Identifier
Mp00024:
Dyck paths
—to 321-avoiding permutation⟶
Permutations
Mp00109: Permutations —descent word⟶ Binary words
Mp00104: Binary words —reverse⟶ Binary words
Mp00109: Permutations —descent word⟶ Binary words
Mp00104: Binary words —reverse⟶ Binary words
Images
=>
Cc0005;cc-rep-0
[1,0]=>[1]=>=>
[1,0,1,0]=>[2,1]=>1=>1
[1,1,0,0]=>[1,2]=>0=>0
[1,0,1,0,1,0]=>[2,1,3]=>10=>01
[1,0,1,1,0,0]=>[2,3,1]=>01=>10
[1,1,0,0,1,0]=>[3,1,2]=>10=>01
[1,1,0,1,0,0]=>[1,3,2]=>01=>10
[1,1,1,0,0,0]=>[1,2,3]=>00=>00
[1,0,1,0,1,0,1,0]=>[2,1,4,3]=>101=>101
[1,0,1,0,1,1,0,0]=>[2,4,1,3]=>010=>010
[1,0,1,1,0,0,1,0]=>[2,1,3,4]=>100=>001
[1,0,1,1,0,1,0,0]=>[2,3,1,4]=>010=>010
[1,0,1,1,1,0,0,0]=>[2,3,4,1]=>001=>100
[1,1,0,0,1,0,1,0]=>[3,1,4,2]=>101=>101
[1,1,0,0,1,1,0,0]=>[3,4,1,2]=>010=>010
[1,1,0,1,0,0,1,0]=>[3,1,2,4]=>100=>001
[1,1,0,1,0,1,0,0]=>[1,3,2,4]=>010=>010
[1,1,0,1,1,0,0,0]=>[1,3,4,2]=>001=>100
[1,1,1,0,0,0,1,0]=>[4,1,2,3]=>100=>001
[1,1,1,0,0,1,0,0]=>[1,4,2,3]=>010=>010
[1,1,1,0,1,0,0,0]=>[1,2,4,3]=>001=>100
[1,1,1,1,0,0,0,0]=>[1,2,3,4]=>000=>000
[1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,5]=>1010=>0101
[1,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,5]=>0100=>0010
[1,0,1,0,1,1,0,0,1,0]=>[2,1,4,5,3]=>1001=>1001
[1,0,1,0,1,1,0,1,0,0]=>[2,4,1,5,3]=>0101=>1010
[1,0,1,0,1,1,1,0,0,0]=>[2,4,5,1,3]=>0010=>0100
[1,0,1,1,0,0,1,0,1,0]=>[2,1,5,3,4]=>1010=>0101
[1,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,4]=>0100=>0010
[1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,4]=>1001=>1001
[1,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,4]=>0101=>1010
[1,0,1,1,0,1,1,0,0,0]=>[2,3,5,1,4]=>0010=>0100
[1,0,1,1,1,0,0,0,1,0]=>[2,1,3,4,5]=>1000=>0001
[1,0,1,1,1,0,0,1,0,0]=>[2,3,1,4,5]=>0100=>0010
[1,0,1,1,1,0,1,0,0,0]=>[2,3,4,1,5]=>0010=>0100
[1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>0001=>1000
[1,1,0,0,1,0,1,0,1,0]=>[3,1,4,2,5]=>1010=>0101
[1,1,0,0,1,0,1,1,0,0]=>[3,4,1,2,5]=>0100=>0010
[1,1,0,0,1,1,0,0,1,0]=>[3,1,4,5,2]=>1001=>1001
[1,1,0,0,1,1,0,1,0,0]=>[3,4,1,5,2]=>0101=>1010
[1,1,0,0,1,1,1,0,0,0]=>[3,4,5,1,2]=>0010=>0100
[1,1,0,1,0,0,1,0,1,0]=>[3,1,5,2,4]=>1010=>0101
[1,1,0,1,0,0,1,1,0,0]=>[3,5,1,2,4]=>0100=>0010
[1,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,4]=>1001=>1001
[1,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4]=>0101=>1010
[1,1,0,1,0,1,1,0,0,0]=>[1,3,5,2,4]=>0010=>0100
[1,1,0,1,1,0,0,0,1,0]=>[3,1,2,4,5]=>1000=>0001
[1,1,0,1,1,0,0,1,0,0]=>[1,3,2,4,5]=>0100=>0010
[1,1,0,1,1,0,1,0,0,0]=>[1,3,4,2,5]=>0010=>0100
[1,1,0,1,1,1,0,0,0,0]=>[1,3,4,5,2]=>0001=>1000
[1,1,1,0,0,0,1,0,1,0]=>[4,1,5,2,3]=>1010=>0101
[1,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,3]=>0100=>0010
[1,1,1,0,0,1,0,0,1,0]=>[4,1,2,5,3]=>1001=>1001
[1,1,1,0,0,1,0,1,0,0]=>[1,4,2,5,3]=>0101=>1010
[1,1,1,0,0,1,1,0,0,0]=>[1,4,5,2,3]=>0010=>0100
[1,1,1,0,1,0,0,0,1,0]=>[4,1,2,3,5]=>1000=>0001
[1,1,1,0,1,0,0,1,0,0]=>[1,4,2,3,5]=>0100=>0010
[1,1,1,0,1,0,1,0,0,0]=>[1,2,4,3,5]=>0010=>0100
[1,1,1,0,1,1,0,0,0,0]=>[1,2,4,5,3]=>0001=>1000
[1,1,1,1,0,0,0,0,1,0]=>[5,1,2,3,4]=>1000=>0001
[1,1,1,1,0,0,0,1,0,0]=>[1,5,2,3,4]=>0100=>0010
[1,1,1,1,0,0,1,0,0,0]=>[1,2,5,3,4]=>0010=>0100
[1,1,1,1,0,1,0,0,0,0]=>[1,2,3,5,4]=>0001=>1000
[1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5]=>0000=>0000
[1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,6,5]=>10101=>10101
[1,0,1,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,6,5]=>01001=>10010
[1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,4,6,3,5]=>10010=>01001
[1,0,1,0,1,0,1,1,0,1,0,0]=>[2,4,1,6,3,5]=>01010=>01010
[1,0,1,0,1,0,1,1,1,0,0,0]=>[2,4,6,1,3,5]=>00100=>00100
[1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>10100=>00101
[1,0,1,0,1,1,0,0,1,1,0,0]=>[2,4,1,3,5,6]=>01000=>00010
[1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>10010=>01001
[1,0,1,0,1,1,0,1,0,1,0,0]=>[2,4,1,5,3,6]=>01010=>01010
[1,0,1,0,1,1,0,1,1,0,0,0]=>[2,4,5,1,3,6]=>00100=>00100
[1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,4,5,6,3]=>10001=>10001
[1,0,1,0,1,1,1,0,0,1,0,0]=>[2,4,1,5,6,3]=>01001=>10010
[1,0,1,0,1,1,1,0,1,0,0,0]=>[2,4,5,1,6,3]=>00101=>10100
[1,0,1,0,1,1,1,1,0,0,0,0]=>[2,4,5,6,1,3]=>00010=>01000
[1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,5,3,6,4]=>10101=>10101
[1,0,1,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,6,4]=>01001=>10010
[1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,5,6,3,4]=>10010=>01001
[1,0,1,1,0,0,1,1,0,1,0,0]=>[2,5,1,6,3,4]=>01010=>01010
[1,0,1,1,0,0,1,1,1,0,0,0]=>[2,5,6,1,3,4]=>00100=>00100
[1,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,5,3,4,6]=>10100=>00101
[1,0,1,1,0,1,0,0,1,1,0,0]=>[2,5,1,3,4,6]=>01000=>00010
[1,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,3,5,4,6]=>10010=>01001
[1,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,4,6]=>01010=>01010
[1,0,1,1,0,1,0,1,1,0,0,0]=>[2,3,5,1,4,6]=>00100=>00100
[1,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,3,5,6,4]=>10001=>10001
[1,0,1,1,0,1,1,0,0,1,0,0]=>[2,3,1,5,6,4]=>01001=>10010
[1,0,1,1,0,1,1,0,1,0,0,0]=>[2,3,5,1,6,4]=>00101=>10100
[1,0,1,1,0,1,1,1,0,0,0,0]=>[2,3,5,6,1,4]=>00010=>01000
[1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,6,3,4,5]=>10100=>00101
[1,0,1,1,1,0,0,0,1,1,0,0]=>[2,6,1,3,4,5]=>01000=>00010
[1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,3,6,4,5]=>10010=>01001
[1,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,1,6,4,5]=>01010=>01010
[1,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,6,1,4,5]=>00100=>00100
[1,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,3,4,6,5]=>10001=>10001
[1,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,1,4,6,5]=>01001=>10010
[1,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,4,1,6,5]=>00101=>10100
[1,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,4,6,1,5]=>00010=>01000
[1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,3,4,5,6]=>10000=>00001
[1,0,1,1,1,1,0,0,0,1,0,0]=>[2,3,1,4,5,6]=>01000=>00010
[1,0,1,1,1,1,0,0,1,0,0,0]=>[2,3,4,1,5,6]=>00100=>00100
[1,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,4,5,1,6]=>00010=>01000
[1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>00001=>10000
[1,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,6,5]=>10101=>10101
[1,1,0,0,1,0,1,0,1,1,0,0]=>[3,4,1,2,6,5]=>01001=>10010
[1,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,4,6,2,5]=>10010=>01001
[1,1,0,0,1,0,1,1,0,1,0,0]=>[3,4,1,6,2,5]=>01010=>01010
[1,1,0,0,1,0,1,1,1,0,0,0]=>[3,4,6,1,2,5]=>00100=>00100
[1,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,4,2,5,6]=>10100=>00101
[1,1,0,0,1,1,0,0,1,1,0,0]=>[3,4,1,2,5,6]=>01000=>00010
[1,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,4,5,2,6]=>10010=>01001
[1,1,0,0,1,1,0,1,0,1,0,0]=>[3,4,1,5,2,6]=>01010=>01010
[1,1,0,0,1,1,0,1,1,0,0,0]=>[3,4,5,1,2,6]=>00100=>00100
[1,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,4,5,6,2]=>10001=>10001
[1,1,0,0,1,1,1,0,0,1,0,0]=>[3,4,1,5,6,2]=>01001=>10010
[1,1,0,0,1,1,1,0,1,0,0,0]=>[3,4,5,1,6,2]=>00101=>10100
[1,1,0,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,1,2]=>00010=>01000
[1,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,5,2,6,4]=>10101=>10101
[1,1,0,1,0,0,1,0,1,1,0,0]=>[3,5,1,2,6,4]=>01001=>10010
[1,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,5,6,2,4]=>10010=>01001
[1,1,0,1,0,0,1,1,0,1,0,0]=>[3,5,1,6,2,4]=>01010=>01010
[1,1,0,1,0,0,1,1,1,0,0,0]=>[3,5,6,1,2,4]=>00100=>00100
[1,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,5,2,4,6]=>10100=>00101
[1,1,0,1,0,1,0,0,1,1,0,0]=>[3,5,1,2,4,6]=>01000=>00010
[1,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,4,6]=>10010=>01001
[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,6]=>01010=>01010
[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,5,2,4,6]=>00100=>00100
[1,1,0,1,0,1,1,0,0,0,1,0]=>[3,1,2,5,6,4]=>10001=>10001
[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,2,5,6,4]=>01001=>10010
[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,5,2,6,4]=>00101=>10100
[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,5,6,2,4]=>00010=>01000
[1,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,6,2,4,5]=>10100=>00101
[1,1,0,1,1,0,0,0,1,1,0,0]=>[3,6,1,2,4,5]=>01000=>00010
[1,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,2,6,4,5]=>10010=>01001
[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,2,6,4,5]=>01010=>01010
[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,6,2,4,5]=>00100=>00100
[1,1,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,4,6,5]=>10001=>10001
[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,2,4,6,5]=>01001=>10010
[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,4,2,6,5]=>00101=>10100
[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,4,6,2,5]=>00010=>01000
[1,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,2,4,5,6]=>10000=>00001
[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,2,4,5,6]=>01000=>00010
[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,4,2,5,6]=>00100=>00100
[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,4,5,2,6]=>00010=>01000
[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,4,5,6,2]=>00001=>10000
[1,1,1,0,0,0,1,0,1,0,1,0]=>[4,1,5,2,6,3]=>10101=>10101
[1,1,1,0,0,0,1,0,1,1,0,0]=>[4,5,1,2,6,3]=>01001=>10010
[1,1,1,0,0,0,1,1,0,0,1,0]=>[4,1,5,6,2,3]=>10010=>01001
[1,1,1,0,0,0,1,1,0,1,0,0]=>[4,5,1,6,2,3]=>01010=>01010
[1,1,1,0,0,0,1,1,1,0,0,0]=>[4,5,6,1,2,3]=>00100=>00100
[1,1,1,0,0,1,0,0,1,0,1,0]=>[4,1,5,2,3,6]=>10100=>00101
[1,1,1,0,0,1,0,0,1,1,0,0]=>[4,5,1,2,3,6]=>01000=>00010
[1,1,1,0,0,1,0,1,0,0,1,0]=>[4,1,2,5,3,6]=>10010=>01001
[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,5,3,6]=>01010=>01010
[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,5,2,3,6]=>00100=>00100
[1,1,1,0,0,1,1,0,0,0,1,0]=>[4,1,2,5,6,3]=>10001=>10001
[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,5,6,3]=>01001=>10010
[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,5,2,6,3]=>00101=>10100
[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,5,6,2,3]=>00010=>01000
[1,1,1,0,1,0,0,0,1,0,1,0]=>[4,1,6,2,3,5]=>10100=>00101
[1,1,1,0,1,0,0,0,1,1,0,0]=>[4,6,1,2,3,5]=>01000=>00010
[1,1,1,0,1,0,0,1,0,0,1,0]=>[4,1,2,6,3,5]=>10010=>01001
[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,2,6,3,5]=>01010=>01010
[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,6,2,3,5]=>00100=>00100
[1,1,1,0,1,0,1,0,0,0,1,0]=>[4,1,2,3,6,5]=>10001=>10001
[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,2,3,6,5]=>01001=>10010
[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,2,4,3,6,5]=>00101=>10100
[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,2,4,6,3,5]=>00010=>01000
[1,1,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,3,5,6]=>10000=>00001
[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,2,3,5,6]=>01000=>00010
[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,2,4,3,5,6]=>00100=>00100
[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,2,4,5,3,6]=>00010=>01000
[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,4,5,6,3]=>00001=>10000
[1,1,1,1,0,0,0,0,1,0,1,0]=>[5,1,6,2,3,4]=>10100=>00101
[1,1,1,1,0,0,0,0,1,1,0,0]=>[5,6,1,2,3,4]=>01000=>00010
[1,1,1,1,0,0,0,1,0,0,1,0]=>[5,1,2,6,3,4]=>10010=>01001
[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,2,6,3,4]=>01010=>01010
[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,6,2,3,4]=>00100=>00100
[1,1,1,1,0,0,1,0,0,0,1,0]=>[5,1,2,3,6,4]=>10001=>10001
[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,2,3,6,4]=>01001=>10010
[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,2,5,3,6,4]=>00101=>10100
[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,2,5,6,3,4]=>00010=>01000
[1,1,1,1,0,1,0,0,0,0,1,0]=>[5,1,2,3,4,6]=>10000=>00001
[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,5,2,3,4,6]=>01000=>00010
[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,2,5,3,4,6]=>00100=>00100
[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,2,3,5,4,6]=>00010=>01000
[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,2,3,5,6,4]=>00001=>10000
[1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5]=>10000=>00001
[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,2,3,4,5]=>01000=>00010
[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,6,3,4,5]=>00100=>00100
[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,2,3,6,4,5]=>00010=>01000
[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,3,4,6,5]=>00001=>10000
[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,5,6]=>00000=>00000
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,7]=>101010=>010101
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,6,5,7]=>010010=>010010
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,4,6,3,5,7]=>100100=>001001
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,4,1,6,3,5,7]=>010100=>001010
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,4,6,1,3,5,7]=>001000=>000100
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,6,7,5]=>101001=>100101
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,4,1,3,6,7,5]=>010001=>100010
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,4,6,3,7,5]=>100101=>101001
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,4,1,6,3,7,5]=>010101=>101010
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,4,6,1,3,7,5]=>001001=>100100
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,4,6,7,3,5]=>100010=>010001
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,4,1,6,7,3,5]=>010010=>010010
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,4,6,1,7,3,5]=>001010=>010100
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,4,6,7,1,3,5]=>000100=>001000
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,7,5,6]=>101010=>010101
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,4,1,3,7,5,6]=>010010=>010010
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,7,3,5,6]=>100100=>001001
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,4,1,7,3,5,6]=>010100=>001010
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,7,1,3,5,6]=>001000=>000100
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,3,5,7,6]=>101001=>100101
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[2,4,1,3,5,7,6]=>010001=>100010
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,3,7,6]=>100101=>101001
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,4,1,5,3,7,6]=>010101=>101010
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,4,5,1,3,7,6]=>001001=>100100
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,5,7,3,6]=>100010=>010001
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[2,4,1,5,7,3,6]=>010010=>010010
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,4,5,1,7,3,6]=>001010=>010100
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,4,5,7,1,3,6]=>000100=>001000
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>101000=>000101
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,3,5,6,7]=>010000=>000010
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,4,5,3,6,7]=>100100=>001001
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,4,1,5,3,6,7]=>010100=>001010
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,4,5,1,3,6,7]=>001000=>000100
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,4,5,6,3,7]=>100010=>010001
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,4,1,5,6,3,7]=>010010=>010010
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,4,5,1,6,3,7]=>001010=>010100
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,4,5,6,1,3,7]=>000100=>001000
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,5,6,7,3]=>100001=>100001
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[2,4,1,5,6,7,3]=>010001=>100010
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[2,4,5,1,6,7,3]=>001001=>100100
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,4,5,6,1,7,3]=>000101=>101000
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,4,5,6,7,1,3]=>000010=>010000
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,5,3,6,4,7]=>101010=>010101
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,5,1,3,6,4,7]=>010010=>010010
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,5,6,3,4,7]=>100100=>001001
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,5,1,6,3,4,7]=>010100=>001010
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,5,6,1,3,4,7]=>001000=>000100
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,5,3,6,7,4]=>101001=>100101
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,6,7,4]=>010001=>100010
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,5,6,3,7,4]=>100101=>101001
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,5,1,6,3,7,4]=>010101=>101010
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,5,6,1,3,7,4]=>001001=>100100
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,6,7,3,4]=>100010=>010001
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,5,1,6,7,3,4]=>010010=>010010
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,5,6,1,7,3,4]=>001010=>010100
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,5,6,7,1,3,4]=>000100=>001000
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,5,3,7,4,6]=>101010=>010101
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,7,4,6]=>010010=>010010
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,5,7,3,4,6]=>100100=>001001
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[2,5,1,7,3,4,6]=>010100=>001010
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,5,7,1,3,4,6]=>001000=>000100
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[2,1,5,3,4,7,6]=>101001=>100101
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,5,1,3,4,7,6]=>010001=>100010
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,3,5,4,7,6]=>100101=>101001
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,4,7,6]=>010101=>101010
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,5,1,4,7,6]=>001001=>100100
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,3,5,7,4,6]=>100010=>010001
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,1,5,7,4,6]=>010010=>010010
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,1,7,4,6]=>001010=>010100
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,5,7,1,4,6]=>000100=>001000
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,5,3,4,6,7]=>101000=>000101
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,5,1,3,4,6,7]=>010000=>000010
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[2,1,3,5,4,6,7]=>100100=>001001
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,1,5,4,6,7]=>010100=>001010
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,1,4,6,7]=>001000=>000100
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[2,1,3,5,6,4,7]=>100010=>010001
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,1,5,6,4,7]=>010010=>010010
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,1,6,4,7]=>001010=>010100
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,5,6,1,4,7]=>000100=>001000
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,3,5,6,7,4]=>100001=>100001
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,1,5,6,7,4]=>010001=>100010
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,5,1,6,7,4]=>001001=>100100
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,5,6,1,7,4]=>000101=>101000
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,5,6,7,1,4]=>000010=>010000
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,6,3,7,4,5]=>101010=>010101
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,6,1,3,7,4,5]=>010010=>010010
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,1,6,7,3,4,5]=>100100=>001001
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,6,1,7,3,4,5]=>010100=>001010
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,6,7,1,3,4,5]=>001000=>000100
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[2,1,6,3,4,7,5]=>101001=>100101
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,6,1,3,4,7,5]=>010001=>100010
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[2,1,3,6,4,7,5]=>100101=>101001
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,1,6,4,7,5]=>010101=>101010
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,3,6,1,4,7,5]=>001001=>100100
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[2,1,3,6,7,4,5]=>100010=>010001
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,1,6,7,4,5]=>010010=>010010
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,6,1,7,4,5]=>001010=>010100
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,6,7,1,4,5]=>000100=>001000
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,1,6,3,4,5,7]=>101000=>000101
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,6,1,3,4,5,7]=>010000=>000010
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[2,1,3,6,4,5,7]=>100100=>001001
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,3,1,6,4,5,7]=>010100=>001010
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[2,3,6,1,4,5,7]=>001000=>000100
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[2,1,3,4,6,5,7]=>100010=>010001
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,3,1,4,6,5,7]=>010010=>010010
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,4,1,6,5,7]=>001010=>010100
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[2,3,4,6,1,5,7]=>000100=>001000
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[2,1,3,4,6,7,5]=>100001=>100001
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,3,1,4,6,7,5]=>010001=>100010
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,3,4,1,6,7,5]=>001001=>100100
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,4,6,1,7,5]=>000101=>101000
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,4,6,7,1,5]=>000010=>010000
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,1,7,3,4,5,6]=>101000=>000101
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,7,1,3,4,5,6]=>010000=>000010
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[2,1,3,7,4,5,6]=>100100=>001001
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,1,7,4,5,6]=>010100=>001010
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,7,1,4,5,6]=>001000=>000100
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[2,1,3,4,7,5,6]=>100010=>010001
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,3,1,4,7,5,6]=>010010=>010010
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,3,4,1,7,5,6]=>001010=>010100
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,4,7,1,5,6]=>000100=>001000
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[2,1,3,4,5,7,6]=>100001=>100001
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,3,1,4,5,7,6]=>010001=>100010
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,3,4,1,5,7,6]=>001001=>100100
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,4,5,1,7,6]=>000101=>101000
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,4,5,7,1,6]=>000010=>010000
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7]=>100000=>000001
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,1,4,5,6,7]=>010000=>000010
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,3,4,1,5,6,7]=>001000=>000100
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,3,4,5,1,6,7]=>000100=>001000
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,3,4,5,6,1,7]=>000010=>010000
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1]=>000001=>100000
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,6,5,7]=>101010=>010101
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,4,1,2,6,5,7]=>010010=>010010
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,4,6,2,5,7]=>100100=>001001
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,4,1,6,2,5,7]=>010100=>001010
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,4,6,1,2,5,7]=>001000=>000100
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[3,1,4,2,6,7,5]=>101001=>100101
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[3,4,1,2,6,7,5]=>010001=>100010
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,4,6,2,7,5]=>100101=>101001
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[3,4,1,6,2,7,5]=>010101=>101010
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,4,6,1,2,7,5]=>001001=>100100
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,1,4,6,7,2,5]=>100010=>010001
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,4,1,6,7,2,5]=>010010=>010010
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,4,6,1,7,2,5]=>001010=>010100
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,4,6,7,1,2,5]=>000100=>001000
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[3,1,4,2,7,5,6]=>101010=>010101
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[3,4,1,2,7,5,6]=>010010=>010010
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,4,7,2,5,6]=>100100=>001001
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,4,1,7,2,5,6]=>010100=>001010
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,4,7,1,2,5,6]=>001000=>000100
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[3,1,4,2,5,7,6]=>101001=>100101
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[3,4,1,2,5,7,6]=>010001=>100010
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[3,1,4,5,2,7,6]=>100101=>101001
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,4,1,5,2,7,6]=>010101=>101010
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,4,5,1,2,7,6]=>001001=>100100
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,1,4,5,7,2,6]=>100010=>010001
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,4,1,5,7,2,6]=>010010=>010010
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,4,5,1,7,2,6]=>001010=>010100
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,4,5,7,1,2,6]=>000100=>001000
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[3,1,4,2,5,6,7]=>101000=>000101
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,4,1,2,5,6,7]=>010000=>000010
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,1,4,5,2,6,7]=>100100=>001001
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,4,1,5,2,6,7]=>010100=>001010
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,4,5,1,2,6,7]=>001000=>000100
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[3,1,4,5,6,2,7]=>100010=>010001
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,4,1,5,6,2,7]=>010010=>010010
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,4,5,1,6,2,7]=>001010=>010100
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,4,5,6,1,2,7]=>000100=>001000
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,5,6,7,2]=>100001=>100001
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,4,1,5,6,7,2]=>010001=>100010
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,4,5,1,6,7,2]=>001001=>100100
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,4,5,6,1,7,2]=>000101=>101000
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,1,2]=>000010=>010000
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,6,4,7]=>101010=>010101
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,5,1,2,6,4,7]=>010010=>010010
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,5,6,2,4,7]=>100100=>001001
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,5,1,6,2,4,7]=>010100=>001010
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,5,6,1,2,4,7]=>001000=>000100
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,5,2,6,7,4]=>101001=>100101
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,5,1,2,6,7,4]=>010001=>100010
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,5,6,2,7,4]=>100101=>101001
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,5,1,6,2,7,4]=>010101=>101010
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,5,6,1,2,7,4]=>001001=>100100
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,5,6,7,2,4]=>100010=>010001
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,5,1,6,7,2,4]=>010010=>010010
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,5,6,1,7,2,4]=>001010=>010100
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,5,6,7,1,2,4]=>000100=>001000
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,5,2,7,4,6]=>101010=>010101
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[3,5,1,2,7,4,6]=>010010=>010010
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,5,7,2,4,6]=>100100=>001001
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[3,5,1,7,2,4,6]=>010100=>001010
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,5,7,1,2,4,6]=>001000=>000100
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,5,2,4,7,6]=>101001=>100101
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[3,5,1,2,4,7,6]=>010001=>100010
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,4,7,6]=>100101=>101001
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,7,6]=>010101=>101010
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,5,2,4,7,6]=>001001=>100100
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[3,1,2,5,7,4,6]=>100010=>010001
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,2,5,7,4,6]=>010010=>010010
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,5,2,7,4,6]=>001010=>010100
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,5,7,2,4,6]=>000100=>001000
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,5,2,4,6,7]=>101000=>000101
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[3,5,1,2,4,6,7]=>010000=>000010
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,2,5,4,6,7]=>100100=>001001
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,2,5,4,6,7]=>010100=>001010
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,2,4,6,7]=>001000=>000100
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,5,6,4,7]=>100010=>010001
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,2,5,6,4,7]=>010010=>010010
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,2,6,4,7]=>001010=>010100
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,6,2,4,7]=>000100=>001000
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,2,5,6,7,4]=>100001=>100001
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,2,5,6,7,4]=>010001=>100010
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,5,2,6,7,4]=>001001=>100100
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,5,6,2,7,4]=>000101=>101000
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,5,6,7,2,4]=>000010=>010000
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,6,2,7,4,5]=>101010=>010101
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[3,6,1,2,7,4,5]=>010010=>010010
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,6,7,2,4,5]=>100100=>001001
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,6,1,7,2,4,5]=>010100=>001010
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,6,7,1,2,4,5]=>001000=>000100
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,6,2,4,7,5]=>101001=>100101
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,6,1,2,4,7,5]=>010001=>100010
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[3,1,2,6,4,7,5]=>100101=>101001
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,3,2,6,4,7,5]=>010101=>101010
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,6,2,4,7,5]=>001001=>100100
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,1,2,6,7,4,5]=>100010=>010001
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,6,7,4,5]=>010010=>010010
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,6,2,7,4,5]=>001010=>010100
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,6,7,2,4,5]=>000100=>001000
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[3,1,6,2,4,5,7]=>101000=>000101
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,6,1,2,4,5,7]=>010000=>000010
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[3,1,2,6,4,5,7]=>100100=>001001
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,3,2,6,4,5,7]=>010100=>001010
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,6,2,4,5,7]=>001000=>000100
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[3,1,2,4,6,5,7]=>100010=>010001
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,3,2,4,6,5,7]=>010010=>010010
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,4,2,6,5,7]=>001010=>010100
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,3,4,6,2,5,7]=>000100=>001000
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,1,2,4,6,7,5]=>100001=>100001
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,2,4,6,7,5]=>010001=>100010
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,4,2,6,7,5]=>001001=>100100
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,4,6,2,7,5]=>000101=>101000
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,4,6,7,2,5]=>000010=>010000
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[3,1,7,2,4,5,6]=>101000=>000101
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,7,1,2,4,5,6]=>010000=>000010
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[3,1,2,7,4,5,6]=>100100=>001001
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,3,2,7,4,5,6]=>010100=>001010
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,3,7,2,4,5,6]=>001000=>000100
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[3,1,2,4,7,5,6]=>100010=>010001
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,3,2,4,7,5,6]=>010010=>010010
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,3,4,2,7,5,6]=>001010=>010100
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,3,4,7,2,5,6]=>000100=>001000
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,1,2,4,5,7,6]=>100001=>100001
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,3,2,4,5,7,6]=>010001=>100010
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,3,4,2,5,7,6]=>001001=>100100
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,3,4,5,2,7,6]=>000101=>101000
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,3,4,5,7,2,6]=>000010=>010000
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,1,2,4,5,6,7]=>100000=>000001
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,3,2,4,5,6,7]=>010000=>000010
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,3,4,2,5,6,7]=>001000=>000100
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,3,4,5,2,6,7]=>000100=>001000
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,3,4,5,6,2,7]=>000010=>010000
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,4,5,6,7,2]=>000001=>100000
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,5,2,6,3,7]=>101010=>010101
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[4,5,1,2,6,3,7]=>010010=>010010
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[4,1,5,6,2,3,7]=>100100=>001001
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[4,5,1,6,2,3,7]=>010100=>001010
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[4,5,6,1,2,3,7]=>001000=>000100
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[4,1,5,2,6,7,3]=>101001=>100101
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[4,5,1,2,6,7,3]=>010001=>100010
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[4,1,5,6,2,7,3]=>100101=>101001
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[4,5,1,6,2,7,3]=>010101=>101010
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[4,5,6,1,2,7,3]=>001001=>100100
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[4,1,5,6,7,2,3]=>100010=>010001
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[4,5,1,6,7,2,3]=>010010=>010010
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[4,5,6,1,7,2,3]=>001010=>010100
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,1,2,3]=>000100=>001000
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[4,1,5,2,7,3,6]=>101010=>010101
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[4,5,1,2,7,3,6]=>010010=>010010
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[4,1,5,7,2,3,6]=>100100=>001001
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[4,5,1,7,2,3,6]=>010100=>001010
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[4,5,7,1,2,3,6]=>001000=>000100
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[4,1,5,2,3,7,6]=>101001=>100101
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[4,5,1,2,3,7,6]=>010001=>100010
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[4,1,2,5,3,7,6]=>100101=>101001
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,4,2,5,3,7,6]=>010101=>101010
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,4,5,2,3,7,6]=>001001=>100100
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[4,1,2,5,7,3,6]=>100010=>010001
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,4,2,5,7,3,6]=>010010=>010010
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,4,5,2,7,3,6]=>001010=>010100
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,4,5,7,2,3,6]=>000100=>001000
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[4,1,5,2,3,6,7]=>101000=>000101
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,3,6,7]=>010000=>000010
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[4,1,2,5,3,6,7]=>100100=>001001
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,4,2,5,3,6,7]=>010100=>001010
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,5,2,3,6,7]=>001000=>000100
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[4,1,2,5,6,3,7]=>100010=>010001
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,4,2,5,6,3,7]=>010010=>010010
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,4,5,2,6,3,7]=>001010=>010100
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,4,5,6,2,3,7]=>000100=>001000
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[4,1,2,5,6,7,3]=>100001=>100001
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,4,2,5,6,7,3]=>010001=>100010
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,4,5,2,6,7,3]=>001001=>100100
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,4,5,6,2,7,3]=>000101=>101000
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,4,5,6,7,2,3]=>000010=>010000
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[4,1,6,2,7,3,5]=>101010=>010101
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[4,6,1,2,7,3,5]=>010010=>010010
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[4,1,6,7,2,3,5]=>100100=>001001
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,6,1,7,2,3,5]=>010100=>001010
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,6,7,1,2,3,5]=>001000=>000100
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[4,1,6,2,3,7,5]=>101001=>100101
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[4,6,1,2,3,7,5]=>010001=>100010
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[4,1,2,6,3,7,5]=>100101=>101001
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,6,3,7,5]=>010101=>101010
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,4,6,2,3,7,5]=>001001=>100100
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[4,1,2,6,7,3,5]=>100010=>010001
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,6,7,3,5]=>010010=>010010
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,4,6,2,7,3,5]=>001010=>010100
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,4,6,7,2,3,5]=>000100=>001000
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[4,1,6,2,3,5,7]=>101000=>000101
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[4,6,1,2,3,5,7]=>010000=>000010
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[4,1,2,6,3,5,7]=>100100=>001001
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,4,2,6,3,5,7]=>010100=>001010
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,4,6,2,3,5,7]=>001000=>000100
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[4,1,2,3,6,5,7]=>100010=>010001
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,4,2,3,6,5,7]=>010010=>010010
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,2,4,3,6,5,7]=>001010=>010100
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,2,4,6,3,5,7]=>000100=>001000
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,3,6,7,5]=>100001=>100001
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,4,2,3,6,7,5]=>010001=>100010
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,2,4,3,6,7,5]=>001001=>100100
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,2,4,6,3,7,5]=>000101=>101000
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,2,4,6,7,3,5]=>000010=>010000
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[4,1,7,2,3,5,6]=>101000=>000101
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[4,7,1,2,3,5,6]=>010000=>000010
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[4,1,2,7,3,5,6]=>100100=>001001
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,4,2,7,3,5,6]=>010100=>001010
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,4,7,2,3,5,6]=>001000=>000100
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[4,1,2,3,7,5,6]=>100010=>010001
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,4,2,3,7,5,6]=>010010=>010010
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,2,4,3,7,5,6]=>001010=>010100
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,2,4,7,3,5,6]=>000100=>001000
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[4,1,2,3,5,7,6]=>100001=>100001
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,4,2,3,5,7,6]=>010001=>100010
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,2,4,3,5,7,6]=>001001=>100100
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,2,4,5,3,7,6]=>000101=>101000
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,2,4,5,7,3,6]=>000010=>010000
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[4,1,2,3,5,6,7]=>100000=>000001
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,4,2,3,5,6,7]=>010000=>000010
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,2,4,3,5,6,7]=>001000=>000100
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,2,4,5,3,6,7]=>000100=>001000
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,2,4,5,6,3,7]=>000010=>010000
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,5,6,7,3]=>000001=>100000
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[5,1,6,2,7,3,4]=>101010=>010101
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[5,6,1,2,7,3,4]=>010010=>010010
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[5,1,6,7,2,3,4]=>100100=>001001
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[5,6,1,7,2,3,4]=>010100=>001010
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,6,7,1,2,3,4]=>001000=>000100
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[5,1,6,2,3,7,4]=>101001=>100101
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[5,6,1,2,3,7,4]=>010001=>100010
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[5,1,2,6,3,7,4]=>100101=>101001
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,5,2,6,3,7,4]=>010101=>101010
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,5,6,2,3,7,4]=>001001=>100100
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[5,1,2,6,7,3,4]=>100010=>010001
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,5,2,6,7,3,4]=>010010=>010010
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,5,6,2,7,3,4]=>001010=>010100
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,5,6,7,2,3,4]=>000100=>001000
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[5,1,6,2,3,4,7]=>101000=>000101
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[5,6,1,2,3,4,7]=>010000=>000010
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[5,1,2,6,3,4,7]=>100100=>001001
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,5,2,6,3,4,7]=>010100=>001010
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,5,6,2,3,4,7]=>001000=>000100
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[5,1,2,3,6,4,7]=>100010=>010001
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,5,2,3,6,4,7]=>010010=>010010
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,2,5,3,6,4,7]=>001010=>010100
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,2,5,6,3,4,7]=>000100=>001000
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[5,1,2,3,6,7,4]=>100001=>100001
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,5,2,3,6,7,4]=>010001=>100010
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,2,5,3,6,7,4]=>001001=>100100
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,2,5,6,3,7,4]=>000101=>101000
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,2,5,6,7,3,4]=>000010=>010000
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[5,1,7,2,3,4,6]=>101000=>000101
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[5,7,1,2,3,4,6]=>010000=>000010
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[5,1,2,7,3,4,6]=>100100=>001001
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,5,2,7,3,4,6]=>010100=>001010
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,5,7,2,3,4,6]=>001000=>000100
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[5,1,2,3,7,4,6]=>100010=>010001
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,5,2,3,7,4,6]=>010010=>010010
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,2,5,3,7,4,6]=>001010=>010100
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,2,5,7,3,4,6]=>000100=>001000
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[5,1,2,3,4,7,6]=>100001=>100001
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,5,2,3,4,7,6]=>010001=>100010
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,2,5,3,4,7,6]=>001001=>100100
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,2,3,5,4,7,6]=>000101=>101000
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,2,3,5,7,4,6]=>000010=>010000
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[5,1,2,3,4,6,7]=>100000=>000001
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,5,2,3,4,6,7]=>010000=>000010
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,2,5,3,4,6,7]=>001000=>000100
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,2,3,5,4,6,7]=>000100=>001000
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,2,3,5,6,4,7]=>000010=>010000
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,2,3,5,6,7,4]=>000001=>100000
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[6,1,7,2,3,4,5]=>101000=>000101
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,7,1,2,3,4,5]=>010000=>000010
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[6,1,2,7,3,4,5]=>100100=>001001
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,6,2,7,3,4,5]=>010100=>001010
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,6,7,2,3,4,5]=>001000=>000100
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,1,2,3,7,4,5]=>100010=>010001
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,6,2,3,7,4,5]=>010010=>010010
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,2,6,3,7,4,5]=>001010=>010100
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,2,6,7,3,4,5]=>000100=>001000
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,1,2,3,4,7,5]=>100001=>100001
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,6,2,3,4,7,5]=>010001=>100010
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,2,6,3,4,7,5]=>001001=>100100
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,2,3,6,4,7,5]=>000101=>101000
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,2,3,6,7,4,5]=>000010=>010000
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,7]=>100000=>000001
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,6,2,3,4,5,7]=>010000=>000010
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,2,6,3,4,5,7]=>001000=>000100
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,2,3,6,4,5,7]=>000100=>001000
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,2,3,4,6,5,7]=>000010=>010000
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,2,3,4,6,7,5]=>000001=>100000
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6]=>100000=>000001
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,7,2,3,4,5,6]=>010000=>000010
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,2,7,3,4,5,6]=>001000=>000100
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,2,3,7,4,5,6]=>000100=>001000
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,2,3,4,7,5,6]=>000010=>010000
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,2,3,4,5,7,6]=>000001=>100000
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7]=>000000=>000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,6,5,8,7]=>0100101=>1010010
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,4,6,3,5,8,7]=>1001001=>1001001
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,4,1,6,3,5,8,7]=>0101001=>1001010
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,4,6,1,3,5,8,7]=>0010001=>1000100
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,6,8,5,7]=>1010010=>0100101
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,4,1,3,6,8,5,7]=>0100010=>0100010
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,4,6,3,8,5,7]=>1001010=>0101001
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,4,1,6,3,8,5,7]=>0101010=>0101010
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,4,6,1,3,8,5,7]=>0010010=>0100100
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,4,6,8,3,5,7]=>1000100=>0010001
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,4,1,6,8,3,5,7]=>0100100=>0010010
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,4,6,1,8,3,5,7]=>0010100=>0010100
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,4,6,8,1,3,5,7]=>0001000=>0001000
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,7,8]=>1010100=>0010101
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,4,1,3,6,5,7,8]=>0100100=>0010010
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,4,1,6,3,7,5,8]=>0101010=>0101010
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,4,6,1,3,7,5,8]=>0010010=>0100100
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,4,6,7,1,3,5,8]=>0001000=>0001000
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,4,3,6,7,8,5]=>1010001=>1000101
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,3,6,7,8,5]=>0100001=>1000010
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,4,6,3,7,8,5]=>1001001=>1001001
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,4,1,6,3,7,8,5]=>0101001=>1001010
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,4,6,1,3,7,8,5]=>0010001=>1000100
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,4,1,6,7,3,8,5]=>0100101=>1010010
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,4,6,1,7,3,8,5]=>0010101=>1010100
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,4,6,7,1,3,8,5]=>0001001=>1001000
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[2,4,1,6,7,8,3,5]=>0100010=>0100010
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[2,4,6,1,7,8,3,5]=>0010010=>0100100
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,4,6,7,1,8,3,5]=>0001010=>0101000
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,4,6,7,8,1,3,5]=>0000100=>0010000
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,7,5,8,6]=>1010101=>1010101
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,7,5,8,6]=>0100101=>1010010
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,4,1,7,3,5,8,6]=>0101001=>1001010
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,4,7,1,3,5,8,6]=>0010001=>1000100
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,7,8,5,6]=>1010010=>0100101
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,3,7,8,5,6]=>0100010=>0100010
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,4,1,7,3,8,5,6]=>0101010=>0101010
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,4,1,7,8,3,5,6]=>0100100=>0010010
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,4,7,1,8,3,5,6]=>0010100=>0010100
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,1,5,3,7,6,8]=>0101010=>0101010
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,4,5,1,7,3,6,8]=>0010100=>0010100
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,1,3,5,7,8,6]=>0100001=>1000010
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,1,5,3,7,8,6]=>0101001=>1001010
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,5,1,3,7,8,6]=>0010001=>1000100
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[2,1,4,5,7,3,8,6]=>1000101=>1010001
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,1,5,7,3,8,6]=>0100101=>1010010
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,5,1,7,3,8,6]=>0010101=>1010100
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,5,7,1,3,8,6]=>0001001=>1001000
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,4,5,7,8,1,3,6]=>0000100=>0010000
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,4,3,8,5,6,7]=>1010100=>0010101
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,4,1,3,8,5,6,7]=>0100100=>0010010
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,1,4,8,3,5,6,7]=>1001000=>0001001
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,1,8,3,5,6,7]=>0101000=>0001010
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,1,5,3,8,6,7]=>0101010=>0101010
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[2,1,4,5,8,3,6,7]=>1000100=>0010001
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,1,5,8,3,6,7]=>0100100=>0010010
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,5,8,1,3,6,7]=>0001000=>0001000
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,1,4,3,5,6,8,7]=>1010001=>1000101
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[2,1,4,5,3,6,8,7]=>1001001=>1001001
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[2,1,4,5,6,3,8,7]=>1000101=>1010001
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,4,1,5,6,3,8,7]=>0100101=>1010010
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[2,1,4,5,6,8,3,7]=>1000010=>0100001
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,4,5,1,6,8,3,7]=>0010010=>0100100
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,4,5,6,1,8,3,7]=>0001010=>0101000
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,4,5,6,8,1,3,7]=>0000100=>0010000
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,1,4,3,5,6,7,8]=>1010000=>0000101
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,4,1,3,5,6,7,8]=>0100000=>0000010
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,4,1,5,6,3,7,8]=>0100100=>0010010
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,4,5,1,6,3,7,8]=>0010100=>0010100
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,4,5,6,1,3,7,8]=>0001000=>0001000
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,4,5,6,7,1,3,8]=>0000100=>0010000
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,4,5,6,7,8,3]=>1000001=>1000001
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,4,1,5,6,7,8,3]=>0100001=>1000010
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,4,5,6,7,1,8,3]=>0000101=>1010000
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,5,3,6,4,8,7]=>1010101=>1010101
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,5,6,3,4,8,7]=>1001001=>1001001
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,5,3,6,8,4,7]=>1010010=>0100101
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,6,8,4,7]=>0100010=>0100010
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,5,1,6,8,3,4,7]=>0100100=>0010010
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,5,6,3,4,7,8]=>1001000=>0001001
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,5,1,6,3,4,7,8]=>0101000=>0001010
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,5,3,6,7,4,8]=>1010010=>0100101
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,5,6,3,7,4,8]=>1001010=>0101001
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,5,1,6,3,7,4,8]=>0101010=>0101010
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,5,6,1,3,7,4,8]=>0010010=>0100100
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,5,6,7,3,4,8]=>1000100=>0010001
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,5,1,6,7,3,4,8]=>0100100=>0010010
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,5,3,6,7,8,4]=>1010001=>1000101
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,5,1,3,6,7,8,4]=>0100001=>1000010
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,6,3,7,8,4]=>1001001=>1001001
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,5,1,6,3,7,8,4]=>0101001=>1001010
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,5,6,1,3,7,8,4]=>0010001=>1000100
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,5,6,7,3,8,4]=>1000101=>1010001
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,5,1,6,7,3,8,4]=>0100101=>1010010
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,5,6,7,8,3,4]=>1000010=>0100001
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,5,1,6,7,8,3,4]=>0100010=>0100010
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,5,6,1,7,8,3,4]=>0010010=>0100100
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,5,6,7,8,1,3,4]=>0000100=>0010000
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,5,3,7,4,8,6]=>1010101=>1010101
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,5,1,3,7,4,8,6]=>0100101=>1010010
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,5,7,3,4,8,6]=>1001001=>1001001
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,5,1,7,3,4,8,6]=>0101001=>1001010
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,5,7,1,3,4,8,6]=>0010001=>1000100
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,5,3,7,8,4,6]=>1010010=>0100101
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,7,8,4,6]=>0100010=>0100010
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,5,7,3,8,4,6]=>1001010=>0101001
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,7,8,3,4,6]=>1000100=>0010001
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,5,1,7,8,3,4,6]=>0100100=>0010010
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,7,4,6,8]=>0100100=>0010010
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,5,7,3,4,6,8]=>1001000=>0001001
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,4,7,6,8]=>0101010=>0101010
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,5,7,1,4,6,8]=>0001000=>0001000
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,1,7,4,8,6]=>0010101=>1010100
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,5,7,1,4,8,6]=>0001001=>1001000
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,5,7,1,8,4,6]=>0001010=>0101000
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,5,3,8,4,6,7]=>1010100=>0010101
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,1,5,8,3,4,6,7]=>1001000=>0001001
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,5,1,8,3,4,6,7]=>0101000=>0001010
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,3,5,1,4,8,6,7]=>0010010=>0100100
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,5,8,1,4,6,7]=>0001000=>0001000
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,1,5,3,4,6,8,7]=>1010001=>1000101
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,1,3,5,4,6,8,7]=>1001001=>1001001
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,5,1,6,4,8,7]=>0010101=>1010100
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,3,5,6,1,4,8,7]=>0001001=>1001000
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,5,6,1,8,4,7]=>0001010=>0101000
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,5,6,8,1,4,7]=>0000100=>0010000
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,5,6,1,4,7,8]=>0001000=>0001000
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,3,1,5,6,7,4,8]=>0100010=>0100010
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,5,6,1,7,4,8]=>0001010=>0101000
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,1,5,6,7,8,4]=>0100001=>1000010
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,3,5,1,6,7,8,4]=>0010001=>1000100
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,3,5,6,1,7,8,4]=>0001001=>1001000
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,3,5,6,7,1,8,4]=>0000101=>1010000
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,5,6,7,8,1,4]=>0000010=>0100000
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,1,6,3,7,4,8,5]=>1010101=>1010101
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[2,6,1,3,7,4,8,5]=>0100101=>1010010
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[2,6,7,1,3,4,8,5]=>0010001=>1000100
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,1,6,3,7,8,4,5]=>1010010=>0100101
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[2,1,6,7,3,8,4,5]=>1001010=>0101001
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[2,6,1,7,3,8,4,5]=>0101010=>0101010
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,1,6,7,8,3,4,5]=>1000100=>0010001
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,6,1,7,8,3,4,5]=>0100100=>0010010
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,6,7,8,1,3,4,5]=>0001000=>0001000
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[2,6,1,7,3,4,5,8]=>0101000=>0001010
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[2,6,7,1,3,4,5,8]=>0010000=>0000100
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,6,4,7,5,8]=>0101010=>0101010
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[2,3,6,1,4,7,5,8]=>0010010=>0100100
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,7,1,4,5,8]=>0001000=>0001000
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[2,1,6,3,4,7,8,5]=>1010001=>1000101
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,3,6,1,4,7,8,5]=>0010001=>1000100
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[2,1,3,6,7,4,8,5]=>1000101=>1010001
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[2,3,6,7,1,4,8,5]=>0001001=>1001000
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[2,3,1,6,7,8,4,5]=>0100010=>0100010
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[2,3,6,1,7,8,4,5]=>0010010=>0100100
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[2,3,6,7,1,8,4,5]=>0001010=>0101000
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,3,6,7,8,1,4,5]=>0000100=>0010000
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[2,6,1,8,3,4,5,7]=>0101000=>0001010
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[2,6,8,1,3,4,5,7]=>0010000=>0000100
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[2,1,6,3,4,8,5,7]=>1010010=>0100101
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[2,3,1,6,4,8,5,7]=>0101010=>0101010
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[2,3,6,1,4,8,5,7]=>0010010=>0100100
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[2,3,1,6,8,4,5,7]=>0100100=>0010010
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[2,3,6,1,8,4,5,7]=>0010100=>0010100
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[2,3,6,8,1,4,5,7]=>0001000=>0001000
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[2,1,6,3,4,5,8,7]=>1010001=>1000101
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[2,6,1,3,4,5,8,7]=>0100001=>1000010
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[2,3,6,1,4,5,8,7]=>0010001=>1000100
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[2,1,3,4,6,5,8,7]=>1000101=>1010001
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,3,4,1,6,5,8,7]=>0010101=>1010100
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[2,3,4,1,6,8,5,7]=>0010010=>0100100
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[2,3,4,6,1,8,5,7]=>0001010=>0101000
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[2,3,6,1,4,5,7,8]=>0010000=>0000100
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[2,1,3,4,6,5,7,8]=>1000100=>0010001
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[2,3,4,1,6,5,7,8]=>0010100=>0010100
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[2,3,1,4,6,7,5,8]=>0100010=>0100010
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[2,3,4,1,6,7,5,8]=>0010010=>0100100
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[2,1,3,4,6,7,8,5]=>1000001=>1000001
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[2,3,1,4,6,7,8,5]=>0100001=>1000010
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[2,3,4,1,6,7,8,5]=>0010001=>1000100
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,6,7,8,1,5]=>0000010=>0100000
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[2,7,1,3,8,4,5,6]=>0100100=>0010010
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,1,7,8,3,4,5,6]=>1001000=>0001001
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[2,7,1,8,3,4,5,6]=>0101000=>0001010
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,7,8,1,3,4,5,6]=>0010000=>0000100
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[2,1,7,3,4,8,5,6]=>1010010=>0100101
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[2,1,3,7,4,8,5,6]=>1001010=>0101001
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[2,3,1,7,4,8,5,6]=>0101010=>0101010
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[2,3,1,7,8,4,5,6]=>0100100=>0010010
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[2,3,7,8,1,4,5,6]=>0001000=>0001000
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[2,1,7,3,4,5,8,6]=>1010001=>1000101
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[2,3,1,7,4,5,8,6]=>0101001=>1001010
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[2,3,7,1,4,5,8,6]=>0010001=>1000100
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,3,4,1,7,5,8,6]=>0010101=>1010100
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[2,3,4,7,1,5,8,6]=>0001001=>1001000
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[2,1,3,4,7,8,5,6]=>1000010=>0100001
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[2,3,1,4,7,8,5,6]=>0100010=>0100010
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[2,3,4,1,7,8,5,6]=>0010010=>0100100
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,3,4,7,8,1,5,6]=>0000100=>0010000
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[2,3,4,1,7,5,6,8]=>0010100=>0010100
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[2,3,4,7,1,5,6,8]=>0001000=>0001000
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[2,3,4,1,5,7,6,8]=>0010010=>0100100
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[2,3,1,4,5,7,8,6]=>0100001=>1000010
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[2,3,4,1,5,7,8,6]=>0010001=>1000100
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,1,8,3,4,5,6,7]=>1010000=>0000101
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,8,1,3,4,5,6,7]=>0100000=>0000010
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[2,3,8,1,4,5,6,7]=>0010000=>0000100
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[2,1,3,4,8,5,6,7]=>1000100=>0010001
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[2,3,1,4,8,5,6,7]=>0100100=>0010010
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[2,3,4,1,8,5,6,7]=>0010100=>0010100
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[2,3,4,8,1,5,6,7]=>0001000=>0001000
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[2,3,4,1,5,8,6,7]=>0010010=>0100100
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,3,4,5,8,1,6,7]=>0000100=>0010000
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,8,7]=>1000001=>1000001
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[2,3,4,1,5,6,8,7]=>0010001=>1000100
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,3,4,5,6,1,8,7]=>0000101=>1010000
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7,8]=>1000000=>0000001
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[2,3,1,4,5,6,7,8]=>0100000=>0000010
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[2,3,4,1,5,6,7,8]=>0010000=>0000100
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[2,3,4,5,1,6,7,8]=>0001000=>0001000
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1]=>0000001=>1000000
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,6,5,8,7]=>1010101=>1010101
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[3,4,1,2,6,5,8,7]=>0100101=>1010010
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[3,1,4,2,6,8,5,7]=>1010010=>0100101
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[3,4,1,2,6,8,5,7]=>0100010=>0100010
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,4,6,2,8,5,7]=>1001010=>0101001
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[3,1,4,6,8,2,5,7]=>1000100=>0010001
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[3,4,1,6,8,2,5,7]=>0100100=>0010010
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[3,1,4,2,6,5,7,8]=>1010100=>0010101
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[3,4,1,2,6,5,7,8]=>0100100=>0010010
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[3,1,4,2,6,7,5,8]=>1010010=>0100101
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[3,4,1,2,6,7,5,8]=>0100010=>0100010
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[3,4,1,6,2,7,5,8]=>0101010=>0101010
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[3,4,6,1,2,7,5,8]=>0010010=>0100100
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[3,1,4,2,6,7,8,5]=>1010001=>1000101
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[3,4,1,2,6,7,8,5]=>0100001=>1000010
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[3,4,6,1,2,7,8,5]=>0010001=>1000100
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[3,4,6,1,7,2,8,5]=>0010101=>1010100
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,6,7,8,2,5]=>1000010=>0100001
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[3,4,6,1,7,8,2,5]=>0010010=>0100100
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[3,4,6,7,1,8,2,5]=>0001010=>0101000
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,6,7,8,1,2,5]=>0000100=>0010000
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,7,5,8,6]=>1010101=>1010101
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[3,4,1,2,7,5,8,6]=>0100101=>1010010
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[3,4,7,1,2,5,8,6]=>0010001=>1000100
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,4,2,7,8,5,6]=>1010010=>0100101
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,4,1,2,7,8,5,6]=>0100010=>0100010
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[3,4,7,1,8,2,5,6]=>0010100=>0010100
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,4,2,7,5,6,8]=>1010100=>0010101
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[3,4,1,2,7,5,6,8]=>0100100=>0010010
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[3,4,1,2,5,7,6,8]=>0100010=>0100010
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,4,5,2,7,6,8]=>1001010=>0101001
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,1,5,2,7,6,8]=>0101010=>0101010
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[3,4,1,5,7,2,6,8]=>0100100=>0010010
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,4,2,5,7,8,6]=>1010001=>1000101
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[3,4,1,2,5,7,8,6]=>0100001=>1000010
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,4,5,2,7,8,6]=>1001001=>1001001
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[3,4,1,5,7,2,8,6]=>0100101=>1010010
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[3,4,5,7,1,2,8,6]=>0001001=>1001000
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,4,5,7,8,2,6]=>1000010=>0100001
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[3,4,1,5,7,8,2,6]=>0100010=>0100010
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[3,4,5,1,7,8,2,6]=>0010010=>0100100
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,4,2,8,5,6,7]=>1010100=>0010101
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[3,4,1,2,8,5,6,7]=>0100100=>0010010
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,4,8,2,5,6,7]=>1001000=>0001001
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[3,4,1,8,2,5,6,7]=>0101000=>0001010
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[3,4,8,1,2,5,6,7]=>0010000=>0000100
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,4,2,5,8,6,7]=>1010010=>0100101
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[3,4,1,2,5,8,6,7]=>0100010=>0100010
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[3,4,1,5,2,8,6,7]=>0101010=>0101010
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[3,4,5,1,2,8,6,7]=>0010010=>0100100
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[3,4,1,5,8,2,6,7]=>0100100=>0010010
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[3,4,5,8,1,2,6,7]=>0001000=>0001000
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[3,4,1,2,5,6,8,7]=>0100001=>1000010
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[3,1,4,5,6,2,8,7]=>1000101=>1010001
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,1,6,2,8,7]=>0010101=>1010100
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,5,6,1,2,8,7]=>0001001=>1001000
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[3,4,1,5,6,8,2,7]=>0100010=>0100010
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[3,4,5,6,1,8,2,7]=>0001010=>0101000
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,6,8,1,2,7]=>0000100=>0010000
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[3,1,4,2,5,6,7,8]=>1010000=>0000101
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[3,4,1,2,5,6,7,8]=>0100000=>0000010
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[3,4,1,5,6,2,7,8]=>0100100=>0010010
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[3,4,5,1,6,2,7,8]=>0010100=>0010100
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[3,4,1,5,6,7,2,8]=>0100010=>0100010
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[3,4,5,6,1,7,2,8]=>0001010=>0101000
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,5,6,7,1,2,8]=>0000100=>0010000
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,8,2]=>1000001=>1000001
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[3,4,5,1,6,7,8,2]=>0010001=>1000100
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[3,4,5,6,1,7,8,2]=>0001001=>1001000
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,8,1,2]=>0000010=>0100000
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,6,4,8,7]=>1010101=>1010101
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,5,6,2,4,8,7]=>1001001=>1001001
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,5,1,6,2,4,8,7]=>0101001=>1001010
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,5,6,1,2,4,8,7]=>0010001=>1000100
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[3,5,1,2,6,8,4,7]=>0100010=>0100010
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,5,6,2,8,4,7]=>1001010=>0101001
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,5,6,1,2,8,4,7]=>0010010=>0100100
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,1,5,6,8,2,4,7]=>1000100=>0010001
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,5,6,1,8,2,4,7]=>0010100=>0010100
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,6,2,4,7,8]=>1001000=>0001001
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,5,1,6,2,4,7,8]=>0101000=>0001010
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,5,6,1,2,4,7,8]=>0010000=>0000100
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,5,1,6,2,7,4,8]=>0101010=>0101010
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,5,6,1,2,7,4,8]=>0010010=>0100100
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,5,6,1,7,2,4,8]=>0010100=>0010100
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[3,1,5,2,6,7,8,4]=>1010001=>1000101
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,5,1,2,6,7,8,4]=>0100001=>1000010
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,1,5,6,2,7,8,4]=>1001001=>1001001
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,5,1,6,2,7,8,4]=>0101001=>1001010
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,5,6,1,2,7,8,4]=>0010001=>1000100
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[3,1,5,6,7,2,8,4]=>1000101=>1010001
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,5,1,6,7,2,8,4]=>0100101=>1010010
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,5,6,1,7,2,8,4]=>0010101=>1010100
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,5,6,7,8,2,4]=>1000010=>0100001
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,5,1,6,7,8,2,4]=>0100010=>0100010
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,5,6,1,7,8,2,4]=>0010010=>0100100
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,5,6,7,8,1,2,4]=>0000100=>0010000
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,7,4,8,6]=>1010101=>1010101
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,5,1,2,7,4,8,6]=>0100101=>1010010
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,5,7,2,4,8,6]=>1001001=>1001001
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,5,1,7,2,4,8,6]=>0101001=>1001010
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,5,7,1,2,4,8,6]=>0010001=>1000100
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,5,2,7,8,4,6]=>1010010=>0100101
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,5,1,2,7,8,4,6]=>0100010=>0100010
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,5,7,2,8,4,6]=>1001010=>0101001
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,5,1,7,2,8,4,6]=>0101010=>0101010
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,5,7,8,2,4,6]=>1000100=>0010001
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,5,1,7,8,2,4,6]=>0100100=>0010010
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,5,7,8,1,2,4,6]=>0001000=>0001000
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,5,2,7,4,6,8]=>1010100=>0010101
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[3,5,1,2,7,4,6,8]=>0100100=>0010010
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,5,7,2,4,6,8]=>1001000=>0001001
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[3,5,1,7,2,4,6,8]=>0101000=>0001010
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,5,7,1,2,4,6,8]=>0010000=>0000100
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,5,2,4,7,6,8]=>1010010=>0100101
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[3,5,1,2,4,7,6,8]=>0100010=>0100010
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,4,7,6,8]=>1001010=>0101001
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,7,6,8]=>0101010=>0101010
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,5,2,4,7,6,8]=>0010010=>0100100
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[3,1,2,5,7,4,6,8]=>1000100=>0010001
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,2,5,7,4,6,8]=>0100100=>0010010
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,5,2,7,4,6,8]=>0010100=>0010100
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,5,7,2,4,6,8]=>0001000=>0001000
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[3,5,1,2,4,7,8,6]=>0100001=>1000010
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,2,5,4,7,8,6]=>0101001=>1001010
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,2,4,7,8,6]=>0010001=>1000100
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,5,7,4,8,6]=>1000101=>1010001
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,2,5,7,4,8,6]=>0100101=>1010010
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,2,7,4,8,6]=>0010101=>1010100
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,7,2,4,8,6]=>0001001=>1001000
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,2,5,7,8,4,6]=>0100010=>0100010
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,5,2,7,8,4,6]=>0010010=>0100100
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,5,7,2,8,4,6]=>0001010=>0101000
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,5,7,8,2,4,6]=>0000100=>0010000
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,5,2,8,4,6,7]=>1010100=>0010101
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[3,5,1,2,8,4,6,7]=>0100100=>0010010
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,5,8,2,4,6,7]=>1001000=>0001001
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,5,1,8,2,4,6,7]=>0101000=>0001010
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,5,2,4,8,6,7]=>1010010=>0100101
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,5,1,2,4,8,6,7]=>0100010=>0100010
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,8,6,7]=>0101010=>0101010
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,5,2,4,8,6,7]=>0010010=>0100100
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,1,2,5,8,4,6,7]=>1000100=>0010001
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,5,8,4,6,7]=>0100100=>0010010
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,5,2,8,4,6,7]=>0010100=>0010100
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,5,8,2,4,6,7]=>0001000=>0001000
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,5,1,2,4,6,8,7]=>0100001=>1000010
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[3,1,2,5,4,6,8,7]=>1001001=>1001001
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,5,2,4,6,8,7]=>0010001=>1000100
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,3,5,6,2,4,8,7]=>0001001=>1001000
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,1,2,5,6,8,4,7]=>1000010=>0100001
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,5,2,6,8,4,7]=>0010010=>0100100
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,5,1,2,4,6,7,8]=>0100000=>0000010
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,3,2,5,4,6,7,8]=>0101000=>0001010
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,3,5,2,4,6,7,8]=>0010000=>0000100
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,3,2,5,6,4,7,8]=>0100100=>0010010
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,3,5,2,6,4,7,8]=>0010100=>0010100
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,3,5,6,2,4,7,8]=>0001000=>0001000
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,1,2,5,6,7,4,8]=>1000010=>0100001
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,3,2,5,6,7,4,8]=>0100010=>0100010
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,3,5,2,6,7,4,8]=>0010010=>0100100
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,3,5,6,2,7,4,8]=>0001010=>0101000
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,3,5,6,7,2,4,8]=>0000100=>0010000
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,1,2,5,6,7,8,4]=>1000001=>1000001
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,3,5,6,2,7,8,4]=>0001001=>1001000
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,5,6,7,8,2,4]=>0000010=>0100000
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,1,6,2,7,4,8,5]=>1010101=>1010101
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,6,1,2,7,4,8,5]=>0100101=>1010010
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,6,1,7,2,4,8,5]=>0101001=>1001010
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,6,7,1,2,4,8,5]=>0010001=>1000100
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,1,6,7,2,8,4,5]=>1001010=>0101001
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,6,1,7,2,8,4,5]=>0101010=>0101010
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,6,7,1,2,8,4,5]=>0010010=>0100100
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,6,1,7,8,2,4,5]=>0100100=>0010010
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,6,7,8,1,2,4,5]=>0001000=>0001000
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,1,6,7,2,4,5,8]=>1001000=>0001001
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,6,7,1,2,4,5,8]=>0010000=>0000100
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,1,6,2,4,7,5,8]=>1010010=>0100101
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,6,1,2,4,7,5,8]=>0100010=>0100010
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,1,2,6,4,7,5,8]=>1001010=>0101001
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,3,2,6,4,7,5,8]=>0101010=>0101010
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,3,6,2,4,7,5,8]=>0010010=>0100100
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,3,2,6,7,4,5,8]=>0100100=>0010010
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,1,6,2,4,7,8,5]=>1010001=>1000101
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,6,1,2,4,7,8,5]=>0100001=>1000010
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,1,2,6,4,7,8,5]=>1001001=>1001001
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,3,2,6,4,7,8,5]=>0101001=>1001010
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,3,6,2,4,7,8,5]=>0010001=>1000100
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,6,7,4,8,5]=>1000101=>1010001
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,3,6,2,7,4,8,5]=>0010101=>1010100
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,3,6,2,7,8,4,5]=>0010010=>0100100
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,1,6,2,8,4,5,7]=>1010100=>0010101
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,1,6,8,2,4,5,7]=>1001000=>0001001
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,6,8,1,2,4,5,7]=>0010000=>0000100
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,1,6,2,4,8,5,7]=>1010010=>0100101
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,6,1,2,4,8,5,7]=>0100010=>0100010
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,3,2,6,4,8,5,7]=>0101010=>0101010
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,3,6,2,4,8,5,7]=>0010010=>0100100
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,1,6,2,4,5,8,7]=>1010001=>1000101
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,1,2,6,4,5,8,7]=>1001001=>1001001
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,3,2,4,6,5,8,7]=>0100101=>1010010
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,3,4,6,2,5,8,7]=>0001001=>1001000
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,1,2,4,6,8,5,7]=>1000010=>0100001
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,3,2,4,6,8,5,7]=>0100010=>0100010
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,3,4,6,8,2,5,7]=>0000100=>0010000
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,1,6,2,4,5,7,8]=>1010000=>0000101
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,3,2,6,4,5,7,8]=>0101000=>0001010
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,3,6,2,4,5,7,8]=>0010000=>0000100
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,3,2,4,6,5,7,8]=>0100100=>0010010
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,1,2,4,6,7,5,8]=>1000010=>0100001
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,3,4,2,6,7,5,8]=>0010010=>0100100
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,1,2,4,6,7,8,5]=>1000001=>1000001
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,3,2,4,6,7,8,5]=>0100001=>1000010
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,3,4,2,6,7,8,5]=>0010001=>1000100
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,3,4,6,7,2,8,5]=>0000101=>1010000
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[3,7,1,2,8,4,5,6]=>0100100=>0010010
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[3,1,7,8,2,4,5,6]=>1001000=>0001001
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[3,1,2,7,4,8,5,6]=>1001010=>0101001
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,3,2,7,4,8,5,6]=>0101010=>0101010
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,3,7,2,4,8,5,6]=>0010010=>0100100
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[3,1,2,7,8,4,5,6]=>1000100=>0010001
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[3,7,1,2,4,5,8,6]=>0100001=>1000010
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,3,7,2,4,5,8,6]=>0010001=>1000100
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[3,1,2,4,7,5,8,6]=>1000101=>1010001
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,3,2,4,7,5,8,6]=>0100101=>1010010
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[3,1,2,4,7,8,5,6]=>1000010=>0100001
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,3,2,4,7,8,5,6]=>0100010=>0100010
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,3,4,2,7,8,5,6]=>0010010=>0100100
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[3,7,1,2,4,5,6,8]=>0100000=>0000010
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,3,2,7,4,5,6,8]=>0101000=>0001010
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[3,1,2,4,7,5,6,8]=>1000100=>0010001
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,3,2,4,5,7,6,8]=>0100010=>0100010
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,3,4,2,5,7,6,8]=>0010010=>0100100
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,3,4,5,2,7,6,8]=>0001010=>0101000
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,3,4,5,7,2,6,8]=>0000100=>0010000
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,3,2,4,5,7,8,6]=>0100001=>1000010
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,3,4,2,5,7,8,6]=>0010001=>1000100
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,3,4,5,2,7,8,6]=>0001001=>1001000
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,3,4,5,7,2,8,6]=>0000101=>1010000
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,3,4,5,7,8,2,6]=>0000010=>0100000
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[3,1,8,2,4,5,6,7]=>1010000=>0000101
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,3,2,8,4,5,6,7]=>0101000=>0001010
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,3,8,2,4,5,6,7]=>0010000=>0000100
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[3,1,2,4,8,5,6,7]=>1000100=>0010001
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,3,2,4,8,5,6,7]=>0100100=>0010010
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,3,4,2,8,5,6,7]=>0010100=>0010100
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,3,4,8,2,5,6,7]=>0001000=>0001000
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[3,1,2,4,5,8,6,7]=>1000010=>0100001
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,3,2,4,5,8,6,7]=>0100010=>0100010
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,3,4,2,5,8,6,7]=>0010010=>0100100
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,3,4,5,2,8,6,7]=>0001010=>0101000
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,3,4,5,8,2,6,7]=>0000100=>0010000
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,3,4,2,5,6,8,7]=>0010001=>1000100
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,3,4,5,2,6,8,7]=>0001001=>1001000
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,1,2,4,5,6,7,8]=>1000000=>0000001
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,3,2,4,5,6,7,8]=>0100000=>0000010
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,3,4,2,5,6,7,8]=>0010000=>0000100
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,3,4,5,2,6,7,8]=>0001000=>0001000
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,3,4,5,6,7,2,8]=>0000010=>0100000
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,5,2,6,3,8,7]=>1010101=>1010101
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[4,1,5,6,2,3,8,7]=>1001001=>1001001
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[4,5,1,6,2,3,8,7]=>0101001=>1001010
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[4,5,6,1,2,3,8,7]=>0010001=>1000100
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[4,1,5,2,6,8,3,7]=>1010010=>0100101
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[4,5,1,2,6,8,3,7]=>0100010=>0100010
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[4,1,5,6,2,8,3,7]=>1001010=>0101001
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[4,5,1,6,2,8,3,7]=>0101010=>0101010
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[4,1,5,6,8,2,3,7]=>1000100=>0010001
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[4,5,6,8,1,2,3,7]=>0001000=>0001000
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[4,1,5,6,2,3,7,8]=>1001000=>0001001
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[4,5,1,6,2,3,7,8]=>0101000=>0001010
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[4,5,1,6,2,7,3,8]=>0101010=>0101010
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[4,1,5,6,7,2,3,8]=>1000100=>0010001
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[4,5,1,6,7,2,3,8]=>0100100=>0010010
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[4,5,6,7,1,2,3,8]=>0001000=>0001000
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[4,1,5,2,6,7,8,3]=>1010001=>1000101
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,6,7,8,3]=>0100001=>1000010
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[4,5,1,6,2,7,8,3]=>0101001=>1001010
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[4,1,5,6,7,2,8,3]=>1000101=>1010001
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[4,5,1,6,7,2,8,3]=>0100101=>1010010
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[4,5,6,1,7,2,8,3]=>0010101=>1010100
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[4,5,6,7,1,2,8,3]=>0001001=>1001000
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[4,1,5,6,7,8,2,3]=>1000010=>0100001
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[4,5,1,6,7,8,2,3]=>0100010=>0100010
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,5,6,7,1,8,2,3]=>0001010=>0101000
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,1,2,3]=>0000100=>0010000
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[4,1,5,2,7,3,8,6]=>1010101=>1010101
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[4,5,1,7,2,3,8,6]=>0101001=>1001010
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[4,1,5,2,7,8,3,6]=>1010010=>0100101
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[4,5,1,2,7,8,3,6]=>0100010=>0100010
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[4,1,5,7,2,8,3,6]=>1001010=>0101001
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[4,5,1,7,2,8,3,6]=>0101010=>0101010
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[4,5,7,1,2,8,3,6]=>0010010=>0100100
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[4,5,1,7,8,2,3,6]=>0100100=>0010010
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[4,1,5,2,7,3,6,8]=>1010100=>0010101
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[4,5,1,2,7,3,6,8]=>0100100=>0010010
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[4,1,5,7,2,3,6,8]=>1001000=>0001001
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[4,5,1,7,2,3,6,8]=>0101000=>0001010
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[4,5,1,2,3,7,6,8]=>0100010=>0100010
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,4,2,5,3,7,6,8]=>0101010=>0101010
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,4,5,2,3,7,6,8]=>0010010=>0100100
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[4,1,2,5,7,3,6,8]=>1000100=>0010001
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,4,2,5,7,3,6,8]=>0100100=>0010010
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,4,5,2,7,3,6,8]=>0010100=>0010100
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,4,5,7,2,3,6,8]=>0001000=>0001000
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[4,1,5,2,3,7,8,6]=>1010001=>1000101
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[4,1,2,5,3,7,8,6]=>1001001=>1001001
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,4,2,5,3,7,8,6]=>0101001=>1001010
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,4,5,2,3,7,8,6]=>0010001=>1000100
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[4,1,2,5,7,3,8,6]=>1000101=>1010001
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,4,2,5,7,3,8,6]=>0100101=>1010010
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,4,5,2,7,3,8,6]=>0010101=>1010100
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,4,5,7,2,3,8,6]=>0001001=>1001000
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[4,1,2,5,7,8,3,6]=>1000010=>0100001
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,4,2,5,7,8,3,6]=>0100010=>0100010
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,4,5,2,7,8,3,6]=>0010010=>0100100
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,4,5,7,8,2,3,6]=>0000100=>0010000
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[4,1,5,2,8,3,6,7]=>1010100=>0010101
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[4,5,1,2,8,3,6,7]=>0100100=>0010010
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[4,1,5,8,2,3,6,7]=>1001000=>0001001
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[4,5,1,8,2,3,6,7]=>0101000=>0001010
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[4,5,8,1,2,3,6,7]=>0010000=>0000100
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[4,1,5,2,3,8,6,7]=>1010010=>0100101
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[4,5,1,2,3,8,6,7]=>0100010=>0100010
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[4,1,2,5,3,8,6,7]=>1001010=>0101001
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,5,3,8,6,7]=>0101010=>0101010
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,5,2,3,8,6,7]=>0010010=>0100100
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[4,1,2,5,8,3,6,7]=>1000100=>0010001
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,5,8,3,6,7]=>0100100=>0010010
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,5,2,8,3,6,7]=>0010100=>0010100
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,5,8,2,3,6,7]=>0001000=>0001000
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,2,5,3,6,8,7]=>0101001=>1001010
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[4,1,2,5,6,3,8,7]=>1000101=>1010001
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,2,6,3,8,7]=>0010101=>1010100
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,5,6,8,3,7]=>1000010=>0100001
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,4,5,2,6,8,3,7]=>0010010=>0100100
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,4,5,6,2,8,3,7]=>0001010=>0101000
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,4,5,6,8,2,3,7]=>0000100=>0010000
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[4,5,1,2,3,6,7,8]=>0100000=>0000010
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,4,2,5,3,6,7,8]=>0101000=>0001010
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,4,5,2,3,6,7,8]=>0010000=>0000100
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[4,1,2,5,6,3,7,8]=>1000100=>0010001
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,4,5,2,6,3,7,8]=>0010100=>0010100
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[4,1,2,5,6,7,3,8]=>1000010=>0100001
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,4,2,5,6,7,3,8]=>0100010=>0100010
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,4,5,6,7,2,3,8]=>0000100=>0010000
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[4,1,2,5,6,7,8,3]=>1000001=>1000001
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,4,5,2,6,7,8,3]=>0010001=>1000100
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,4,5,6,7,2,8,3]=>0000101=>1010000
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,6,2,7,3,8,5]=>1010101=>1010101
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[4,1,6,7,2,3,8,5]=>1001001=>1001001
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[4,6,7,1,2,3,8,5]=>0010001=>1000100
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[4,6,7,1,2,8,3,5]=>0010010=>0100100
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[4,6,7,1,8,2,3,5]=>0010100=>0010100
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,6,7,8,1,2,3,5]=>0001000=>0001000
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[4,1,6,2,7,3,5,8]=>1010100=>0010101
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[4,6,1,2,7,3,5,8]=>0100100=>0010010
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[4,1,6,7,2,3,5,8]=>1001000=>0001001
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[4,6,1,7,2,3,5,8]=>0101000=>0001010
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[4,1,6,2,3,7,5,8]=>1010010=>0100101
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[4,6,1,2,3,7,5,8]=>0100010=>0100010
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[4,1,2,6,3,7,5,8]=>1001010=>0101001
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,4,2,6,3,7,5,8]=>0101010=>0101010
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[4,1,2,6,7,3,5,8]=>1000100=>0010001
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,4,2,6,7,3,5,8]=>0100100=>0010010
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,4,6,2,7,3,5,8]=>0010100=>0010100
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[4,1,6,2,3,7,8,5]=>1010001=>1000101
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[4,1,2,6,3,7,8,5]=>1001001=>1001001
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,6,2,3,7,8,5]=>0010001=>1000100
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[4,1,2,6,7,3,8,5]=>1000101=>1010001
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,4,6,2,7,3,8,5]=>0010101=>1010100
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,4,2,6,7,8,3,5]=>0100010=>0100010
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,4,6,2,7,8,3,5]=>0010010=>0100100
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,4,6,7,2,8,3,5]=>0001010=>0101000
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[4,1,6,2,8,3,5,7]=>1010100=>0010101
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[4,6,1,2,8,3,5,7]=>0100100=>0010010
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[4,1,6,8,2,3,5,7]=>1001000=>0001001
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,6,1,8,2,3,5,7]=>0101000=>0001010
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,6,8,1,2,3,5,7]=>0010000=>0000100
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[4,6,1,2,3,8,5,7]=>0100010=>0100010
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[4,1,2,6,3,8,5,7]=>1001010=>0101001
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,6,3,8,5,7]=>0101010=>0101010
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,4,6,2,3,8,5,7]=>0010010=>0100100
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,6,8,3,5,7]=>0100100=>0010010
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,4,6,2,8,3,5,7]=>0010100=>0010100
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[4,1,2,6,3,5,8,7]=>1001001=>1001001
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,4,2,6,3,5,8,7]=>0101001=>1001010
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[4,1,2,3,6,5,8,7]=>1000101=>1010001
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,4,2,3,6,5,8,7]=>0100101=>1010010
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,2,4,3,6,5,8,7]=>0010101=>1010100
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,3,6,8,5,7]=>1000010=>0100001
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,2,4,3,6,8,5,7]=>0010010=>0100100
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,2,4,6,8,3,5,7]=>0000100=>0010000
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,4,2,6,3,5,7,8]=>0101000=>0001010
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[4,1,2,3,6,5,7,8]=>1000100=>0010001
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,4,2,3,6,5,7,8]=>0100100=>0010010
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,2,4,3,6,5,7,8]=>0010100=>0010100
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,2,4,6,3,5,7,8]=>0001000=>0001000
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[4,1,2,3,6,7,5,8]=>1000010=>0100001
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,2,4,3,6,7,5,8]=>0010010=>0100100
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[4,1,2,3,6,7,8,5]=>1000001=>1000001
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,4,2,3,6,7,8,5]=>0100001=>1000010
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,2,4,3,6,7,8,5]=>0010001=>1000100
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,2,4,6,7,3,8,5]=>0000101=>1010000
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,1,7,2,8,3,5,6]=>1010100=>0010101
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,7,1,2,8,3,5,6]=>0100100=>0010010
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,7,1,8,2,3,5,6]=>0101000=>0001010
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,4,2,7,3,8,5,6]=>0101010=>0101010
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,1,2,7,8,3,5,6]=>1000100=>0010001
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,4,2,7,8,3,5,6]=>0100100=>0010010
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[4,1,7,2,3,5,8,6]=>1010001=>1000101
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,1,2,7,3,5,8,6]=>1001001=>1001001
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,4,2,7,3,5,8,6]=>0101001=>1001010
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,4,7,2,3,5,8,6]=>0010001=>1000100
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[4,1,2,3,7,5,8,6]=>1000101=>1010001
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,2,4,3,7,5,8,6]=>0010101=>1010100
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,1,2,3,7,8,5,6]=>1000010=>0100001
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,4,2,3,7,8,5,6]=>0100010=>0100010
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,2,4,3,7,8,5,6]=>0010010=>0100100
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,2,4,7,8,3,5,6]=>0000100=>0010000
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,4,2,7,3,5,6,8]=>0101000=>0001010
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,1,2,3,7,5,6,8]=>1000100=>0010001
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,4,2,3,7,5,6,8]=>0100100=>0010010
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,1,2,3,5,7,6,8]=>1000010=>0100001
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,4,2,3,5,7,6,8]=>0100010=>0100010
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,1,2,3,5,7,8,6]=>1000001=>1000001
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,4,2,3,5,7,8,6]=>0100001=>1000010
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,2,4,3,5,7,8,6]=>0010001=>1000100
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,2,4,5,3,7,8,6]=>0001001=>1001000
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,2,4,5,7,3,8,6]=>0000101=>1010000
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[4,8,1,2,3,5,6,7]=>0100000=>0000010
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[4,1,2,8,3,5,6,7]=>1001000=>0001001
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,4,2,8,3,5,6,7]=>0101000=>0001010
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,4,8,2,3,5,6,7]=>0010000=>0000100
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[4,1,2,3,8,5,6,7]=>1000100=>0010001
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,4,2,3,8,5,6,7]=>0100100=>0010010
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,2,4,3,8,5,6,7]=>0010100=>0010100
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,2,4,8,3,5,6,7]=>0001000=>0001000
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[4,1,2,3,5,8,6,7]=>1000010=>0100001
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,4,2,3,5,8,6,7]=>0100010=>0100010
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,2,4,3,5,8,6,7]=>0010010=>0100100
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,2,4,5,3,8,6,7]=>0001010=>0101000
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,2,4,5,8,3,6,7]=>0000100=>0010000
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[4,1,2,3,5,6,8,7]=>1000001=>1000001
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,4,2,3,5,6,8,7]=>0100001=>1000010
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,2,4,3,5,6,8,7]=>0010001=>1000100
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,2,4,5,6,8,3,7]=>0000010=>0100000
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[4,1,2,3,5,6,7,8]=>1000000=>0000001
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,4,2,3,5,6,7,8]=>0100000=>0000010
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,2,4,3,5,6,7,8]=>0010000=>0000100
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,2,4,5,6,3,7,8]=>0000100=>0010000
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[5,1,6,2,7,3,8,4]=>1010101=>1010101
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[5,6,1,2,7,3,8,4]=>0100101=>1010010
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[5,1,6,7,2,3,8,4]=>1001001=>1001001
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[5,6,1,7,2,3,8,4]=>0101001=>1001010
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,1,2,3,8,4]=>0010001=>1000100
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[5,1,6,7,2,8,3,4]=>1001010=>0101001
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[5,6,7,1,2,8,3,4]=>0010010=>0100100
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[5,1,6,7,8,2,3,4]=>1000100=>0010001
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[5,6,1,7,8,2,3,4]=>0100100=>0010010
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[5,6,7,1,8,2,3,4]=>0010100=>0010100
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,1,2,3,4]=>0001000=>0001000
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[5,1,6,2,7,3,4,8]=>1010100=>0010101
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,1,2,3,4,8]=>0010000=>0000100
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[5,1,6,2,3,7,4,8]=>1010010=>0100101
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[5,1,2,6,3,7,4,8]=>1001010=>0101001
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,5,2,6,3,7,4,8]=>0101010=>0101010
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[5,1,2,6,7,3,4,8]=>1000100=>0010001
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[1,5,2,6,7,3,4,8]=>0100100=>0010010
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[1,5,6,7,2,3,4,8]=>0001000=>0001000
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[5,1,6,2,3,7,8,4]=>1010001=>1000101
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[5,6,1,2,3,7,8,4]=>0100001=>1000010
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[5,1,2,6,3,7,8,4]=>1001001=>1001001
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[1,5,2,6,3,7,8,4]=>0101001=>1001010
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[1,5,6,2,3,7,8,4]=>0010001=>1000100
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[5,1,2,6,7,3,8,4]=>1000101=>1010001
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[1,5,6,7,2,3,8,4]=>0001001=>1001000
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[5,1,2,6,7,8,3,4]=>1000010=>0100001
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,5,6,7,8,2,3,4]=>0000100=>0010000
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[5,1,6,2,8,3,4,7]=>1010100=>0010101
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[5,6,1,2,8,3,4,7]=>0100100=>0010010
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[5,6,8,1,2,3,4,7]=>0010000=>0000100
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[5,1,6,2,3,8,4,7]=>1010010=>0100101
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[5,6,1,2,3,8,4,7]=>0100010=>0100010
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[5,1,2,6,3,8,4,7]=>1001010=>0101001
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[1,5,2,6,3,8,4,7]=>0101010=>0101010
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[1,5,6,2,3,8,4,7]=>0010010=>0100100
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[5,1,2,6,8,3,4,7]=>1000100=>0010001
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[1,5,2,6,8,3,4,7]=>0100100=>0010010
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,5,6,2,8,3,4,7]=>0010100=>0010100
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[1,5,6,8,2,3,4,7]=>0001000=>0001000
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[5,1,2,6,3,4,8,7]=>1001001=>1001001
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[1,5,2,6,3,4,8,7]=>0101001=>1001010
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[1,5,6,2,3,4,8,7]=>0010001=>1000100
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,2,5,3,6,4,8,7]=>0010101=>1010100
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[1,2,5,6,3,4,8,7]=>0001001=>1001000
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[5,1,2,3,6,8,4,7]=>1000010=>0100001
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[1,5,2,3,6,8,4,7]=>0100010=>0100010
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[1,2,5,6,3,8,4,7]=>0001010=>0101000
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[5,1,6,2,3,4,7,8]=>1010000=>0000101
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[5,1,2,6,3,4,7,8]=>1001000=>0001001
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[1,5,2,6,3,4,7,8]=>0101000=>0001010
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,2,5,6,3,4,7,8]=>0001000=>0001000
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[5,1,2,3,6,7,4,8]=>1000010=>0100001
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[1,2,5,6,3,7,4,8]=>0001010=>0101000
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[5,1,2,3,6,7,8,4]=>1000001=>1000001
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[1,5,2,3,6,7,8,4]=>0100001=>1000010
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[1,2,5,3,6,7,8,4]=>0010001=>1000100
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[1,2,5,6,3,7,8,4]=>0001001=>1001000
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,2,5,6,7,8,3,4]=>0000010=>0100000
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[5,1,7,2,8,3,4,6]=>1010100=>0010101
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[5,7,1,2,8,3,4,6]=>0100100=>0010010
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[5,7,8,1,2,3,4,6]=>0010000=>0000100
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[5,1,2,7,3,8,4,6]=>1001010=>0101001
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,5,2,7,3,8,4,6]=>0101010=>0101010
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[1,5,7,2,3,8,4,6]=>0010010=>0100100
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[5,1,2,7,8,3,4,6]=>1000100=>0010001
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[1,5,2,7,8,3,4,6]=>0100100=>0010010
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,5,7,2,8,3,4,6]=>0010100=>0010100
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[1,5,7,8,2,3,4,6]=>0001000=>0001000
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[5,1,7,2,3,4,8,6]=>1010001=>1000101
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[5,1,2,7,3,4,8,6]=>1001001=>1001001
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[1,5,2,7,3,4,8,6]=>0101001=>1001010
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[1,5,7,2,3,4,8,6]=>0010001=>1000100
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[5,1,2,3,7,4,8,6]=>1000101=>1010001
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[1,5,2,3,7,4,8,6]=>0100101=>1010010
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,2,5,3,7,4,8,6]=>0010101=>1010100
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[1,2,5,7,3,4,8,6]=>0001001=>1001000
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[5,1,2,3,7,8,4,6]=>1000010=>0100001
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[1,5,2,3,7,8,4,6]=>0100010=>0100010
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,2,5,7,3,8,4,6]=>0001010=>0101000
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[5,7,1,2,3,4,6,8]=>0100000=>0000010
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[5,1,2,7,3,4,6,8]=>1001000=>0001001
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,5,2,7,3,4,6,8]=>0101000=>0001010
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[1,2,5,7,3,4,6,8]=>0001000=>0001000
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,5,2,3,4,7,6,8]=>0100010=>0100010
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,2,3,5,4,7,6,8]=>0001010=>0101000
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,2,3,5,7,4,6,8]=>0000100=>0010000
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[1,5,2,3,4,7,8,6]=>0100001=>1000010
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[1,2,5,3,4,7,8,6]=>0010001=>1000100
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[1,2,3,5,4,7,8,6]=>0001001=>1001000
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[1,2,3,5,7,4,8,6]=>0000101=>1010000
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,2,3,5,7,8,4,6]=>0000010=>0100000
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[5,1,2,8,3,4,6,7]=>1001000=>0001001
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[1,5,2,8,3,4,6,7]=>0101000=>0001010
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[1,5,2,3,8,4,6,7]=>0100100=>0010010
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[1,2,5,3,8,4,6,7]=>0010100=>0010100
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[1,2,5,8,3,4,6,7]=>0001000=>0001000
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[1,5,2,3,4,8,6,7]=>0100010=>0100010
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[1,2,5,3,4,8,6,7]=>0010010=>0100100
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[1,2,3,5,4,8,6,7]=>0001010=>0101000
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[1,2,3,5,8,4,6,7]=>0000100=>0010000
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,5,2,3,4,6,8,7]=>0100001=>1000010
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,2,3,5,6,4,8,7]=>0000101=>1010000
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,2,3,5,6,8,4,7]=>0000010=>0100000
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[5,1,2,3,4,6,7,8]=>1000000=>0000001
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[1,5,2,3,4,6,7,8]=>0100000=>0000010
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[1,2,3,5,4,6,7,8]=>0001000=>0001000
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[1,2,3,5,6,4,7,8]=>0000100=>0010000
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,2,3,5,6,7,4,8]=>0000010=>0100000
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,5,6,7,8,4]=>0000001=>1000000
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[6,1,7,2,8,3,4,5]=>1010100=>0010101
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[6,1,7,8,2,3,4,5]=>1001000=>0001001
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[6,7,1,8,2,3,4,5]=>0101000=>0001010
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,1,2,3,4,5]=>0010000=>0000100
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[6,1,7,2,3,8,4,5]=>1010010=>0100101
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[6,7,1,2,3,8,4,5]=>0100010=>0100010
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[6,1,2,7,3,8,4,5]=>1001010=>0101001
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,6,2,7,3,8,4,5]=>0101010=>0101010
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[1,6,7,2,3,8,4,5]=>0010010=>0100100
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[1,6,7,2,8,3,4,5]=>0010100=>0010100
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,6,7,8,2,3,4,5]=>0001000=>0001000
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[6,1,7,2,3,4,8,5]=>1010001=>1000101
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[6,7,1,2,3,4,8,5]=>0100001=>1000010
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[6,1,2,7,3,4,8,5]=>1001001=>1001001
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[1,6,2,7,3,4,8,5]=>0101001=>1001010
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[1,6,7,2,3,4,8,5]=>0010001=>1000100
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[1,6,2,3,7,4,8,5]=>0100101=>1010010
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[1,2,6,3,7,4,8,5]=>0010101=>1010100
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[6,1,2,3,7,8,4,5]=>1000010=>0100001
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[1,2,6,3,7,8,4,5]=>0010010=>0100100
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[1,2,6,7,3,8,4,5]=>0001010=>0101000
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[6,1,7,2,3,4,5,8]=>1010000=>0000101
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[6,7,1,2,3,4,5,8]=>0100000=>0000010
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[1,6,2,7,3,4,5,8]=>0101000=>0001010
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[1,6,7,2,3,4,5,8]=>0010000=>0000100
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[1,6,2,3,4,7,5,8]=>0100010=>0100010
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[1,2,6,3,4,7,5,8]=>0010010=>0100100
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,2,3,6,4,7,5,8]=>0001010=>0101000
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,2,3,6,7,4,5,8]=>0000100=>0010000
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,7,8,5]=>1000001=>1000001
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[1,6,2,3,4,7,8,5]=>0100001=>1000010
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[1,2,6,3,4,7,8,5]=>0010001=>1000100
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[1,2,3,6,4,7,8,5]=>0001001=>1001000
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,2,3,6,7,4,8,5]=>0000101=>1010000
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[1,2,3,6,7,8,4,5]=>0000010=>0100000
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[6,1,8,2,3,4,5,7]=>1010000=>0000101
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[6,1,2,8,3,4,5,7]=>1001000=>0001001
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[1,6,2,8,3,4,5,7]=>0101000=>0001010
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[1,6,8,2,3,4,5,7]=>0010000=>0000100
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,6,2,3,8,4,5,7]=>0100100=>0010010
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[1,2,6,3,8,4,5,7]=>0010100=>0010100
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[1,2,6,8,3,4,5,7]=>0001000=>0001000
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,6,2,3,4,8,5,7]=>0100010=>0100010
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,2,6,3,4,8,5,7]=>0010010=>0100100
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,2,3,6,4,8,5,7]=>0001010=>0101000
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,8,7]=>1000001=>1000001
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[1,6,2,3,4,5,8,7]=>0100001=>1000010
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,2,6,3,4,5,8,7]=>0010001=>1000100
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,2,3,6,4,5,8,7]=>0001001=>1001000
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,2,3,4,6,5,8,7]=>0000101=>1010000
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,2,3,4,6,8,5,7]=>0000010=>0100000
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[1,6,2,3,4,5,7,8]=>0100000=>0000010
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[1,2,6,3,4,5,7,8]=>0010000=>0000100
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[1,2,3,6,4,5,7,8]=>0001000=>0001000
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,2,3,4,6,5,7,8]=>0000100=>0010000
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,2,3,4,6,7,5,8]=>0000010=>0100000
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,6,7,8,5]=>0000001=>1000000
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[7,8,1,2,3,4,5,6]=>0100000=>0000010
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,1,2,8,3,4,5,6]=>1001000=>0001001
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,7,2,8,3,4,5,6]=>0101000=>0001010
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,7,8,2,3,4,5,6]=>0010000=>0000100
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,1,2,3,8,4,5,6]=>1000100=>0010001
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[1,2,7,8,3,4,5,6]=>0001000=>0001000
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[1,2,7,3,4,8,5,6]=>0010010=>0100100
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,2,3,7,4,8,5,6]=>0001010=>0101000
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,2,3,7,8,4,5,6]=>0000100=>0010000
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,2,7,3,4,5,8,6]=>0010001=>1000100
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[1,2,3,7,4,5,8,6]=>0001001=>1001000
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,2,3,4,7,5,8,6]=>0000101=>1010000
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,2,3,4,7,8,5,6]=>0000010=>0100000
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6,8]=>1000000=>0000001
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,7,2,3,4,5,6,8]=>0100000=>0000010
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[1,2,7,3,4,5,6,8]=>0010000=>0000100
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,2,3,7,4,5,6,8]=>0001000=>0001000
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,2,3,4,7,5,6,8]=>0000100=>0010000
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,2,3,4,5,7,6,8]=>0000010=>0100000
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,7,8,6]=>0000001=>1000000
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[8,1,2,3,4,5,6,7]=>1000000=>0000001
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,8,2,3,4,5,6,7]=>0100000=>0000010
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,2,8,3,4,5,6,7]=>0010000=>0000100
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,2,3,8,4,5,6,7]=>0001000=>0001000
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,2,3,4,8,5,6,7]=>0000100=>0010000
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,2,3,4,5,8,6,7]=>0000010=>0100000
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,8,7]=>0000001=>1000000
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8]=>0000000=>0000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,8,7,10,9]=>101010101=>101010101
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,4,6,8,10,1,3,5,7,9]=>000010000=>000010000
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,4,2,6,3,8,5,10,7,9]=>010101010=>010101010
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,7,4,9,6,8,10]=>101010100=>001010101
Map
to 321-avoiding permutation
Description
Sends a Dyck path to a 321-avoiding permutation.
This bijection defined in [3, pp. 60] and in [2, Section 3.1].
It is shown in [1] that it sends the number of centered tunnels to the number of fixed points, the number of right tunnels to the number of exceedences, and the semilength plus the height of the middle point to 2 times the length of the longest increasing subsequence.
This bijection defined in [3, pp. 60] and in [2, Section 3.1].
It is shown in [1] that it sends the number of centered tunnels to the number of fixed points, the number of right tunnels to the number of exceedences, and the semilength plus the height of the middle point to 2 times the length of the longest increasing subsequence.
Map
descent word
Description
The descent positions of a permutation as a binary word.
For a permutation $\pi$ of $n$ letters and each $1\leq i\leq n-1$ such that $\pi(i) > \pi(i+1)$ we set $w_i=1$, otherwise $w_i=0$.
Thus, the length of the word is one less the size of the permutation. In particular, the descent word is undefined for the empty permutation.
For a permutation $\pi$ of $n$ letters and each $1\leq i\leq n-1$ such that $\pi(i) > \pi(i+1)$ we set $w_i=1$, otherwise $w_i=0$.
Thus, the length of the word is one less the size of the permutation. In particular, the descent word is undefined for the empty permutation.
Map
reverse
Description
Return the reversal of a binary word.
searching the database
Sorry, this map was not found in the database.