Identifier
Mp00120:
Dyck paths
—Lalanne-Kreweras involution⟶
Dyck paths
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00131: Permutations —descent bottoms⟶ Binary words
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00131: Permutations —descent bottoms⟶ Binary words
Images
=>
Cc0005;cc-rep-0Cc0005;cc-rep-1
[1,0]=>[1,0]=>[1]=>
[1,0,1,0]=>[1,1,0,0]=>[1,2]=>0
[1,1,0,0]=>[1,0,1,0]=>[2,1]=>1
[1,0,1,0,1,0]=>[1,1,1,0,0,0]=>[1,2,3]=>00
[1,0,1,1,0,0]=>[1,1,0,0,1,0]=>[3,1,2]=>10
[1,1,0,0,1,0]=>[1,0,1,1,0,0]=>[2,3,1]=>10
[1,1,0,1,0,0]=>[1,1,0,1,0,0]=>[2,1,3]=>10
[1,1,1,0,0,0]=>[1,0,1,0,1,0]=>[3,2,1]=>11
[1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0]=>[1,2,3,4]=>000
[1,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,0]=>[4,1,2,3]=>100
[1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0]=>[3,4,1,2]=>100
[1,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,0]=>[3,1,2,4]=>100
[1,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,0]=>[4,3,1,2]=>101
[1,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0]=>[2,3,4,1]=>100
[1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0]=>[4,2,3,1]=>110
[1,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,0]=>[2,3,1,4]=>100
[1,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0]=>[2,1,3,4]=>100
[1,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,0]=>[4,2,1,3]=>110
[1,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0]=>[3,4,2,1]=>110
[1,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,0]=>[3,2,4,1]=>110
[1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,0]=>[3,2,1,4]=>110
[1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0]=>[4,3,2,1]=>111
[1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5]=>0000
[1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,0]=>[5,1,2,3,4]=>1000
[1,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,3]=>1000
[1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0]=>[4,1,2,3,5]=>1000
[1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0]=>[5,4,1,2,3]=>1001
[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0]=>[3,4,5,1,2]=>1000
[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>[5,3,4,1,2]=>1010
[1,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0]=>[3,4,1,2,5]=>1000
[1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0]=>[3,1,2,4,5]=>1000
[1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0]=>[5,3,1,2,4]=>1010
[1,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0]=>[4,5,3,1,2]=>1010
[1,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,0]=>[4,3,5,1,2]=>1010
[1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0]=>[4,3,1,2,5]=>1010
[1,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0]=>[5,4,3,1,2]=>1011
[1,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>1000
[1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,0]=>[5,2,3,4,1]=>1100
[1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0]=>[4,5,2,3,1]=>1100
[1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0]=>[4,2,3,5,1]=>1100
[1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0]=>[5,4,2,3,1]=>1101
[1,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,0]=>[2,3,4,1,5]=>1000
[1,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]=>[5,2,3,1,4]=>1100
[1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,0]=>[2,3,1,4,5]=>1000
[1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,0]=>[2,1,3,4,5]=>1000
[1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0]=>[5,2,1,3,4]=>1100
[1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0]=>[4,5,2,1,3]=>1100
[1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0]=>[4,2,3,1,5]=>1100
[1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0]=>[4,2,1,3,5]=>1100
[1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0]=>[5,4,2,1,3]=>1101
[1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0]=>[3,4,5,2,1]=>1100
[1,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0]=>[5,3,4,2,1]=>1110
[1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0]=>[3,4,2,5,1]=>1100
[1,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0]=>[3,2,4,5,1]=>1100
[1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0]=>[5,3,2,4,1]=>1110
[1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,0]=>[3,4,2,1,5]=>1100
[1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0]=>[3,2,4,1,5]=>1100
[1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0]=>[3,2,1,4,5]=>1100
[1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0]=>[5,3,2,1,4]=>1110
[1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0]=>[4,5,3,2,1]=>1110
[1,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]=>[4,3,5,2,1]=>1110
[1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0]=>[4,3,2,5,1]=>1110
[1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0]=>[4,3,2,1,5]=>1110
[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>[5,4,3,2,1]=>1111
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,5,6]=>00000
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5]=>10000
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[5,6,1,2,3,4]=>10000
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,2,3,4,6]=>10000
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,2,3,4]=>10001
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[4,5,6,1,2,3]=>10000
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[6,4,5,1,2,3]=>10010
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,5,1,2,3,6]=>10000
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,2,3,5,6]=>10000
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,2,3,5]=>10010
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[5,6,4,1,2,3]=>10010
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[5,4,6,1,2,3]=>10010
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,2,3,6]=>10010
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[6,5,4,1,2,3]=>10011
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,1,2]=>10000
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[6,3,4,5,1,2]=>10100
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[5,6,3,4,1,2]=>10100
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[5,3,4,6,1,2]=>10100
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,1,2]=>10101
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,4,5,1,2,6]=>10000
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[6,3,4,1,2,5]=>10100
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[3,4,1,2,5,6]=>10000
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,2,4,5,6]=>10000
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,2,4,5]=>10100
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[5,6,3,1,2,4]=>10100
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[5,3,4,1,2,6]=>10100
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,2,4,6]=>10100
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[6,5,3,1,2,4]=>10101
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,1,2]=>10100
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[6,4,5,3,1,2]=>10110
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[4,5,3,6,1,2]=>10100
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[4,3,5,6,1,2]=>10100
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[6,4,3,5,1,2]=>10110
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[4,5,3,1,2,6]=>10100
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[4,3,5,1,2,6]=>10100
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,2,5,6]=>10100
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[6,4,3,1,2,5]=>10110
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[5,6,4,3,1,2]=>10110
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[5,4,6,3,1,2]=>10110
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[5,4,3,6,1,2]=>10110
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[5,4,3,1,2,6]=>10110
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,1,2]=>10111
[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>10000
[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[6,2,3,4,5,1]=>11000
[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[5,6,2,3,4,1]=>11000
[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,6,1]=>11000
[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[6,5,2,3,4,1]=>11001
[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[4,5,6,2,3,1]=>11000
[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[6,4,5,2,3,1]=>11010
[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[4,5,2,3,6,1]=>11000
[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[4,2,3,5,6,1]=>11000
[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[6,4,2,3,5,1]=>11010
[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[5,6,4,2,3,1]=>11010
[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[5,4,6,2,3,1]=>11010
[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,6,1]=>11010
[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,3,1]=>11011
[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,1,6]=>10000
[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[6,2,3,4,1,5]=>11000
[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[5,6,2,3,1,4]=>11000
[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,1,6]=>11000
[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[6,5,2,3,1,4]=>11001
[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,4,1,5,6]=>10000
[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[6,2,3,1,4,5]=>11000
[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,1,4,5,6]=>10000
[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,3,4,5,6]=>10000
[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,3,4,5]=>11000
[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[5,6,2,1,3,4]=>11000
[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,3,1,4,6]=>11000
[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,3,4,6]=>11000
[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[6,5,2,1,3,4]=>11001
[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[4,5,6,2,1,3]=>11000
[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[6,4,5,2,1,3]=>11010
[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[4,5,2,3,1,6]=>11000
[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[4,2,3,5,1,6]=>11000
[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[6,4,2,3,1,5]=>11010
[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[4,5,2,1,3,6]=>11000
[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[4,2,3,1,5,6]=>11000
[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,3,5,6]=>11000
[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[6,4,2,1,3,5]=>11010
[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[5,6,4,2,1,3]=>11010
[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[5,4,6,2,1,3]=>11010
[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,1,6]=>11010
[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[5,4,2,1,3,6]=>11010
[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,1,3]=>11011
[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,2,1]=>11000
[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[6,3,4,5,2,1]=>11100
[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[5,6,3,4,2,1]=>11100
[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[5,3,4,6,2,1]=>11100
[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,2,1]=>11101
[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,6,1]=>11000
[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[6,3,4,2,5,1]=>11100
[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,6,1]=>11000
[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,6,1]=>11000
[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[6,3,2,4,5,1]=>11100
[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[5,6,3,2,4,1]=>11100
[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[5,3,4,2,6,1]=>11100
[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,6,1]=>11100
[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,4,1]=>11101
[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,1,6]=>11000
[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[6,3,4,2,1,5]=>11100
[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,1,6]=>11000
[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,1,6]=>11000
[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[6,3,2,4,1,5]=>11100
[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,2,1,5,6]=>11000
[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,4,1,5,6]=>11000
[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,4,5,6]=>11000
[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[6,3,2,1,4,5]=>11100
[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[5,6,3,2,1,4]=>11100
[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[5,3,4,2,1,6]=>11100
[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,1,6]=>11100
[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[5,3,2,1,4,6]=>11100
[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,1,4]=>11101
[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,2,1]=>11100
[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[6,4,5,3,2,1]=>11110
[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[4,5,3,6,2,1]=>11100
[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>11100
[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[6,4,3,5,2,1]=>11110
[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[4,5,3,2,6,1]=>11100
[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[4,3,5,2,6,1]=>11100
[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,6,1]=>11100
[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,5,1]=>11110
[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[4,5,3,2,1,6]=>11100
[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[4,3,5,2,1,6]=>11100
[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,1,6]=>11100
[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[4,3,2,1,5,6]=>11100
[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,1,5]=>11110
[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[5,6,4,3,2,1]=>11110
[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[5,4,6,3,2,1]=>11110
[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[5,4,3,6,2,1]=>11110
[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,6,1]=>11110
[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,1,6]=>11110
[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,2,1]=>11111
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7]=>000000
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6]=>100000
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,7,1,2,3,4,5]=>100000
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,2,3,4,5,7]=>100000
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,2,3,4,5]=>100001
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,6,7,1,2,3,4]=>100000
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[7,5,6,1,2,3,4]=>100010
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,6,1,2,3,4,7]=>100000
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,2,3,4,6,7]=>100000
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,2,3,4,6]=>100010
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[6,7,5,1,2,3,4]=>100010
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[6,5,7,1,2,3,4]=>100010
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,2,3,4,7]=>100010
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[7,6,5,1,2,3,4]=>100011
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,1,2,3]=>100000
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,1,2,3]=>100100
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,1,2,3]=>100100
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,1,2,3]=>100100
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,1,2,3]=>100101
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,5,6,1,2,3,7]=>100000
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,5,1,2,3,6]=>100100
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,5,1,2,3,6,7]=>100000
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,2,3,5,6,7]=>100000
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,2,3,5,6]=>100100
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[6,7,4,1,2,3,5]=>100100
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,5,1,2,3,7]=>100100
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,2,3,5,7]=>100100
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[7,6,4,1,2,3,5]=>100101
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,1,2,3]=>100100
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,1,2,3]=>100110
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,1,2,3]=>100100
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,1,2,3]=>100100
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,1,2,3]=>100110
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[5,6,4,1,2,3,7]=>100100
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,6,1,2,3,7]=>100100
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,2,3,6,7]=>100100
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[7,5,4,1,2,3,6]=>100110
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,1,2,3]=>100110
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,1,2,3]=>100110
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,1,2,3]=>100110
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1,2,3,7]=>100110
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,1,2,3]=>100111
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,1,2]=>100000
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,6,1,2]=>101000
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,5,1,2]=>101000
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,7,1,2]=>101000
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,5,1,2]=>101001
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,4,1,2]=>101000
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,4,1,2]=>101010
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,7,1,2]=>101000
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,7,1,2]=>101000
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,6,1,2]=>101010
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,4,1,2]=>101010
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,4,1,2]=>101010
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,7,1,2]=>101010
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,4,1,2]=>101011
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,1,2,7]=>100000
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,1,2,6]=>101000
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,1,2,5]=>101000
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,1,2,7]=>101000
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,1,2,5]=>101001
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,4,5,1,2,6,7]=>100000
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,4,1,2,5,6]=>101000
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,4,1,2,5,6,7]=>100000
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,2,4,5,6,7]=>100000
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,2,4,5,6]=>101000
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[6,7,3,1,2,4,5]=>101000
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,4,1,2,5,7]=>101000
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,2,4,5,7]=>101000
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[7,6,3,1,2,4,5]=>101001
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,1,2,4]=>101000
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,1,2,4]=>101010
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,1,2,7]=>101000
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,1,2,7]=>101000
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,1,2,6]=>101010
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,6,3,1,2,4,7]=>101000
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,4,1,2,6,7]=>101000
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,2,4,6,7]=>101000
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[7,5,3,1,2,4,6]=>101010
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,1,2,4]=>101010
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,1,2,4]=>101010
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,1,2,7]=>101010
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[6,5,3,1,2,4,7]=>101010
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,1,2,4]=>101011
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,3,1,2]=>101000
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,3,1,2]=>101100
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,3,1,2]=>101100
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,3,1,2]=>101100
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,3,1,2]=>101101
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,7,1,2]=>101000
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,6,1,2]=>101100
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,7,1,2]=>101000
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,7,1,2]=>101000
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,6,1,2]=>101100
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,5,1,2]=>101100
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,7,1,2]=>101100
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,7,1,2]=>101100
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,5,1,2]=>101101
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,1,2,7]=>101000
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,1,2,6]=>101100
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,1,2,7]=>101000
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,1,2,7]=>101000
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,1,2,6]=>101100
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,5,3,1,2,6,7]=>101000
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,5,1,2,6,7]=>101000
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,2,5,6,7]=>101000
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[7,4,3,1,2,5,6]=>101100
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,1,2,5]=>101100
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,1,2,7]=>101100
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,1,2,7]=>101100
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1,2,5,7]=>101100
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,1,2,5]=>101101
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,3,1,2]=>101100
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,3,1,2]=>101110
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,3,1,2]=>101100
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,3,1,2]=>101100
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,3,1,2]=>101110
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,7,1,2]=>101100
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,7,1,2]=>101100
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,1,2]=>101100
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,6,1,2]=>101110
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,1,2,7]=>101100
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,1,2,7]=>101100
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,1,2,7]=>101100
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1,2,6,7]=>101100
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,1,2,6]=>101110
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,3,1,2]=>101110
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,3,1,2]=>101110
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,3,1,2]=>101110
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,7,1,2]=>101110
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,1,2,7]=>101110
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,1,2]=>101111
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1]=>100000
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,5,6,1]=>110000
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,4,5,1]=>110000
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,5,7,1]=>110000
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,4,5,1]=>110001
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,3,4,1]=>110000
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,3,4,1]=>110010
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,4,7,1]=>110000
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,6,7,1]=>110000
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,4,6,1]=>110010
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,3,4,1]=>110010
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,3,4,1]=>110010
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,4,7,1]=>110010
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,3,4,1]=>110011
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,2,3,1]=>110000
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,2,3,1]=>110100
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,2,3,1]=>110100
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,2,3,1]=>110100
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,2,3,1]=>110101
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,3,7,1]=>110000
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,3,6,1]=>110100
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,6,7,1]=>110000
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,6,7,1]=>110000
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,5,6,1]=>110100
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,3,5,1]=>110100
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,3,7,1]=>110100
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,5,7,1]=>110100
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,3,5,1]=>110101
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,2,3,1]=>110100
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,2,3,1]=>110110
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,2,3,1]=>110100
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,2,3,1]=>110100
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,2,3,1]=>110110
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,3,7,1]=>110100
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,3,7,1]=>110100
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,6,7,1]=>110100
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,3,6,1]=>110110
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,2,3,1]=>110110
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,2,3,1]=>110110
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,2,3,1]=>110110
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,3,7,1]=>110110
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,3,1]=>110111
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,1,7]=>100000
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,5,1,6]=>110000
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,4,1,5]=>110000
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,5,1,7]=>110000
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,4,1,5]=>110001
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,3,1,4]=>110000
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,3,1,4]=>110010
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,4,1,7]=>110000
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,6,1,7]=>110000
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,4,1,6]=>110010
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,3,1,4]=>110010
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,3,1,4]=>110010
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,4,1,7]=>110010
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,3,1,4]=>110011
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,1,6,7]=>100000
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,1,5,6]=>110000
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,1,4,5]=>110000
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,1,5,7]=>110000
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,1,4,5]=>110001
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,3,4,1,5,6,7]=>100000
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,3,1,4,5,6]=>110000
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,3,1,4,5,6,7]=>100000
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,3,4,5,6,7]=>100000
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,3,4,5,6]=>110000
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[6,7,2,1,3,4,5]=>110000
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,3,1,4,5,7]=>110000
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,3,4,5,7]=>110000
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[7,6,2,1,3,4,5]=>110001
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,1,3,4]=>110000
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,1,3,4]=>110010
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,1,4,7]=>110000
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,1,6,7]=>110000
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,1,4,6]=>110010
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,6,2,1,3,4,7]=>110000
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,3,1,4,6,7]=>110000
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,3,4,6,7]=>110000
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[7,5,2,1,3,4,6]=>110010
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,1,3,4]=>110010
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,1,3,4]=>110010
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,1,4,7]=>110010
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,3,4,7]=>110010
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,1,3,4]=>110011
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,2,1,3]=>110000
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,2,1,3]=>110100
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,2,1,3]=>110100
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,2,1,3]=>110100
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,2,1,3]=>110101
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,3,1,7]=>110000
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,3,1,6]=>110100
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,6,1,7]=>110000
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,6,1,7]=>110000
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,5,1,6]=>110100
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,3,1,5]=>110100
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,3,1,7]=>110100
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,5,1,7]=>110100
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,3,1,5]=>110101
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,1,3,7]=>110000
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,1,3,6]=>110100
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,1,6,7]=>110000
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,1,6,7]=>110000
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,1,5,6]=>110100
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,2,1,3,6,7]=>110000
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,3,1,5,6,7]=>110000
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,3,5,6,7]=>110000
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1,3,5,6]=>110100
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,1,3,5]=>110100
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,1,3,7]=>110100
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,1,5,7]=>110100
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1,3,5,7]=>110100
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,1,3,5]=>110101
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,2,1,3]=>110100
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,2,1,3]=>110110
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,2,1,3]=>110100
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,2,1,3]=>110100
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,2,1,3]=>110110
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,3,1,7]=>110100
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,3,1,7]=>110100
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,6,1,7]=>110100
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,3,1,6]=>110110
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,1,3,7]=>110100
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,1,3,7]=>110100
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,1,6,7]=>110100
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1,3,6,7]=>110100
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,1,3,6]=>110110
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,2,1,3]=>110110
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,2,1,3]=>110110
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,2,1,3]=>110110
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,3,1,7]=>110110
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,1,3,7]=>110110
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,1,3]=>110111
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,2,1]=>110000
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,6,2,1]=>111000
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,5,2,1]=>111000
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,7,2,1]=>111000
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,5,2,1]=>111001
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,4,2,1]=>111000
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,4,2,1]=>111010
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,7,2,1]=>111000
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,7,2,1]=>111000
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,6,2,1]=>111010
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,4,2,1]=>111010
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,4,2,1]=>111010
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,7,2,1]=>111010
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,4,2,1]=>111011
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,2,7,1]=>110000
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,2,6,1]=>111000
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,2,5,1]=>111000
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,2,7,1]=>111000
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,2,5,1]=>111001
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,6,7,1]=>110000
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,5,6,1]=>111000
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,6,7,1]=>110000
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,6,7,1]=>110000
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,5,6,1]=>111000
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,4,5,1]=>111000
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,5,7,1]=>111000
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,5,7,1]=>111000
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,4,5,1]=>111001
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,2,4,1]=>111000
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,2,4,1]=>111010
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,2,7,1]=>111000
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,2,7,1]=>111000
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,2,6,1]=>111010
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,4,7,1]=>111000
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,6,7,1]=>111000
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,6,7,1]=>111000
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,4,6,1]=>111010
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,2,4,1]=>111010
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,2,4,1]=>111010
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,2,7,1]=>111010
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,4,7,1]=>111010
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,4,1]=>111011
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,2,1,7]=>110000
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,2,1,6]=>111000
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,2,1,5]=>111000
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,2,1,7]=>111000
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,2,1,5]=>111001
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,6,1,7]=>110000
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,5,1,6]=>111000
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,6,1,7]=>110000
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,6,1,7]=>110000
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,5,1,6]=>111000
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,4,1,5]=>111000
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,5,1,7]=>111000
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,5,1,7]=>111000
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,4,1,5]=>111001
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,1,6,7]=>110000
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,1,5,6]=>111000
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,1,6,7]=>110000
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,1,6,7]=>110000
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,1,5,6]=>111000
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,4,2,1,5,6,7]=>110000
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,4,1,5,6,7]=>110000
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,4,5,6,7]=>110000
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1,4,5,6]=>111000
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,1,4,5]=>111000
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,1,5,7]=>111000
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,1,5,7]=>111000
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1,4,5,7]=>111000
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,1,4,5]=>111001
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,2,1,4]=>111000
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,2,1,4]=>111010
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,2,1,7]=>111000
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,2,1,7]=>111000
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,2,1,6]=>111010
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,4,1,7]=>111000
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,6,1,7]=>111000
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,6,1,7]=>111000
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,4,1,6]=>111010
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,1,4,7]=>111000
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,1,6,7]=>111000
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,1,6,7]=>111000
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1,4,6,7]=>111000
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,1,4,6]=>111010
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,2,1,4]=>111010
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,2,1,4]=>111010
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,2,1,7]=>111010
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,4,1,7]=>111010
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,1,4,7]=>111010
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,1,4]=>111011
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,3,2,1]=>111000
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,3,2,1]=>111100
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,3,2,1]=>111100
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,3,2,1]=>111100
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,3,2,1]=>111101
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,7,2,1]=>111000
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,6,2,1]=>111100
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,7,2,1]=>111000
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,7,2,1]=>111000
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,6,2,1]=>111100
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,5,2,1]=>111100
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,7,2,1]=>111100
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,7,2,1]=>111100
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,5,2,1]=>111101
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,2,7,1]=>111000
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,2,6,1]=>111100
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,2,7,1]=>111000
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,2,7,1]=>111000
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,2,6,1]=>111100
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,6,7,1]=>111000
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,6,7,1]=>111000
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,6,7,1]=>111000
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,5,6,1]=>111100
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,2,5,1]=>111100
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,2,7,1]=>111100
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,2,7,1]=>111100
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,5,7,1]=>111100
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,5,1]=>111101
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,2,1,7]=>111000
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,2,1,6]=>111100
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,2,1,7]=>111000
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,2,1,7]=>111000
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,2,1,6]=>111100
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,6,1,7]=>111000
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,6,1,7]=>111000
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,6,1,7]=>111000
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,5,1,6]=>111100
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,1,6,7]=>111000
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,1,6,7]=>111000
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,1,6,7]=>111000
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,5,6,7]=>111000
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,1,5,6]=>111100
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,2,1,5]=>111100
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,2,1,7]=>111100
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,2,1,7]=>111100
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,5,1,7]=>111100
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,1,5,7]=>111100
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,1,5]=>111101
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,3,2,1]=>111100
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,3,2,1]=>111110
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,3,2,1]=>111100
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,3,2,1]=>111100
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,3,2,1]=>111110
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,7,2,1]=>111100
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,7,2,1]=>111100
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,2,1]=>111100
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,6,2,1]=>111110
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,2,7,1]=>111100
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,2,7,1]=>111100
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,2,7,1]=>111100
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,6,7,1]=>111100
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,6,1]=>111110
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,2,1,7]=>111100
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,2,1,7]=>111100
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,2,1,7]=>111100
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,6,1,7]=>111100
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,1,6,7]=>111100
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,1,6]=>111110
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,3,2,1]=>111110
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,3,2,1]=>111110
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,3,2,1]=>111110
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,7,2,1]=>111110
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,7,1]=>111110
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,1,7]=>111110
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,2,1]=>111111
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[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
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[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
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[7,8,1,2,3,4,5,6]=>1000000
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,1,2,3,4,5,6,8]=>1000000
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,1,2,3,4,5]=>1000000
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[8,6,7,1,2,3,4,5]=>1000010
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[6,7,1,2,3,4,5,8]=>1000000
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[7,8,6,1,2,3,4,5]=>1000010
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[7,6,8,1,2,3,4,5]=>1000010
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,1,2,3,4,5]=>1000011
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,1,2,3,4]=>1000000
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,1,2,3,4]=>1000100
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,1,2,3,4]=>1000100
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,1,2,3,4]=>1000100
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,1,2,3,4]=>1000101
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,1,2,3,4,8]=>1000000
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[8,5,6,1,2,3,4,7]=>1000100
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[5,1,2,3,4,6,7,8]=>1000000
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[7,8,5,1,2,3,4,6]=>1000100
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[7,5,6,1,2,3,4,8]=>1000100
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[7,5,1,2,3,4,6,8]=>1000100
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[8,7,5,1,2,3,4,6]=>1000101
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,1,2,3,4]=>1000100
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,1,2,3,4]=>1000110
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,1,2,3,4]=>1000100
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,1,2,3,4]=>1000100
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,1,2,3,4]=>1000110
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[6,7,5,1,2,3,4,8]=>1000100
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[6,5,7,1,2,3,4,8]=>1000100
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[8,6,5,1,2,3,4,7]=>1000110
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,1,2,3,4]=>1000110
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,1,2,3,4]=>1000110
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,1,2,3,4]=>1000110
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,1,2,3,4,8]=>1000110
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,1,2,3,4]=>1000111
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,1,2,3]=>1000000
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,8,1,2,3]=>1001000
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,5,1,2,3]=>1001010
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,8,1,2,3]=>1001000
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,8,1,2,3]=>1001000
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,7,1,2,3]=>1001010
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,8,1,2,3]=>1001010
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,1,2,3,8]=>1000000
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,1,2,3,7]=>1001000
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,1,2,3,8]=>1001000
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,1,2,3,6]=>1001001
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[4,5,1,2,3,6,7,8]=>1000000
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[4,1,2,3,5,6,7,8]=>1000000
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[7,8,4,1,2,3,5,6]=>1001000
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[7,4,5,1,2,3,6,8]=>1001000
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,1,2,3,5]=>1001000
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,1,2,3,5]=>1001010
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,1,2,3,5]=>1001010
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,1,2,3,8]=>1001010
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,1,2,3,5]=>1001011
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,1,2,3]=>1001000
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,4,1,2,3]=>1001100
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,1,2,3]=>1001100
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,8,1,2,3]=>1001000
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,7,1,2,3]=>1001100
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,8,1,2,3]=>1001000
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,8,1,2,3]=>1001000
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,8,1,2,3]=>1001100
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,8,1,2,3]=>1001100
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,6,1,2,3]=>1001101
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,1,2,3,8]=>1001000
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,1,2,3,7]=>1001100
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,1,2,3,8]=>1001000
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,1,2,3,8]=>1001000
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[5,4,1,2,3,6,7,8]=>1001000
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,1,2,3,6]=>1001100
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,1,2,3,8]=>1001100
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,1,2,3,8]=>1001100
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,1,2,3]=>1001100
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,1,2,3]=>1001100
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,4,1,2,3]=>1001100
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,8,1,2,3]=>1001100
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,1,2,3]=>1001100
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,8,1,2,3]=>1001100
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,7,1,2,3]=>1001110
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,1,2,3]=>1001110
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,8,1,2,3]=>1001110
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,1,2,3,8]=>1001110
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,1,2,3]=>1001111
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,8,1,2]=>1000000
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,5,6,1,2]=>1010000
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,7,8,1,2]=>1010000
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,4,5,1,2]=>1010010
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[7,6,3,4,5,8,1,2]=>1010010
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,5,1,2]=>1010011
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,4,1,2]=>1010000
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,3,4,1,2]=>1010100
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,4,1,2]=>1010100
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,3,4,1,2]=>1010100
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,4,1,2]=>1010101
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,7,8,1,2]=>1010000
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[5,3,4,6,7,8,1,2]=>1010000
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[8,5,3,4,6,7,1,2]=>1010100
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,4,6,1,2]=>1010100
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,4,8,1,2]=>1010100
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,4,6,8,1,2]=>1010100
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,3,4,1,2]=>1010100
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,4,1,2]=>1010100
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,3,4,1,2]=>1010100
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,4,1,2]=>1010110
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,4,1,2]=>1010110
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,4,1,2]=>1010111
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,1,2,8]=>1000000
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,1,2,7]=>1010000
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,4,1,2,5]=>1010000
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[6,7,3,4,5,1,2,8]=>1010000
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,5,1,2,7]=>1010010
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,1,2,5]=>1010011
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,1,2,5,6]=>1010000
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,1,2,5,6]=>1010001
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[8,3,4,1,2,5,6,7]=>1010000
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[3,4,1,2,5,6,7,8]=>1000000
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8]=>1000000
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[8,3,1,2,4,5,6,7]=>1010000
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[7,8,3,1,2,4,5,6]=>1010000
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[7,3,4,1,2,5,6,8]=>1010000
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[7,3,1,2,4,5,6,8]=>1010000
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,1,2,4,5]=>1010000
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,1,2,5,7]=>1010010
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[6,7,3,1,2,4,5,8]=>1010000
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,1,2,4,5]=>1010010
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,1,2,4,5]=>1010011
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,1,2,4]=>1010000
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,1,2,4]=>1010100
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,3,1,2,4]=>1010100
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,4,1,2,7]=>1010100
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,4,1,2,6]=>1010100
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,4,1,2,8]=>1010100
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,4,6,1,2,8]=>1010100
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,4,1,2,6]=>1010101
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,1,2,4,8]=>1010000
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,1,2,4,7]=>1010100
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,1,2,7,8]=>1010000
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[8,5,3,4,1,2,6,7]=>1010100
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[5,3,4,1,2,6,7,8]=>1010000
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[5,3,1,2,4,6,7,8]=>1010000
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,1,2,4,6]=>1010100
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,1,2,4,8]=>1010100
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,4,1,2,6,8]=>1010100
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,1,2,4,6,8]=>1010100
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,1,2,4,6]=>1010101
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,1,2,4]=>1010100
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,3,1,2,4]=>1010100
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,4,1,2,8]=>1010100
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,1,2,4]=>1010110
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,1,2,4]=>1010110
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,1,2,4]=>1010111
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,3,1,2]=>1010000
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,6,3,1,2]=>1011000
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,5,3,1,2]=>1011010
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,8,3,1,2]=>1011000
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,5,3,1,2]=>1011010
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,8,3,1,2]=>1011010
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,3,8,1,2]=>1010000
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,3,6,1,2]=>1011000
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,3,6,1,2]=>1011001
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,7,8,1,2]=>1010000
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[4,5,3,6,7,8,1,2]=>1010000
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[4,3,5,6,7,8,1,2]=>1010000
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,6,7,1,2]=>1011000
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,5,6,1,2]=>1011000
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[7,4,5,3,6,8,1,2]=>1011000
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,5,6,1,2]=>1011001
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,3,8,1,2]=>1011000
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[6,4,3,5,7,8,1,2]=>1011000
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,3,1,2,8]=>1010000
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,3,1,2,8]=>1011000
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,6,1,2,7]=>1011000
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,6,1,2,7]=>1011000
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[4,3,1,2,5,6,7,8]=>1010000
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,1,2,5,6]=>1011000
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[7,4,3,1,2,5,6,8]=>1011000
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,3,1,2,5]=>1011000
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,3,1,2,7]=>1011010
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[6,4,5,3,7,1,2,8]=>1011000
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[6,4,3,5,1,2,7,8]=>1011000
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[6,4,3,1,2,5,7,8]=>1011000
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3,1,2,5]=>1011011
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,3,1,2]=>1011000
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,3,1,2]=>1011100
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,4,3,1,2]=>1011100
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,4,3,1,2]=>1011101
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,7,3,1,2]=>1011100
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,8,3,1,2]=>1011000
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,6,3,1,2]=>1011101
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,3,8,1,2]=>1011000
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,3,8,1,2]=>1011000
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,3,8,1,2]=>1011000
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,3,7,1,2]=>1011100
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,7,8,1,2]=>1011000
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,7,8,1,2]=>1011000
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,6,7,1,2]=>1011100
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,3,6,1,2]=>1011100
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,3,8,1,2]=>1011100
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,6,8,1,2]=>1011100
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,3,1,2,8]=>1011000
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[5,6,4,3,1,2,7,8]=>1011000
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,1,2,7,8]=>1011000
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,1,2,7,8]=>1011000
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,1,2,6,7,8]=>1011000
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,3,1,2,6]=>1011100
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,3,1,2,6]=>1011101
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,3,1,2]=>1011100
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,3,1,2]=>1011100
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,3,8,1,2]=>1011100
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,8,1,2]=>1011100
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,1,2,8]=>1011100
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,1,2,7,8]=>1011100
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,3,1,2]=>1011110
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,3,1,2]=>1011110
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,8,1,2]=>1011110
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,3,1,2]=>1011111
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1]=>1000000
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,2,3,4,5,1]=>1100000
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[8,6,7,2,3,4,5,1]=>1100010
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[6,7,2,3,4,5,8,1]=>1100000
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[7,8,6,2,3,4,5,1]=>1100010
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[7,6,8,2,3,4,5,1]=>1100010
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,3,4,5,1]=>1100011
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,2,3,4,1]=>1100000
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,2,3,4,1]=>1100100
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,2,3,4,1]=>1100100
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,2,3,4,1]=>1100101
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,2,3,4,8,1]=>1100000
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,4,6,7,8,1]=>1100000
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[7,5,2,3,4,6,8,1]=>1100100
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,2,3,4,1]=>1100100
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,2,3,4,1]=>1100110
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,2,3,4,1]=>1100100
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,2,3,4,1]=>1100100
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,2,3,4,1]=>1100110
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[6,5,2,3,4,7,8,1]=>1100100
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,2,3,4,1]=>1100110
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,2,3,4,1]=>1100110
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,2,3,4,8,1]=>1100110
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,2,3,4,1]=>1100111
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,2,3,1]=>1100000
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,6,2,3,1]=>1101001
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,5,2,3,1]=>1101000
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,5,2,3,1]=>1101010
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,7,2,3,1]=>1101010
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,5,2,3,1]=>1101010
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,5,2,3,1]=>1101011
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,2,3,8,1]=>1100000
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,2,3,8,1]=>1101000
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[4,5,2,3,6,7,8,1]=>1100000
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,2,3,5,1]=>1101000
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,2,3,8,1]=>1101000
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,2,3,8,1]=>1101000
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[6,4,5,2,3,7,8,1]=>1101000
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,2,3,5,7,1]=>1101010
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,2,3,5,1]=>1101010
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[7,6,4,2,3,5,8,1]=>1101010
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,2,3,1]=>1101000
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,4,2,3,1]=>1101100
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,4,2,3,1]=>1101100
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,7,2,3,1]=>1101100
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,6,2,3,1]=>1101101
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,2,3,8,1]=>1101000
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,2,3,7,1]=>1101100
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,2,3,8,1]=>1101000
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,2,3,8,1]=>1101000
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[5,6,4,2,3,7,8,1]=>1101000
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[5,4,6,2,3,7,8,1]=>1101000
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,2,3,6,7,8,1]=>1101000
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[8,5,4,2,3,6,7,1]=>1101100
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,2,3,8,1]=>1101100
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,4,2,3,1]=>1101110
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,2,3,1]=>1101100
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,2,3,1]=>1101100
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,7,2,3,1]=>1101110
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,2,3,8,1]=>1101100
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,2,3,8,1]=>1101100
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,2,3,8,1]=>1101100
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[6,5,4,2,3,7,8,1]=>1101100
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,2,3,1]=>1101110
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,2,3,1]=>1101110
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,2,3,1]=>1101111
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,2,3,4,1,5]=>1100000
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[6,7,2,3,4,5,1,8]=>1100000
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,2,3,4,5,7,1,8]=>1100000
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[7,6,2,3,4,5,1,8]=>1100010
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,3,4,1,5]=>1100011
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,2,3,1,4]=>1100000
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,2,3,1,4]=>1100100
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,2,3,1,4]=>1100100
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,2,3,1,4]=>1100100
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,2,3,1,4]=>1100101
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,2,3,4,1,8]=>1100000
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[8,5,6,2,3,4,1,7]=>1100100
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[8,5,2,3,4,6,1,7]=>1100100
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[7,5,6,2,3,4,1,8]=>1100100
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,2,3,1,4]=>1100100
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,2,3,1,4]=>1100110
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,2,3,1,4]=>1100100
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,2,3,1,4]=>1100100
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,2,3,1,4]=>1100110
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[6,7,5,2,3,4,1,8]=>1100100
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[6,5,7,2,3,4,1,8]=>1100100
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[8,6,5,2,3,4,1,7]=>1100110
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,2,3,1,4]=>1100110
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,2,3,1,4]=>1100110
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,2,3,1,4]=>1100110
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,2,3,4,1,8]=>1100110
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,2,3,1,4]=>1100111
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,3,4,1,5,6]=>1100000
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[7,2,3,4,5,1,6,8]=>1100000
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,2,3,1,4,5]=>1100000
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[6,7,2,3,4,1,5,8]=>1100000
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[7,6,8,2,3,1,4,5]=>1100010
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[7,6,2,3,4,1,5,8]=>1100010
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,3,1,4,5]=>1100011
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,1,6,7,8]=>1000000
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[8,2,3,4,1,5,6,7]=>1100000
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,3,1,4,5,6]=>1100000
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,1,5,6,7,8]=>1000000
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[8,2,3,1,4,5,6,7]=>1100000
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8]=>1000000
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8]=>1000000
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,1,3,4,5,6]=>1100000
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[8,7,2,1,3,4,5,6]=>1100001
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,2,1,3,4,5]=>1100000
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[7,8,6,2,1,3,4,5]=>1100010
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[7,6,2,3,1,4,5,8]=>1100010
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,1,3,4,5]=>1100011
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,2,1,3,4]=>1100000
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,2,1,3,4]=>1100100
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,2,1,3,4]=>1100100
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,2,1,3,4]=>1100100
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,2,3,1,4,8]=>1100000
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[8,5,6,2,3,1,4,7]=>1100100
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,6,2,3,4,1,7,8]=>1100000
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[7,5,6,2,3,1,4,8]=>1100100
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[7,5,2,3,4,1,6,8]=>1100100
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[8,7,5,2,3,1,4,6]=>1100101
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,2,1,3,4,8]=>1100000
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[8,5,6,2,1,3,4,7]=>1100100
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,4,1,6,7,8]=>1100000
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,1,4,6,7,8]=>1100000
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[5,2,1,3,4,6,7,8]=>1100000
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[7,8,5,2,1,3,4,6]=>1100100
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[8,7,5,2,1,3,4,6]=>1100101
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,2,1,3,4]=>1100100
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,2,1,3,4]=>1100100
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,2,1,3,4]=>1100100
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,2,1,3,4]=>1100110
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[6,7,5,2,3,1,4,8]=>1100100
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[6,5,7,2,3,1,4,8]=>1100100
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[6,5,2,3,4,1,7,8]=>1100100
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[8,6,5,2,3,1,4,7]=>1100110
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[8,6,5,2,1,3,4,7]=>1100110
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,2,1,3,4]=>1100110
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,2,1,3,4]=>1100110
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,2,3,1,4,8]=>1100110
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,2,1,3,4,8]=>1100110
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,2,1,3,4]=>1100111
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,2,1,3]=>1100000
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,6,2,1,3]=>1101001
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,5,2,1,3]=>1101010
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,8,2,1,3]=>1101010
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,2,3,1,8]=>1100000
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,2,3,1,6]=>1101000
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,2,3,1,8]=>1101000
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,2,3,1,6]=>1101001
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[4,5,2,3,6,7,1,8]=>1100000
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[7,4,5,2,3,6,1,8]=>1101000
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,2,3,1,5]=>1101000
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,2,3,1,8]=>1101000
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,2,3,5,1,7]=>1101010
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,2,3,1,5]=>1101010
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,2,3,1,8]=>1101010
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[7,6,4,2,3,5,1,8]=>1101010
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,2,3,1,5]=>1101011
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,2,1,3,8]=>1100000
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,2,1,3,8]=>1101000
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[8,4,5,2,3,1,6,7]=>1101000
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[8,4,2,3,5,1,6,7]=>1101000
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[7,8,4,2,3,1,5,6]=>1101000
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[7,4,2,3,5,1,6,8]=>1101000
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[4,5,2,3,1,6,7,8]=>1100000
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[4,2,3,5,1,6,7,8]=>1100000
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[4,2,3,1,5,6,7,8]=>1100000
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[4,2,1,3,5,6,7,8]=>1100000
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[8,4,2,1,3,5,6,7]=>1101000
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[7,8,4,2,1,3,5,6]=>1101000
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,2,1,3,5]=>1101000
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,2,1,3,5]=>1101010
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,2,3,1,5,7]=>1101010
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[6,4,5,2,1,3,7,8]=>1101000
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[6,4,2,1,3,5,7,8]=>1101000
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,2,1,3,5,7]=>1101010
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,2,1,3,5]=>1101010
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[7,6,4,2,3,1,5,8]=>1101010
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[7,6,4,2,1,3,5,8]=>1101010
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,2,1,3,5]=>1101011
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,2,1,3]=>1101000
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,2,1,3]=>1101100
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,4,2,1,3]=>1101100
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,4,2,1,3]=>1101101
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,8,2,1,3]=>1101100
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,2,3,1,8]=>1101000
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,2,3,1,7]=>1101100
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,2,3,1,8]=>1101000
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,2,3,1,8]=>1101000
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,2,3,1,8]=>1101100
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,2,1,3,7]=>1101100
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[5,4,6,2,3,1,7,8]=>1101000
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[5,6,4,2,1,3,7,8]=>1101000
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[5,4,6,2,1,3,7,8]=>1101000
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,2,3,1,6,7,8]=>1101000
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[5,4,2,1,3,6,7,8]=>1101000
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[8,5,4,2,1,3,6,7]=>1101100
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,2,1,3,6]=>1101100
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,2,1,3]=>1101100
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,2,1,3]=>1101100
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,4,2,1,3]=>1101100
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,8,2,1,3]=>1101100
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,2,3,1,8]=>1101100
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,2,3,1,7]=>1101110
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,2,1,3,7]=>1101110
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,2,1,3]=>1101110
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,2,1,3]=>1101110
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,2,1,3]=>1101111
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,5,6,2,1]=>1110001
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,4,5,2,1]=>1110000
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,4,5,2,1]=>1110010
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,4,5,2,1]=>1110010
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,4,5,2,1]=>1110010
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[7,6,3,4,5,8,2,1]=>1110010
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,5,2,1]=>1110011
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,4,2,1]=>1110000
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,3,4,2,1]=>1110100
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,4,2,1]=>1110100
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,4,2,1]=>1110101
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,4,6,2,1]=>1110100
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,4,6,8,2,1]=>1110100
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,4,2,1]=>1110100
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,4,2,1]=>1110110
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,3,4,2,1]=>1110110
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,4,2,1]=>1110110
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,4,2,1]=>1110111
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,4,2,5,1]=>1110010
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,5,2,7,1]=>1110010
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,4,2,5,1]=>1110010
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,2,5,1]=>1110011
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,2,7,8,1]=>1100000
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,2,5,6,1]=>1110000
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,4,2,5,6,7,8,1]=>1100000
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,4,5,6,7,8,1]=>1100000
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[7,8,3,2,4,5,6,1]=>1110000
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,2,4,5,1]=>1110000
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,2,4,5,1]=>1110010
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[6,7,3,2,4,5,8,1]=>1110000
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,2,4,1]=>1110000
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,3,2,4,1]=>1110100
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,7,2,8,1]=>1110000
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,4,2,6,1]=>1110100
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,4,2,6,1]=>1110101
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[8,5,3,4,2,6,7,1]=>1110100
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,2,4,6,1]=>1110101
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,3,2,4,1]=>1110100
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,3,2,4,1]=>1110110
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,2,4,1]=>1110100
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,3,2,4,1]=>1110110
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[6,5,3,4,7,2,8,1]=>1110100
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[6,7,5,3,2,4,8,1]=>1110100
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,2,4,8,1]=>1110100
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,2,4,1]=>1110110
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,3,2,4,1]=>1110110
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,2,4,1]=>1110110
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,2,4,1]=>1110111
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,2,1,7]=>1110000
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,5,2,1,6]=>1110000
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[7,3,4,5,6,2,1,8]=>1110000
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,5,2,1,6]=>1110001
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,4,2,1,5]=>1110000
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,4,2,1,5]=>1110010
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[7,6,3,4,5,2,1,8]=>1110010
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,2,1,5]=>1110011
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,2,7,1,8]=>1100000
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,2,5,1,6]=>1110000
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,2,5,1,6]=>1110001
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,2,4,1,5]=>1110000
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,2,4,1,5]=>1110010
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[6,7,3,4,2,5,1,8]=>1110000
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,2,7,1,8]=>1110000
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[6,7,3,2,4,5,1,8]=>1110000
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[6,3,2,4,5,7,1,8]=>1110000
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[8,6,3,2,4,5,1,7]=>1110010
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[7,6,3,2,4,5,1,8]=>1110010
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,2,4,1,5]=>1110011
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,2,1,7,8]=>1100000
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,2,1,6,7]=>1110000
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,2,1,5,6]=>1110000
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,2,1,5,6]=>1110001
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[7,8,3,2,4,1,5,6]=>1110000
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[8,7,3,2,4,1,5,6]=>1110001
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[3,4,5,2,1,6,7,8]=>1100000
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[3,4,2,5,1,6,7,8]=>1100000
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,4,5,1,6,7,8]=>1100000
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[3,4,2,1,5,6,7,8]=>1100000
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[3,2,4,1,5,6,7,8]=>1100000
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1,4,5,6,7,8]=>1100000
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[8,3,2,1,4,5,6,7]=>1110000
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[7,8,3,2,1,4,5,6]=>1110000
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[8,7,3,2,1,4,5,6]=>1110001
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,2,1,4,5]=>1110000
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[6,7,3,4,2,1,5,8]=>1110000
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,2,1,5,7]=>1110010
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[8,6,3,2,4,1,5,7]=>1110010
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[6,7,3,2,1,4,5,8]=>1110000
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[6,3,4,2,1,5,7,8]=>1110000
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[8,6,3,2,1,4,5,7]=>1110010
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,2,1,4,5]=>1110010
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[7,6,3,2,4,1,5,8]=>1110010
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[7,6,3,2,1,4,5,8]=>1110010
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,2,1,4,5]=>1110011
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,2,1,4]=>1110000
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,3,2,1,4]=>1110100
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,2,1,4]=>1110100
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,3,2,1,4]=>1110100
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,2,1,4]=>1110101
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,4,2,1,8]=>1110000
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,4,2,1,7]=>1110100
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,4,2,1,8]=>1110100
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,4,2,1,6]=>1110101
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,2,4,1,8]=>1110000
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,2,7,1,8]=>1110000
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,4,2,6,1,8]=>1110100
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,2,4,6,1,8]=>1110100
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,2,4,1,6]=>1110101
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,2,1,4,7]=>1110100
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[5,6,3,2,4,1,7,8]=>1110000
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,4,6,1,7,8]=>1110000
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[5,6,3,2,1,4,7,8]=>1110000
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[5,3,4,2,1,6,7,8]=>1110000
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,4,1,6,7,8]=>1110000
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,1,4,6,7,8]=>1110000
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[8,5,3,2,1,4,6,7]=>1110100
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,2,1,4,6]=>1110100
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,2,1,4,6,8]=>1110100
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,2,1,4,6]=>1110101
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,3,2,1,4]=>1110100
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,3,2,1,4]=>1110110
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,2,1,4]=>1110100
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,3,2,1,4]=>1110100
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,3,2,1,4]=>1110110
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[6,7,5,3,4,2,1,8]=>1110100
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,4,2,1,8]=>1110100
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[8,6,5,3,4,2,1,7]=>1110110
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[6,5,3,2,4,7,1,8]=>1110100
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[8,6,5,3,2,4,1,7]=>1110110
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[6,5,3,4,2,1,7,8]=>1110100
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[8,6,5,3,2,1,4,7]=>1110110
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,2,1,4]=>1110110
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,3,2,1,4]=>1110110
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,2,1,4]=>1110110
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,4,2,1,8]=>1110110
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,2,1,4]=>1110111
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,3,2,1]=>1110000
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,8,3,2,1]=>1111000
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,5,3,2,1]=>1111010
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,8,3,2,1]=>1111000
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,8,3,2,1]=>1111000
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,7,3,2,1]=>1111010
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,5,3,2,1]=>1111010
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,8,3,2,1]=>1111010
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,5,3,2,1]=>1111011
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,3,8,2,1]=>1110000
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,3,8,2,1]=>1111000
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,5,6,2,1]=>1111001
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,3,5,2,1]=>1111000
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,3,8,2,1]=>1111000
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,3,5,2,1]=>1111010
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,3,5,2,1]=>1111010
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3,5,2,1]=>1111011
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,3,2,8,1]=>1110000
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,3,2,8,1]=>1111000
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,7,2,8,1]=>1110000
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,6,2,7,1]=>1111000
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,5,2,6,1]=>1111000
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,3,5,2,6,7,8,1]=>1110000
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,5,6,7,8,1]=>1110000
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,2,5,6,1]=>1111000
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,3,2,5,1]=>1111000
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,3,2,5,1]=>1111010
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,3,2,8,1]=>1111000
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[6,4,5,3,7,2,8,1]=>1111000
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,5,2,7,1]=>1111010
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[6,7,4,3,2,5,8,1]=>1111000
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,3,2,5,1]=>1111010
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,3,2,5,1]=>1111010
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3,2,5,1]=>1111011
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,3,2,1,8]=>1110000
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,3,2,1,7]=>1111000
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,3,2,1,8]=>1111000
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,6,2,1,7]=>1111000
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[7,4,5,3,6,2,1,8]=>1111000
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[4,5,3,6,2,7,1,8]=>1110000
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,2,5,1,6]=>1111000
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[7,4,5,3,2,6,1,8]=>1111000
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[7,4,3,5,2,6,1,8]=>1111000
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,2,5,1,6]=>1111001
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,2,1,7,8]=>1110000
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,2,1,6,7]=>1111000
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,2,1,6,7]=>1111000
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,3,2,6,1,7,8]=>1110000
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,3,2,1,6,7,8]=>1110000
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[4,3,5,2,1,6,7,8]=>1110000
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,5,1,6,7,8]=>1110000
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,1,5,6,7,8]=>1110000
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[8,4,3,2,1,5,6,7]=>1111000
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,2,1,5,6]=>1111000
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[7,4,3,2,1,5,6,8]=>1111000
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,2,1,5,6]=>1111001
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,3,2,1,5]=>1111000
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,3,2,1,5]=>1111010
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[6,7,4,3,2,5,1,8]=>1111000
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[6,7,4,3,2,1,5,8]=>1111000
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[6,4,3,2,5,1,7,8]=>1111000
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[6,4,3,2,1,5,7,8]=>1111000
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,2,1,5,7]=>1111010
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,3,2,1,5]=>1111010
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,3,2,1,5]=>1111010
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,3,2,1,8]=>1111010
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,2,1,5,8]=>1111010
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3,2,1,5]=>1111011
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,3,2,1]=>1111000
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,4,3,2,1]=>1111100
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,3,2,1]=>1111100
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,4,3,2,1]=>1111100
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,4,3,2,1]=>1111101
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,8,3,2,1]=>1111000
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,7,3,2,1]=>1111100
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,8,3,2,1]=>1111000
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,8,3,2,1]=>1111000
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,8,3,2,1]=>1111100
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,8,3,2,1]=>1111100
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,6,3,2,1]=>1111101
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,3,8,2,1]=>1111000
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,3,6,2,1]=>1111100
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,3,8,2,1]=>1111100
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,6,8,2,1]=>1111100
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,3,6,2,1]=>1111101
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,7,2,8,1]=>1111000
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,7,2,8,1]=>1111000
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,2,7,8,1]=>1111000
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,2,7,8,1]=>1111000
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,6,7,8,1]=>1111000
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,3,2,1,8]=>1111000
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,3,2,1,7]=>1111100
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,3,2,1,8]=>1111000
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,7,2,1,8]=>1111000
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,7,2,1,8]=>1111000
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,2,7,1,8]=>1111000
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,2,7,1,8]=>1111000
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,6,7,1,8]=>1111000
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[5,6,4,3,2,1,7,8]=>1111000
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,2,1,7,8]=>1111000
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,2,1,7,8]=>1111000
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,6,1,7,8]=>1111000
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,1,6,7,8]=>1111000
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,3,2,1,6]=>1111100
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,3,2,1,8]=>1111100
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,3,2,1,6]=>1111101
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,3,2,1]=>1111100
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,4,3,2,1]=>1111110
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,3,2,1]=>1111100
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,4,3,2,1]=>1111100
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,4,3,2,1]=>1111110
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,8,3,2,1]=>1111100
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,3,2,1]=>1111100
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,8,3,2,1]=>1111100
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,7,3,2,1]=>1111110
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,8,2,1]=>1111100
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,2,8,1]=>1111100
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,2,7,8,1]=>1111100
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,2,7,1]=>1111110
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,3,2,1,8]=>1111100
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,3,2,1,8]=>1111100
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,3,2,1,8]=>1111100
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,2,1,8]=>1111100
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,2,1,7]=>1111110
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,3,2,1]=>1111110
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,3,2,1]=>1111110
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,3,2,1]=>1111110
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,8,3,2,1]=>1111110
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,8,2,1]=>1111110
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,2,1,8]=>1111110
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,3,2,1]=>1111111
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[6,7,8,9,10,5,4,3,2,1]=>111110000
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[5,4,3,2,1,6,7,8,9,10]=>111100000
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[6,5,4,3,7,8,9,10,1,2]=>101110000
Map
Lalanne-Kreweras involution
Description
The Lalanne-Kreweras involution on Dyck paths.
Label the upsteps from left to right and record the labels on the first up step of each double rise. Do the same for the downsteps. Then form the Dyck path whose ascent lengths and descent lengths are the consecutives differences of the labels.
Label the upsteps from left to right and record the labels on the first up step of each double rise. Do the same for the downsteps. Then form the Dyck path whose ascent lengths and descent lengths are the consecutives differences of the labels.
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
This bijection is defined in [1, Section 2].
Map
descent bottoms
Description
The descent bottoms of a permutation as a binary word.
searching the database
Sorry, this map was not found in the database.