Identifier
-
Mp00129:
Dyck paths
—to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶
Permutations
St000337: Permutations ⟶ ℤ
Values
=>
Cc0005;cc-rep-0
[1,0]=>[1]=>0
[1,0,1,0]=>[2,1]=>1
[1,1,0,0]=>[1,2]=>0
[1,0,1,0,1,0]=>[2,3,1]=>1
[1,0,1,1,0,0]=>[2,1,3]=>1
[1,1,0,0,1,0]=>[1,3,2]=>1
[1,1,0,1,0,0]=>[3,1,2]=>2
[1,1,1,0,0,0]=>[1,2,3]=>0
[1,0,1,0,1,0,1,0]=>[2,3,4,1]=>1
[1,0,1,0,1,1,0,0]=>[2,3,1,4]=>1
[1,0,1,1,0,0,1,0]=>[2,1,4,3]=>2
[1,0,1,1,0,1,0,0]=>[2,4,1,3]=>2
[1,0,1,1,1,0,0,0]=>[2,1,3,4]=>1
[1,1,0,0,1,0,1,0]=>[1,3,4,2]=>1
[1,1,0,0,1,1,0,0]=>[1,3,2,4]=>1
[1,1,0,1,0,0,1,0]=>[3,1,4,2]=>2
[1,1,0,1,0,1,0,0]=>[3,4,1,2]=>2
[1,1,0,1,1,0,0,0]=>[3,1,2,4]=>2
[1,1,1,0,0,0,1,0]=>[1,2,4,3]=>1
[1,1,1,0,0,1,0,0]=>[1,4,2,3]=>2
[1,1,1,0,1,0,0,0]=>[4,1,2,3]=>3
[1,1,1,1,0,0,0,0]=>[1,2,3,4]=>0
[1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,1]=>1
[1,0,1,0,1,0,1,1,0,0]=>[2,3,4,1,5]=>1
[1,0,1,0,1,1,0,0,1,0]=>[2,3,1,5,4]=>2
[1,0,1,0,1,1,0,1,0,0]=>[2,3,5,1,4]=>2
[1,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,5]=>1
[1,0,1,1,0,0,1,0,1,0]=>[2,1,4,5,3]=>2
[1,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,5]=>2
[1,0,1,1,0,1,0,0,1,0]=>[2,4,1,5,3]=>2
[1,0,1,1,0,1,0,1,0,0]=>[2,4,5,1,3]=>2
[1,0,1,1,0,1,1,0,0,0]=>[2,4,1,3,5]=>2
[1,0,1,1,1,0,0,0,1,0]=>[2,1,3,5,4]=>2
[1,0,1,1,1,0,0,1,0,0]=>[2,1,5,3,4]=>3
[1,0,1,1,1,0,1,0,0,0]=>[2,5,1,3,4]=>3
[1,0,1,1,1,1,0,0,0,0]=>[2,1,3,4,5]=>1
[1,1,0,0,1,0,1,0,1,0]=>[1,3,4,5,2]=>1
[1,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5]=>1
[1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4]=>2
[1,1,0,0,1,1,0,1,0,0]=>[1,3,5,2,4]=>2
[1,1,0,0,1,1,1,0,0,0]=>[1,3,2,4,5]=>1
[1,1,0,1,0,0,1,0,1,0]=>[3,1,4,5,2]=>2
[1,1,0,1,0,0,1,1,0,0]=>[3,1,4,2,5]=>2
[1,1,0,1,0,1,0,0,1,0]=>[3,4,1,5,2]=>2
[1,1,0,1,0,1,0,1,0,0]=>[3,4,5,1,2]=>2
[1,1,0,1,0,1,1,0,0,0]=>[3,4,1,2,5]=>2
[1,1,0,1,1,0,0,0,1,0]=>[3,1,2,5,4]=>3
[1,1,0,1,1,0,0,1,0,0]=>[3,1,5,2,4]=>3
[1,1,0,1,1,0,1,0,0,0]=>[3,5,1,2,4]=>3
[1,1,0,1,1,1,0,0,0,0]=>[3,1,2,4,5]=>2
[1,1,1,0,0,0,1,0,1,0]=>[1,2,4,5,3]=>1
[1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5]=>1
[1,1,1,0,0,1,0,0,1,0]=>[1,4,2,5,3]=>2
[1,1,1,0,0,1,0,1,0,0]=>[1,4,5,2,3]=>2
[1,1,1,0,0,1,1,0,0,0]=>[1,4,2,3,5]=>2
[1,1,1,0,1,0,0,0,1,0]=>[4,1,2,5,3]=>3
[1,1,1,0,1,0,0,1,0,0]=>[4,1,5,2,3]=>3
[1,1,1,0,1,0,1,0,0,0]=>[4,5,1,2,3]=>3
[1,1,1,0,1,1,0,0,0,0]=>[4,1,2,3,5]=>3
[1,1,1,1,0,0,0,0,1,0]=>[1,2,3,5,4]=>1
[1,1,1,1,0,0,0,1,0,0]=>[1,2,5,3,4]=>2
[1,1,1,1,0,0,1,0,0,0]=>[1,5,2,3,4]=>3
[1,1,1,1,0,1,0,0,0,0]=>[5,1,2,3,4]=>4
[1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5]=>0
[1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,1]=>1
[1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,1,6]=>1
[1,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,4,1,6,5]=>2
[1,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,4,6,1,5]=>2
[1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,1,5,6]=>1
[1,0,1,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,6,4]=>2
[1,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,6]=>2
[1,0,1,0,1,1,0,1,0,0,1,0]=>[2,3,5,1,6,4]=>2
[1,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,5,6,1,4]=>2
[1,0,1,0,1,1,0,1,1,0,0,0]=>[2,3,5,1,4,6]=>2
[1,0,1,0,1,1,1,0,0,0,1,0]=>[2,3,1,4,6,5]=>2
[1,0,1,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,4,5]=>3
[1,0,1,0,1,1,1,0,1,0,0,0]=>[2,3,6,1,4,5]=>3
[1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,1,4,5,6]=>1
[1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,5,6,3]=>2
[1,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,5,3,6]=>2
[1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5]=>3
[1,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,6,3,5]=>3
[1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,5,6]=>2
[1,0,1,1,0,1,0,0,1,0,1,0]=>[2,4,1,5,6,3]=>2
[1,0,1,1,0,1,0,0,1,1,0,0]=>[2,4,1,5,3,6]=>2
[1,0,1,1,0,1,0,1,0,0,1,0]=>[2,4,5,1,6,3]=>2
[1,0,1,1,0,1,0,1,0,1,0,0]=>[2,4,5,6,1,3]=>2
[1,0,1,1,0,1,0,1,1,0,0,0]=>[2,4,5,1,3,6]=>2
[1,0,1,1,0,1,1,0,0,0,1,0]=>[2,4,1,3,6,5]=>3
[1,0,1,1,0,1,1,0,0,1,0,0]=>[2,4,1,6,3,5]=>3
[1,0,1,1,0,1,1,0,1,0,0,0]=>[2,4,6,1,3,5]=>3
[1,0,1,1,0,1,1,1,0,0,0,0]=>[2,4,1,3,5,6]=>2
[1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,3,5,6,4]=>2
[1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,5,4,6]=>2
[1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,3,6,4]=>3
[1,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,6,3,4]=>3
[1,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,3,4,6]=>3
[1,0,1,1,1,0,1,0,0,0,1,0]=>[2,5,1,3,6,4]=>3
[1,0,1,1,1,0,1,0,0,1,0,0]=>[2,5,1,6,3,4]=>3
[1,0,1,1,1,0,1,0,1,0,0,0]=>[2,5,6,1,3,4]=>3
[1,0,1,1,1,0,1,1,0,0,0,0]=>[2,5,1,3,4,6]=>3
[1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,3,4,6,5]=>2
[1,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,3,6,4,5]=>3
[1,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,6,3,4,5]=>4
[1,0,1,1,1,1,0,1,0,0,0,0]=>[2,6,1,3,4,5]=>4
[1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,3,4,5,6]=>1
[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,6,2]=>1
[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,4,5,2,6]=>1
[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,4,2,6,5]=>2
[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,4,6,2,5]=>2
[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,4,2,5,6]=>1
[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,6,4]=>2
[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,6]=>2
[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,5,2,6,4]=>2
[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,5,6,2,4]=>2
[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,5,2,4,6]=>2
[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,4,6,5]=>2
[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,4,5]=>3
[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,6,2,4,5]=>3
[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,4,5,6]=>1
[1,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,4,5,6,2]=>2
[1,1,0,1,0,0,1,0,1,1,0,0]=>[3,1,4,5,2,6]=>2
[1,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,4,2,6,5]=>3
[1,1,0,1,0,0,1,1,0,1,0,0]=>[3,1,4,6,2,5]=>3
[1,1,0,1,0,0,1,1,1,0,0,0]=>[3,1,4,2,5,6]=>2
[1,1,0,1,0,1,0,0,1,0,1,0]=>[3,4,1,5,6,2]=>2
[1,1,0,1,0,1,0,0,1,1,0,0]=>[3,4,1,5,2,6]=>2
[1,1,0,1,0,1,0,1,0,0,1,0]=>[3,4,5,1,6,2]=>2
[1,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,6,1,2]=>2
[1,1,0,1,0,1,0,1,1,0,0,0]=>[3,4,5,1,2,6]=>2
[1,1,0,1,0,1,1,0,0,0,1,0]=>[3,4,1,2,6,5]=>3
[1,1,0,1,0,1,1,0,0,1,0,0]=>[3,4,1,6,2,5]=>3
[1,1,0,1,0,1,1,0,1,0,0,0]=>[3,4,6,1,2,5]=>3
[1,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,1,2,5,6]=>2
[1,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,2,5,6,4]=>3
[1,1,0,1,1,0,0,0,1,1,0,0]=>[3,1,2,5,4,6]=>3
[1,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,5,2,6,4]=>3
[1,1,0,1,1,0,0,1,0,1,0,0]=>[3,1,5,6,2,4]=>3
[1,1,0,1,1,0,0,1,1,0,0,0]=>[3,1,5,2,4,6]=>3
[1,1,0,1,1,0,1,0,0,0,1,0]=>[3,5,1,2,6,4]=>3
[1,1,0,1,1,0,1,0,0,1,0,0]=>[3,5,1,6,2,4]=>3
[1,1,0,1,1,0,1,0,1,0,0,0]=>[3,5,6,1,2,4]=>3
[1,1,0,1,1,0,1,1,0,0,0,0]=>[3,5,1,2,4,6]=>3
[1,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,2,4,6,5]=>3
[1,1,0,1,1,1,0,0,0,1,0,0]=>[3,1,2,6,4,5]=>4
[1,1,0,1,1,1,0,0,1,0,0,0]=>[3,1,6,2,4,5]=>4
[1,1,0,1,1,1,0,1,0,0,0,0]=>[3,6,1,2,4,5]=>4
[1,1,0,1,1,1,1,0,0,0,0,0]=>[3,1,2,4,5,6]=>2
[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,2,4,5,6,3]=>1
[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,2,4,5,3,6]=>1
[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5]=>2
[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,2,4,6,3,5]=>2
[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,4,3,5,6]=>1
[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,2,5,6,3]=>2
[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,2,5,3,6]=>2
[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,5,2,6,3]=>2
[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,5,6,2,3]=>2
[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,5,2,3,6]=>2
[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,2,3,6,5]=>3
[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,6,3,5]=>3
[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,6,2,3,5]=>3
[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,2,3,5,6]=>2
[1,1,1,0,1,0,0,0,1,0,1,0]=>[4,1,2,5,6,3]=>3
[1,1,1,0,1,0,0,0,1,1,0,0]=>[4,1,2,5,3,6]=>3
[1,1,1,0,1,0,0,1,0,0,1,0]=>[4,1,5,2,6,3]=>3
[1,1,1,0,1,0,0,1,0,1,0,0]=>[4,1,5,6,2,3]=>3
[1,1,1,0,1,0,0,1,1,0,0,0]=>[4,1,5,2,3,6]=>3
[1,1,1,0,1,0,1,0,0,0,1,0]=>[4,5,1,2,6,3]=>3
[1,1,1,0,1,0,1,0,0,1,0,0]=>[4,5,1,6,2,3]=>3
[1,1,1,0,1,0,1,0,1,0,0,0]=>[4,5,6,1,2,3]=>3
[1,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,1,2,3,6]=>3
[1,1,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,3,6,5]=>4
[1,1,1,0,1,1,0,0,0,1,0,0]=>[4,1,2,6,3,5]=>4
[1,1,1,0,1,1,0,0,1,0,0,0]=>[4,1,6,2,3,5]=>4
[1,1,1,0,1,1,0,1,0,0,0,0]=>[4,6,1,2,3,5]=>4
[1,1,1,0,1,1,1,0,0,0,0,0]=>[4,1,2,3,5,6]=>3
[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,2,3,5,6,4]=>1
[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,2,3,5,4,6]=>1
[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,2,5,3,6,4]=>2
[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,2,5,6,3,4]=>2
[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,2,5,3,4,6]=>2
[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,5,2,3,6,4]=>3
[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,2,6,3,4]=>3
[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,5,6,2,3,4]=>3
[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,5,2,3,4,6]=>3
[1,1,1,1,0,1,0,0,0,0,1,0]=>[5,1,2,3,6,4]=>4
[1,1,1,1,0,1,0,0,0,1,0,0]=>[5,1,2,6,3,4]=>4
[1,1,1,1,0,1,0,0,1,0,0,0]=>[5,1,6,2,3,4]=>4
[1,1,1,1,0,1,0,1,0,0,0,0]=>[5,6,1,2,3,4]=>4
[1,1,1,1,0,1,1,0,0,0,0,0]=>[5,1,2,3,4,6]=>4
[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,2,3,4,6,5]=>1
[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,2,3,6,4,5]=>2
[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,6,3,4,5]=>3
[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,6,2,3,4,5]=>4
[1,1,1,1,1,0,1,0,0,0,0,0]=>[6,1,2,3,4,5]=>5
[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,5,6]=>0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,1]=>1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,6,1,7]=>1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,4,5,1,7,6]=>2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,4,5,7,1,6]=>2
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,5,1,6,7]=>1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,3,4,6,1,7,5]=>2
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,4,6,7,1,5]=>2
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,3,4,1,5,7,6]=>2
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,3,4,7,1,5,6]=>3
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,4,1,5,6,7]=>1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,5,6,7,1,4]=>2
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,1,4,5,6,7]=>1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,4,1,3,5,6,7]=>2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,5,7,1,3,4,6]=>4
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,5,1,3,4,6,7]=>3
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,1,6,3,4,5,7]=>4
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,6,1,7,3,4,5]=>4
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,6,7,1,3,4,5]=>4
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,6,1,3,4,5,7]=>4
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,1,3,4,7,5,6]=>3
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,1,3,7,4,5,6]=>4
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,1,7,3,4,5,6]=>5
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,7,1,3,4,5,6]=>5
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,3,4,5,6,7]=>1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,3,7,2,4,5,6]=>4
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,4,5,6,7]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,6,7,1,2]=>2
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,1,2,5,6,7]=>2
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[3,5,6,1,2,4,7]=>3
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,6,1,2,4,5,7]=>4
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,1,2,4,5,7,6]=>3
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,1,2,4,5,6,7]=>2
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,4,6,7,2,3,5]=>3
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,4,7,2,3,5,6]=>4
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[4,5,1,6,2,3,7]=>3
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,5,6,1,2,3,7]=>3
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,1,6,2,3,5,7]=>4
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[4,6,1,2,3,7,5]=>4
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[4,6,1,2,3,5,7]=>4
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[4,1,2,3,5,7,6]=>4
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[4,1,2,3,5,6,7]=>3
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,5,6,2,7,3,4]=>3
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,5,6,7,2,3,4]=>3
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,5,2,3,4,7,6]=>4
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,5,2,7,3,4,6]=>4
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,5,7,2,3,4,6]=>4
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[5,1,2,3,6,7,4]=>4
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[5,1,2,3,6,4,7]=>4
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,1,2,6,3,4,7]=>4
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[5,1,6,2,3,7,4]=>4
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[5,1,6,2,3,4,7]=>4
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[5,6,1,2,3,7,4]=>4
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[5,6,7,1,2,3,4]=>4
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[5,6,1,2,3,4,7]=>4
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[5,1,2,3,4,7,6]=>5
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[5,1,2,3,7,4,6]=>5
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[5,1,2,3,4,6,7]=>4
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,6,5,7]=>1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,2,3,6,4,7,5]=>2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,2,6,3,4,7,5]=>3
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,6,2,3,4,7,5]=>4
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,6,2,3,7,4,5]=>4
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,6,2,7,3,4,5]=>4
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,6,7,2,3,4,5]=>4
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,7,5]=>5
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,1,2,3,7,4,5]=>5
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[6,1,2,7,3,4,5]=>5
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[6,7,1,2,3,4,5]=>5
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[6,1,2,3,4,5,7]=>5
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,2,3,4,5,7,6]=>1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,7,2,3,4,5,6]=>5
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[7,1,2,3,4,5,6]=>6
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7]=>0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,8,1]=>1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,6,7,1,8]=>1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,4,5,6,1,8,7]=>2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,4,5,6,8,1,7]=>2
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,5,6,1,7,8]=>1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,4,5,7,8,1,6]=>2
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1,6,7,8]=>1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,6,7,8,5]=>2
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,5,6,1,7,8,4]=>2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,1,4,5,7,8,6]=>2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7]=>4
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,4,3,7,5,8,6]=>4
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,4,3,7,8,5,6]=>4
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,4,3,8,5,6,7]=>5
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,4,5,6,7,1,8,3]=>2
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,4,6,1,7,3,8,5]=>3
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,4,6,8,1,3,5,7]=>4
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,4,1,3,7,5,8,6]=>4
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,4,7,8,1,3,5,6]=>4
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,1,5,3,6,4,8,7]=>4
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[2,1,5,6,3,4,8,7]=>4
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[2,1,5,3,7,4,8,6]=>4
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[2,1,5,7,3,8,4,6]=>4
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[2,5,6,8,1,3,4,7]=>4
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[2,5,1,7,3,4,8,6]=>4
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[2,5,7,8,1,3,4,6]=>4
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[2,1,6,3,4,7,8,5]=>4
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[2,1,6,3,7,4,8,5]=>4
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,1,6,7,8,3,4,5]=>4
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[2,1,6,3,4,5,8,7]=>5
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[2,6,7,1,3,4,8,5]=>4
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,6,7,8,1,3,4,5]=>4
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,6,1,3,4,5,7,8]=>4
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,7,8,1,3,4,5,6]=>5
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,7,1,3,4,5,6,8]=>5
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,8,7]=>2
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[2,1,3,8,4,5,6,7]=>5
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,1,8,3,4,5,6,7]=>6
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,8,1,3,4,5,6,7]=>6
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8]=>1
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,6,7,5,8]=>2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,8]=>3
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,5,4,8,6,7]=>4
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,5,4,6,7,8]=>2
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,5,6,2,7,4,8]=>2
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,5,8,2,4,6,7]=>4
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,3,2,6,4,7,5,8]=>3
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,6,4,8,5,7]=>4
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,2,6,4,5,7,8]=>3
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>2
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,3,2,7,4,8,5,6]=>4
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,3,2,7,4,5,6,8]=>4
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,3,2,4,5,8,6,7]=>3
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,3,2,8,4,5,6,7]=>5
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8]=>1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,4,2,6,5,8,7]=>4
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,1,4,2,6,8,5,7]=>4
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,1,4,2,7,5,8,6]=>4
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,6,7,8,1,2]=>2
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,4,1,2,6,5,8,7]=>4
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,4,6,8,1,2,5,7]=>4
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[3,4,1,2,7,8,5,6]=>4
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[3,4,7,8,1,2,5,6]=>4
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,1,2,5,6,7,8]=>2
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,6,4,8,7]=>4
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,1,5,6,2,8,4,7]=>4
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,1,5,2,7,4,8,6]=>4
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,5,1,6,2,4,8,7]=>4
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,5,6,8,1,2,4,7]=>4
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,5,1,7,2,8,4,6]=>4
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,5,7,8,1,2,4,6]=>4
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[3,1,2,6,7,4,8,5]=>4
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[3,1,6,2,7,4,8,5]=>4
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[3,6,1,7,8,2,4,5]=>4
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[3,6,7,1,2,8,4,5]=>4
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,6,7,8,1,2,4,5]=>4
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[3,1,2,4,5,8,6,7]=>4
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,6,5,7,8]=>2
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,4,2,5,3,7,6,8]=>3
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,4,2,5,3,8,6,7]=>4
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,4,2,5,3,6,7,8]=>2
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,4,5,6,7,2,3,8]=>2
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,2,6,3,7,5,8]=>3
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,6,7,8,3,5]=>3
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,6,3,8,5,7]=>4
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,2,6,3,5,7,8]=>3
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,4,2,3,5,7,6,8]=>3
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,4,2,3,7,5,6,8]=>4
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,4,2,7,3,8,5,6]=>4
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,4,2,7,3,5,6,8]=>4
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,4,2,3,5,8,6,7]=>4
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,4,2,8,3,5,6,7]=>5
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,4,2,3,5,6,7,8]=>2
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[4,1,5,2,6,3,8,7]=>4
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[4,1,5,6,8,2,3,7]=>4
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[4,1,5,2,7,3,8,6]=>4
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[4,1,5,2,7,8,3,6]=>4
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[4,5,6,1,2,3,8,7]=>4
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,5,6,8,1,2,3,7]=>4
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,1,2,3,7,8]=>3
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[4,5,1,7,8,2,3,6]=>4
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[4,5,7,1,2,8,3,6]=>4
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,5,7,8,1,2,3,6]=>4
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,1,2,3,6,5,8,7]=>5
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,1,6,2,7,3,8,5]=>4
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,6,7,1,8,2,3,5]=>4
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,6,7,8,1,2,3,5]=>4
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[4,7,1,2,3,5,6,8]=>5
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[4,1,2,3,8,5,6,7]=>6
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,2,3,5,6,7,8,4]=>1
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6,8]=>2
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,5,4,8,6,7]=>3
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,5,4,6,7,8]=>1
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[1,2,5,6,3,4,7,8]=>2
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[1,5,2,6,3,7,4,8]=>3
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[1,5,2,6,3,8,4,7]=>4
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[1,5,2,6,3,4,7,8]=>3
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[1,5,2,3,4,7,6,8]=>4
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[1,5,2,7,3,8,4,6]=>4
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,5,2,7,3,4,6,8]=>4
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[1,5,2,3,4,8,6,7]=>5
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[1,5,2,8,3,4,6,7]=>5
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[1,5,8,2,3,4,6,7]=>5
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,5,2,3,4,6,7,8]=>3
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[5,1,6,2,7,3,8,4]=>4
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,6,7,8,1,2,3,4]=>4
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[5,6,7,1,2,3,4,8]=>4
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[5,7,1,2,3,4,6,8]=>5
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[5,1,2,3,4,6,8,7]=>5
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[5,1,2,8,3,4,6,7]=>6
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[5,1,2,3,4,6,7,8]=>4
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[1,2,3,6,4,7,5,8]=>2
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[1,2,3,6,4,8,5,7]=>3
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,2,3,6,4,5,7,8]=>2
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[1,6,2,3,4,7,5,8]=>4
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,6,2,7,3,8,4,5]=>4
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[1,6,2,7,3,4,5,8]=>4
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,6,7,8,2,3,4,5]=>4
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,6,7,2,3,4,5,8]=>4
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[1,6,2,3,4,8,5,7]=>5
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[1,6,2,8,3,4,5,7]=>5
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,6,8,2,3,4,5,7]=>5
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[1,6,2,3,4,5,7,8]=>4
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[6,1,2,7,3,4,5,8]=>5
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[6,1,7,2,3,4,5,8]=>5
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[6,7,1,2,3,4,8,5]=>5
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[6,7,8,1,2,3,4,5]=>5
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[6,7,1,2,3,4,5,8]=>5
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,8,7]=>6
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[6,1,8,2,3,4,5,7]=>6
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[6,1,2,3,4,5,7,8]=>5
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,5,7,6,8]=>1
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[1,2,3,7,4,8,5,6]=>3
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[1,2,3,7,4,5,6,8]=>3
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[1,2,7,3,4,5,8,6]=>4
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[1,7,2,3,4,5,8,6]=>5
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[1,7,2,3,4,8,5,6]=>5
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,7,2,3,8,4,5,6]=>5
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[1,7,2,8,3,4,5,6]=>5
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,7,8,2,3,4,5,6]=>5
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,7,2,3,4,5,6,8]=>5
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,8,6]=>6
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[7,1,2,3,4,8,5,6]=>6
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[7,8,1,2,3,4,5,6]=>6
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[7,1,2,3,4,5,6,8]=>6
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,2,3,4,5,6,8,7]=>1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,2,3,4,5,8,6,7]=>2
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,2,3,8,4,5,6,7]=>4
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,8,2,3,4,5,6,7]=>6
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[8,1,2,3,4,5,6,7]=>7
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8]=>0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,2,3,4,5,6,7,9,8]=>1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9]=>1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[1,2,3,4,5,6,7,8,10,9]=>1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[8,1,2,3,4,5,6,9,7]=>7
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,9,1,3,4,5,6,7,8]=>7
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9,10]=>1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[1,2,3,4,5,6,7,8,9,11,10]=>1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[9,1,2,3,4,5,6,7,10,8]=>8
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[1,8,2,3,4,5,6,9,7]=>6
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6,9,8]=>7
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[2,1,9,3,4,5,6,7,8]=>7
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[2,8,1,3,4,5,6,7,9]=>6
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[2,10,1,3,4,5,6,7,8,9]=>8
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9,10,11]=>1
[]=>[]=>0
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,1,2,5,6,7,8,9]=>2
[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[4,5,6,1,2,3,7,8,9]=>3
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[5,6,7,8,1,2,3,4,9]=>4
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[6,7,8,9,1,2,3,4,5]=>5
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[6,8,1,2,3,4,5,7,9]=>6
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]=>[1,7,9,2,3,4,5,6,8]=>6
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]=>[7,1,8,2,3,4,5,6,9]=>6
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[7,8,9,1,2,3,4,5,6]=>6
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[7,8,1,2,3,4,5,6,9]=>6
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[7,1,2,3,4,5,6,8,9]=>6
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[1,8,2,9,3,4,5,6,7]=>6
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[1,8,9,2,3,4,5,6,7]=>6
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[8,9,1,2,3,4,5,6,7]=>7
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[8,1,2,3,4,5,6,7,9]=>7
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,9,2,3,4,5,6,7,8]=>7
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[9,1,2,3,4,5,6,7,8]=>8
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9]=>0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,8,9,1]=>1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,6,7,8,1,9]=>1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,4,5,6,7,9,1,8]=>2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,8,9,10,1]=>1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,6,7,8,9,1,10]=>1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,5,6,7,1,8,9]=>1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,8,9,10,11,1]=>1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7,10,9]=>5
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9,10]=>0
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[9,1,2,3,4,5,6,7,8,10]=>8
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[1,10,2,3,4,5,6,7,8,9]=>8
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]=>[10,1,2,3,4,5,6,7,8,9,11]=>9
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[8,9,1,2,3,4,5,6,7,10]=>7
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[1,9,10,2,3,4,5,6,7,8]=>7
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>[1,11,2,3,4,5,6,7,8,9,10]=>9
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[10,1,2,3,4,5,6,7,8,9]=>9
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[11,1,2,3,4,5,6,7,8,9,10]=>10
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[2,7,8,9,10,1,3,4,5,6]=>5
[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,4,1,2,5,6,7,8,9,10]=>2
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,4,6,8,10,1,3,5,7,9]=>5
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,4,6,8,10,12,1,3,5,7,9,11]=>6
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[6,7,8,9,10,1,2,3,4,5]=>5
[1,1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[3,7,8,9,10,1,2,4,5,6]=>5
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[9,10,1,2,3,4,5,6,7,8]=>8
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[7,8,9,10,1,2,3,4,5,6]=>6
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[8,9,10,1,2,3,4,5,6,7]=>7
[1,1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[5,6,7,8,1,2,3,4,9,10]=>4
[1,1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,5,6,1,2,3,7,8,9,10]=>3
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,7,8,9,10,1,2,3,4,6]=>5
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[4,7,8,9,10,1,2,3,5,6]=>5
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[5,6,7,8,10,1,2,3,4,9]=>5
[1,1,0,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,4,6,8,10,1,2,5,7,9]=>5
[1,1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[4,5,6,9,10,1,2,3,7,8]=>5
[1,1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[4,5,8,9,10,1,2,3,6,7]=>5
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>6
[1,0,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[2,6,8,9,10,1,3,4,5,7]=>5
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[2,8,9,10,11,12,1,3,4,5,6,7]=>6
search for individual values
searching the database for the individual values of this statistic
/
search for generating function
searching the database for statistics with the same generating function
Description
The lec statistic, the sum of the inversion numbers of the hook factors of a permutation.
For a permutation $\sigma = p \tau_{1} \tau_{2} \cdots \tau_{k}$ in its hook factorization, [1] defines $$ \textrm{lec} \, \sigma = \sum_{1 \leq i \leq k} \textrm{inv} \, \tau_{i} \, ,$$ where $\textrm{inv} \, \tau_{i}$ is the number of inversions of $\tau_{i}$.
For a permutation $\sigma = p \tau_{1} \tau_{2} \cdots \tau_{k}$ in its hook factorization, [1] defines $$ \textrm{lec} \, \sigma = \sum_{1 \leq i \leq k} \textrm{inv} \, \tau_{i} \, ,$$ where $\textrm{inv} \, \tau_{i}$ is the number of inversions of $\tau_{i}$.
Map
to 321-avoiding permutation (Billey-Jockusch-Stanley)
Description
The Billey-Jockusch-Stanley bijection to 321-avoiding permutations.
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!