Identifier
-
Mp00146:
Dyck paths
—to tunnel matching⟶
Perfect matchings
St000041: Perfect matchings ⟶ ℤ
Values
=>
Cc0005;cc-rep-0
Cc0012;cc-rep
[1,0]=>[(1,2)]=>0
[1,0,1,0]=>[(1,2),(3,4)]=>0
[1,1,0,0]=>[(1,4),(2,3)]=>1
[1,0,1,0,1,0]=>[(1,2),(3,4),(5,6)]=>0
[1,0,1,1,0,0]=>[(1,2),(3,6),(4,5)]=>1
[1,1,0,0,1,0]=>[(1,4),(2,3),(5,6)]=>1
[1,1,0,1,0,0]=>[(1,6),(2,3),(4,5)]=>2
[1,1,1,0,0,0]=>[(1,6),(2,5),(3,4)]=>3
[1,0,1,0,1,0,1,0]=>[(1,2),(3,4),(5,6),(7,8)]=>0
[1,0,1,0,1,1,0,0]=>[(1,2),(3,4),(5,8),(6,7)]=>1
[1,0,1,1,0,0,1,0]=>[(1,2),(3,6),(4,5),(7,8)]=>1
[1,0,1,1,0,1,0,0]=>[(1,2),(3,8),(4,5),(6,7)]=>2
[1,0,1,1,1,0,0,0]=>[(1,2),(3,8),(4,7),(5,6)]=>3
[1,1,0,0,1,0,1,0]=>[(1,4),(2,3),(5,6),(7,8)]=>1
[1,1,0,0,1,1,0,0]=>[(1,4),(2,3),(5,8),(6,7)]=>2
[1,1,0,1,0,0,1,0]=>[(1,6),(2,3),(4,5),(7,8)]=>2
[1,1,0,1,0,1,0,0]=>[(1,8),(2,3),(4,5),(6,7)]=>3
[1,1,0,1,1,0,0,0]=>[(1,8),(2,3),(4,7),(5,6)]=>4
[1,1,1,0,0,0,1,0]=>[(1,6),(2,5),(3,4),(7,8)]=>3
[1,1,1,0,0,1,0,0]=>[(1,8),(2,5),(3,4),(6,7)]=>4
[1,1,1,0,1,0,0,0]=>[(1,8),(2,7),(3,4),(5,6)]=>5
[1,1,1,1,0,0,0,0]=>[(1,8),(2,7),(3,6),(4,5)]=>6
[1,0,1,0,1,0,1,0,1,0]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>0
[1,0,1,0,1,0,1,1,0,0]=>[(1,2),(3,4),(5,6),(7,10),(8,9)]=>1
[1,0,1,0,1,1,0,0,1,0]=>[(1,2),(3,4),(5,8),(6,7),(9,10)]=>1
[1,0,1,0,1,1,0,1,0,0]=>[(1,2),(3,4),(5,10),(6,7),(8,9)]=>2
[1,0,1,0,1,1,1,0,0,0]=>[(1,2),(3,4),(5,10),(6,9),(7,8)]=>3
[1,0,1,1,0,0,1,0,1,0]=>[(1,2),(3,6),(4,5),(7,8),(9,10)]=>1
[1,0,1,1,0,0,1,1,0,0]=>[(1,2),(3,6),(4,5),(7,10),(8,9)]=>2
[1,0,1,1,0,1,0,0,1,0]=>[(1,2),(3,8),(4,5),(6,7),(9,10)]=>2
[1,0,1,1,0,1,0,1,0,0]=>[(1,2),(3,10),(4,5),(6,7),(8,9)]=>3
[1,0,1,1,0,1,1,0,0,0]=>[(1,2),(3,10),(4,5),(6,9),(7,8)]=>4
[1,0,1,1,1,0,0,0,1,0]=>[(1,2),(3,8),(4,7),(5,6),(9,10)]=>3
[1,0,1,1,1,0,0,1,0,0]=>[(1,2),(3,10),(4,7),(5,6),(8,9)]=>4
[1,0,1,1,1,0,1,0,0,0]=>[(1,2),(3,10),(4,9),(5,6),(7,8)]=>5
[1,0,1,1,1,1,0,0,0,0]=>[(1,2),(3,10),(4,9),(5,8),(6,7)]=>6
[1,1,0,0,1,0,1,0,1,0]=>[(1,4),(2,3),(5,6),(7,8),(9,10)]=>1
[1,1,0,0,1,0,1,1,0,0]=>[(1,4),(2,3),(5,6),(7,10),(8,9)]=>2
[1,1,0,0,1,1,0,0,1,0]=>[(1,4),(2,3),(5,8),(6,7),(9,10)]=>2
[1,1,0,0,1,1,0,1,0,0]=>[(1,4),(2,3),(5,10),(6,7),(8,9)]=>3
[1,1,0,0,1,1,1,0,0,0]=>[(1,4),(2,3),(5,10),(6,9),(7,8)]=>4
[1,1,0,1,0,0,1,0,1,0]=>[(1,6),(2,3),(4,5),(7,8),(9,10)]=>2
[1,1,0,1,0,0,1,1,0,0]=>[(1,6),(2,3),(4,5),(7,10),(8,9)]=>3
[1,1,0,1,0,1,0,0,1,0]=>[(1,8),(2,3),(4,5),(6,7),(9,10)]=>3
[1,1,0,1,0,1,0,1,0,0]=>[(1,10),(2,3),(4,5),(6,7),(8,9)]=>4
[1,1,0,1,0,1,1,0,0,0]=>[(1,10),(2,3),(4,5),(6,9),(7,8)]=>5
[1,1,0,1,1,0,0,0,1,0]=>[(1,8),(2,3),(4,7),(5,6),(9,10)]=>4
[1,1,0,1,1,0,0,1,0,0]=>[(1,10),(2,3),(4,7),(5,6),(8,9)]=>5
[1,1,0,1,1,0,1,0,0,0]=>[(1,10),(2,3),(4,9),(5,6),(7,8)]=>6
[1,1,0,1,1,1,0,0,0,0]=>[(1,10),(2,3),(4,9),(5,8),(6,7)]=>7
[1,1,1,0,0,0,1,0,1,0]=>[(1,6),(2,5),(3,4),(7,8),(9,10)]=>3
[1,1,1,0,0,0,1,1,0,0]=>[(1,6),(2,5),(3,4),(7,10),(8,9)]=>4
[1,1,1,0,0,1,0,0,1,0]=>[(1,8),(2,5),(3,4),(6,7),(9,10)]=>4
[1,1,1,0,0,1,0,1,0,0]=>[(1,10),(2,5),(3,4),(6,7),(8,9)]=>5
[1,1,1,0,0,1,1,0,0,0]=>[(1,10),(2,5),(3,4),(6,9),(7,8)]=>6
[1,1,1,0,1,0,0,0,1,0]=>[(1,8),(2,7),(3,4),(5,6),(9,10)]=>5
[1,1,1,0,1,0,0,1,0,0]=>[(1,10),(2,7),(3,4),(5,6),(8,9)]=>6
[1,1,1,0,1,0,1,0,0,0]=>[(1,10),(2,9),(3,4),(5,6),(7,8)]=>7
[1,1,1,0,1,1,0,0,0,0]=>[(1,10),(2,9),(3,4),(5,8),(6,7)]=>8
[1,1,1,1,0,0,0,0,1,0]=>[(1,8),(2,7),(3,6),(4,5),(9,10)]=>6
[1,1,1,1,0,0,0,1,0,0]=>[(1,10),(2,7),(3,6),(4,5),(8,9)]=>7
[1,1,1,1,0,0,1,0,0,0]=>[(1,10),(2,9),(3,6),(4,5),(7,8)]=>8
[1,1,1,1,0,1,0,0,0,0]=>[(1,10),(2,9),(3,8),(4,5),(6,7)]=>9
[1,1,1,1,1,0,0,0,0,0]=>[(1,10),(2,9),(3,8),(4,7),(5,6)]=>10
[1,0,1,0,1,0,1,0,1,0,1,0]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>0
[1,0,1,0,1,0,1,0,1,1,0,0]=>[(1,2),(3,4),(5,6),(7,8),(9,12),(10,11)]=>1
[1,0,1,0,1,0,1,1,0,0,1,0]=>[(1,2),(3,4),(5,6),(7,10),(8,9),(11,12)]=>1
[1,0,1,0,1,0,1,1,0,1,0,0]=>[(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)]=>2
[1,0,1,0,1,0,1,1,1,0,0,0]=>[(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)]=>3
[1,0,1,0,1,1,0,0,1,0,1,0]=>[(1,2),(3,4),(5,8),(6,7),(9,10),(11,12)]=>1
[1,0,1,0,1,1,0,0,1,1,0,0]=>[(1,2),(3,4),(5,8),(6,7),(9,12),(10,11)]=>2
[1,0,1,0,1,1,0,1,0,0,1,0]=>[(1,2),(3,4),(5,10),(6,7),(8,9),(11,12)]=>2
[1,0,1,0,1,1,0,1,0,1,0,0]=>[(1,2),(3,4),(5,12),(6,7),(8,9),(10,11)]=>3
[1,0,1,0,1,1,0,1,1,0,0,0]=>[(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)]=>4
[1,0,1,0,1,1,1,0,0,0,1,0]=>[(1,2),(3,4),(5,10),(6,9),(7,8),(11,12)]=>3
[1,0,1,0,1,1,1,0,0,1,0,0]=>[(1,2),(3,4),(5,12),(6,9),(7,8),(10,11)]=>4
[1,0,1,0,1,1,1,0,1,0,0,0]=>[(1,2),(3,4),(5,12),(6,11),(7,8),(9,10)]=>5
[1,0,1,0,1,1,1,1,0,0,0,0]=>[(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)]=>6
[1,0,1,1,0,0,1,0,1,0,1,0]=>[(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)]=>1
[1,0,1,1,0,0,1,0,1,1,0,0]=>[(1,2),(3,6),(4,5),(7,8),(9,12),(10,11)]=>2
[1,0,1,1,0,0,1,1,0,0,1,0]=>[(1,2),(3,6),(4,5),(7,10),(8,9),(11,12)]=>2
[1,0,1,1,0,0,1,1,0,1,0,0]=>[(1,2),(3,6),(4,5),(7,12),(8,9),(10,11)]=>3
[1,0,1,1,0,0,1,1,1,0,0,0]=>[(1,2),(3,6),(4,5),(7,12),(8,11),(9,10)]=>4
[1,0,1,1,0,1,0,0,1,0,1,0]=>[(1,2),(3,8),(4,5),(6,7),(9,10),(11,12)]=>2
[1,0,1,1,0,1,0,0,1,1,0,0]=>[(1,2),(3,8),(4,5),(6,7),(9,12),(10,11)]=>3
[1,0,1,1,0,1,0,1,0,0,1,0]=>[(1,2),(3,10),(4,5),(6,7),(8,9),(11,12)]=>3
[1,0,1,1,0,1,0,1,0,1,0,0]=>[(1,2),(3,12),(4,5),(6,7),(8,9),(10,11)]=>4
[1,0,1,1,0,1,0,1,1,0,0,0]=>[(1,2),(3,12),(4,5),(6,7),(8,11),(9,10)]=>5
[1,0,1,1,0,1,1,0,0,0,1,0]=>[(1,2),(3,10),(4,5),(6,9),(7,8),(11,12)]=>4
[1,0,1,1,0,1,1,0,0,1,0,0]=>[(1,2),(3,12),(4,5),(6,9),(7,8),(10,11)]=>5
[1,0,1,1,0,1,1,0,1,0,0,0]=>[(1,2),(3,12),(4,5),(6,11),(7,8),(9,10)]=>6
[1,0,1,1,0,1,1,1,0,0,0,0]=>[(1,2),(3,12),(4,5),(6,11),(7,10),(8,9)]=>7
[1,0,1,1,1,0,0,0,1,0,1,0]=>[(1,2),(3,8),(4,7),(5,6),(9,10),(11,12)]=>3
[1,0,1,1,1,0,0,0,1,1,0,0]=>[(1,2),(3,8),(4,7),(5,6),(9,12),(10,11)]=>4
[1,0,1,1,1,0,0,1,0,0,1,0]=>[(1,2),(3,10),(4,7),(5,6),(8,9),(11,12)]=>4
[1,0,1,1,1,0,0,1,0,1,0,0]=>[(1,2),(3,12),(4,7),(5,6),(8,9),(10,11)]=>5
[1,0,1,1,1,0,0,1,1,0,0,0]=>[(1,2),(3,12),(4,7),(5,6),(8,11),(9,10)]=>6
[1,0,1,1,1,0,1,0,0,0,1,0]=>[(1,2),(3,10),(4,9),(5,6),(7,8),(11,12)]=>5
[1,0,1,1,1,0,1,0,0,1,0,0]=>[(1,2),(3,12),(4,9),(5,6),(7,8),(10,11)]=>6
[1,0,1,1,1,0,1,0,1,0,0,0]=>[(1,2),(3,12),(4,11),(5,6),(7,8),(9,10)]=>7
[1,0,1,1,1,0,1,1,0,0,0,0]=>[(1,2),(3,12),(4,11),(5,6),(7,10),(8,9)]=>8
[1,0,1,1,1,1,0,0,0,0,1,0]=>[(1,2),(3,10),(4,9),(5,8),(6,7),(11,12)]=>6
[1,0,1,1,1,1,0,0,0,1,0,0]=>[(1,2),(3,12),(4,9),(5,8),(6,7),(10,11)]=>7
[1,0,1,1,1,1,0,0,1,0,0,0]=>[(1,2),(3,12),(4,11),(5,8),(6,7),(9,10)]=>8
[1,0,1,1,1,1,0,1,0,0,0,0]=>[(1,2),(3,12),(4,11),(5,10),(6,7),(8,9)]=>9
[1,0,1,1,1,1,1,0,0,0,0,0]=>[(1,2),(3,12),(4,11),(5,10),(6,9),(7,8)]=>10
[1,1,0,0,1,0,1,0,1,0,1,0]=>[(1,4),(2,3),(5,6),(7,8),(9,10),(11,12)]=>1
[1,1,0,0,1,0,1,0,1,1,0,0]=>[(1,4),(2,3),(5,6),(7,8),(9,12),(10,11)]=>2
[1,1,0,0,1,0,1,1,0,0,1,0]=>[(1,4),(2,3),(5,6),(7,10),(8,9),(11,12)]=>2
[1,1,0,0,1,0,1,1,0,1,0,0]=>[(1,4),(2,3),(5,6),(7,12),(8,9),(10,11)]=>3
[1,1,0,0,1,0,1,1,1,0,0,0]=>[(1,4),(2,3),(5,6),(7,12),(8,11),(9,10)]=>4
[1,1,0,0,1,1,0,0,1,0,1,0]=>[(1,4),(2,3),(5,8),(6,7),(9,10),(11,12)]=>2
[1,1,0,0,1,1,0,0,1,1,0,0]=>[(1,4),(2,3),(5,8),(6,7),(9,12),(10,11)]=>3
[1,1,0,0,1,1,0,1,0,0,1,0]=>[(1,4),(2,3),(5,10),(6,7),(8,9),(11,12)]=>3
[1,1,0,0,1,1,0,1,0,1,0,0]=>[(1,4),(2,3),(5,12),(6,7),(8,9),(10,11)]=>4
[1,1,0,0,1,1,0,1,1,0,0,0]=>[(1,4),(2,3),(5,12),(6,7),(8,11),(9,10)]=>5
[1,1,0,0,1,1,1,0,0,0,1,0]=>[(1,4),(2,3),(5,10),(6,9),(7,8),(11,12)]=>4
[1,1,0,0,1,1,1,0,0,1,0,0]=>[(1,4),(2,3),(5,12),(6,9),(7,8),(10,11)]=>5
[1,1,0,0,1,1,1,0,1,0,0,0]=>[(1,4),(2,3),(5,12),(6,11),(7,8),(9,10)]=>6
[1,1,0,0,1,1,1,1,0,0,0,0]=>[(1,4),(2,3),(5,12),(6,11),(7,10),(8,9)]=>7
[1,1,0,1,0,0,1,0,1,0,1,0]=>[(1,6),(2,3),(4,5),(7,8),(9,10),(11,12)]=>2
[1,1,0,1,0,0,1,0,1,1,0,0]=>[(1,6),(2,3),(4,5),(7,8),(9,12),(10,11)]=>3
[1,1,0,1,0,0,1,1,0,0,1,0]=>[(1,6),(2,3),(4,5),(7,10),(8,9),(11,12)]=>3
[1,1,0,1,0,0,1,1,0,1,0,0]=>[(1,6),(2,3),(4,5),(7,12),(8,9),(10,11)]=>4
[1,1,0,1,0,0,1,1,1,0,0,0]=>[(1,6),(2,3),(4,5),(7,12),(8,11),(9,10)]=>5
[1,1,0,1,0,1,0,0,1,0,1,0]=>[(1,8),(2,3),(4,5),(6,7),(9,10),(11,12)]=>3
[1,1,0,1,0,1,0,0,1,1,0,0]=>[(1,8),(2,3),(4,5),(6,7),(9,12),(10,11)]=>4
[1,1,0,1,0,1,0,1,0,0,1,0]=>[(1,10),(2,3),(4,5),(6,7),(8,9),(11,12)]=>4
[1,1,0,1,0,1,0,1,0,1,0,0]=>[(1,12),(2,3),(4,5),(6,7),(8,9),(10,11)]=>5
[1,1,0,1,0,1,0,1,1,0,0,0]=>[(1,12),(2,3),(4,5),(6,7),(8,11),(9,10)]=>6
[1,1,0,1,0,1,1,0,0,0,1,0]=>[(1,10),(2,3),(4,5),(6,9),(7,8),(11,12)]=>5
[1,1,0,1,0,1,1,0,0,1,0,0]=>[(1,12),(2,3),(4,5),(6,9),(7,8),(10,11)]=>6
[1,1,0,1,0,1,1,0,1,0,0,0]=>[(1,12),(2,3),(4,5),(6,11),(7,8),(9,10)]=>7
[1,1,0,1,0,1,1,1,0,0,0,0]=>[(1,12),(2,3),(4,5),(6,11),(7,10),(8,9)]=>8
[1,1,0,1,1,0,0,0,1,0,1,0]=>[(1,8),(2,3),(4,7),(5,6),(9,10),(11,12)]=>4
[1,1,0,1,1,0,0,0,1,1,0,0]=>[(1,8),(2,3),(4,7),(5,6),(9,12),(10,11)]=>5
[1,1,0,1,1,0,0,1,0,0,1,0]=>[(1,10),(2,3),(4,7),(5,6),(8,9),(11,12)]=>5
[1,1,0,1,1,0,0,1,0,1,0,0]=>[(1,12),(2,3),(4,7),(5,6),(8,9),(10,11)]=>6
[1,1,0,1,1,0,0,1,1,0,0,0]=>[(1,12),(2,3),(4,7),(5,6),(8,11),(9,10)]=>7
[1,1,0,1,1,0,1,0,0,0,1,0]=>[(1,10),(2,3),(4,9),(5,6),(7,8),(11,12)]=>6
[1,1,0,1,1,0,1,0,0,1,0,0]=>[(1,12),(2,3),(4,9),(5,6),(7,8),(10,11)]=>7
[1,1,0,1,1,0,1,0,1,0,0,0]=>[(1,12),(2,3),(4,11),(5,6),(7,8),(9,10)]=>8
[1,1,0,1,1,0,1,1,0,0,0,0]=>[(1,12),(2,3),(4,11),(5,6),(7,10),(8,9)]=>9
[1,1,0,1,1,1,0,0,0,0,1,0]=>[(1,10),(2,3),(4,9),(5,8),(6,7),(11,12)]=>7
[1,1,0,1,1,1,0,0,0,1,0,0]=>[(1,12),(2,3),(4,9),(5,8),(6,7),(10,11)]=>8
[1,1,0,1,1,1,0,0,1,0,0,0]=>[(1,12),(2,3),(4,11),(5,8),(6,7),(9,10)]=>9
[1,1,0,1,1,1,0,1,0,0,0,0]=>[(1,12),(2,3),(4,11),(5,10),(6,7),(8,9)]=>10
[1,1,0,1,1,1,1,0,0,0,0,0]=>[(1,12),(2,3),(4,11),(5,10),(6,9),(7,8)]=>11
[1,1,1,0,0,0,1,0,1,0,1,0]=>[(1,6),(2,5),(3,4),(7,8),(9,10),(11,12)]=>3
[1,1,1,0,0,0,1,0,1,1,0,0]=>[(1,6),(2,5),(3,4),(7,8),(9,12),(10,11)]=>4
[1,1,1,0,0,0,1,1,0,0,1,0]=>[(1,6),(2,5),(3,4),(7,10),(8,9),(11,12)]=>4
[1,1,1,0,0,0,1,1,0,1,0,0]=>[(1,6),(2,5),(3,4),(7,12),(8,9),(10,11)]=>5
[1,1,1,0,0,0,1,1,1,0,0,0]=>[(1,6),(2,5),(3,4),(7,12),(8,11),(9,10)]=>6
[1,1,1,0,0,1,0,0,1,0,1,0]=>[(1,8),(2,5),(3,4),(6,7),(9,10),(11,12)]=>4
[1,1,1,0,0,1,0,0,1,1,0,0]=>[(1,8),(2,5),(3,4),(6,7),(9,12),(10,11)]=>5
[1,1,1,0,0,1,0,1,0,0,1,0]=>[(1,10),(2,5),(3,4),(6,7),(8,9),(11,12)]=>5
[1,1,1,0,0,1,0,1,0,1,0,0]=>[(1,12),(2,5),(3,4),(6,7),(8,9),(10,11)]=>6
[1,1,1,0,0,1,0,1,1,0,0,0]=>[(1,12),(2,5),(3,4),(6,7),(8,11),(9,10)]=>7
[1,1,1,0,0,1,1,0,0,0,1,0]=>[(1,10),(2,5),(3,4),(6,9),(7,8),(11,12)]=>6
[1,1,1,0,0,1,1,0,0,1,0,0]=>[(1,12),(2,5),(3,4),(6,9),(7,8),(10,11)]=>7
[1,1,1,0,0,1,1,0,1,0,0,0]=>[(1,12),(2,5),(3,4),(6,11),(7,8),(9,10)]=>8
[1,1,1,0,0,1,1,1,0,0,0,0]=>[(1,12),(2,5),(3,4),(6,11),(7,10),(8,9)]=>9
[1,1,1,0,1,0,0,0,1,0,1,0]=>[(1,8),(2,7),(3,4),(5,6),(9,10),(11,12)]=>5
[1,1,1,0,1,0,0,0,1,1,0,0]=>[(1,8),(2,7),(3,4),(5,6),(9,12),(10,11)]=>6
[1,1,1,0,1,0,0,1,0,0,1,0]=>[(1,10),(2,7),(3,4),(5,6),(8,9),(11,12)]=>6
[1,1,1,0,1,0,0,1,0,1,0,0]=>[(1,12),(2,7),(3,4),(5,6),(8,9),(10,11)]=>7
[1,1,1,0,1,0,0,1,1,0,0,0]=>[(1,12),(2,7),(3,4),(5,6),(8,11),(9,10)]=>8
[1,1,1,0,1,0,1,0,0,0,1,0]=>[(1,10),(2,9),(3,4),(5,6),(7,8),(11,12)]=>7
[1,1,1,0,1,0,1,0,0,1,0,0]=>[(1,12),(2,9),(3,4),(5,6),(7,8),(10,11)]=>8
[1,1,1,0,1,0,1,0,1,0,0,0]=>[(1,12),(2,11),(3,4),(5,6),(7,8),(9,10)]=>9
[1,1,1,0,1,0,1,1,0,0,0,0]=>[(1,12),(2,11),(3,4),(5,6),(7,10),(8,9)]=>10
[1,1,1,0,1,1,0,0,0,0,1,0]=>[(1,10),(2,9),(3,4),(5,8),(6,7),(11,12)]=>8
[1,1,1,0,1,1,0,0,0,1,0,0]=>[(1,12),(2,9),(3,4),(5,8),(6,7),(10,11)]=>9
[1,1,1,0,1,1,0,0,1,0,0,0]=>[(1,12),(2,11),(3,4),(5,8),(6,7),(9,10)]=>10
[1,1,1,0,1,1,0,1,0,0,0,0]=>[(1,12),(2,11),(3,4),(5,10),(6,7),(8,9)]=>11
[1,1,1,0,1,1,1,0,0,0,0,0]=>[(1,12),(2,11),(3,4),(5,10),(6,9),(7,8)]=>12
[1,1,1,1,0,0,0,0,1,0,1,0]=>[(1,8),(2,7),(3,6),(4,5),(9,10),(11,12)]=>6
[1,1,1,1,0,0,0,0,1,1,0,0]=>[(1,8),(2,7),(3,6),(4,5),(9,12),(10,11)]=>7
[1,1,1,1,0,0,0,1,0,0,1,0]=>[(1,10),(2,7),(3,6),(4,5),(8,9),(11,12)]=>7
[1,1,1,1,0,0,0,1,0,1,0,0]=>[(1,12),(2,7),(3,6),(4,5),(8,9),(10,11)]=>8
[1,1,1,1,0,0,0,1,1,0,0,0]=>[(1,12),(2,7),(3,6),(4,5),(8,11),(9,10)]=>9
[1,1,1,1,0,0,1,0,0,0,1,0]=>[(1,10),(2,9),(3,6),(4,5),(7,8),(11,12)]=>8
[1,1,1,1,0,0,1,0,0,1,0,0]=>[(1,12),(2,9),(3,6),(4,5),(7,8),(10,11)]=>9
[1,1,1,1,0,0,1,0,1,0,0,0]=>[(1,12),(2,11),(3,6),(4,5),(7,8),(9,10)]=>10
[1,1,1,1,0,0,1,1,0,0,0,0]=>[(1,12),(2,11),(3,6),(4,5),(7,10),(8,9)]=>11
[1,1,1,1,0,1,0,0,0,0,1,0]=>[(1,10),(2,9),(3,8),(4,5),(6,7),(11,12)]=>9
[1,1,1,1,0,1,0,0,0,1,0,0]=>[(1,12),(2,9),(3,8),(4,5),(6,7),(10,11)]=>10
[1,1,1,1,0,1,0,0,1,0,0,0]=>[(1,12),(2,11),(3,8),(4,5),(6,7),(9,10)]=>11
[1,1,1,1,0,1,0,1,0,0,0,0]=>[(1,12),(2,11),(3,10),(4,5),(6,7),(8,9)]=>12
[1,1,1,1,0,1,1,0,0,0,0,0]=>[(1,12),(2,11),(3,10),(4,5),(6,9),(7,8)]=>13
[1,1,1,1,1,0,0,0,0,0,1,0]=>[(1,10),(2,9),(3,8),(4,7),(5,6),(11,12)]=>10
[1,1,1,1,1,0,0,0,0,1,0,0]=>[(1,12),(2,9),(3,8),(4,7),(5,6),(10,11)]=>11
[1,1,1,1,1,0,0,0,1,0,0,0]=>[(1,12),(2,11),(3,8),(4,7),(5,6),(9,10)]=>12
[1,1,1,1,1,0,0,1,0,0,0,0]=>[(1,12),(2,11),(3,10),(4,7),(5,6),(8,9)]=>13
[1,1,1,1,1,0,1,0,0,0,0,0]=>[(1,12),(2,11),(3,10),(4,9),(5,6),(7,8)]=>14
[1,1,1,1,1,1,0,0,0,0,0,0]=>[(1,12),(2,11),(3,10),(4,9),(5,8),(6,7)]=>15
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,14)]=>0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,14),(12,13)]=>1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[(1,2),(3,4),(5,6),(7,8),(9,12),(10,11),(13,14)]=>1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[(1,2),(3,4),(5,6),(7,8),(9,14),(10,11),(12,13)]=>2
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[(1,2),(3,4),(5,6),(7,8),(9,14),(10,13),(11,12)]=>3
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[(1,2),(3,4),(5,6),(7,10),(8,9),(11,12),(13,14)]=>1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[(1,2),(3,4),(5,6),(7,10),(8,9),(11,14),(12,13)]=>2
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[(1,2),(3,4),(5,6),(7,14),(8,9),(10,11),(12,13)]=>3
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[(1,2),(3,4),(5,6),(7,12),(8,11),(9,10),(13,14)]=>3
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[(1,2),(3,4),(5,6),(7,14),(8,11),(9,10),(12,13)]=>4
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[(1,2),(3,4),(5,6),(7,14),(8,13),(9,10),(11,12)]=>5
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[(1,2),(3,4),(5,6),(7,14),(8,13),(9,12),(10,11)]=>6
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[(1,2),(3,4),(5,8),(6,7),(9,10),(11,12),(13,14)]=>1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[(1,2),(3,4),(5,8),(6,7),(9,10),(11,14),(12,13)]=>2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[(1,2),(3,4),(5,8),(6,7),(9,12),(10,11),(13,14)]=>2
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[(1,2),(3,4),(5,8),(6,7),(9,14),(10,13),(11,12)]=>4
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[(1,2),(3,4),(5,14),(6,7),(8,9),(10,11),(12,13)]=>4
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[(1,2),(3,4),(5,10),(6,9),(7,8),(11,12),(13,14)]=>3
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[(1,2),(3,4),(5,10),(6,9),(7,8),(11,14),(12,13)]=>4
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[(1,2),(3,4),(5,14),(6,9),(7,8),(10,11),(12,13)]=>5
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[(1,2),(3,4),(5,14),(6,11),(7,8),(9,10),(12,13)]=>6
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[(1,2),(3,4),(5,14),(6,13),(7,8),(9,10),(11,12)]=>7
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[(1,2),(3,4),(5,14),(6,13),(7,8),(9,12),(10,11)]=>8
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[(1,2),(3,4),(5,12),(6,11),(7,10),(8,9),(13,14)]=>6
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[(1,2),(3,4),(5,14),(6,11),(7,10),(8,9),(12,13)]=>7
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[(1,2),(3,4),(5,14),(6,13),(7,12),(8,9),(10,11)]=>9
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[(1,2),(3,4),(5,14),(6,13),(7,12),(8,11),(9,10)]=>10
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[(1,2),(3,6),(4,5),(7,8),(9,10),(11,12),(13,14)]=>1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[(1,2),(3,6),(4,5),(7,8),(9,10),(11,14),(12,13)]=>2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[(1,2),(3,6),(4,5),(7,8),(9,12),(10,11),(13,14)]=>2
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[(1,2),(3,6),(4,5),(7,8),(9,14),(10,13),(11,12)]=>4
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[(1,2),(3,6),(4,5),(7,10),(8,9),(11,12),(13,14)]=>2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[(1,2),(3,6),(4,5),(7,10),(8,9),(11,14),(12,13)]=>3
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[(1,2),(3,6),(4,5),(7,12),(8,11),(9,10),(13,14)]=>4
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[(1,2),(3,6),(4,5),(7,14),(8,13),(9,12),(10,11)]=>7
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[(1,2),(3,14),(4,5),(6,7),(8,9),(10,11),(12,13)]=>5
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[(1,2),(3,14),(4,5),(6,13),(7,12),(8,11),(9,10)]=>11
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[(1,2),(3,8),(4,7),(5,6),(9,10),(11,12),(13,14)]=>3
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[(1,2),(3,8),(4,7),(5,6),(9,10),(11,14),(12,13)]=>4
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[(1,2),(3,8),(4,7),(5,6),(9,12),(10,11),(13,14)]=>4
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[(1,2),(3,8),(4,7),(5,6),(9,14),(10,13),(11,12)]=>6
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[(1,2),(3,14),(4,7),(5,6),(8,9),(10,11),(12,13)]=>6
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[(1,2),(3,14),(4,9),(5,6),(7,8),(10,11),(12,13)]=>7
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[(1,2),(3,14),(4,11),(5,6),(7,8),(9,10),(12,13)]=>8
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[(1,2),(3,14),(4,11),(5,6),(7,10),(8,9),(12,13)]=>9
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[(1,2),(3,14),(4,13),(5,6),(7,12),(8,9),(10,11)]=>11
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[(1,2),(3,14),(4,13),(5,6),(7,12),(8,11),(9,10)]=>12
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[(1,2),(3,10),(4,9),(5,8),(6,7),(11,12),(13,14)]=>6
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[(1,2),(3,10),(4,9),(5,8),(6,7),(11,14),(12,13)]=>7
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[(1,2),(3,14),(4,9),(5,8),(6,7),(10,11),(12,13)]=>8
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[(1,2),(3,14),(4,13),(5,8),(6,7),(9,12),(10,11)]=>11
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[(1,2),(3,14),(4,11),(5,10),(6,7),(8,9),(12,13)]=>10
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[(1,2),(3,14),(4,13),(5,10),(6,7),(8,9),(11,12)]=>11
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[(1,2),(3,14),(4,13),(5,12),(6,7),(8,9),(10,11)]=>12
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[(1,2),(3,14),(4,13),(5,12),(6,7),(8,11),(9,10)]=>13
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[(1,2),(3,12),(4,11),(5,10),(6,9),(7,8),(13,14)]=>10
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[(1,2),(3,14),(4,11),(5,10),(6,9),(7,8),(12,13)]=>11
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[(1,2),(3,14),(4,13),(5,10),(6,9),(7,8),(11,12)]=>12
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[(1,2),(3,14),(4,13),(5,12),(6,9),(7,8),(10,11)]=>13
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[(1,2),(3,14),(4,13),(5,12),(6,11),(7,8),(9,10)]=>14
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[(1,2),(3,14),(4,13),(5,12),(6,11),(7,10),(8,9)]=>15
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[(1,4),(2,3),(5,6),(7,8),(9,10),(11,12),(13,14)]=>1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[(1,4),(2,3),(5,6),(7,8),(9,10),(11,14),(12,13)]=>2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[(1,4),(2,3),(5,6),(7,8),(9,12),(10,11),(13,14)]=>2
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[(1,4),(2,3),(5,6),(7,8),(9,14),(10,13),(11,12)]=>4
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[(1,4),(2,3),(5,6),(7,10),(8,9),(11,12),(13,14)]=>2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[(1,4),(2,3),(5,6),(7,10),(8,9),(11,14),(12,13)]=>3
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[(1,4),(2,3),(5,6),(7,12),(8,11),(9,10),(13,14)]=>4
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[(1,4),(2,3),(5,6),(7,14),(8,13),(9,12),(10,11)]=>7
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[(1,4),(2,3),(5,8),(6,7),(9,10),(11,12),(13,14)]=>2
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[(1,4),(2,3),(5,8),(6,7),(9,10),(11,14),(12,13)]=>3
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[(1,4),(2,3),(5,8),(6,7),(9,12),(10,11),(13,14)]=>3
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[(1,4),(2,3),(5,8),(6,7),(9,14),(10,13),(11,12)]=>5
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[(1,4),(2,3),(5,10),(6,9),(7,8),(11,12),(13,14)]=>4
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[(1,4),(2,3),(5,10),(6,9),(7,8),(11,14),(12,13)]=>5
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[(1,4),(2,3),(5,12),(6,11),(7,10),(8,9),(13,14)]=>7
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[(1,4),(2,3),(5,14),(6,13),(7,12),(8,11),(9,10)]=>11
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[(1,14),(2,3),(4,5),(6,7),(8,9),(10,11),(12,13)]=>6
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[(1,14),(2,3),(4,5),(6,7),(8,9),(10,13),(11,12)]=>7
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[(1,14),(2,3),(4,5),(6,7),(8,11),(9,10),(12,13)]=>7
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[(1,14),(2,3),(4,5),(6,7),(8,13),(9,10),(11,12)]=>8
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[(1,14),(2,3),(4,5),(6,7),(8,13),(9,12),(10,11)]=>9
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[(1,14),(2,3),(4,5),(6,9),(7,8),(10,11),(12,13)]=>7
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[(1,14),(2,3),(4,5),(6,9),(7,8),(10,13),(11,12)]=>8
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[(1,14),(2,3),(4,5),(6,11),(7,8),(9,10),(12,13)]=>8
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[(1,14),(2,3),(4,5),(6,13),(7,8),(9,10),(11,12)]=>9
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[(1,14),(2,3),(4,5),(6,13),(7,8),(9,12),(10,11)]=>10
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[(1,14),(2,3),(4,5),(6,11),(7,10),(8,9),(12,13)]=>9
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[(1,14),(2,3),(4,5),(6,13),(7,10),(8,9),(11,12)]=>10
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[(1,14),(2,3),(4,5),(6,13),(7,12),(8,9),(10,11)]=>11
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[(1,14),(2,3),(4,5),(6,13),(7,12),(8,11),(9,10)]=>12
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[(1,14),(2,3),(4,7),(5,6),(8,9),(10,11),(12,13)]=>7
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[(1,14),(2,3),(4,7),(5,6),(8,9),(10,13),(11,12)]=>8
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[(1,14),(2,3),(4,7),(5,6),(8,11),(9,10),(12,13)]=>8
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[(1,14),(2,3),(4,7),(5,6),(8,13),(9,10),(11,12)]=>9
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[(1,14),(2,3),(4,7),(5,6),(8,13),(9,12),(10,11)]=>10
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[(1,14),(2,3),(4,9),(5,6),(7,8),(10,11),(12,13)]=>8
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[(1,14),(2,3),(4,9),(5,6),(7,8),(10,13),(11,12)]=>9
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[(1,14),(2,3),(4,11),(5,6),(7,8),(9,10),(12,13)]=>9
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[(1,14),(2,3),(4,13),(5,6),(7,8),(9,10),(11,12)]=>10
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[(1,14),(2,3),(4,13),(5,6),(7,8),(9,12),(10,11)]=>11
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[(1,14),(2,3),(4,11),(5,6),(7,10),(8,9),(12,13)]=>10
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[(1,14),(2,3),(4,13),(5,6),(7,10),(8,9),(11,12)]=>11
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[(1,14),(2,3),(4,13),(5,6),(7,12),(8,9),(10,11)]=>12
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[(1,14),(2,3),(4,13),(5,6),(7,12),(8,11),(9,10)]=>13
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[(1,14),(2,3),(4,9),(5,8),(6,7),(10,11),(12,13)]=>9
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[(1,14),(2,3),(4,9),(5,8),(6,7),(10,13),(11,12)]=>10
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[(1,14),(2,3),(4,11),(5,8),(6,7),(9,10),(12,13)]=>10
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[(1,14),(2,3),(4,13),(5,8),(6,7),(9,10),(11,12)]=>11
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[(1,14),(2,3),(4,13),(5,8),(6,7),(9,12),(10,11)]=>12
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[(1,14),(2,3),(4,11),(5,10),(6,7),(8,9),(12,13)]=>11
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[(1,14),(2,3),(4,13),(5,10),(6,7),(8,9),(11,12)]=>12
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[(1,14),(2,3),(4,13),(5,12),(6,7),(8,9),(10,11)]=>13
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[(1,14),(2,3),(4,13),(5,12),(6,7),(8,11),(9,10)]=>14
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[(1,12),(2,3),(4,11),(5,10),(6,9),(7,8),(13,14)]=>11
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[(1,14),(2,3),(4,11),(5,10),(6,9),(7,8),(12,13)]=>12
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[(1,14),(2,3),(4,13),(5,10),(6,9),(7,8),(11,12)]=>13
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[(1,14),(2,3),(4,13),(5,12),(6,9),(7,8),(10,11)]=>14
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[(1,14),(2,3),(4,13),(5,12),(6,11),(7,8),(9,10)]=>15
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[(1,14),(2,3),(4,13),(5,12),(6,11),(7,10),(8,9)]=>16
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[(1,6),(2,5),(3,4),(7,8),(9,10),(11,12),(13,14)]=>3
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[(1,6),(2,5),(3,4),(7,8),(9,10),(11,14),(12,13)]=>4
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[(1,6),(2,5),(3,4),(7,8),(9,12),(10,11),(13,14)]=>4
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[(1,6),(2,5),(3,4),(7,8),(9,14),(10,13),(11,12)]=>6
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[(1,6),(2,5),(3,4),(7,10),(8,9),(11,12),(13,14)]=>4
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[(1,6),(2,5),(3,4),(7,10),(8,9),(11,14),(12,13)]=>5
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[(1,6),(2,5),(3,4),(7,12),(8,11),(9,10),(13,14)]=>6
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[(1,6),(2,5),(3,4),(7,14),(8,13),(9,12),(10,11)]=>9
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[(1,14),(2,5),(3,4),(6,7),(8,9),(10,11),(12,13)]=>7
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[(1,14),(2,5),(3,4),(6,7),(8,9),(10,13),(11,12)]=>8
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[(1,14),(2,5),(3,4),(6,7),(8,11),(9,10),(12,13)]=>8
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[(1,14),(2,5),(3,4),(6,7),(8,13),(9,10),(11,12)]=>9
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[(1,14),(2,5),(3,4),(6,7),(8,13),(9,12),(10,11)]=>10
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[(1,14),(2,5),(3,4),(6,9),(7,8),(10,11),(12,13)]=>8
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[(1,14),(2,5),(3,4),(6,9),(7,8),(10,13),(11,12)]=>9
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[(1,14),(2,5),(3,4),(6,11),(7,8),(9,10),(12,13)]=>9
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[(1,14),(2,5),(3,4),(6,13),(7,8),(9,10),(11,12)]=>10
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[(1,14),(2,5),(3,4),(6,13),(7,8),(9,12),(10,11)]=>11
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[(1,14),(2,5),(3,4),(6,11),(7,10),(8,9),(12,13)]=>10
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[(1,14),(2,5),(3,4),(6,13),(7,10),(8,9),(11,12)]=>11
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[(1,14),(2,5),(3,4),(6,13),(7,12),(8,9),(10,11)]=>12
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[(1,14),(2,5),(3,4),(6,13),(7,12),(8,11),(9,10)]=>13
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[(1,14),(2,7),(3,4),(5,6),(8,9),(10,11),(12,13)]=>8
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[(1,14),(2,7),(3,4),(5,6),(8,9),(10,13),(11,12)]=>9
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[(1,14),(2,7),(3,4),(5,6),(8,11),(9,10),(12,13)]=>9
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[(1,14),(2,7),(3,4),(5,6),(8,13),(9,10),(11,12)]=>10
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[(1,14),(2,7),(3,4),(5,6),(8,13),(9,12),(10,11)]=>11
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[(1,14),(2,9),(3,4),(5,6),(7,8),(10,11),(12,13)]=>9
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[(1,14),(2,9),(3,4),(5,6),(7,8),(10,13),(11,12)]=>10
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[(1,14),(2,11),(3,4),(5,6),(7,8),(9,10),(12,13)]=>10
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[(1,14),(2,13),(3,4),(5,6),(7,8),(9,10),(11,12)]=>11
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[(1,14),(2,13),(3,4),(5,6),(7,8),(9,12),(10,11)]=>12
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[(1,14),(2,11),(3,4),(5,6),(7,10),(8,9),(12,13)]=>11
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[(1,14),(2,13),(3,4),(5,6),(7,10),(8,9),(11,12)]=>12
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[(1,14),(2,13),(3,4),(5,6),(7,12),(8,9),(10,11)]=>13
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[(1,14),(2,13),(3,4),(5,6),(7,12),(8,11),(9,10)]=>14
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[(1,14),(2,9),(3,4),(5,8),(6,7),(10,11),(12,13)]=>10
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[(1,14),(2,9),(3,4),(5,8),(6,7),(10,13),(11,12)]=>11
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[(1,14),(2,11),(3,4),(5,8),(6,7),(9,10),(12,13)]=>11
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[(1,14),(2,13),(3,4),(5,8),(6,7),(9,10),(11,12)]=>12
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[(1,14),(2,13),(3,4),(5,8),(6,7),(9,12),(10,11)]=>13
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[(1,12),(2,11),(3,4),(5,10),(6,7),(8,9),(13,14)]=>11
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[(1,14),(2,11),(3,4),(5,10),(6,7),(8,9),(12,13)]=>12
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[(1,14),(2,13),(3,4),(5,10),(6,7),(8,9),(11,12)]=>13
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[(1,14),(2,13),(3,4),(5,12),(6,7),(8,9),(10,11)]=>14
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[(1,14),(2,13),(3,4),(5,12),(6,7),(8,11),(9,10)]=>15
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[(1,12),(2,11),(3,4),(5,10),(6,9),(7,8),(13,14)]=>12
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[(1,14),(2,11),(3,4),(5,10),(6,9),(7,8),(12,13)]=>13
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[(1,14),(2,13),(3,4),(5,10),(6,9),(7,8),(11,12)]=>14
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[(1,14),(2,13),(3,4),(5,12),(6,9),(7,8),(10,11)]=>15
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[(1,14),(2,13),(3,4),(5,12),(6,11),(7,8),(9,10)]=>16
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[(1,14),(2,13),(3,4),(5,12),(6,11),(7,10),(8,9)]=>17
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[(1,8),(2,7),(3,6),(4,5),(9,10),(11,12),(13,14)]=>6
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[(1,8),(2,7),(3,6),(4,5),(9,10),(11,14),(12,13)]=>7
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[(1,8),(2,7),(3,6),(4,5),(9,12),(10,11),(13,14)]=>7
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[(1,8),(2,7),(3,6),(4,5),(9,14),(10,13),(11,12)]=>9
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[(1,14),(2,7),(3,6),(4,5),(8,9),(10,11),(12,13)]=>9
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[(1,14),(2,7),(3,6),(4,5),(8,9),(10,13),(11,12)]=>10
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[(1,14),(2,7),(3,6),(4,5),(8,11),(9,10),(12,13)]=>10
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[(1,14),(2,7),(3,6),(4,5),(8,13),(9,10),(11,12)]=>11
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[(1,14),(2,7),(3,6),(4,5),(8,13),(9,12),(10,11)]=>12
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[(1,14),(2,9),(3,6),(4,5),(7,8),(10,11),(12,13)]=>10
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[(1,14),(2,9),(3,6),(4,5),(7,8),(10,13),(11,12)]=>11
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[(1,14),(2,11),(3,6),(4,5),(7,8),(9,10),(12,13)]=>11
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[(1,14),(2,13),(3,6),(4,5),(7,8),(9,10),(11,12)]=>12
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[(1,14),(2,13),(3,6),(4,5),(7,8),(9,12),(10,11)]=>13
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[(1,12),(2,11),(3,6),(4,5),(7,10),(8,9),(13,14)]=>11
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[(1,14),(2,11),(3,6),(4,5),(7,10),(8,9),(12,13)]=>12
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[(1,14),(2,13),(3,6),(4,5),(7,10),(8,9),(11,12)]=>13
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[(1,14),(2,13),(3,6),(4,5),(7,12),(8,9),(10,11)]=>14
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[(1,14),(2,13),(3,6),(4,5),(7,12),(8,11),(9,10)]=>15
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[(1,14),(2,9),(3,8),(4,5),(6,7),(10,11),(12,13)]=>11
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[(1,14),(2,9),(3,8),(4,5),(6,7),(10,13),(11,12)]=>12
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[(1,12),(2,11),(3,8),(4,5),(6,7),(9,10),(13,14)]=>11
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[(1,14),(2,11),(3,8),(4,5),(6,7),(9,10),(12,13)]=>12
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[(1,14),(2,13),(3,8),(4,5),(6,7),(9,10),(11,12)]=>13
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[(1,14),(2,13),(3,8),(4,5),(6,7),(9,12),(10,11)]=>14
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[(1,12),(2,11),(3,10),(4,5),(6,7),(8,9),(13,14)]=>12
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[(1,14),(2,11),(3,10),(4,5),(6,7),(8,9),(12,13)]=>13
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[(1,14),(2,13),(3,10),(4,5),(6,7),(8,9),(11,12)]=>14
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[(1,14),(2,13),(3,12),(4,5),(6,7),(8,9),(10,11)]=>15
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[(1,14),(2,13),(3,12),(4,5),(6,7),(8,11),(9,10)]=>16
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[(1,12),(2,11),(3,10),(4,5),(6,9),(7,8),(13,14)]=>13
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[(1,14),(2,11),(3,10),(4,5),(6,9),(7,8),(12,13)]=>14
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[(1,14),(2,13),(3,10),(4,5),(6,9),(7,8),(11,12)]=>15
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[(1,14),(2,13),(3,12),(4,5),(6,9),(7,8),(10,11)]=>16
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[(1,14),(2,13),(3,12),(4,5),(6,11),(7,8),(9,10)]=>17
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[(1,14),(2,13),(3,12),(4,5),(6,11),(7,10),(8,9)]=>18
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[(1,10),(2,9),(3,8),(4,7),(5,6),(11,12),(13,14)]=>10
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[(1,10),(2,9),(3,8),(4,7),(5,6),(11,14),(12,13)]=>11
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[(1,12),(2,9),(3,8),(4,7),(5,6),(10,11),(13,14)]=>11
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[(1,14),(2,9),(3,8),(4,7),(5,6),(10,11),(12,13)]=>12
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[(1,14),(2,9),(3,8),(4,7),(5,6),(10,13),(11,12)]=>13
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[(1,12),(2,11),(3,8),(4,7),(5,6),(9,10),(13,14)]=>12
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[(1,14),(2,11),(3,8),(4,7),(5,6),(9,10),(12,13)]=>13
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[(1,14),(2,13),(3,8),(4,7),(5,6),(9,10),(11,12)]=>14
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[(1,14),(2,13),(3,8),(4,7),(5,6),(9,12),(10,11)]=>15
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[(1,12),(2,11),(3,10),(4,7),(5,6),(8,9),(13,14)]=>13
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[(1,14),(2,11),(3,10),(4,7),(5,6),(8,9),(12,13)]=>14
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[(1,14),(2,13),(3,10),(4,7),(5,6),(8,9),(11,12)]=>15
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[(1,14),(2,13),(3,12),(4,7),(5,6),(8,9),(10,11)]=>16
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[(1,14),(2,13),(3,12),(4,7),(5,6),(8,11),(9,10)]=>17
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[(1,12),(2,11),(3,10),(4,9),(5,6),(7,8),(13,14)]=>14
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[(1,14),(2,11),(3,10),(4,9),(5,6),(7,8),(12,13)]=>15
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[(1,14),(2,13),(3,10),(4,9),(5,6),(7,8),(11,12)]=>16
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[(1,14),(2,13),(3,12),(4,9),(5,6),(7,8),(10,11)]=>17
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[(1,14),(2,13),(3,12),(4,11),(5,6),(7,8),(9,10)]=>18
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[(1,14),(2,13),(3,12),(4,11),(5,6),(7,10),(8,9)]=>19
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[(1,12),(2,11),(3,10),(4,9),(5,8),(6,7),(13,14)]=>15
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[(1,14),(2,11),(3,10),(4,9),(5,8),(6,7),(12,13)]=>16
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[(1,14),(2,13),(3,10),(4,9),(5,8),(6,7),(11,12)]=>17
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[(1,14),(2,13),(3,12),(4,9),(5,8),(6,7),(10,11)]=>18
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[(1,14),(2,13),(3,12),(4,11),(5,8),(6,7),(9,10)]=>19
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[(1,14),(2,13),(3,12),(4,11),(5,10),(6,7),(8,9)]=>20
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[(1,14),(2,13),(3,12),(4,11),(5,10),(6,9),(7,8)]=>21
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16)]=>0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,16),(14,15)]=>1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,16),(12,13),(14,15)]=>2
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,16),(12,15),(13,14)]=>3
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[(1,2),(3,4),(5,6),(7,8),(9,16),(10,11),(12,13),(14,15)]=>3
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[(1,2),(3,4),(5,6),(7,8),(9,16),(10,13),(11,12),(14,15)]=>4
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[(1,2),(3,4),(5,6),(7,8),(9,16),(10,15),(11,12),(13,14)]=>5
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[(1,2),(3,4),(5,6),(7,8),(9,16),(10,15),(11,14),(12,13)]=>6
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[(1,2),(3,4),(5,6),(7,16),(8,9),(10,11),(12,13),(14,15)]=>4
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[(1,2),(3,4),(5,6),(7,16),(8,11),(9,10),(12,13),(14,15)]=>5
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[(1,2),(3,4),(5,6),(7,16),(8,13),(9,10),(11,12),(14,15)]=>6
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[(1,2),(3,4),(5,6),(7,16),(8,13),(9,12),(10,11),(14,15)]=>7
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[(1,2),(3,4),(5,16),(6,7),(8,9),(10,11),(12,13),(14,15)]=>5
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[(1,2),(3,4),(5,16),(6,9),(7,8),(10,11),(12,13),(14,15)]=>6
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[(1,2),(3,4),(5,16),(6,11),(7,8),(9,10),(12,13),(14,15)]=>7
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[(1,2),(3,4),(5,16),(6,11),(7,10),(8,9),(12,13),(14,15)]=>8
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[(1,2),(3,16),(4,5),(6,7),(8,9),(10,11),(12,13),(14,15)]=>6
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[(1,2),(3,16),(4,7),(5,6),(8,9),(10,11),(12,13),(14,15)]=>7
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[(1,2),(3,16),(4,9),(5,6),(7,8),(10,11),(12,13),(14,15)]=>8
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[(1,2),(3,16),(4,9),(5,8),(6,7),(10,11),(12,13),(14,15)]=>9
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[(1,2),(3,16),(4,15),(5,14),(6,7),(8,13),(9,12),(10,11)]=>18
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[(1,2),(3,16),(4,15),(5,14),(6,13),(7,8),(9,10),(11,12)]=>18
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[(1,2),(3,16),(4,15),(5,14),(6,13),(7,8),(9,12),(10,11)]=>19
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[(1,2),(3,16),(4,15),(5,14),(6,11),(7,10),(8,9),(12,13)]=>18
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[(1,2),(3,16),(4,15),(5,14),(6,13),(7,10),(8,9),(11,12)]=>19
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[(1,2),(3,16),(4,15),(5,14),(6,13),(7,12),(8,9),(10,11)]=>20
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[(1,2),(3,16),(4,15),(5,14),(6,13),(7,12),(8,11),(9,10)]=>21
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[(1,16),(2,3),(4,5),(6,7),(8,9),(10,11),(12,13),(14,15)]=>7
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[(1,16),(2,5),(3,4),(6,7),(8,9),(10,11),(12,13),(14,15)]=>8
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[(1,16),(2,7),(3,4),(5,6),(8,9),(10,11),(12,13),(14,15)]=>9
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[(1,16),(2,7),(3,6),(4,5),(8,9),(10,11),(12,13),(14,15)]=>10
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[(1,14),(2,13),(3,12),(4,5),(6,11),(7,10),(8,9),(15,16)]=>18
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[(1,14),(2,13),(3,12),(4,11),(5,6),(7,8),(9,10),(15,16)]=>18
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[(1,14),(2,13),(3,12),(4,11),(5,6),(7,10),(8,9),(15,16)]=>19
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[(1,14),(2,13),(3,12),(4,9),(5,8),(6,7),(10,11),(15,16)]=>18
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[(1,14),(2,13),(3,12),(4,11),(5,8),(6,7),(9,10),(15,16)]=>19
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[(1,14),(2,13),(3,12),(4,11),(5,10),(6,7),(8,9),(15,16)]=>20
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[(1,14),(2,13),(3,12),(4,11),(5,10),(6,9),(7,8),(15,16)]=>21
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[(1,16),(2,15),(3,14),(4,13),(5,12),(6,11),(7,10),(8,9),(17,18)]=>28
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[(1,2),(3,18),(4,17),(5,16),(6,15),(7,14),(8,13),(9,12),(10,11)]=>28
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[(1,18),(2,17),(3,16),(4,15),(5,14),(6,13),(7,12),(8,11),(9,10),(19,20)]=>36
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[(1,16),(2,15),(3,14),(4,13),(5,12),(6,11),(7,8),(9,10),(17,18)]=>27
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[(1,2),(3,18),(4,17),(5,16),(6,15),(7,14),(8,13),(9,10),(11,12)]=>27
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[(1,2),(3,20),(4,19),(5,18),(6,17),(7,16),(8,15),(9,14),(10,13),(11,12)]=>36
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[(1,20),(2,19),(3,18),(4,17),(5,16),(6,15),(7,14),(8,13),(9,12),(10,11),(21,22)]=>45
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[(1,18),(2,17),(3,16),(4,15),(5,14),(6,13),(7,12),(8,9),(10,11),(19,20)]=>35
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[(1,16),(2,15),(3,14),(4,13),(5,12),(6,9),(7,8),(10,11),(17,18)]=>26
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[(1,16),(2,15),(3,14),(4,13),(5,12),(6,7),(8,11),(9,10),(17,18)]=>26
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[(1,2),(3,18),(4,17),(5,16),(6,15),(7,14),(8,11),(9,10),(12,13)]=>26
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[(1,2),(3,18),(4,17),(5,16),(6,15),(7,14),(8,9),(10,13),(11,12)]=>26
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[(1,2),(3,20),(4,19),(5,18),(6,17),(7,16),(8,15),(9,14),(10,11),(12,13)]=>35
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[(1,2),(3,22),(4,21),(5,20),(6,19),(7,18),(8,17),(9,16),(10,15),(11,14),(12,13)]=>45
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[(1,18),(2,3),(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17)]=>8
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[(1,18),(2,5),(3,4),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17)]=>9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16),(17,18)]=>0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,18),(16,17)]=>1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,18),(14,15),(16,17)]=>2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,18),(12,13),(14,15),(16,17)]=>3
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[(1,2),(3,4),(5,6),(7,8),(9,18),(10,11),(12,13),(14,15),(16,17)]=>4
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[(1,2),(3,4),(5,6),(7,18),(8,9),(10,11),(12,13),(14,15),(16,17)]=>5
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[(1,2),(3,4),(5,18),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17)]=>6
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[(1,2),(3,18),(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17)]=>7
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16),(17,18),(19,20)]=>0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16),(17,20),(18,19)]=>1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,18),(14,17),(15,16)]=>3
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,20),(16,17),(18,19)]=>2
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,18),(12,15),(13,14),(16,17)]=>4
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,20),(14,15),(16,17),(18,19)]=>3
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[(1,2),(3,4),(5,6),(7,8),(9,18),(10,13),(11,12),(14,15),(16,17)]=>5
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,20),(12,13),(14,15),(16,17),(18,19)]=>4
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[(1,2),(3,4),(5,6),(7,18),(8,11),(9,10),(12,13),(14,15),(16,17)]=>6
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[(1,2),(3,4),(5,6),(7,8),(9,20),(10,11),(12,13),(14,15),(16,17),(18,19)]=>5
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[(1,2),(3,4),(5,18),(6,9),(7,8),(10,11),(12,13),(14,15),(16,17)]=>7
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[(1,2),(3,4),(5,6),(7,20),(8,9),(10,11),(12,13),(14,15),(16,17),(18,19)]=>6
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[(1,2),(3,18),(4,7),(5,6),(8,9),(10,11),(12,13),(14,15),(16,17)]=>8
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[(1,2),(3,4),(5,20),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17),(18,19)]=>7
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[(1,2),(3,20),(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17),(18,19)]=>8
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[(1,20),(2,3),(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17),(18,19)]=>9
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 number of nestings of a perfect matching.
This is the number of pairs of edges $((a,b), (c,d))$ such that $a\le c\le d\le b$. i.e., the edge $(c,d)$ is nested inside $(a,b)$.
This is the number of pairs of edges $((a,b), (c,d))$ such that $a\le c\le d\le b$. i.e., the edge $(c,d)$ is nested inside $(a,b)$.
Map
to tunnel matching
Description
Sends a Dyck path of semilength n to the noncrossing perfect matching given by matching an up-step with the corresponding down-step.
This is, for a Dyck path $D$ of semilength $n$, the perfect matching of $\{1,\dots,2n\}$ with $i < j$ being matched if $D_i$ is an up-step and $D_j$ is the down-step connected to $D_i$ by a tunnel.
This is, for a Dyck path $D$ of semilength $n$, the perfect matching of $\{1,\dots,2n\}$ with $i < j$ being matched if $D_i$ is an up-step and $D_j$ is the down-step connected to $D_i$ by a tunnel.
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!