Identifier
-
Mp00027:
Dyck paths
—to partition⟶
Integer partitions
Mp00179: Integer partitions —to skew partition⟶ Skew partitions
Mp00185: Skew partitions —cell poset⟶ Posets
St000100: Posets ⟶ ℤ
Values
=>
Cc0005;cc-rep-0
Cc0002;cc-rep-1
Cc0028;cc-rep-2
Cc0014;cc-rep
[1,0,1,0,1,0]=>[2,1]=>[[2,1],[]]=>([(0,1),(0,2)],3)=>2
[1,0,1,1,0,0]=>[1,1]=>[[1,1],[]]=>([(0,1)],2)=>1
[1,1,0,0,1,0]=>[2]=>[[2],[]]=>([(0,1)],2)=>1
[1,0,1,0,1,0,1,0]=>[3,2,1]=>[[3,2,1],[]]=>([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)=>16
[1,0,1,0,1,1,0,0]=>[2,2,1]=>[[2,2,1],[]]=>([(0,2),(0,3),(2,4),(3,1),(3,4)],5)=>5
[1,0,1,1,0,0,1,0]=>[3,1,1]=>[[3,1,1],[]]=>([(0,3),(0,4),(3,2),(4,1)],5)=>6
[1,0,1,1,0,1,0,0]=>[2,1,1]=>[[2,1,1],[]]=>([(0,2),(0,3),(3,1)],4)=>3
[1,0,1,1,1,0,0,0]=>[1,1,1]=>[[1,1,1],[]]=>([(0,2),(2,1)],3)=>1
[1,1,0,0,1,0,1,0]=>[3,2]=>[[3,2],[]]=>([(0,2),(0,3),(2,4),(3,1),(3,4)],5)=>5
[1,1,0,0,1,1,0,0]=>[2,2]=>[[2,2],[]]=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[1,1,0,1,0,0,1,0]=>[3,1]=>[[3,1],[]]=>([(0,2),(0,3),(3,1)],4)=>3
[1,1,0,1,0,1,0,0]=>[2,1]=>[[2,1],[]]=>([(0,1),(0,2)],3)=>2
[1,1,0,1,1,0,0,0]=>[1,1]=>[[1,1],[]]=>([(0,1)],2)=>1
[1,1,1,0,0,0,1,0]=>[3]=>[[3],[]]=>([(0,2),(2,1)],3)=>1
[1,1,1,0,0,1,0,0]=>[2]=>[[2],[]]=>([(0,1)],2)=>1
[1,0,1,0,1,0,1,0,1,0]=>[4,3,2,1]=>[[4,3,2,1],[]]=>([(0,5),(0,6),(3,2),(3,8),(4,1),(4,9),(5,3),(5,7),(6,4),(6,7),(7,8),(7,9)],10)=>768
[1,0,1,0,1,0,1,1,0,0]=>[3,3,2,1]=>[[3,3,2,1],[]]=>([(0,4),(0,5),(2,7),(3,1),(3,8),(4,2),(4,6),(5,3),(5,6),(6,7),(6,8)],9)=>168
[1,0,1,0,1,1,0,0,1,0]=>[4,2,2,1]=>[[4,2,2,1],[]]=>([(0,5),(0,6),(3,1),(4,2),(4,8),(5,3),(5,7),(6,4),(6,7),(7,8)],9)=>216
[1,0,1,0,1,1,0,1,0,0]=>[3,2,2,1]=>[[3,2,2,1],[]]=>([(0,4),(0,5),(3,2),(3,7),(4,3),(4,6),(5,1),(5,6),(6,7)],8)=>70
[1,0,1,0,1,1,1,0,0,0]=>[2,2,2,1]=>[[2,2,2,1],[]]=>([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7)=>14
[1,0,1,1,0,0,1,0,1,0]=>[4,3,1,1]=>[[4,3,1,1],[]]=>([(0,5),(0,6),(3,1),(4,2),(4,8),(5,3),(5,7),(6,4),(6,7),(7,8)],9)=>216
[1,0,1,1,0,0,1,1,0,0]=>[3,3,1,1]=>[[3,3,1,1],[]]=>([(0,4),(0,5),(1,7),(3,2),(4,3),(4,6),(5,1),(5,6),(6,7)],8)=>56
[1,0,1,1,0,1,0,0,1,0]=>[4,2,1,1]=>[[4,2,1,1],[]]=>([(0,5),(0,6),(3,2),(4,1),(5,3),(5,7),(6,4),(6,7)],8)=>90
[1,0,1,1,0,1,0,1,0,0]=>[3,2,1,1]=>[[3,2,1,1],[]]=>([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)=>35
[1,0,1,1,0,1,1,0,0,0]=>[2,2,1,1]=>[[2,2,1,1],[]]=>([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)=>9
[1,0,1,1,1,0,0,0,1,0]=>[4,1,1,1]=>[[4,1,1,1],[]]=>([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7)=>20
[1,0,1,1,1,0,0,1,0,0]=>[3,1,1,1]=>[[3,1,1,1],[]]=>([(0,4),(0,5),(3,2),(4,3),(5,1)],6)=>10
[1,0,1,1,1,0,1,0,0,0]=>[2,1,1,1]=>[[2,1,1,1],[]]=>([(0,2),(0,4),(3,1),(4,3)],5)=>4
[1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1]=>[[1,1,1,1],[]]=>([(0,3),(2,1),(3,2)],4)=>1
[1,1,0,0,1,0,1,0,1,0]=>[4,3,2]=>[[4,3,2],[]]=>([(0,4),(0,5),(2,7),(3,1),(3,8),(4,2),(4,6),(5,3),(5,6),(6,7),(6,8)],9)=>168
[1,1,0,0,1,0,1,1,0,0]=>[3,3,2]=>[[3,3,2],[]]=>([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7)],8)=>42
[1,1,0,0,1,1,0,0,1,0]=>[4,2,2]=>[[4,2,2],[]]=>([(0,4),(0,5),(1,7),(3,2),(4,3),(4,6),(5,1),(5,6),(6,7)],8)=>56
[1,1,0,0,1,1,0,1,0,0]=>[3,2,2]=>[[3,2,2],[]]=>([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7)=>21
[1,1,0,0,1,1,1,0,0,0]=>[2,2,2]=>[[2,2,2],[]]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>5
[1,1,0,1,0,0,1,0,1,0]=>[4,3,1]=>[[4,3,1],[]]=>([(0,4),(0,5),(3,2),(3,7),(4,3),(4,6),(5,1),(5,6),(6,7)],8)=>70
[1,1,0,1,0,0,1,1,0,0]=>[3,3,1]=>[[3,3,1],[]]=>([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7)=>21
[1,1,0,1,0,1,0,0,1,0]=>[4,2,1]=>[[4,2,1],[]]=>([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)=>35
[1,1,0,1,0,1,0,1,0,0]=>[3,2,1]=>[[3,2,1],[]]=>([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)=>16
[1,1,0,1,0,1,1,0,0,0]=>[2,2,1]=>[[2,2,1],[]]=>([(0,2),(0,3),(2,4),(3,1),(3,4)],5)=>5
[1,1,0,1,1,0,0,0,1,0]=>[4,1,1]=>[[4,1,1],[]]=>([(0,4),(0,5),(3,2),(4,3),(5,1)],6)=>10
[1,1,0,1,1,0,0,1,0,0]=>[3,1,1]=>[[3,1,1],[]]=>([(0,3),(0,4),(3,2),(4,1)],5)=>6
[1,1,0,1,1,0,1,0,0,0]=>[2,1,1]=>[[2,1,1],[]]=>([(0,2),(0,3),(3,1)],4)=>3
[1,1,0,1,1,1,0,0,0,0]=>[1,1,1]=>[[1,1,1],[]]=>([(0,2),(2,1)],3)=>1
[1,1,1,0,0,0,1,0,1,0]=>[4,3]=>[[4,3],[]]=>([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7)=>14
[1,1,1,0,0,0,1,1,0,0]=>[3,3]=>[[3,3],[]]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>5
[1,1,1,0,0,1,0,0,1,0]=>[4,2]=>[[4,2],[]]=>([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)=>9
[1,1,1,0,0,1,0,1,0,0]=>[3,2]=>[[3,2],[]]=>([(0,2),(0,3),(2,4),(3,1),(3,4)],5)=>5
[1,1,1,0,0,1,1,0,0,0]=>[2,2]=>[[2,2],[]]=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[1,1,1,0,1,0,0,0,1,0]=>[4,1]=>[[4,1],[]]=>([(0,2),(0,4),(3,1),(4,3)],5)=>4
[1,1,1,0,1,0,0,1,0,0]=>[3,1]=>[[3,1],[]]=>([(0,2),(0,3),(3,1)],4)=>3
[1,1,1,0,1,0,1,0,0,0]=>[2,1]=>[[2,1],[]]=>([(0,1),(0,2)],3)=>2
[1,1,1,0,1,1,0,0,0,0]=>[1,1]=>[[1,1],[]]=>([(0,1)],2)=>1
[1,1,1,1,0,0,0,0,1,0]=>[4]=>[[4],[]]=>([(0,3),(2,1),(3,2)],4)=>1
[1,1,1,1,0,0,0,1,0,0]=>[3]=>[[3],[]]=>([(0,2),(2,1)],3)=>1
[1,1,1,1,0,0,1,0,0,0]=>[2]=>[[2],[]]=>([(0,1)],2)=>1
[1,0,1,0,1,0,1,0,1,0,1,0]=>[5,4,3,2,1]=>[[5,4,3,2,1],[]]=>([(0,7),(0,8),(3,5),(3,12),(4,6),(4,13),(5,2),(5,10),(6,1),(6,11),(7,3),(7,9),(8,4),(8,9),(9,12),(9,13),(12,10),(12,14),(13,11),(13,14)],15)=>292864
[1,0,1,0,1,1,1,0,1,0,0,0]=>[3,2,2,2,1]=>[[3,2,2,2,1],[]]=>([(0,5),(0,6),(3,4),(3,9),(4,2),(4,8),(5,3),(5,7),(6,1),(6,7),(7,9),(9,8)],10)=>288
[1,0,1,0,1,1,1,1,0,0,0,0]=>[2,2,2,2,1]=>[[2,2,2,2,1],[]]=>([(0,2),(0,5),(2,6),(3,4),(3,8),(4,1),(4,7),(5,3),(5,6),(6,8),(8,7)],9)=>42
[1,0,1,1,0,1,0,1,1,0,0,0]=>[3,3,2,1,1]=>[[3,3,2,1,1],[]]=>([(0,5),(0,6),(2,9),(3,1),(4,3),(4,8),(5,4),(5,7),(6,2),(6,7),(7,8),(7,9)],10)=>450
[1,0,1,1,0,1,1,0,0,1,0,0]=>[4,2,2,1,1]=>[[4,2,2,1,1],[]]=>([(0,6),(0,7),(3,4),(3,9),(4,1),(5,2),(6,5),(6,8),(7,3),(7,8),(8,9)],10)=>567
[1,0,1,1,0,1,1,0,1,0,0,0]=>[3,2,2,1,1]=>[[3,2,2,1,1],[]]=>([(0,5),(0,6),(3,4),(3,8),(4,2),(5,3),(5,7),(6,1),(6,7),(7,8)],9)=>162
[1,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,2,1,1]=>[[2,2,2,1,1],[]]=>([(0,2),(0,5),(2,6),(3,4),(3,7),(4,1),(5,3),(5,6),(6,7)],8)=>28
[1,0,1,1,1,0,0,1,0,1,0,0]=>[4,3,1,1,1]=>[[4,3,1,1,1],[]]=>([(0,6),(0,7),(3,4),(4,1),(5,2),(5,9),(6,5),(6,8),(7,3),(7,8),(8,9)],10)=>525
[1,0,1,1,1,0,0,1,1,0,0,0]=>[3,3,1,1,1]=>[[3,3,1,1,1],[]]=>([(0,5),(0,6),(2,8),(3,4),(4,1),(5,3),(5,7),(6,2),(6,7),(7,8)],9)=>120
[1,0,1,1,1,0,1,0,0,0,1,0]=>[5,2,1,1,1]=>[[5,2,1,1,1],[]]=>([(0,7),(0,8),(3,5),(4,6),(5,2),(6,1),(7,3),(7,9),(8,4),(8,9)],10)=>448
[1,0,1,1,1,0,1,0,0,1,0,0]=>[4,2,1,1,1]=>[[4,2,1,1,1],[]]=>([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(6,8),(7,3),(7,8)],9)=>189
[1,0,1,1,1,0,1,0,1,0,0,0]=>[3,2,1,1,1]=>[[3,2,1,1,1],[]]=>([(0,5),(0,6),(3,4),(4,2),(5,3),(5,7),(6,1),(6,7)],8)=>64
[1,0,1,1,1,0,1,1,0,0,0,0]=>[2,2,1,1,1]=>[[2,2,1,1,1],[]]=>([(0,2),(0,5),(2,6),(3,4),(4,1),(5,3),(5,6)],7)=>14
[1,0,1,1,1,1,0,0,0,0,1,0]=>[5,1,1,1,1]=>[[5,1,1,1,1],[]]=>([(0,7),(0,8),(3,5),(4,6),(5,2),(6,1),(7,3),(8,4)],9)=>70
[1,0,1,1,1,1,0,0,0,1,0,0]=>[4,1,1,1,1]=>[[4,1,1,1,1],[]]=>([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(7,3)],8)=>35
[1,0,1,1,1,1,0,0,1,0,0,0]=>[3,1,1,1,1]=>[[3,1,1,1,1],[]]=>([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)=>15
[1,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,1,1,1]=>[[2,1,1,1,1],[]]=>([(0,2),(0,5),(3,4),(4,1),(5,3)],6)=>5
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1]=>[[1,1,1,1,1],[]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[1,1,0,0,1,1,0,1,1,0,0,0]=>[3,3,2,2]=>[[3,3,2,2],[]]=>([(0,4),(0,5),(1,8),(2,7),(3,2),(3,9),(4,3),(4,6),(5,1),(5,6),(6,8),(6,9),(9,7)],10)=>252
[1,1,0,0,1,1,1,0,0,1,0,0]=>[4,2,2,2]=>[[4,2,2,2],[]]=>([(0,5),(0,6),(2,8),(3,1),(4,2),(4,9),(5,3),(5,7),(6,4),(6,7),(7,9),(9,8)],10)=>300
[1,1,0,0,1,1,1,0,1,0,0,0]=>[3,2,2,2]=>[[3,2,2,2],[]]=>([(0,4),(0,5),(2,7),(3,2),(3,8),(4,3),(4,6),(5,1),(5,6),(6,8),(8,7)],9)=>84
[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,2,2,2]=>[[2,2,2,2],[]]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)=>14
[1,1,0,1,0,0,1,1,1,0,0,0]=>[3,3,3,1]=>[[3,3,3,1],[]]=>([(0,4),(0,5),(2,7),(3,1),(3,8),(4,2),(4,6),(5,3),(5,6),(6,7),(6,8),(7,9),(8,9)],10)=>210
[1,1,0,1,0,1,0,1,0,1,0,0]=>[4,3,2,1]=>[[4,3,2,1],[]]=>([(0,5),(0,6),(3,2),(3,8),(4,1),(4,9),(5,3),(5,7),(6,4),(6,7),(7,8),(7,9)],10)=>768
[1,1,0,1,0,1,0,1,1,0,0,0]=>[3,3,2,1]=>[[3,3,2,1],[]]=>([(0,4),(0,5),(2,7),(3,1),(3,8),(4,2),(4,6),(5,3),(5,6),(6,7),(6,8)],9)=>168
[1,1,0,1,0,1,1,0,0,0,1,0]=>[5,2,2,1]=>[[5,2,2,1],[]]=>([(0,6),(0,7),(3,4),(4,1),(5,2),(5,9),(6,5),(6,8),(7,3),(7,8),(8,9)],10)=>525
[1,1,0,1,0,1,1,0,0,1,0,0]=>[4,2,2,1]=>[[4,2,2,1],[]]=>([(0,5),(0,6),(3,1),(4,2),(4,8),(5,3),(5,7),(6,4),(6,7),(7,8)],9)=>216
[1,1,0,1,0,1,1,0,1,0,0,0]=>[3,2,2,1]=>[[3,2,2,1],[]]=>([(0,4),(0,5),(3,2),(3,7),(4,3),(4,6),(5,1),(5,6),(6,7)],8)=>70
[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,2,2,1]=>[[2,2,2,1],[]]=>([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7)=>14
[1,1,0,1,1,0,0,0,1,1,0,0]=>[4,4,1,1]=>[[4,4,1,1],[]]=>([(0,5),(0,6),(2,8),(3,1),(4,2),(4,9),(5,3),(5,7),(6,4),(6,7),(7,9),(9,8)],10)=>300
[1,1,0,1,1,0,0,1,0,0,1,0]=>[5,3,1,1]=>[[5,3,1,1],[]]=>([(0,6),(0,7),(3,4),(3,9),(4,1),(5,2),(6,5),(6,8),(7,3),(7,8),(8,9)],10)=>567
[1,1,0,1,1,0,0,1,0,1,0,0]=>[4,3,1,1]=>[[4,3,1,1],[]]=>([(0,5),(0,6),(3,1),(4,2),(4,8),(5,3),(5,7),(6,4),(6,7),(7,8)],9)=>216
[1,1,0,1,1,0,0,1,1,0,0,0]=>[3,3,1,1]=>[[3,3,1,1],[]]=>([(0,4),(0,5),(1,7),(3,2),(4,3),(4,6),(5,1),(5,6),(6,7)],8)=>56
[1,1,0,1,1,0,1,0,0,0,1,0]=>[5,2,1,1]=>[[5,2,1,1],[]]=>([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(6,8),(7,3),(7,8)],9)=>189
[1,1,0,1,1,0,1,0,0,1,0,0]=>[4,2,1,1]=>[[4,2,1,1],[]]=>([(0,5),(0,6),(3,2),(4,1),(5,3),(5,7),(6,4),(6,7)],8)=>90
[1,1,0,1,1,0,1,0,1,0,0,0]=>[3,2,1,1]=>[[3,2,1,1],[]]=>([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)=>35
[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,1,1]=>[[2,2,1,1],[]]=>([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)=>9
[1,1,0,1,1,1,0,0,0,0,1,0]=>[5,1,1,1]=>[[5,1,1,1],[]]=>([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(7,3)],8)=>35
[1,1,0,1,1,1,0,0,0,1,0,0]=>[4,1,1,1]=>[[4,1,1,1],[]]=>([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7)=>20
[1,1,0,1,1,1,0,0,1,0,0,0]=>[3,1,1,1]=>[[3,1,1,1],[]]=>([(0,4),(0,5),(3,2),(4,3),(5,1)],6)=>10
[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,1,1]=>[[2,1,1,1],[]]=>([(0,2),(0,4),(3,1),(4,3)],5)=>4
[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1]=>[[1,1,1,1],[]]=>([(0,3),(2,1),(3,2)],4)=>1
[1,1,1,0,0,0,1,1,0,1,0,0]=>[4,3,3]=>[[4,3,3],[]]=>([(0,4),(0,5),(2,7),(3,1),(3,8),(4,2),(4,6),(5,3),(5,6),(6,7),(6,8),(7,9),(8,9)],10)=>210
[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,3,3]=>[[3,3,3],[]]=>([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)=>42
[1,1,1,0,0,1,0,0,1,1,0,0]=>[4,4,2]=>[[4,4,2],[]]=>([(0,4),(0,5),(1,8),(2,7),(3,2),(3,9),(4,3),(4,6),(5,1),(5,6),(6,8),(6,9),(9,7)],10)=>252
[1,1,1,0,0,1,0,1,0,0,1,0]=>[5,3,2]=>[[5,3,2],[]]=>([(0,5),(0,6),(2,9),(3,1),(4,3),(4,8),(5,4),(5,7),(6,2),(6,7),(7,8),(7,9)],10)=>450
[1,1,1,0,0,1,0,1,0,1,0,0]=>[4,3,2]=>[[4,3,2],[]]=>([(0,4),(0,5),(2,7),(3,1),(3,8),(4,2),(4,6),(5,3),(5,6),(6,7),(6,8)],9)=>168
[1,1,1,0,0,1,0,1,1,0,0,0]=>[3,3,2]=>[[3,3,2],[]]=>([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7)],8)=>42
[1,1,1,0,0,1,1,0,0,0,1,0]=>[5,2,2]=>[[5,2,2],[]]=>([(0,5),(0,6),(2,8),(3,4),(4,1),(5,3),(5,7),(6,2),(6,7),(7,8)],9)=>120
[1,1,1,0,0,1,1,0,0,1,0,0]=>[4,2,2]=>[[4,2,2],[]]=>([(0,4),(0,5),(1,7),(3,2),(4,3),(4,6),(5,1),(5,6),(6,7)],8)=>56
[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,2]=>[[3,2,2],[]]=>([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7)=>21
[1,1,1,0,0,1,1,1,0,0,0,0]=>[2,2,2]=>[[2,2,2],[]]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>5
[1,1,1,0,1,0,0,0,1,0,1,0]=>[5,4,1]=>[[5,4,1],[]]=>([(0,5),(0,6),(3,4),(3,9),(4,2),(4,8),(5,3),(5,7),(6,1),(6,7),(7,9),(9,8)],10)=>288
[1,1,1,0,1,0,0,0,1,1,0,0]=>[4,4,1]=>[[4,4,1],[]]=>([(0,4),(0,5),(2,7),(3,2),(3,8),(4,3),(4,6),(5,1),(5,6),(6,8),(8,7)],9)=>84
[1,1,1,0,1,0,0,1,0,0,1,0]=>[5,3,1]=>[[5,3,1],[]]=>([(0,5),(0,6),(3,4),(3,8),(4,2),(5,3),(5,7),(6,1),(6,7),(7,8)],9)=>162
[1,1,1,0,1,0,0,1,0,1,0,0]=>[4,3,1]=>[[4,3,1],[]]=>([(0,4),(0,5),(3,2),(3,7),(4,3),(4,6),(5,1),(5,6),(6,7)],8)=>70
[1,1,1,0,1,0,0,1,1,0,0,0]=>[3,3,1]=>[[3,3,1],[]]=>([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7)=>21
[1,1,1,0,1,0,1,0,0,0,1,0]=>[5,2,1]=>[[5,2,1],[]]=>([(0,5),(0,6),(3,4),(4,2),(5,3),(5,7),(6,1),(6,7)],8)=>64
[1,1,1,0,1,0,1,0,0,1,0,0]=>[4,2,1]=>[[4,2,1],[]]=>([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)=>35
[1,1,1,0,1,0,1,0,1,0,0,0]=>[3,2,1]=>[[3,2,1],[]]=>([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)=>16
[1,1,1,0,1,0,1,1,0,0,0,0]=>[2,2,1]=>[[2,2,1],[]]=>([(0,2),(0,3),(2,4),(3,1),(3,4)],5)=>5
[1,1,1,0,1,1,0,0,0,0,1,0]=>[5,1,1]=>[[5,1,1],[]]=>([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)=>15
[1,1,1,0,1,1,0,0,0,1,0,0]=>[4,1,1]=>[[4,1,1],[]]=>([(0,4),(0,5),(3,2),(4,3),(5,1)],6)=>10
[1,1,1,0,1,1,0,0,1,0,0,0]=>[3,1,1]=>[[3,1,1],[]]=>([(0,3),(0,4),(3,2),(4,1)],5)=>6
[1,1,1,0,1,1,0,1,0,0,0,0]=>[2,1,1]=>[[2,1,1],[]]=>([(0,2),(0,3),(3,1)],4)=>3
[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1]=>[[1,1,1],[]]=>([(0,2),(2,1)],3)=>1
[1,1,1,1,0,0,0,0,1,0,1,0]=>[5,4]=>[[5,4],[]]=>([(0,2),(0,5),(2,6),(3,4),(3,8),(4,1),(4,7),(5,3),(5,6),(6,8),(8,7)],9)=>42
[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,4]=>[[4,4],[]]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)=>14
[1,1,1,1,0,0,0,1,0,0,1,0]=>[5,3]=>[[5,3],[]]=>([(0,2),(0,5),(2,6),(3,4),(3,7),(4,1),(5,3),(5,6),(6,7)],8)=>28
[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3]=>[[4,3],[]]=>([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7)=>14
[1,1,1,1,0,0,0,1,1,0,0,0]=>[3,3]=>[[3,3],[]]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>5
[1,1,1,1,0,0,1,0,0,0,1,0]=>[5,2]=>[[5,2],[]]=>([(0,2),(0,5),(2,6),(3,4),(4,1),(5,3),(5,6)],7)=>14
[1,1,1,1,0,0,1,0,0,1,0,0]=>[4,2]=>[[4,2],[]]=>([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)=>9
[1,1,1,1,0,0,1,0,1,0,0,0]=>[3,2]=>[[3,2],[]]=>([(0,2),(0,3),(2,4),(3,1),(3,4)],5)=>5
[1,1,1,1,0,0,1,1,0,0,0,0]=>[2,2]=>[[2,2],[]]=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[1,1,1,1,0,1,0,0,0,0,1,0]=>[5,1]=>[[5,1],[]]=>([(0,2),(0,5),(3,4),(4,1),(5,3)],6)=>5
[1,1,1,1,0,1,0,0,0,1,0,0]=>[4,1]=>[[4,1],[]]=>([(0,2),(0,4),(3,1),(4,3)],5)=>4
[1,1,1,1,0,1,0,0,1,0,0,0]=>[3,1]=>[[3,1],[]]=>([(0,2),(0,3),(3,1)],4)=>3
[1,1,1,1,0,1,0,1,0,0,0,0]=>[2,1]=>[[2,1],[]]=>([(0,1),(0,2)],3)=>2
[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1]=>[[1,1],[]]=>([(0,1)],2)=>1
[1,1,1,1,1,0,0,0,0,0,1,0]=>[5]=>[[5],[]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[1,1,1,1,1,0,0,0,0,1,0,0]=>[4]=>[[4],[]]=>([(0,3),(2,1),(3,2)],4)=>1
[1,1,1,1,1,0,0,0,1,0,0,0]=>[3]=>[[3],[]]=>([(0,2),(2,1)],3)=>1
[1,1,1,1,1,0,0,1,0,0,0,0]=>[2]=>[[2],[]]=>([(0,1)],2)=>1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1,1]=>[[2,2,2,2,1,1],[]]=>([(0,2),(0,6),(2,7),(3,1),(4,3),(4,8),(5,4),(5,9),(6,5),(6,7),(7,9),(9,8)],10)=>90
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1,1,1]=>[[3,2,2,1,1,1],[]]=>([(0,6),(0,7),(3,5),(4,3),(4,9),(5,2),(6,4),(6,8),(7,1),(7,8),(8,9)],10)=>315
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1,1]=>[[2,2,2,1,1,1],[]]=>([(0,2),(0,6),(2,7),(3,5),(4,3),(4,8),(5,1),(6,4),(6,7),(7,8)],9)=>48
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1,1,1]=>[[3,3,1,1,1,1],[]]=>([(0,6),(0,7),(2,9),(3,5),(4,3),(5,1),(6,4),(6,8),(7,2),(7,8),(8,9)],10)=>225
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,1,1,1]=>[[4,2,1,1,1,1],[]]=>([(0,7),(0,8),(3,5),(4,3),(5,2),(6,1),(7,6),(7,9),(8,4),(8,9)],10)=>350
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1,1,1]=>[[3,2,1,1,1,1],[]]=>([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(6,8),(7,1),(7,8)],9)=>105
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1,1]=>[[2,2,1,1,1,1],[]]=>([(0,2),(0,6),(2,7),(3,5),(4,3),(5,1),(6,4),(6,7)],8)=>20
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1,1]=>[[5,1,1,1,1,1],[]]=>([(0,8),(0,9),(3,7),(4,3),(5,6),(6,1),(7,2),(8,4),(9,5)],10)=>126
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1,1]=>[[4,1,1,1,1,1],[]]=>([(0,7),(0,8),(3,5),(4,3),(5,2),(6,1),(7,6),(8,4)],9)=>56
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1,1]=>[[3,1,1,1,1,1],[]]=>([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(7,1)],8)=>21
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1,1]=>[[2,1,1,1,1,1],[]]=>([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7)=>6
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[[1,1,1,1,1,1],[]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2]=>[[2,2,2,2,2],[]]=>([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)=>42
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,1]=>[[5,4,3,2,1],[]]=>([(0,7),(0,8),(3,5),(3,12),(4,6),(4,13),(5,2),(5,10),(6,1),(6,11),(7,3),(7,9),(8,4),(8,9),(9,12),(9,13),(12,10),(12,14),(13,11),(13,14)],15)=>292864
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,2,2,1]=>[[3,2,2,2,1],[]]=>([(0,5),(0,6),(3,4),(3,9),(4,2),(4,8),(5,3),(5,7),(6,1),(6,7),(7,9),(9,8)],10)=>288
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1]=>[[2,2,2,2,1],[]]=>([(0,2),(0,5),(2,6),(3,4),(3,8),(4,1),(4,7),(5,3),(5,6),(6,8),(8,7)],9)=>42
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[3,3,2,1,1]=>[[3,3,2,1,1],[]]=>([(0,5),(0,6),(2,9),(3,1),(4,3),(4,8),(5,4),(5,7),(6,2),(6,7),(7,8),(7,9)],10)=>450
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[4,2,2,1,1]=>[[4,2,2,1,1],[]]=>([(0,6),(0,7),(3,4),(3,9),(4,1),(5,2),(6,5),(6,8),(7,3),(7,8),(8,9)],10)=>567
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1,1]=>[[3,2,2,1,1],[]]=>([(0,5),(0,6),(3,4),(3,8),(4,2),(5,3),(5,7),(6,1),(6,7),(7,8)],9)=>162
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1]=>[[2,2,2,1,1],[]]=>([(0,2),(0,5),(2,6),(3,4),(3,7),(4,1),(5,3),(5,6),(6,7)],8)=>28
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,1,1]=>[[4,3,1,1,1],[]]=>([(0,6),(0,7),(3,4),(4,1),(5,2),(5,9),(6,5),(6,8),(7,3),(7,8),(8,9)],10)=>525
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1,1]=>[[3,3,1,1,1],[]]=>([(0,5),(0,6),(2,8),(3,4),(4,1),(5,3),(5,7),(6,2),(6,7),(7,8)],9)=>120
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,1,1]=>[[5,2,1,1,1],[]]=>([(0,7),(0,8),(3,5),(4,6),(5,2),(6,1),(7,3),(7,9),(8,4),(8,9)],10)=>448
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,1,1]=>[[4,2,1,1,1],[]]=>([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(6,8),(7,3),(7,8)],9)=>189
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1,1]=>[[3,2,1,1,1],[]]=>([(0,5),(0,6),(3,4),(4,2),(5,3),(5,7),(6,1),(6,7)],8)=>64
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1]=>[[2,2,1,1,1],[]]=>([(0,2),(0,5),(2,6),(3,4),(4,1),(5,3),(5,6)],7)=>14
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1]=>[[6,1,1,1,1],[]]=>([(0,8),(0,9),(3,7),(4,3),(5,6),(6,1),(7,2),(8,4),(9,5)],10)=>126
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1]=>[[5,1,1,1,1],[]]=>([(0,7),(0,8),(3,5),(4,6),(5,2),(6,1),(7,3),(8,4)],9)=>70
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1]=>[[4,1,1,1,1],[]]=>([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(7,3)],8)=>35
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1]=>[[3,1,1,1,1],[]]=>([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)=>15
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1]=>[[2,1,1,1,1],[]]=>([(0,2),(0,5),(3,4),(4,1),(5,3)],6)=>5
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[[1,1,1,1,1],[]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,3,2,2]=>[[3,3,2,2],[]]=>([(0,4),(0,5),(1,8),(2,7),(3,2),(3,9),(4,3),(4,6),(5,1),(5,6),(6,8),(6,9),(9,7)],10)=>252
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[4,2,2,2]=>[[4,2,2,2],[]]=>([(0,5),(0,6),(2,8),(3,1),(4,2),(4,9),(5,3),(5,7),(6,4),(6,7),(7,9),(9,8)],10)=>300
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,2,2]=>[[3,2,2,2],[]]=>([(0,4),(0,5),(2,7),(3,2),(3,8),(4,3),(4,6),(5,1),(5,6),(6,8),(8,7)],9)=>84
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2]=>[[2,2,2,2],[]]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)=>14
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,3,3,1]=>[[3,3,3,1],[]]=>([(0,4),(0,5),(2,7),(3,1),(3,8),(4,2),(4,6),(5,3),(5,6),(6,7),(6,8),(7,9),(8,9)],10)=>210
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[4,3,2,1]=>[[4,3,2,1],[]]=>([(0,5),(0,6),(3,2),(3,8),(4,1),(4,9),(5,3),(5,7),(6,4),(6,7),(7,8),(7,9)],10)=>768
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,3,2,1]=>[[3,3,2,1],[]]=>([(0,4),(0,5),(2,7),(3,1),(3,8),(4,2),(4,6),(5,3),(5,6),(6,7),(6,8)],9)=>168
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[5,2,2,1]=>[[5,2,2,1],[]]=>([(0,6),(0,7),(3,4),(4,1),(5,2),(5,9),(6,5),(6,8),(7,3),(7,8),(8,9)],10)=>525
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[4,2,2,1]=>[[4,2,2,1],[]]=>([(0,5),(0,6),(3,1),(4,2),(4,8),(5,3),(5,7),(6,4),(6,7),(7,8)],9)=>216
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1]=>[[3,2,2,1],[]]=>([(0,4),(0,5),(3,2),(3,7),(4,3),(4,6),(5,1),(5,6),(6,7)],8)=>70
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1]=>[[2,2,2,1],[]]=>([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7)=>14
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[4,4,1,1]=>[[4,4,1,1],[]]=>([(0,5),(0,6),(2,8),(3,1),(4,2),(4,9),(5,3),(5,7),(6,4),(6,7),(7,9),(9,8)],10)=>300
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,1]=>[[5,3,1,1],[]]=>([(0,6),(0,7),(3,4),(3,9),(4,1),(5,2),(6,5),(6,8),(7,3),(7,8),(8,9)],10)=>567
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,1]=>[[4,3,1,1],[]]=>([(0,5),(0,6),(3,1),(4,2),(4,8),(5,3),(5,7),(6,4),(6,7),(7,8)],9)=>216
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1]=>[[3,3,1,1],[]]=>([(0,4),(0,5),(1,7),(3,2),(4,3),(4,6),(5,1),(5,6),(6,7)],8)=>56
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,1]=>[[6,2,1,1],[]]=>([(0,7),(0,8),(3,5),(4,3),(5,2),(6,1),(7,6),(7,9),(8,4),(8,9)],10)=>350
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,1]=>[[5,2,1,1],[]]=>([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(6,8),(7,3),(7,8)],9)=>189
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,1]=>[[4,2,1,1],[]]=>([(0,5),(0,6),(3,2),(4,1),(5,3),(5,7),(6,4),(6,7)],8)=>90
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1]=>[[3,2,1,1],[]]=>([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)=>35
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1]=>[[2,2,1,1],[]]=>([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)=>9
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1]=>[[6,1,1,1],[]]=>([(0,7),(0,8),(3,5),(4,3),(5,2),(6,1),(7,6),(8,4)],9)=>56
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1]=>[[5,1,1,1],[]]=>([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(7,3)],8)=>35
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1]=>[[4,1,1,1],[]]=>([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7)=>20
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1]=>[[3,1,1,1],[]]=>([(0,4),(0,5),(3,2),(4,3),(5,1)],6)=>10
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1]=>[[2,1,1,1],[]]=>([(0,2),(0,4),(3,1),(4,3)],5)=>4
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[[1,1,1,1],[]]=>([(0,3),(2,1),(3,2)],4)=>1
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,3]=>[[4,3,3],[]]=>([(0,4),(0,5),(2,7),(3,1),(3,8),(4,2),(4,6),(5,3),(5,6),(6,7),(6,8),(7,9),(8,9)],10)=>210
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,3,3]=>[[3,3,3],[]]=>([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)=>42
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,4,2]=>[[4,4,2],[]]=>([(0,4),(0,5),(1,8),(2,7),(3,2),(3,9),(4,3),(4,6),(5,1),(5,6),(6,8),(6,9),(9,7)],10)=>252
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[5,3,2]=>[[5,3,2],[]]=>([(0,5),(0,6),(2,9),(3,1),(4,3),(4,8),(5,4),(5,7),(6,2),(6,7),(7,8),(7,9)],10)=>450
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,3,2]=>[[4,3,2],[]]=>([(0,4),(0,5),(2,7),(3,1),(3,8),(4,2),(4,6),(5,3),(5,6),(6,7),(6,8)],9)=>168
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[3,3,2]=>[[3,3,2],[]]=>([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7)],8)=>42
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[6,2,2]=>[[6,2,2],[]]=>([(0,6),(0,7),(2,9),(3,5),(4,3),(5,1),(6,4),(6,8),(7,2),(7,8),(8,9)],10)=>225
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[5,2,2]=>[[5,2,2],[]]=>([(0,5),(0,6),(2,8),(3,4),(4,1),(5,3),(5,7),(6,2),(6,7),(7,8)],9)=>120
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,2,2]=>[[4,2,2],[]]=>([(0,4),(0,5),(1,7),(3,2),(4,3),(4,6),(5,1),(5,6),(6,7)],8)=>56
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[3,2,2]=>[[3,2,2],[]]=>([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7)=>21
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[[2,2,2],[]]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>5
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[5,4,1]=>[[5,4,1],[]]=>([(0,5),(0,6),(3,4),(3,9),(4,2),(4,8),(5,3),(5,7),(6,1),(6,7),(7,9),(9,8)],10)=>288
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,4,1]=>[[4,4,1],[]]=>([(0,4),(0,5),(2,7),(3,2),(3,8),(4,3),(4,6),(5,1),(5,6),(6,8),(8,7)],9)=>84
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[6,3,1]=>[[6,3,1],[]]=>([(0,6),(0,7),(3,5),(4,3),(4,9),(5,2),(6,4),(6,8),(7,1),(7,8),(8,9)],10)=>315
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[5,3,1]=>[[5,3,1],[]]=>([(0,5),(0,6),(3,4),(3,8),(4,2),(5,3),(5,7),(6,1),(6,7),(7,8)],9)=>162
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,3,1]=>[[4,3,1],[]]=>([(0,4),(0,5),(3,2),(3,7),(4,3),(4,6),(5,1),(5,6),(6,7)],8)=>70
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[3,3,1]=>[[3,3,1],[]]=>([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7)=>21
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[6,2,1]=>[[6,2,1],[]]=>([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(6,8),(7,1),(7,8)],9)=>105
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[5,2,1]=>[[5,2,1],[]]=>([(0,5),(0,6),(3,4),(4,2),(5,3),(5,7),(6,1),(6,7)],8)=>64
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,2,1]=>[[4,2,1],[]]=>([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)=>35
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,2,1]=>[[3,2,1],[]]=>([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)=>16
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,2,1]=>[[2,2,1],[]]=>([(0,2),(0,3),(2,4),(3,1),(3,4)],5)=>5
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[6,1,1]=>[[6,1,1],[]]=>([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(7,1)],8)=>21
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[5,1,1]=>[[5,1,1],[]]=>([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)=>15
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,1,1]=>[[4,1,1],[]]=>([(0,4),(0,5),(3,2),(4,3),(5,1)],6)=>10
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,1,1]=>[[3,1,1],[]]=>([(0,3),(0,4),(3,2),(4,1)],5)=>6
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,1,1]=>[[2,1,1],[]]=>([(0,2),(0,3),(3,1)],4)=>3
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[[1,1,1],[]]=>([(0,2),(2,1)],3)=>1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,5]=>[[5,5],[]]=>([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)=>42
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[6,4]=>[[6,4],[]]=>([(0,2),(0,6),(2,7),(3,1),(4,3),(4,8),(5,4),(5,9),(6,5),(6,7),(7,9),(9,8)],10)=>90
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4]=>[[5,4],[]]=>([(0,2),(0,5),(2,6),(3,4),(3,8),(4,1),(4,7),(5,3),(5,6),(6,8),(8,7)],9)=>42
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,4]=>[[4,4],[]]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)=>14
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,3]=>[[6,3],[]]=>([(0,2),(0,6),(2,7),(3,5),(4,3),(4,8),(5,1),(6,4),(6,7),(7,8)],9)=>48
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,3]=>[[5,3],[]]=>([(0,2),(0,5),(2,6),(3,4),(3,7),(4,1),(5,3),(5,6),(6,7)],8)=>28
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[4,3]=>[[4,3],[]]=>([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7)=>14
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[[3,3],[]]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>5
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,2]=>[[6,2],[]]=>([(0,2),(0,6),(2,7),(3,5),(4,3),(5,1),(6,4),(6,7)],8)=>20
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,2]=>[[5,2],[]]=>([(0,2),(0,5),(2,6),(3,4),(4,1),(5,3),(5,6)],7)=>14
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[4,2]=>[[4,2],[]]=>([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)=>9
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,2]=>[[3,2],[]]=>([(0,2),(0,3),(2,4),(3,1),(3,4)],5)=>5
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[[2,2],[]]=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1]=>[[6,1],[]]=>([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7)=>6
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,1]=>[[5,1],[]]=>([(0,2),(0,5),(3,4),(4,1),(5,3)],6)=>5
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[4,1]=>[[4,1],[]]=>([(0,2),(0,4),(3,1),(4,3)],5)=>4
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,1]=>[[3,1],[]]=>([(0,2),(0,3),(3,1)],4)=>3
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,1]=>[[2,1],[]]=>([(0,1),(0,2)],3)=>2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[[1,1],[]]=>([(0,1)],2)=>1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6]=>[[6],[]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[5]=>[[5],[]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[4]=>[[4],[]]=>([(0,3),(2,1),(3,2)],4)=>1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[3]=>[[3],[]]=>([(0,2),(2,1)],3)=>1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2]=>[[2],[]]=>([(0,1)],2)=>1
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[[2,2,2,1,1,1,1],[]]=>([(0,2),(0,7),(2,8),(3,4),(4,6),(5,3),(5,9),(6,1),(7,5),(7,8),(8,9)],10)=>75
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1,1,1]=>[[3,2,1,1,1,1,1],[]]=>([(0,7),(0,8),(3,4),(4,6),(5,3),(6,2),(7,5),(7,9),(8,1),(8,9)],10)=>160
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[[2,2,1,1,1,1,1],[]]=>([(0,2),(0,7),(2,8),(3,4),(4,6),(5,3),(6,1),(7,5),(7,8)],9)=>27
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[[4,1,1,1,1,1,1],[]]=>([(0,8),(0,9),(3,4),(4,6),(5,3),(6,2),(7,1),(8,7),(9,5)],10)=>84
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[[3,1,1,1,1,1,1],[]]=>([(0,7),(0,8),(3,4),(4,6),(5,3),(6,2),(7,5),(8,1)],9)=>28
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[[2,1,1,1,1,1,1],[]]=>([(0,2),(0,7),(3,4),(4,6),(5,3),(6,1),(7,5)],8)=>7
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[[1,1,1,1,1,1,1],[]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>1
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[[2,2,2,2,1,1],[]]=>([(0,2),(0,6),(2,7),(3,1),(4,3),(4,8),(5,4),(5,9),(6,5),(6,7),(7,9),(9,8)],10)=>90
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1,1]=>[[3,2,2,1,1,1],[]]=>([(0,6),(0,7),(3,5),(4,3),(4,9),(5,2),(6,4),(6,8),(7,1),(7,8),(8,9)],10)=>315
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[[2,2,2,1,1,1],[]]=>([(0,2),(0,6),(2,7),(3,5),(4,3),(4,8),(5,1),(6,4),(6,7),(7,8)],9)=>48
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[[3,3,1,1,1,1],[]]=>([(0,6),(0,7),(2,9),(3,5),(4,3),(5,1),(6,4),(6,8),(7,2),(7,8),(8,9)],10)=>225
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1,1]=>[[4,2,1,1,1,1],[]]=>([(0,7),(0,8),(3,5),(4,3),(5,2),(6,1),(7,6),(7,9),(8,4),(8,9)],10)=>350
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1,1]=>[[3,2,1,1,1,1],[]]=>([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(6,8),(7,1),(7,8)],9)=>105
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[[2,2,1,1,1,1],[]]=>([(0,2),(0,6),(2,7),(3,5),(4,3),(5,1),(6,4),(6,7)],8)=>20
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[[5,1,1,1,1,1],[]]=>([(0,8),(0,9),(3,7),(4,3),(5,6),(6,1),(7,2),(8,4),(9,5)],10)=>126
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[[4,1,1,1,1,1],[]]=>([(0,7),(0,8),(3,5),(4,3),(5,2),(6,1),(7,6),(8,4)],9)=>56
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[[3,1,1,1,1,1],[]]=>([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(7,1)],8)=>21
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[[2,1,1,1,1,1],[]]=>([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7)=>6
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[[1,1,1,1,1,1],[]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>1
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[[2,2,2,2,2],[]]=>([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)=>42
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,1]=>[[5,4,3,2,1],[]]=>([(0,7),(0,8),(3,5),(3,12),(4,6),(4,13),(5,2),(5,10),(6,1),(6,11),(7,3),(7,9),(8,4),(8,9),(9,12),(9,13),(12,10),(12,14),(13,11),(13,14)],15)=>292864
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1]=>[[3,2,2,2,1],[]]=>([(0,5),(0,6),(3,4),(3,9),(4,2),(4,8),(5,3),(5,7),(6,1),(6,7),(7,9),(9,8)],10)=>288
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[[2,2,2,2,1],[]]=>([(0,2),(0,5),(2,6),(3,4),(3,8),(4,1),(4,7),(5,3),(5,6),(6,8),(8,7)],9)=>42
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1]=>[[3,3,2,1,1],[]]=>([(0,5),(0,6),(2,9),(3,1),(4,3),(4,8),(5,4),(5,7),(6,2),(6,7),(7,8),(7,9)],10)=>450
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1]=>[[4,2,2,1,1],[]]=>([(0,6),(0,7),(3,4),(3,9),(4,1),(5,2),(6,5),(6,8),(7,3),(7,8),(8,9)],10)=>567
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1]=>[[3,2,2,1,1],[]]=>([(0,5),(0,6),(3,4),(3,8),(4,2),(5,3),(5,7),(6,1),(6,7),(7,8)],9)=>162
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[[2,2,2,1,1],[]]=>([(0,2),(0,5),(2,6),(3,4),(3,7),(4,1),(5,3),(5,6),(6,7)],8)=>28
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1]=>[[4,3,1,1,1],[]]=>([(0,6),(0,7),(3,4),(4,1),(5,2),(5,9),(6,5),(6,8),(7,3),(7,8),(8,9)],10)=>525
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[[3,3,1,1,1],[]]=>([(0,5),(0,6),(2,8),(3,4),(4,1),(5,3),(5,7),(6,2),(6,7),(7,8)],9)=>120
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1]=>[[5,2,1,1,1],[]]=>([(0,7),(0,8),(3,5),(4,6),(5,2),(6,1),(7,3),(7,9),(8,4),(8,9)],10)=>448
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1]=>[[4,2,1,1,1],[]]=>([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(6,8),(7,3),(7,8)],9)=>189
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1]=>[[3,2,1,1,1],[]]=>([(0,5),(0,6),(3,4),(4,2),(5,3),(5,7),(6,1),(6,7)],8)=>64
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[[2,2,1,1,1],[]]=>([(0,2),(0,5),(2,6),(3,4),(4,1),(5,3),(5,6)],7)=>14
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[[6,1,1,1,1],[]]=>([(0,8),(0,9),(3,7),(4,3),(5,6),(6,1),(7,2),(8,4),(9,5)],10)=>126
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[[5,1,1,1,1],[]]=>([(0,7),(0,8),(3,5),(4,6),(5,2),(6,1),(7,3),(8,4)],9)=>70
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[[4,1,1,1,1],[]]=>([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(7,3)],8)=>35
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[[3,1,1,1,1],[]]=>([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)=>15
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[[2,1,1,1,1],[]]=>([(0,2),(0,5),(3,4),(4,1),(5,3)],6)=>5
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[[1,1,1,1,1],[]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]=>[[3,3,2,2],[]]=>([(0,4),(0,5),(1,8),(2,7),(3,2),(3,9),(4,3),(4,6),(5,1),(5,6),(6,8),(6,9),(9,7)],10)=>252
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[[4,2,2,2],[]]=>([(0,5),(0,6),(2,8),(3,1),(4,2),(4,9),(5,3),(5,7),(6,4),(6,7),(7,9),(9,8)],10)=>300
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2]=>[[3,2,2,2],[]]=>([(0,4),(0,5),(2,7),(3,2),(3,8),(4,3),(4,6),(5,1),(5,6),(6,8),(8,7)],9)=>84
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[[2,2,2,2],[]]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)=>14
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1]=>[[3,3,3,1],[]]=>([(0,4),(0,5),(2,7),(3,1),(3,8),(4,2),(4,6),(5,3),(5,6),(6,7),(6,8),(7,9),(8,9)],10)=>210
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1]=>[[4,3,2,1],[]]=>([(0,5),(0,6),(3,2),(3,8),(4,1),(4,9),(5,3),(5,7),(6,4),(6,7),(7,8),(7,9)],10)=>768
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1]=>[[3,3,2,1],[]]=>([(0,4),(0,5),(2,7),(3,1),(3,8),(4,2),(4,6),(5,3),(5,6),(6,7),(6,8)],9)=>168
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1]=>[[5,2,2,1],[]]=>([(0,6),(0,7),(3,4),(4,1),(5,2),(5,9),(6,5),(6,8),(7,3),(7,8),(8,9)],10)=>525
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1]=>[[4,2,2,1],[]]=>([(0,5),(0,6),(3,1),(4,2),(4,8),(5,3),(5,7),(6,4),(6,7),(7,8)],9)=>216
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1]=>[[3,2,2,1],[]]=>([(0,4),(0,5),(3,2),(3,7),(4,3),(4,6),(5,1),(5,6),(6,7)],8)=>70
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[[2,2,2,1],[]]=>([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7)=>14
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1]=>[[4,4,1,1],[]]=>([(0,5),(0,6),(2,8),(3,1),(4,2),(4,9),(5,3),(5,7),(6,4),(6,7),(7,9),(9,8)],10)=>300
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1]=>[[5,3,1,1],[]]=>([(0,6),(0,7),(3,4),(3,9),(4,1),(5,2),(6,5),(6,8),(7,3),(7,8),(8,9)],10)=>567
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1]=>[[4,3,1,1],[]]=>([(0,5),(0,6),(3,1),(4,2),(4,8),(5,3),(5,7),(6,4),(6,7),(7,8)],9)=>216
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[[3,3,1,1],[]]=>([(0,4),(0,5),(1,7),(3,2),(4,3),(4,6),(5,1),(5,6),(6,7)],8)=>56
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1]=>[[6,2,1,1],[]]=>([(0,7),(0,8),(3,5),(4,3),(5,2),(6,1),(7,6),(7,9),(8,4),(8,9)],10)=>350
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1]=>[[5,2,1,1],[]]=>([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(6,8),(7,3),(7,8)],9)=>189
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1]=>[[4,2,1,1],[]]=>([(0,5),(0,6),(3,2),(4,1),(5,3),(5,7),(6,4),(6,7)],8)=>90
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1]=>[[3,2,1,1],[]]=>([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)=>35
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[[2,2,1,1],[]]=>([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)=>9
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[[7,1,1,1],[]]=>([(0,8),(0,9),(3,4),(4,6),(5,3),(6,2),(7,1),(8,7),(9,5)],10)=>84
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[[6,1,1,1],[]]=>([(0,7),(0,8),(3,5),(4,3),(5,2),(6,1),(7,6),(8,4)],9)=>56
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[[5,1,1,1],[]]=>([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(7,3)],8)=>35
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[[4,1,1,1],[]]=>([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7)=>20
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[[3,1,1,1],[]]=>([(0,4),(0,5),(3,2),(4,3),(5,1)],6)=>10
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[[2,1,1,1],[]]=>([(0,2),(0,4),(3,1),(4,3)],5)=>4
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[[1,1,1,1],[]]=>([(0,3),(2,1),(3,2)],4)=>1
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[4,3,3]=>[[4,3,3],[]]=>([(0,4),(0,5),(2,7),(3,1),(3,8),(4,2),(4,6),(5,3),(5,6),(6,7),(6,8),(7,9),(8,9)],10)=>210
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[[3,3,3],[]]=>([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)=>42
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]=>[[4,4,2],[]]=>([(0,4),(0,5),(1,8),(2,7),(3,2),(3,9),(4,3),(4,6),(5,1),(5,6),(6,8),(6,9),(9,7)],10)=>252
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[5,3,2]=>[[5,3,2],[]]=>([(0,5),(0,6),(2,9),(3,1),(4,3),(4,8),(5,4),(5,7),(6,2),(6,7),(7,8),(7,9)],10)=>450
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[4,3,2]=>[[4,3,2],[]]=>([(0,4),(0,5),(2,7),(3,1),(3,8),(4,2),(4,6),(5,3),(5,6),(6,7),(6,8)],9)=>168
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[[3,3,2],[]]=>([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7)],8)=>42
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[[6,2,2],[]]=>([(0,6),(0,7),(2,9),(3,5),(4,3),(5,1),(6,4),(6,8),(7,2),(7,8),(8,9)],10)=>225
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[[5,2,2],[]]=>([(0,5),(0,6),(2,8),(3,4),(4,1),(5,3),(5,7),(6,2),(6,7),(7,8)],9)=>120
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[[4,2,2],[]]=>([(0,4),(0,5),(1,7),(3,2),(4,3),(4,6),(5,1),(5,6),(6,7)],8)=>56
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[[3,2,2],[]]=>([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7)=>21
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[[2,2,2],[]]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>5
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[5,4,1]=>[[5,4,1],[]]=>([(0,5),(0,6),(3,4),(3,9),(4,2),(4,8),(5,3),(5,7),(6,1),(6,7),(7,9),(9,8)],10)=>288
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[4,4,1]=>[[4,4,1],[]]=>([(0,4),(0,5),(2,7),(3,2),(3,8),(4,3),(4,6),(5,1),(5,6),(6,8),(8,7)],9)=>84
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[6,3,1]=>[[6,3,1],[]]=>([(0,6),(0,7),(3,5),(4,3),(4,9),(5,2),(6,4),(6,8),(7,1),(7,8),(8,9)],10)=>315
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[5,3,1]=>[[5,3,1],[]]=>([(0,5),(0,6),(3,4),(3,8),(4,2),(5,3),(5,7),(6,1),(6,7),(7,8)],9)=>162
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[4,3,1]=>[[4,3,1],[]]=>([(0,4),(0,5),(3,2),(3,7),(4,3),(4,6),(5,1),(5,6),(6,7)],8)=>70
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[[3,3,1],[]]=>([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7)=>21
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[7,2,1]=>[[7,2,1],[]]=>([(0,7),(0,8),(3,4),(4,6),(5,3),(6,2),(7,5),(7,9),(8,1),(8,9)],10)=>160
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[6,2,1]=>[[6,2,1],[]]=>([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(6,8),(7,1),(7,8)],9)=>105
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[5,2,1]=>[[5,2,1],[]]=>([(0,5),(0,6),(3,4),(4,2),(5,3),(5,7),(6,1),(6,7)],8)=>64
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[4,2,1]=>[[4,2,1],[]]=>([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)=>35
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[3,2,1]=>[[3,2,1],[]]=>([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)=>16
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[[2,2,1],[]]=>([(0,2),(0,3),(2,4),(3,1),(3,4)],5)=>5
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[[7,1,1],[]]=>([(0,7),(0,8),(3,4),(4,6),(5,3),(6,2),(7,5),(8,1)],9)=>28
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[[6,1,1],[]]=>([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(7,1)],8)=>21
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[[5,1,1],[]]=>([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)=>15
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[[4,1,1],[]]=>([(0,4),(0,5),(3,2),(4,3),(5,1)],6)=>10
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[[3,1,1],[]]=>([(0,3),(0,4),(3,2),(4,1)],5)=>6
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[[2,1,1],[]]=>([(0,2),(0,3),(3,1)],4)=>3
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[[1,1,1],[]]=>([(0,2),(2,1)],3)=>1
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[[5,5],[]]=>([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)=>42
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[[6,4],[]]=>([(0,2),(0,6),(2,7),(3,1),(4,3),(4,8),(5,4),(5,9),(6,5),(6,7),(7,9),(9,8)],10)=>90
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[[5,4],[]]=>([(0,2),(0,5),(2,6),(3,4),(3,8),(4,1),(4,7),(5,3),(5,6),(6,8),(8,7)],9)=>42
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[[4,4],[]]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)=>14
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[[7,3],[]]=>([(0,2),(0,7),(2,8),(3,4),(4,6),(5,3),(5,9),(6,1),(7,5),(7,8),(8,9)],10)=>75
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[[6,3],[]]=>([(0,2),(0,6),(2,7),(3,5),(4,3),(4,8),(5,1),(6,4),(6,7),(7,8)],9)=>48
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[[5,3],[]]=>([(0,2),(0,5),(2,6),(3,4),(3,7),(4,1),(5,3),(5,6),(6,7)],8)=>28
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[[4,3],[]]=>([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7)=>14
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[[3,3],[]]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>5
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[[7,2],[]]=>([(0,2),(0,7),(2,8),(3,4),(4,6),(5,3),(6,1),(7,5),(7,8)],9)=>27
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[[6,2],[]]=>([(0,2),(0,6),(2,7),(3,5),(4,3),(5,1),(6,4),(6,7)],8)=>20
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[[5,2],[]]=>([(0,2),(0,5),(2,6),(3,4),(4,1),(5,3),(5,6)],7)=>14
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[[4,2],[]]=>([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)=>9
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[[3,2],[]]=>([(0,2),(0,3),(2,4),(3,1),(3,4)],5)=>5
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[[2,2],[]]=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[[7,1],[]]=>([(0,2),(0,7),(3,4),(4,6),(5,3),(6,1),(7,5)],8)=>7
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[[6,1],[]]=>([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7)=>6
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[[5,1],[]]=>([(0,2),(0,5),(3,4),(4,1),(5,3)],6)=>5
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[[4,1],[]]=>([(0,2),(0,4),(3,1),(4,3)],5)=>4
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[[3,1],[]]=>([(0,2),(0,3),(3,1)],4)=>3
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[[2,1],[]]=>([(0,1),(0,2)],3)=>2
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[[1,1],[]]=>([(0,1)],2)=>1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[7]=>[[7],[]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[6]=>[[6],[]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[5]=>[[5],[]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[4]=>[[4],[]]=>([(0,3),(2,1),(3,2)],4)=>1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[3]=>[[3],[]]=>([(0,2),(2,1)],3)=>1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[2]=>[[2],[]]=>([(0,1)],2)=>1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[8]=>[[8],[]]=>([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)=>1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[[1,1,1,1,1,1,1,1],[]]=>([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)=>1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[9]=>[[9],[]]=>([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)=>1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[8,1]=>[[8,1],[]]=>([(0,2),(0,8),(3,5),(4,3),(5,7),(6,4),(7,1),(8,6)],9)=>8
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,1,1,1,1,1,1,1]=>[[2,1,1,1,1,1,1,1],[]]=>([(0,2),(0,8),(3,5),(4,3),(5,7),(6,4),(7,1),(8,6)],9)=>8
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1]=>[[1,1,1,1,1,1,1,1,1],[]]=>([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)=>1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[10]=>[[10],[]]=>([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)=>1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[9,1]=>[[9,1],[]]=>([(0,2),(0,9),(3,4),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)=>9
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[8,2]=>[[8,2],[]]=>([(0,2),(0,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,1),(8,6),(8,9)],10)=>35
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[8,1,1]=>[[8,1,1],[]]=>([(0,8),(0,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6),(9,1)],10)=>36
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[3,1,1,1,1,1,1,1]=>[[3,1,1,1,1,1,1,1],[]]=>([(0,8),(0,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6),(9,1)],10)=>36
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[2,2,1,1,1,1,1,1]=>[[2,2,1,1,1,1,1,1],[]]=>([(0,2),(0,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,1),(8,6),(8,9)],10)=>35
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[2,1,1,1,1,1,1,1,1]=>[[2,1,1,1,1,1,1,1,1],[]]=>([(0,2),(0,9),(3,4),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)=>9
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1]=>[[1,1,1,1,1,1,1,1,1,1],[]]=>([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)=>1
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[[2,2,2,1,1,1,1],[]]=>([(0,2),(0,7),(2,8),(3,4),(4,6),(5,3),(5,9),(6,1),(7,5),(7,8),(8,9)],10)=>75
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1,1,1,1,1]=>[[3,2,1,1,1,1,1],[]]=>([(0,7),(0,8),(3,4),(4,6),(5,3),(6,2),(7,5),(7,9),(8,1),(8,9)],10)=>160
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[[2,2,1,1,1,1,1],[]]=>([(0,2),(0,7),(2,8),(3,4),(4,6),(5,3),(6,1),(7,5),(7,8)],9)=>27
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[4,1,1,1,1,1,1]=>[[4,1,1,1,1,1,1],[]]=>([(0,8),(0,9),(3,4),(4,6),(5,3),(6,2),(7,1),(8,7),(9,5)],10)=>84
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[[3,1,1,1,1,1,1],[]]=>([(0,7),(0,8),(3,4),(4,6),(5,3),(6,2),(7,5),(8,1)],9)=>28
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[[2,1,1,1,1,1,1],[]]=>([(0,2),(0,7),(3,4),(4,6),(5,3),(6,1),(7,5)],8)=>7
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[[1,1,1,1,1,1,1],[]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>1
[1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[[2,2,2,2,1,1],[]]=>([(0,2),(0,6),(2,7),(3,1),(4,3),(4,8),(5,4),(5,9),(6,5),(6,7),(7,9),(9,8)],10)=>90
[1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[[2,2,2,1,1,1],[]]=>([(0,2),(0,6),(2,7),(3,5),(4,3),(4,8),(5,1),(6,4),(6,7),(7,8)],9)=>48
[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1,1,1,1]=>[[3,2,1,1,1,1],[]]=>([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(6,8),(7,1),(7,8)],9)=>105
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[[2,2,1,1,1,1],[]]=>([(0,2),(0,6),(2,7),(3,5),(4,3),(5,1),(6,4),(6,7)],8)=>20
[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[5,1,1,1,1,1]=>[[5,1,1,1,1,1],[]]=>([(0,8),(0,9),(3,7),(4,3),(5,6),(6,1),(7,2),(8,4),(9,5)],10)=>126
[1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[4,1,1,1,1,1]=>[[4,1,1,1,1,1],[]]=>([(0,7),(0,8),(3,5),(4,3),(5,2),(6,1),(7,6),(8,4)],9)=>56
[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[3,1,1,1,1,1]=>[[3,1,1,1,1,1],[]]=>([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(7,1)],8)=>21
[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[[2,1,1,1,1,1],[]]=>([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7)=>6
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[[1,1,1,1,1,1],[]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>1
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2]=>[[2,2,2,2,2],[]]=>([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)=>42
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,1]=>[[5,4,3,2,1],[]]=>([(0,7),(0,8),(3,5),(3,12),(4,6),(4,13),(5,2),(5,10),(6,1),(6,11),(7,3),(7,9),(8,4),(8,9),(9,12),(9,13),(12,10),(12,14),(13,11),(13,14)],15)=>292864
[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,2,2,1]=>[[3,2,2,2,1],[]]=>([(0,5),(0,6),(3,4),(3,9),(4,2),(4,8),(5,3),(5,7),(6,1),(6,7),(7,9),(9,8)],10)=>288
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,1]=>[[2,2,2,2,1],[]]=>([(0,2),(0,5),(2,6),(3,4),(3,8),(4,1),(4,7),(5,3),(5,6),(6,8),(8,7)],9)=>42
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[3,2,2,1,1]=>[[3,2,2,1,1],[]]=>([(0,5),(0,6),(3,4),(3,8),(4,2),(5,3),(5,7),(6,1),(6,7),(7,8)],9)=>162
[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,1,1]=>[[2,2,2,1,1],[]]=>([(0,2),(0,5),(2,6),(3,4),(3,7),(4,1),(5,3),(5,6),(6,7)],8)=>28
[1,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[4,3,1,1,1]=>[[4,3,1,1,1],[]]=>([(0,6),(0,7),(3,4),(4,1),(5,2),(5,9),(6,5),(6,8),(7,3),(7,8),(8,9)],10)=>525
[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[3,3,1,1,1]=>[[3,3,1,1,1],[]]=>([(0,5),(0,6),(2,8),(3,4),(4,1),(5,3),(5,7),(6,2),(6,7),(7,8)],9)=>120
[1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[5,2,1,1,1]=>[[5,2,1,1,1],[]]=>([(0,7),(0,8),(3,5),(4,6),(5,2),(6,1),(7,3),(7,9),(8,4),(8,9)],10)=>448
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1,1,1]=>[[3,2,1,1,1],[]]=>([(0,5),(0,6),(3,4),(4,2),(5,3),(5,7),(6,1),(6,7)],8)=>64
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[2,2,1,1,1]=>[[2,2,1,1,1],[]]=>([(0,2),(0,5),(2,6),(3,4),(4,1),(5,3),(5,6)],7)=>14
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[6,1,1,1,1]=>[[6,1,1,1,1],[]]=>([(0,8),(0,9),(3,7),(4,3),(5,6),(6,1),(7,2),(8,4),(9,5)],10)=>126
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[5,1,1,1,1]=>[[5,1,1,1,1],[]]=>([(0,7),(0,8),(3,5),(4,6),(5,2),(6,1),(7,3),(8,4)],9)=>70
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,1,1,1,1]=>[[2,1,1,1,1],[]]=>([(0,2),(0,5),(3,4),(4,1),(5,3)],6)=>5
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[[1,1,1,1,1],[]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[1,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0]=>[3,3,2,2]=>[[3,3,2,2],[]]=>([(0,4),(0,5),(1,8),(2,7),(3,2),(3,9),(4,3),(4,6),(5,1),(5,6),(6,8),(6,9),(9,7)],10)=>252
[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0]=>[3,3,3,1]=>[[3,3,3,1],[]]=>([(0,4),(0,5),(2,7),(3,1),(3,8),(4,2),(4,6),(5,3),(5,6),(6,7),(6,8),(7,9),(8,9)],10)=>210
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,1]=>[[4,3,2,1],[]]=>([(0,5),(0,6),(3,2),(3,8),(4,1),(4,9),(5,3),(5,7),(6,4),(6,7),(7,8),(7,9)],10)=>768
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[3,3,2,1]=>[[3,3,2,1],[]]=>([(0,4),(0,5),(2,7),(3,1),(3,8),(4,2),(4,6),(5,3),(5,6),(6,7),(6,8)],9)=>168
[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0]=>[4,2,2,1]=>[[4,2,2,1],[]]=>([(0,5),(0,6),(3,1),(4,2),(4,8),(5,3),(5,7),(6,4),(6,7),(7,8)],9)=>216
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0]=>[3,2,2,1]=>[[3,2,2,1],[]]=>([(0,4),(0,5),(3,2),(3,7),(4,3),(4,6),(5,1),(5,6),(6,7)],8)=>70
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,1]=>[[2,2,2,1],[]]=>([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7)=>14
[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0]=>[4,3,1,1]=>[[4,3,1,1],[]]=>([(0,5),(0,6),(3,1),(4,2),(4,8),(5,3),(5,7),(6,4),(6,7),(7,8)],9)=>216
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0]=>[3,3,1,1]=>[[3,3,1,1],[]]=>([(0,4),(0,5),(1,7),(3,2),(4,3),(4,6),(5,1),(5,6),(6,7)],8)=>56
[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0]=>[4,2,1,1]=>[[4,2,1,1],[]]=>([(0,5),(0,6),(3,2),(4,1),(5,3),(5,7),(6,4),(6,7)],8)=>90
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1,1]=>[[3,2,1,1],[]]=>([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)=>35
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[2,2,1,1]=>[[2,2,1,1],[]]=>([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)=>9
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,1,1,1]=>[[7,1,1,1],[]]=>([(0,8),(0,9),(3,4),(4,6),(5,3),(6,2),(7,1),(8,7),(9,5)],10)=>84
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0]=>[6,1,1,1]=>[[6,1,1,1],[]]=>([(0,7),(0,8),(3,5),(4,3),(5,2),(6,1),(7,6),(8,4)],9)=>56
[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0]=>[5,1,1,1]=>[[5,1,1,1],[]]=>([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(7,3)],8)=>35
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>[4,1,1,1]=>[[4,1,1,1],[]]=>([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7)=>20
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0]=>[3,1,1,1]=>[[3,1,1,1],[]]=>([(0,4),(0,5),(3,2),(4,3),(5,1)],6)=>10
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,1,1,1]=>[[2,1,1,1],[]]=>([(0,2),(0,4),(3,1),(4,3)],5)=>4
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1]=>[[1,1,1,1],[]]=>([(0,3),(2,1),(3,2)],4)=>1
[1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0]=>[4,3,3]=>[[4,3,3],[]]=>([(0,4),(0,5),(2,7),(3,1),(3,8),(4,2),(4,6),(5,3),(5,6),(6,7),(6,8),(7,9),(8,9)],10)=>210
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]=>[3,3,3]=>[[3,3,3],[]]=>([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)=>42
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0]=>[4,4,2]=>[[4,4,2],[]]=>([(0,4),(0,5),(1,8),(2,7),(3,2),(3,9),(4,3),(4,6),(5,1),(5,6),(6,8),(6,9),(9,7)],10)=>252
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0]=>[5,3,2]=>[[5,3,2],[]]=>([(0,5),(0,6),(2,9),(3,1),(4,3),(4,8),(5,4),(5,7),(6,2),(6,7),(7,8),(7,9)],10)=>450
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[4,3,2]=>[[4,3,2],[]]=>([(0,4),(0,5),(2,7),(3,1),(3,8),(4,2),(4,6),(5,3),(5,6),(6,7),(6,8)],9)=>168
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0]=>[3,3,2]=>[[3,3,2],[]]=>([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7)],8)=>42
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0]=>[4,2,2]=>[[4,2,2],[]]=>([(0,4),(0,5),(1,7),(3,2),(4,3),(4,6),(5,1),(5,6),(6,7)],8)=>56
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]=>[3,2,2]=>[[3,2,2],[]]=>([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7)=>21
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]=>[2,2,2]=>[[2,2,2],[]]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>5
[1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0]=>[5,4,1]=>[[5,4,1],[]]=>([(0,5),(0,6),(3,4),(3,9),(4,2),(4,8),(5,3),(5,7),(6,1),(6,7),(7,9),(9,8)],10)=>288
[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0]=>[4,4,1]=>[[4,4,1],[]]=>([(0,4),(0,5),(2,7),(3,2),(3,8),(4,3),(4,6),(5,1),(5,6),(6,8),(8,7)],9)=>84
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0]=>[6,3,1]=>[[6,3,1],[]]=>([(0,6),(0,7),(3,5),(4,3),(4,9),(5,2),(6,4),(6,8),(7,1),(7,8),(8,9)],10)=>315
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0]=>[5,3,1]=>[[5,3,1],[]]=>([(0,5),(0,6),(3,4),(3,8),(4,2),(5,3),(5,7),(6,1),(6,7),(7,8)],9)=>162
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0]=>[4,3,1]=>[[4,3,1],[]]=>([(0,4),(0,5),(3,2),(3,7),(4,3),(4,6),(5,1),(5,6),(6,7)],8)=>70
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]=>[3,3,1]=>[[3,3,1],[]]=>([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7)=>21
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0]=>[7,2,1]=>[[7,2,1],[]]=>([(0,7),(0,8),(3,4),(4,6),(5,3),(6,2),(7,5),(7,9),(8,1),(8,9)],10)=>160
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0]=>[6,2,1]=>[[6,2,1],[]]=>([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(6,8),(7,1),(7,8)],9)=>105
[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0]=>[5,2,1]=>[[5,2,1],[]]=>([(0,5),(0,6),(3,4),(4,2),(5,3),(5,7),(6,1),(6,7)],8)=>64
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[4,2,1]=>[[4,2,1],[]]=>([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)=>35
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1]=>[[3,2,1],[]]=>([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)=>16
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[2,2,1]=>[[2,2,1],[]]=>([(0,2),(0,3),(2,4),(3,1),(3,4)],5)=>5
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[7,1,1]=>[[7,1,1],[]]=>([(0,7),(0,8),(3,4),(4,6),(5,3),(6,2),(7,5),(8,1)],9)=>28
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0]=>[6,1,1]=>[[6,1,1],[]]=>([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(7,1)],8)=>21
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0]=>[4,1,1]=>[[4,1,1],[]]=>([(0,4),(0,5),(3,2),(4,3),(5,1)],6)=>10
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[3,1,1]=>[[3,1,1],[]]=>([(0,3),(0,4),(3,2),(4,1)],5)=>6
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[2,1,1]=>[[2,1,1],[]]=>([(0,2),(0,3),(3,1)],4)=>3
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1]=>[[1,1,1],[]]=>([(0,2),(2,1)],3)=>1
[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0]=>[5,5]=>[[5,5],[]]=>([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)=>42
[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]=>[4,4]=>[[4,4],[]]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)=>14
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0]=>[7,3]=>[[7,3],[]]=>([(0,2),(0,7),(2,8),(3,4),(4,6),(5,3),(5,9),(6,1),(7,5),(7,8),(8,9)],10)=>75
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0]=>[4,3]=>[[4,3],[]]=>([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7)=>14
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[3,3]=>[[3,3],[]]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>5
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[7,2]=>[[7,2],[]]=>([(0,2),(0,7),(2,8),(3,4),(4,6),(5,3),(6,1),(7,5),(7,8)],9)=>27
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[4,2]=>[[4,2],[]]=>([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)=>9
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[3,2]=>[[3,2],[]]=>([(0,2),(0,3),(2,4),(3,1),(3,4)],5)=>5
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[2,2]=>[[2,2],[]]=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[7,1]=>[[7,1],[]]=>([(0,2),(0,7),(3,4),(4,6),(5,3),(6,1),(7,5)],8)=>7
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0]=>[6,1]=>[[6,1],[]]=>([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7)=>6
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0]=>[5,1]=>[[5,1],[]]=>([(0,2),(0,5),(3,4),(4,1),(5,3)],6)=>5
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0]=>[4,1]=>[[4,1],[]]=>([(0,2),(0,4),(3,1),(4,3)],5)=>4
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[3,1]=>[[3,1],[]]=>([(0,2),(0,3),(3,1)],4)=>3
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[2,1]=>[[2,1],[]]=>([(0,1),(0,2)],3)=>2
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1]=>[[1,1],[]]=>([(0,1)],2)=>1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[7]=>[[7],[]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[6]=>[[6],[]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>1
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[5]=>[[5],[]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[4]=>[[4],[]]=>([(0,3),(2,1),(3,2)],4)=>1
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[3]=>[[3],[]]=>([(0,2),(2,1)],3)=>1
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[2]=>[[2],[]]=>([(0,1)],2)=>1
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,1]=>[[1,1],[]]=>([(0,1)],2)=>1
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[2]=>[[2],[]]=>([(0,1)],2)=>1
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1]=>[[1,1],[]]=>([(0,1)],2)=>1
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[2,2,1]=>[[2,2,1],[]]=>([(0,2),(0,3),(2,4),(3,1),(3,4)],5)=>5
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[3,2]=>[[3,2],[]]=>([(0,2),(0,3),(2,4),(3,1),(3,4)],5)=>5
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>[2]=>[[2],[]]=>([(0,1)],2)=>1
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[[1,1,1,1,1,1,1,1],[]]=>([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)=>1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[8]=>[[8],[]]=>([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)=>1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>[9]=>[[9],[]]=>([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)=>1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[8,1]=>[[8,1],[]]=>([(0,2),(0,8),(3,5),(4,3),(5,7),(6,4),(7,1),(8,6)],9)=>8
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1]=>[[1,1,1],[]]=>([(0,2),(2,1)],3)=>1
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1]=>[[1,1,1,1],[]]=>([(0,3),(2,1),(3,2)],4)=>1
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[[1,1,1,1,1],[]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[[1,1,1,1,1,1],[]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>1
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[[1,1,1,1,1,1,1],[]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[7]=>[[7],[]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[6]=>[[6],[]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[5]=>[[5],[]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[4]=>[[4],[]]=>([(0,3),(2,1),(3,2)],4)=>1
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[3]=>[[3],[]]=>([(0,2),(2,1)],3)=>1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0]=>[9,1]=>[[9,1],[]]=>([(0,2),(0,9),(3,4),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)=>9
[1,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[2,1,1,1,1,1,1,1,1]=>[[2,1,1,1,1,1,1,1,1],[]]=>([(0,2),(0,9),(3,4),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)=>9
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[2,2]=>[[2,2],[]]=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]=>[3,3]=>[[3,3],[]]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>5
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0]=>[3,3,3]=>[[3,3,3],[]]=>([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)=>42
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0]=>[2,1,1]=>[[2,1,1],[]]=>([(0,2),(0,3),(3,1)],4)=>3
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[2,1,1,1,1,1,1,1]=>[[2,1,1,1,1,1,1,1],[]]=>([(0,2),(0,8),(3,5),(4,3),(5,7),(6,4),(7,1),(8,6)],9)=>8
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1]=>[[1,1,1,1,1,1,1,1,1],[]]=>([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)=>1
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0]=>[8,1,1]=>[[8,1,1],[]]=>([(0,8),(0,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6),(9,1)],10)=>36
[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[3,1,1,1,1,1,1,1]=>[[3,1,1,1,1,1,1,1],[]]=>([(0,8),(0,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6),(9,1)],10)=>36
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[2,2,1,1,1,1,1,1]=>[[2,2,1,1,1,1,1,1],[]]=>([(0,2),(0,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,1),(8,6),(8,9)],10)=>35
[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1]=>[[1,1,1,1,1,1,1,1,1,1],[]]=>([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)=>1
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,4,3,2,1]=>[[5,4,3,2,1],[]]=>([(0,7),(0,8),(3,5),(3,12),(4,6),(4,13),(5,2),(5,10),(6,1),(6,11),(7,3),(7,9),(8,4),(8,9),(9,12),(9,13),(12,10),(12,14),(13,11),(13,14)],15)=>292864
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2]=>[[4,3,2],[]]=>([(0,4),(0,5),(2,7),(3,1),(3,8),(4,2),(4,6),(5,3),(5,6),(6,7),(6,8)],9)=>168
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]=>[3,1]=>[[3,1],[]]=>([(0,2),(0,3),(3,1)],4)=>3
[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[[2,1,1,1,1,1],[]]=>([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7)=>6
[1,1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[3,1,1,1,1,1]=>[[3,1,1,1,1,1],[]]=>([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(7,1)],8)=>21
[1,1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[4,1,1,1,1,1]=>[[4,1,1,1,1,1],[]]=>([(0,7),(0,8),(3,5),(4,3),(5,2),(6,1),(7,6),(8,4)],9)=>56
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[5,1,1,1,1,1]=>[[5,1,1,1,1,1],[]]=>([(0,8),(0,9),(3,7),(4,3),(5,6),(6,1),(7,2),(8,4),(9,5)],10)=>126
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[[2,1],[]]=>([(0,1),(0,2)],3)=>2
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0]=>[2,1]=>[[2,1],[]]=>([(0,1),(0,2)],3)=>2
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2,1]=>[[4,3,2,1],[]]=>([(0,5),(0,6),(3,2),(3,8),(4,1),(4,9),(5,3),(5,7),(6,4),(6,7),(7,8),(7,9)],10)=>768
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1]=>[[3,2,1],[]]=>([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)=>16
[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0]=>[3]=>[[3],[]]=>([(0,2),(2,1)],3)=>1
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0,0]=>[7,2,1]=>[[7,2,1],[]]=>([(0,7),(0,8),(3,4),(4,6),(5,3),(6,2),(7,5),(7,9),(8,1),(8,9)],10)=>160
[1,1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1,1,1,1,1]=>[[3,2,1,1,1,1,1],[]]=>([(0,7),(0,8),(3,4),(4,6),(5,3),(6,2),(7,5),(7,9),(8,1),(8,9)],10)=>160
[1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0]=>[3,1]=>[[3,1],[]]=>([(0,2),(0,3),(3,1)],4)=>3
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0]=>[4,2]=>[[4,2],[]]=>([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)=>9
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0]=>[5,4,1]=>[[5,4,1],[]]=>([(0,5),(0,6),(3,4),(3,9),(4,2),(4,8),(5,3),(5,7),(6,1),(6,7),(7,9),(9,8)],10)=>288
[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0]=>[4,3,1]=>[[4,3,1],[]]=>([(0,4),(0,5),(3,2),(3,7),(4,3),(4,6),(5,1),(5,6),(6,7)],8)=>70
[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2]=>[[2,2,2],[]]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>5
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0]=>[7,1]=>[[7,1],[]]=>([(0,2),(0,7),(3,4),(4,6),(5,3),(6,1),(7,5)],8)=>7
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0]=>[6,1]=>[[6,1],[]]=>([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7)=>6
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0]=>[5,1]=>[[5,1],[]]=>([(0,2),(0,5),(3,4),(4,1),(5,3)],6)=>5
[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0]=>[4,1]=>[[4,1],[]]=>([(0,2),(0,4),(3,1),(4,3)],5)=>4
[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[2,1,1,1]=>[[2,1,1,1],[]]=>([(0,2),(0,4),(3,1),(4,3)],5)=>4
[1,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[2,1,1,1,1]=>[[2,1,1,1,1],[]]=>([(0,2),(0,5),(3,4),(4,1),(5,3)],6)=>5
[1,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[[2,1,1,1,1,1,1],[]]=>([(0,2),(0,7),(3,4),(4,6),(5,3),(6,1),(7,5)],8)=>7
[1,1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[2,1,1]=>[[2,1,1],[]]=>([(0,2),(0,3),(3,1)],4)=>3
[1,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[3,2,2,1]=>[[3,2,2,1],[]]=>([(0,4),(0,5),(3,2),(3,7),(4,3),(4,6),(5,1),(5,6),(6,7)],8)=>70
[1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1]=>[[1,1,1],[]]=>([(0,2),(2,1)],3)=>1
[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0]=>[3,1,1]=>[[3,1,1],[]]=>([(0,3),(0,4),(3,2),(4,1)],5)=>6
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[2,2,1,1]=>[[2,2,1,1],[]]=>([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)=>9
[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1,1]=>[[3,2,1,1],[]]=>([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)=>35
[1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0]=>[2,2]=>[[2,2],[]]=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[5,4,3,2,1]=>[[5,4,3,2,1],[]]=>([(0,7),(0,8),(3,5),(3,12),(4,6),(4,13),(5,2),(5,10),(6,1),(6,11),(7,3),(7,9),(8,4),(8,9),(9,12),(9,13),(12,10),(12,14),(13,11),(13,14)],15)=>292864
[1,1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0]=>[3,3]=>[[3,3],[]]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>5
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]=>[3]=>[[3],[]]=>([(0,2),(2,1)],3)=>1
[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1]=>[[1,1],[]]=>([(0,1)],2)=>1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0,0]=>[8,1]=>[[8,1],[]]=>([(0,2),(0,8),(3,5),(4,3),(5,7),(6,4),(7,1),(8,6)],9)=>8
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0,0]=>[7,1]=>[[7,1],[]]=>([(0,2),(0,7),(3,4),(4,6),(5,3),(6,1),(7,5)],8)=>7
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0,0]=>[6,1]=>[[6,1],[]]=>([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7)=>6
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0,0]=>[5,1]=>[[5,1],[]]=>([(0,2),(0,5),(3,4),(4,1),(5,3)],6)=>5
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0,0]=>[4,1]=>[[4,1],[]]=>([(0,2),(0,4),(3,1),(4,3)],5)=>4
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]=>[5,5]=>[[5,5],[]]=>([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)=>42
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0]=>[4,4]=>[[4,4],[]]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)=>14
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0]=>[5,3,1]=>[[5,3,1],[]]=>([(0,5),(0,6),(3,4),(3,8),(4,2),(5,3),(5,7),(6,1),(6,7),(7,8)],9)=>162
[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,1]=>[[2,2,2,1],[]]=>([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7)=>14
[1,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0]=>[3,3,2]=>[[3,3,2],[]]=>([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7)],8)=>42
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Description
The number of linear extensions of a poset.
Map
to skew partition
Description
The partition regarded as a skew partition.
Map
cell poset
Description
The Young diagram of a skew partition regarded as a poset.
This is the poset on the cells of the Young diagram, such that a cell $d$ is greater than a cell $c$ if the entry in $d$ must be larger than the entry of $c$ in any standard Young tableau on the skew partition.
This is the poset on the cells of the Young diagram, such that a cell $d$ is greater than a cell $c$ if the entry in $d$ must be larger than the entry of $c$ in any standard Young tableau on the skew partition.
Map
to partition
Description
The cut-out partition of a Dyck path.
The partition $\lambda$ associated to a Dyck path is defined to be the complementary partition inside the staircase partition $(n-1,\ldots,2,1)$ when cutting out $D$ considered as a path from $(0,0)$ to $(n,n)$.
In other words, $\lambda_{i}$ is the number of down-steps before the $(n+1-i)$-th up-step of $D$.
This map is a bijection between Dyck paths of size $n$ and partitions inside the staircase partition $(n-1,\ldots,2,1)$.
The partition $\lambda$ associated to a Dyck path is defined to be the complementary partition inside the staircase partition $(n-1,\ldots,2,1)$ when cutting out $D$ considered as a path from $(0,0)$ to $(n,n)$.
In other words, $\lambda_{i}$ is the number of down-steps before the $(n+1-i)$-th up-step of $D$.
This map is a bijection between Dyck paths of size $n$ and partitions inside the staircase partition $(n-1,\ldots,2,1)$.
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