Your data matches 9 different statistics following compositions of up to 3 maps.
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Matching statistic: St000938
Mp00170: Permutations to signed permutationSigned permutations
Mp00190: Signed permutations Foata-HanSigned permutations
Mp00169: Signed permutations odd cycle typeInteger partitions
St000938: Integer partitions ⟶ ℤResult quality: 100% values known / values provided: 100%distinct values known / distinct values provided: 100%
Values
[2,1] => [2,1] => [-2,1] => [2]
=> 0
[1,3,2] => [1,3,2] => [1,-3,2] => [2]
=> 0
[2,1,3] => [2,1,3] => [-2,1,3] => [2]
=> 0
[1,2,4,3] => [1,2,4,3] => [1,2,-4,3] => [2]
=> 0
[1,3,2,4] => [1,3,2,4] => [1,-3,2,4] => [2]
=> 0
[1,4,2,3] => [1,4,2,3] => [-4,1,2,3] => [4]
=> 0
[2,1,3,4] => [2,1,3,4] => [-2,1,3,4] => [2]
=> 0
[2,1,4,3] => [2,1,4,3] => [-2,1,-4,3] => [2,2]
=> 2
[2,3,4,1] => [2,3,4,1] => [3,4,-2,1] => [4]
=> 0
[2,4,1,3] => [2,4,1,3] => [-2,4,1,3] => [4]
=> 0
[2,4,3,1] => [2,4,3,1] => [3,-2,-4,1] => [3,1]
=> 1
[3,1,4,2] => [3,1,4,2] => [-4,1,-3,2] => [3,1]
=> 1
[3,2,4,1] => [3,2,4,1] => [-2,4,-3,1] => [3,1]
=> 1
[3,4,2,1] => [3,4,2,1] => [2,-4,-3,1] => [3,1]
=> 1
[4,1,3,2] => [4,1,3,2] => [3,1,-4,2] => [4]
=> 0
[4,2,1,3] => [4,2,1,3] => [-4,-2,1,3] => [3,1]
=> 1
[4,2,3,1] => [4,2,3,1] => [2,3,-4,1] => [4]
=> 0
[4,3,1,2] => [4,3,1,2] => [-4,3,1,2] => [4]
=> 0
[4,3,2,1] => [4,3,2,1] => [-2,-3,-4,1] => [4]
=> 0
[1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,-5,4] => [2]
=> 0
[1,2,4,3,5] => [1,2,4,3,5] => [1,2,-4,3,5] => [2]
=> 0
[1,2,5,3,4] => [1,2,5,3,4] => [1,-5,2,3,4] => [4]
=> 0
[1,3,2,4,5] => [1,3,2,4,5] => [1,-3,2,4,5] => [2]
=> 0
[1,3,2,5,4] => [1,3,2,5,4] => [1,-3,2,-5,4] => [2,2]
=> 2
[1,3,4,5,2] => [1,3,4,5,2] => [1,4,5,-3,2] => [4]
=> 0
[1,3,5,2,4] => [1,3,5,2,4] => [1,-3,5,2,4] => [4]
=> 0
[1,3,5,4,2] => [1,3,5,4,2] => [1,4,-3,-5,2] => [3,1]
=> 1
[1,4,2,3,5] => [1,4,2,3,5] => [-4,1,2,3,5] => [4]
=> 0
[1,4,2,5,3] => [1,4,2,5,3] => [1,-5,2,-4,3] => [3,1]
=> 1
[1,4,3,5,2] => [1,4,3,5,2] => [1,-3,5,-4,2] => [3,1]
=> 1
[1,4,5,2,3] => [1,4,5,2,3] => [-4,1,5,2,3] => [3]
=> 0
[1,4,5,3,2] => [1,4,5,3,2] => [1,3,-5,-4,2] => [3,1]
=> 1
[1,5,3,2,4] => [1,5,3,2,4] => [1,-5,-3,2,4] => [3,1]
=> 1
[1,5,4,3,2] => [1,5,4,3,2] => [1,-3,-4,-5,2] => [4]
=> 0
[2,1,3,4,5] => [2,1,3,4,5] => [-2,1,3,4,5] => [2]
=> 0
[2,1,3,5,4] => [2,1,3,5,4] => [-2,1,3,-5,4] => [2,2]
=> 2
[2,1,4,3,5] => [2,1,4,3,5] => [-2,1,-4,3,5] => [2,2]
=> 2
[2,1,4,5,3] => [2,1,4,5,3] => [-2,1,5,-4,3] => [2,1]
=> 1
[2,1,5,4,3] => [2,1,5,4,3] => [-2,1,-4,-5,3] => [2]
=> 0
[2,3,1,5,4] => [2,3,1,5,4] => [3,-2,1,-5,4] => [2,1]
=> 1
[2,3,4,1,5] => [2,3,4,1,5] => [3,4,-2,1,5] => [4]
=> 0
[2,3,4,5,1] => [2,3,4,5,1] => [3,4,5,-2,1] => [2]
=> 0
[2,4,1,3,5] => [2,4,1,3,5] => [-2,4,1,3,5] => [4]
=> 0
[2,4,1,5,3] => [2,4,1,5,3] => [5,-2,1,-4,3] => [1,1]
=> 0
[2,4,3,1,5] => [2,4,3,1,5] => [3,-2,-4,1,5] => [3,1]
=> 1
[2,4,3,5,1] => [2,4,3,5,1] => [3,-2,5,-4,1] => [1,1]
=> 0
[2,4,5,1,3] => [2,4,5,1,3] => [-2,4,5,1,3] => [3]
=> 0
[2,4,5,3,1] => [2,4,5,3,1] => [5,3,-2,-4,1] => [2,1]
=> 1
[2,5,1,3,4] => [2,5,1,3,4] => [-2,1,5,3,4] => [2]
=> 0
[3,1,2,5,4] => [3,1,2,5,4] => [3,1,2,-5,4] => [2]
=> 0
Description
The number of zeros of the symmetric group character corresponding to the partition. For example, the character values of the irreducible representation $S^{(2,2)}$ are $2$ on the conjugacy classes $(4)$ and $(2,2)$, $0$ on the conjugacy classes $(3,1)$ and $(1,1,1,1)$, and $-1$ on the conjugacy class $(2,1,1)$. Therefore, the statistic on the partition $(2,2)$ is $2$.
Matching statistic: St001754
Mp00087: Permutations inverse first fundamental transformationPermutations
Mp00160: Permutations graph of inversionsGraphs
Mp00266: Graphs connected vertex partitionsLattices
St001754: Lattices ⟶ ℤResult quality: 5% values known / values provided: 5%distinct values known / distinct values provided: 18%
Values
[2,1] => [2,1] => ([(0,1)],2)
=> ([(0,1)],2)
=> 2 = 0 + 2
[1,3,2] => [1,3,2] => ([(1,2)],3)
=> ([(0,1)],2)
=> 2 = 0 + 2
[2,1,3] => [2,1,3] => ([(1,2)],3)
=> ([(0,1)],2)
=> 2 = 0 + 2
[1,2,4,3] => [1,2,4,3] => ([(2,3)],4)
=> ([(0,1)],2)
=> 2 = 0 + 2
[1,3,2,4] => [1,3,2,4] => ([(2,3)],4)
=> ([(0,1)],2)
=> 2 = 0 + 2
[1,4,2,3] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[2,1,3,4] => [2,1,3,4] => ([(2,3)],4)
=> ([(0,1)],2)
=> 2 = 0 + 2
[2,1,4,3] => [2,1,4,3] => ([(0,3),(1,2)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4 = 2 + 2
[2,3,4,1] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 0 + 2
[2,4,1,3] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,11),(2,8),(2,9),(2,11),(3,6),(3,7),(3,11),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,12),(7,12),(8,12),(9,12),(10,12),(11,12)],13)
=> ? = 0 + 2
[2,4,3,1] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(6,11),(7,11),(8,11),(9,11),(10,11)],12)
=> ? = 1 + 2
[3,1,4,2] => [4,2,1,3] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? = 1 + 2
[3,2,4,1] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 1 + 2
[3,4,2,1] => [4,1,3,2] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? = 1 + 2
[4,1,3,2] => [3,4,2,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,11),(2,8),(2,9),(2,11),(3,6),(3,7),(3,11),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,12),(7,12),(8,12),(9,12),(10,12),(11,12)],13)
=> ? = 0 + 2
[4,2,1,3] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? = 1 + 2
[4,2,3,1] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 0 + 2
[4,3,1,2] => [4,2,3,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,11),(2,8),(2,9),(2,11),(3,6),(3,7),(3,11),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,12),(7,12),(8,12),(9,12),(10,12),(11,12)],13)
=> ? = 0 + 2
[4,3,2,1] => [3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? = 0 + 2
[1,2,3,5,4] => [1,2,3,5,4] => ([(3,4)],5)
=> ([(0,1)],2)
=> 2 = 0 + 2
[1,2,4,3,5] => [1,2,4,3,5] => ([(3,4)],5)
=> ([(0,1)],2)
=> 2 = 0 + 2
[1,2,5,3,4] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[1,3,2,4,5] => [1,3,2,4,5] => ([(3,4)],5)
=> ([(0,1)],2)
=> 2 = 0 + 2
[1,3,2,5,4] => [1,3,2,5,4] => ([(1,4),(2,3)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4 = 2 + 2
[1,3,4,5,2] => [1,5,2,3,4] => ([(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 0 + 2
[1,3,5,2,4] => [1,5,4,2,3] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,11),(2,8),(2,9),(2,11),(3,6),(3,7),(3,11),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,12),(7,12),(8,12),(9,12),(10,12),(11,12)],13)
=> ? = 0 + 2
[1,3,5,4,2] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(6,11),(7,11),(8,11),(9,11),(10,11)],12)
=> ? = 1 + 2
[1,4,2,3,5] => [1,4,3,2,5] => ([(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[1,4,2,5,3] => [1,5,3,2,4] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? = 1 + 2
[1,4,3,5,2] => [1,3,5,2,4] => ([(1,4),(2,3),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 1 + 2
[1,4,5,2,3] => [1,4,2,5,3] => ([(1,4),(2,3),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 0 + 2
[1,4,5,3,2] => [1,5,2,4,3] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? = 1 + 2
[1,5,3,2,4] => [1,3,5,4,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? = 1 + 2
[1,5,4,3,2] => [1,4,3,5,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? = 0 + 2
[2,1,3,4,5] => [2,1,3,4,5] => ([(3,4)],5)
=> ([(0,1)],2)
=> 2 = 0 + 2
[2,1,3,5,4] => [2,1,3,5,4] => ([(1,4),(2,3)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4 = 2 + 2
[2,1,4,3,5] => [2,1,4,3,5] => ([(1,4),(2,3)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4 = 2 + 2
[2,1,4,5,3] => [2,1,5,3,4] => ([(0,1),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 1 + 2
[2,1,5,4,3] => [2,1,4,5,3] => ([(0,1),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 0 + 2
[2,3,1,5,4] => [3,1,2,5,4] => ([(0,1),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 1 + 2
[2,3,4,1,5] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 0 + 2
[2,3,4,5,1] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? = 0 + 2
[2,4,1,3,5] => [4,3,1,2,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,11),(2,8),(2,9),(2,11),(3,6),(3,7),(3,11),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,12),(7,12),(8,12),(9,12),(10,12),(11,12)],13)
=> ? = 0 + 2
[2,4,1,5,3] => [5,3,1,2,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(1,20),(1,21),(2,9),(2,14),(2,15),(2,21),(3,8),(3,12),(3,13),(3,21),(4,11),(4,13),(4,15),(4,20),(5,10),(5,12),(5,14),(5,20),(6,7),(6,8),(6,9),(6,10),(6,11),(7,22),(7,23),(8,16),(8,17),(8,22),(9,18),(9,19),(9,22),(10,16),(10,18),(10,23),(11,17),(11,19),(11,23),(12,16),(12,24),(13,17),(13,24),(14,18),(14,24),(15,19),(15,24),(16,25),(17,25),(18,25),(19,25),(20,23),(20,24),(21,22),(21,24),(22,25),(23,25),(24,25)],26)
=> ? = 0 + 2
[2,4,3,1,5] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(6,11),(7,11),(8,11),(9,11),(10,11)],12)
=> ? = 1 + 2
[2,4,3,5,1] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,10),(1,11),(1,15),(2,7),(2,8),(2,11),(2,14),(3,6),(3,8),(3,10),(3,13),(4,6),(4,7),(4,9),(4,12),(5,12),(5,13),(5,14),(5,15),(6,18),(6,22),(7,16),(7,22),(8,17),(8,22),(9,19),(9,22),(10,20),(10,22),(11,21),(11,22),(12,16),(12,18),(12,19),(13,17),(13,18),(13,20),(14,16),(14,17),(14,21),(15,19),(15,20),(15,21),(16,23),(17,23),(18,23),(19,23),(20,23),(21,23),(22,23)],24)
=> ? = 0 + 2
[2,4,5,1,3] => [4,1,2,5,3] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? = 0 + 2
[2,4,5,3,1] => [5,1,2,4,3] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,16),(2,8),(2,11),(2,16),(3,7),(3,10),(3,16),(4,6),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(6,13),(6,14),(6,15),(7,13),(7,17),(8,14),(8,17),(9,15),(9,17),(10,13),(10,18),(11,14),(11,18),(12,15),(12,18),(13,19),(14,19),(15,19),(16,17),(16,18),(17,19),(18,19)],20)
=> ? = 1 + 2
[2,5,1,3,4] => [5,4,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,12),(1,15),(1,28),(1,31),(1,34),(2,11),(2,14),(2,28),(2,30),(2,33),(3,10),(3,13),(3,28),(3,29),(3,32),(4,10),(4,16),(4,19),(4,21),(4,30),(4,31),(5,11),(5,17),(5,20),(5,22),(5,29),(5,31),(6,12),(6,18),(6,23),(6,24),(6,29),(6,30),(7,13),(7,16),(7,20),(7,23),(7,33),(7,34),(8,14),(8,17),(8,19),(8,24),(8,32),(8,34),(9,15),(9,18),(9,21),(9,22),(9,32),(9,33),(10,25),(10,35),(10,45),(11,26),(11,36),(11,45),(12,27),(12,37),(12,45),(13,25),(13,38),(13,44),(14,26),(14,39),(14,44),(15,27),(15,40),(15,44),(16,25),(16,42),(16,43),(17,26),(17,41),(17,43),(18,27),(18,41),(18,42),(19,35),(19,39),(19,43),(20,36),(20,38),(20,43),(21,35),(21,40),(21,42),(22,36),(22,40),(22,41),(23,37),(23,38),(23,42),(24,37),(24,39),(24,41),(25,46),(26,46),(27,46),(28,44),(28,45),(29,38),(29,41),(29,45),(30,39),(30,42),(30,45),(31,40),(31,43),(31,45),(32,35),(32,41),(32,44),(33,36),(33,42),(33,44),(34,37),(34,43),(34,44),(35,46),(36,46),(37,46),(38,46),(39,46),(40,46),(41,46),(42,46),(43,46),(44,46),(45,46)],47)
=> ? = 0 + 2
[3,1,2,5,4] => [3,2,1,5,4] => ([(0,1),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? = 0 + 2
[3,1,4,2,5] => [4,2,1,3,5] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? = 1 + 2
[3,2,1,5,4] => [2,3,1,5,4] => ([(0,1),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 0 + 2
[3,2,4,1,5] => [2,4,1,3,5] => ([(1,4),(2,3),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 1 + 2
[3,4,2,1,5] => [4,1,3,2,5] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? = 1 + 2
[3,5,2,1,4] => [5,4,1,3,2] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(1,26),(1,27),(1,28),(2,9),(2,10),(2,11),(2,29),(2,30),(3,13),(3,17),(3,21),(3,28),(3,30),(4,12),(4,16),(4,21),(4,27),(4,29),(5,15),(5,18),(5,20),(5,27),(5,30),(6,14),(6,19),(6,20),(6,28),(6,29),(7,11),(7,16),(7,17),(7,18),(7,19),(7,26),(8,10),(8,12),(8,13),(8,14),(8,15),(8,26),(9,35),(9,38),(10,31),(10,32),(10,35),(11,33),(11,34),(11,35),(12,22),(12,31),(12,36),(13,22),(13,32),(13,37),(14,23),(14,31),(14,37),(15,23),(15,32),(15,36),(16,24),(16,33),(16,36),(17,24),(17,34),(17,37),(18,25),(18,34),(18,36),(19,25),(19,33),(19,37),(20,23),(20,25),(20,38),(21,22),(21,24),(21,38),(22,39),(23,39),(24,39),(25,39),(26,35),(26,36),(26,37),(27,36),(27,38),(28,37),(28,38),(29,31),(29,33),(29,38),(30,32),(30,34),(30,38),(31,39),(32,39),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
=> ? = 1 + 2
[3,5,2,4,1] => [4,5,1,3,2] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,9),(1,10),(1,28),(1,29),(2,12),(2,16),(2,20),(2,22),(2,29),(3,11),(3,15),(3,20),(3,21),(3,28),(4,13),(4,17),(4,19),(4,21),(4,29),(5,14),(5,18),(5,19),(5,22),(5,28),(6,8),(6,10),(6,15),(6,16),(6,17),(6,18),(7,8),(7,9),(7,11),(7,12),(7,13),(7,14),(8,27),(8,34),(8,35),(9,27),(9,30),(9,31),(10,27),(10,32),(10,33),(11,23),(11,30),(11,34),(12,24),(12,31),(12,34),(13,23),(13,31),(13,35),(14,24),(14,30),(14,35),(15,25),(15,32),(15,34),(16,26),(16,33),(16,34),(17,25),(17,33),(17,35),(18,26),(18,32),(18,35),(19,35),(19,36),(20,34),(20,36),(21,23),(21,25),(21,36),(22,24),(22,26),(22,36),(23,37),(24,37),(25,37),(26,37),(27,37),(28,30),(28,32),(28,36),(29,31),(29,33),(29,36),(30,37),(31,37),(32,37),(33,37),(34,37),(35,37),(36,37)],38)
=> ? = 2 + 2
[3,5,4,1,2] => [4,1,3,5,2] => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,16),(2,8),(2,11),(2,16),(3,7),(3,10),(3,16),(4,6),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(6,13),(6,14),(6,15),(7,13),(7,17),(8,14),(8,17),(9,15),(9,17),(10,13),(10,18),(11,14),(11,18),(12,15),(12,18),(13,19),(14,19),(15,19),(16,17),(16,18),(17,19),(18,19)],20)
=> ? = 0 + 2
[4,1,3,2,5] => [3,4,2,1,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,11),(2,8),(2,9),(2,11),(3,6),(3,7),(3,11),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,12),(7,12),(8,12),(9,12),(10,12),(11,12)],13)
=> ? = 0 + 2
[4,1,5,2,3] => [4,2,1,5,3] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,16),(2,8),(2,11),(2,16),(3,7),(3,10),(3,16),(4,6),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(6,13),(6,14),(6,15),(7,13),(7,17),(8,14),(8,17),(9,15),(9,17),(10,13),(10,18),(11,14),(11,18),(12,15),(12,18),(13,19),(14,19),(15,19),(16,17),(16,18),(17,19),(18,19)],20)
=> ? = 0 + 2
[4,2,1,3,5] => [2,4,3,1,5] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? = 1 + 2
[4,2,3,1,5] => [2,3,4,1,5] => ([(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 0 + 2
[4,2,5,1,3] => [2,4,1,5,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? = 1 + 2
[4,3,1,2,5] => [4,2,3,1,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,11),(2,8),(2,9),(2,11),(3,6),(3,7),(3,11),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,12),(7,12),(8,12),(9,12),(10,12),(11,12)],13)
=> ? = 0 + 2
[4,3,2,1,5] => [3,2,4,1,5] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? = 0 + 2
[4,3,5,1,2] => [4,1,5,2,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,10),(1,11),(1,15),(2,7),(2,8),(2,11),(2,14),(3,6),(3,8),(3,10),(3,13),(4,6),(4,7),(4,9),(4,12),(5,12),(5,13),(5,14),(5,15),(6,18),(6,22),(7,16),(7,22),(8,17),(8,22),(9,19),(9,22),(10,20),(10,22),(11,21),(11,22),(12,16),(12,18),(12,19),(13,17),(13,18),(13,20),(14,16),(14,17),(14,21),(15,19),(15,20),(15,21),(16,23),(17,23),(18,23),(19,23),(20,23),(21,23),(22,23)],24)
=> ? = 0 + 2
[4,3,5,2,1] => [5,1,4,2,3] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(1,20),(1,21),(2,9),(2,14),(2,15),(2,21),(3,8),(3,12),(3,13),(3,21),(4,11),(4,13),(4,15),(4,20),(5,10),(5,12),(5,14),(5,20),(6,7),(6,8),(6,9),(6,10),(6,11),(7,22),(7,23),(8,16),(8,17),(8,22),(9,18),(9,19),(9,22),(10,16),(10,18),(10,23),(11,17),(11,19),(11,23),(12,16),(12,24),(13,17),(13,24),(14,18),(14,24),(15,19),(15,24),(16,25),(17,25),(18,25),(19,25),(20,23),(20,24),(21,22),(21,24),(22,25),(23,25),(24,25)],26)
=> ? = 1 + 2
[4,5,3,1,2] => [3,4,1,5,2] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,10),(1,11),(1,15),(2,7),(2,8),(2,11),(2,14),(3,6),(3,8),(3,10),(3,13),(4,6),(4,7),(4,9),(4,12),(5,12),(5,13),(5,14),(5,15),(6,18),(6,22),(7,16),(7,22),(8,17),(8,22),(9,19),(9,22),(10,20),(10,22),(11,21),(11,22),(12,16),(12,18),(12,19),(13,17),(13,18),(13,20),(14,16),(14,17),(14,21),(15,19),(15,20),(15,21),(16,23),(17,23),(18,23),(19,23),(20,23),(21,23),(22,23)],24)
=> ? = 0 + 2
[1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(4,5)],6)
=> ([(0,1)],2)
=> 2 = 0 + 2
[1,2,3,5,4,6] => [1,2,3,5,4,6] => ([(4,5)],6)
=> ([(0,1)],2)
=> 2 = 0 + 2
[1,2,3,6,4,5] => [1,2,3,6,5,4] => ([(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[1,2,4,3,5,6] => [1,2,4,3,5,6] => ([(4,5)],6)
=> ([(0,1)],2)
=> 2 = 0 + 2
[1,2,4,3,6,5] => [1,2,4,3,6,5] => ([(2,5),(3,4)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4 = 2 + 2
[1,2,5,3,4,6] => [1,2,5,4,3,6] => ([(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[1,3,2,4,5,6] => [1,3,2,4,5,6] => ([(4,5)],6)
=> ([(0,1)],2)
=> 2 = 0 + 2
[1,3,2,4,6,5] => [1,3,2,4,6,5] => ([(2,5),(3,4)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4 = 2 + 2
[1,3,2,5,4,6] => [1,3,2,5,4,6] => ([(2,5),(3,4)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4 = 2 + 2
[1,4,2,3,5,6] => [1,4,3,2,5,6] => ([(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[2,1,3,4,5,6] => [2,1,3,4,5,6] => ([(4,5)],6)
=> ([(0,1)],2)
=> 2 = 0 + 2
[2,1,3,4,6,5] => [2,1,3,4,6,5] => ([(2,5),(3,4)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4 = 2 + 2
[2,1,3,5,4,6] => [2,1,3,5,4,6] => ([(2,5),(3,4)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4 = 2 + 2
[2,1,4,3,5,6] => [2,1,4,3,5,6] => ([(2,5),(3,4)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4 = 2 + 2
Description
The number of tolerances of a finite lattice. Let $L$ be a lattice. A tolerance $\tau$ is a reflexive and symmetric relation on $L$ which is compatible with meet and join. Equivalently, a tolerance of $L$ is the image of a congruence by a surjective lattice homomorphism onto $L$. The number of tolerances of a chain of $n$ elements is the Catalan number $\frac{1}{n+1}\binom{2n}{n}$, see [2].
Matching statistic: St001902
Mp00063: Permutations to alternating sign matrixAlternating sign matrices
Mp00001: Alternating sign matrices to semistandard tableau via monotone trianglesSemistandard tableaux
Mp00214: Semistandard tableaux subcrystalPosets
St001902: Posets ⟶ ℤResult quality: 5% values known / values provided: 5%distinct values known / distinct values provided: 18%
Values
[2,1] => [[0,1],[1,0]]
=> [[1,2],[2]]
=> ([(0,1)],2)
=> 0
[1,3,2] => [[1,0,0],[0,0,1],[0,1,0]]
=> [[1,1,1],[2,3],[3]]
=> ([(0,1)],2)
=> 0
[2,1,3] => [[0,1,0],[1,0,0],[0,0,1]]
=> [[1,1,2],[2,2],[3]]
=> ([(0,1)],2)
=> 0
[1,2,4,3] => [[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
=> [[1,1,1,1],[2,2,2],[3,4],[4]]
=> ([(0,1)],2)
=> 0
[1,3,2,4] => [[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,3],[3,3],[4]]
=> ([(0,1)],2)
=> 0
[1,4,2,3] => [[1,0,0,0],[0,0,1,0],[0,0,0,1],[0,1,0,0]]
=> [[1,1,1,1],[2,3,3],[3,4],[4]]
=> ([(0,3),(2,1),(3,2)],4)
=> 0
[2,1,3,4] => [[0,1,0,0],[1,0,0,0],[0,0,1,0],[0,0,0,1]]
=> [[1,1,1,2],[2,2,2],[3,3],[4]]
=> ([(0,1)],2)
=> 0
[2,1,4,3] => [[0,1,0,0],[1,0,0,0],[0,0,0,1],[0,0,1,0]]
=> [[1,1,1,2],[2,2,2],[3,4],[4]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[2,3,4,1] => [[0,0,0,1],[1,0,0,0],[0,1,0,0],[0,0,1,0]]
=> [[1,1,1,4],[2,2,4],[3,4],[4]]
=> ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
=> ? = 0
[2,4,1,3] => [[0,0,1,0],[1,0,0,0],[0,0,0,1],[0,1,0,0]]
=> [[1,1,1,3],[2,3,3],[3,4],[4]]
=> ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> ? = 0
[2,4,3,1] => [[0,0,0,1],[1,0,0,0],[0,0,1,0],[0,1,0,0]]
=> [[1,1,1,4],[2,3,4],[3,4],[4]]
=> ([(0,5),(0,10),(1,16),(2,15),(3,14),(4,13),(5,12),(6,2),(6,13),(7,4),(7,14),(8,1),(9,6),(10,11),(10,12),(11,3),(11,7),(12,9),(13,15),(14,8),(15,16)],17)
=> ? = 1
[3,1,4,2] => [[0,1,0,0],[0,0,0,1],[1,0,0,0],[0,0,1,0]]
=> [[1,1,2,2],[2,2,4],[3,4],[4]]
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 1
[3,2,4,1] => [[0,0,0,1],[0,1,0,0],[1,0,0,0],[0,0,1,0]]
=> [[1,1,2,4],[2,2,4],[3,4],[4]]
=> ([(0,7),(0,8),(1,12),(2,11),(3,10),(4,10),(4,11),(5,3),(6,1),(6,13),(7,9),(8,5),(9,2),(9,4),(10,14),(11,6),(11,14),(13,12),(14,13)],15)
=> ? = 1
[3,4,2,1] => [[0,0,0,1],[0,0,1,0],[1,0,0,0],[0,1,0,0]]
=> [[1,1,3,4],[2,3,4],[3,4],[4]]
=> ([(0,13),(0,15),(1,17),(2,16),(2,17),(3,19),(4,16),(4,18),(5,22),(6,21),(7,20),(8,23),(8,29),(9,4),(9,28),(10,3),(10,28),(11,6),(12,7),(12,24),(13,14),(14,1),(14,2),(15,9),(15,10),(16,25),(17,12),(17,25),(18,26),(18,29),(19,23),(19,26),(20,27),(22,27),(23,30),(24,20),(24,22),(25,24),(26,30),(27,21),(28,8),(28,18),(28,19),(29,5),(29,30),(30,11)],31)
=> ? = 1
[4,1,3,2] => [[0,1,0,0],[0,0,0,1],[0,0,1,0],[1,0,0,0]]
=> [[1,2,2,2],[2,3,4],[3,4],[4]]
=> ([(0,7),(0,8),(1,12),(2,11),(3,10),(4,10),(4,11),(5,3),(6,1),(6,13),(7,9),(8,5),(9,2),(9,4),(10,14),(11,6),(11,14),(13,12),(14,13)],15)
=> ? = 0
[4,2,1,3] => [[0,0,1,0],[0,1,0,0],[0,0,0,1],[1,0,0,0]]
=> [[1,2,2,3],[2,3,3],[3,4],[4]]
=> ([(0,5),(0,10),(1,16),(2,15),(3,14),(4,13),(5,12),(6,2),(6,13),(7,4),(7,14),(8,1),(9,6),(10,11),(10,12),(11,3),(11,7),(12,9),(13,15),(14,8),(15,16)],17)
=> ? = 1
[4,2,3,1] => [[0,0,0,1],[0,1,0,0],[0,0,1,0],[1,0,0,0]]
=> [[1,2,2,4],[2,3,4],[3,4],[4]]
=> ([(0,14),(0,15),(1,19),(2,18),(3,29),(4,30),(5,22),(6,23),(7,24),(7,25),(8,9),(9,7),(9,18),(9,19),(10,5),(11,6),(12,2),(12,29),(13,1),(13,30),(14,16),(14,28),(15,17),(15,28),(16,3),(16,12),(17,4),(17,13),(18,24),(18,27),(19,25),(19,27),(20,26),(21,26),(22,20),(23,21),(24,22),(24,31),(25,23),(25,31),(27,31),(28,8),(29,10),(30,11),(31,20),(31,21)],32)
=> ? = 0
[4,3,1,2] => [[0,0,1,0],[0,0,0,1],[0,1,0,0],[1,0,0,0]]
=> [[1,2,3,3],[2,3,4],[3,4],[4]]
=> ([(0,13),(0,15),(1,17),(2,16),(2,17),(3,19),(4,16),(4,18),(5,22),(6,21),(7,20),(8,23),(8,29),(9,4),(9,28),(10,3),(10,28),(11,6),(12,7),(12,24),(13,14),(14,1),(14,2),(15,9),(15,10),(16,25),(17,12),(17,25),(18,26),(18,29),(19,23),(19,26),(20,27),(22,27),(23,30),(24,20),(24,22),(25,24),(26,30),(27,21),(28,8),(28,18),(28,19),(29,5),(29,30),(30,11)],31)
=> ? = 0
[4,3,2,1] => [[0,0,0,1],[0,0,1,0],[0,1,0,0],[1,0,0,0]]
=> [[1,2,3,4],[2,3,4],[3,4],[4]]
=> ([(0,5),(0,16),(0,17),(1,23),(2,19),(3,11),(3,21),(4,10),(4,20),(5,12),(5,13),(6,50),(7,51),(8,24),(8,58),(9,25),(9,59),(10,14),(10,52),(11,15),(11,53),(12,26),(12,60),(13,27),(13,60),(14,54),(15,55),(16,4),(16,29),(17,3),(17,29),(18,48),(18,49),(19,32),(19,33),(20,46),(20,52),(21,47),(21,53),(22,34),(22,35),(23,18),(23,54),(23,55),(24,40),(24,42),(25,41),(25,43),(26,46),(26,56),(27,47),(27,57),(28,63),(29,1),(30,62),(31,61),(32,61),(33,61),(34,6),(34,62),(35,7),(35,62),(36,58),(37,59),(38,32),(39,33),(40,44),(41,45),(42,38),(43,39),(44,31),(45,31),(46,36),(47,37),(48,40),(48,63),(49,41),(49,63),(50,38),(51,39),(52,8),(52,36),(53,9),(53,37),(54,28),(54,48),(55,28),(55,49),(56,30),(56,34),(57,30),(57,35),(58,42),(58,50),(59,43),(59,51),(60,22),(60,56),(60,57),(62,2),(63,44),(63,45)],64)
=> ? = 0
[1,2,3,5,4] => [[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0]]
=> [[1,1,1,1,1],[2,2,2,2],[3,3,3],[4,5],[5]]
=> ([(0,1)],2)
=> 0
[1,2,4,3,5] => [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [[1,1,1,1,1],[2,2,2,2],[3,3,4],[4,4],[5]]
=> ([(0,1)],2)
=> 0
[1,2,5,3,4] => [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1],[0,0,1,0,0]]
=> [[1,1,1,1,1],[2,2,2,2],[3,4,4],[4,5],[5]]
=> ([(0,3),(2,1),(3,2)],4)
=> 0
[1,3,2,4,5] => [[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
=> [[1,1,1,1,1],[2,2,2,3],[3,3,3],[4,4],[5]]
=> ([(0,1)],2)
=> 0
[1,3,2,5,4] => [[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
=> [[1,1,1,1,1],[2,2,2,3],[3,3,3],[4,5],[5]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[1,3,4,5,2] => [[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0]]
=> [[1,1,1,1,1],[2,2,2,5],[3,3,5],[4,5],[5]]
=> ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
=> ? = 0
[1,3,5,2,4] => [[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,1,0,0]]
=> [[1,1,1,1,1],[2,2,2,4],[3,4,4],[4,5],[5]]
=> ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> ? = 0
[1,3,5,4,2] => [[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0]]
=> [[1,1,1,1,1],[2,2,2,5],[3,4,5],[4,5],[5]]
=> ([(0,5),(0,10),(1,16),(2,15),(3,14),(4,13),(5,12),(6,2),(6,13),(7,4),(7,14),(8,1),(9,6),(10,11),(10,12),(11,3),(11,7),(12,9),(13,15),(14,8),(15,16)],17)
=> ? = 1
[1,4,2,3,5] => [[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [[1,1,1,1,1],[2,2,3,3],[3,3,4],[4,4],[5]]
=> ([(0,3),(2,1),(3,2)],4)
=> 0
[1,4,2,5,3] => [[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,0,1,0]]
=> [[1,1,1,1,1],[2,2,3,3],[3,3,5],[4,5],[5]]
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 1
[1,4,3,5,2] => [[1,0,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0]]
=> [[1,1,1,1,1],[2,2,3,5],[3,3,5],[4,5],[5]]
=> ([(0,7),(0,8),(1,12),(2,11),(3,10),(4,10),(4,11),(5,3),(6,1),(6,13),(7,9),(8,5),(9,2),(9,4),(10,14),(11,6),(11,14),(13,12),(14,13)],15)
=> ? = 1
[1,4,5,2,3] => [[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0]]
=> [[1,1,1,1,1],[2,2,4,4],[3,4,5],[4,5],[5]]
=> ([(0,8),(2,11),(2,12),(3,10),(4,9),(5,4),(5,14),(6,3),(6,14),(7,1),(8,5),(8,6),(9,11),(9,13),(10,12),(10,13),(11,15),(12,15),(13,15),(14,2),(14,9),(14,10),(15,7)],16)
=> ? = 0
[1,4,5,3,2] => [[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0]]
=> [[1,1,1,1,1],[2,2,4,5],[3,4,5],[4,5],[5]]
=> ([(0,13),(0,15),(1,17),(2,16),(2,17),(3,19),(4,16),(4,18),(5,22),(6,21),(7,20),(8,23),(8,29),(9,4),(9,28),(10,3),(10,28),(11,6),(12,7),(12,24),(13,14),(14,1),(14,2),(15,9),(15,10),(16,25),(17,12),(17,25),(18,26),(18,29),(19,23),(19,26),(20,27),(22,27),(23,30),(24,20),(24,22),(25,24),(26,30),(27,21),(28,8),(28,18),(28,19),(29,5),(29,30),(30,11)],31)
=> ? = 1
[1,5,3,2,4] => [[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1],[0,1,0,0,0]]
=> [[1,1,1,1,1],[2,3,3,4],[3,4,4],[4,5],[5]]
=> ([(0,5),(0,10),(1,16),(2,15),(3,14),(4,13),(5,12),(6,2),(6,13),(7,4),(7,14),(8,1),(9,6),(10,11),(10,12),(11,3),(11,7),(12,9),(13,15),(14,8),(15,16)],17)
=> ? = 1
[1,5,4,3,2] => [[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0]]
=> [[1,1,1,1,1],[2,3,4,5],[3,4,5],[4,5],[5]]
=> ([(0,5),(0,16),(0,17),(1,23),(2,19),(3,11),(3,21),(4,10),(4,20),(5,12),(5,13),(6,50),(7,51),(8,24),(8,58),(9,25),(9,59),(10,14),(10,52),(11,15),(11,53),(12,26),(12,60),(13,27),(13,60),(14,54),(15,55),(16,4),(16,29),(17,3),(17,29),(18,48),(18,49),(19,32),(19,33),(20,46),(20,52),(21,47),(21,53),(22,34),(22,35),(23,18),(23,54),(23,55),(24,40),(24,42),(25,41),(25,43),(26,46),(26,56),(27,47),(27,57),(28,63),(29,1),(30,62),(31,61),(32,61),(33,61),(34,6),(34,62),(35,7),(35,62),(36,58),(37,59),(38,32),(39,33),(40,44),(41,45),(42,38),(43,39),(44,31),(45,31),(46,36),(47,37),(48,40),(48,63),(49,41),(49,63),(50,38),(51,39),(52,8),(52,36),(53,9),(53,37),(54,28),(54,48),(55,28),(55,49),(56,30),(56,34),(57,30),(57,35),(58,42),(58,50),(59,43),(59,51),(60,22),(60,56),(60,57),(62,2),(63,44),(63,45)],64)
=> ? = 0
[2,1,3,4,5] => [[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]]
=> [[1,1,1,1,2],[2,2,2,2],[3,3,3],[4,4],[5]]
=> ([(0,1)],2)
=> 0
[2,1,3,5,4] => [[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0]]
=> [[1,1,1,1,2],[2,2,2,2],[3,3,3],[4,5],[5]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[2,1,4,3,5] => [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [[1,1,1,1,2],[2,2,2,2],[3,3,4],[4,4],[5]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[2,1,4,5,3] => [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,0,0,1,0]]
=> [[1,1,1,1,2],[2,2,2,2],[3,3,5],[4,5],[5]]
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 1
[2,1,5,4,3] => [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0]]
=> [[1,1,1,1,2],[2,2,2,2],[3,4,5],[4,5],[5]]
=> ([(0,3),(0,6),(0,7),(1,8),(1,12),(2,8),(2,11),(3,9),(3,10),(4,2),(4,13),(5,1),(5,14),(6,4),(6,9),(7,5),(7,10),(8,15),(9,13),(10,14),(11,15),(12,15),(13,11),(14,12)],16)
=> ? = 0
[2,3,1,5,4] => [[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
=> [[1,1,1,1,3],[2,2,2,3],[3,3,3],[4,5],[5]]
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 1
[2,3,4,1,5] => [[0,0,0,1,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [[1,1,1,1,4],[2,2,2,4],[3,3,4],[4,4],[5]]
=> ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
=> ? = 0
[2,3,4,5,1] => [[0,0,0,0,1],[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0]]
=> [[1,1,1,1,5],[2,2,2,5],[3,3,5],[4,5],[5]]
=> ([(0,9),(1,13),(2,14),(4,12),(5,11),(6,1),(6,12),(7,3),(8,5),(8,15),(9,10),(10,4),(10,6),(11,14),(12,8),(12,13),(13,15),(14,7),(15,2),(15,11)],16)
=> ? = 0
[2,4,1,3,5] => [[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [[1,1,1,1,3],[2,2,3,3],[3,3,4],[4,4],[5]]
=> ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> ? = 0
[2,4,1,5,3] => [[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,0,1,0]]
=> [[1,1,1,1,3],[2,2,3,3],[3,3,5],[4,5],[5]]
=> ([(0,6),(0,7),(1,5),(1,15),(2,4),(2,14),(3,13),(4,12),(5,3),(5,16),(6,9),(7,2),(7,9),(9,1),(9,14),(10,11),(11,8),(12,10),(13,8),(14,12),(14,15),(15,10),(15,16),(16,11),(16,13)],17)
=> ? = 0
[2,4,3,1,5] => [[0,0,0,1,0],[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [[1,1,1,1,4],[2,2,3,4],[3,3,4],[4,4],[5]]
=> ([(0,5),(0,10),(1,16),(2,15),(3,14),(4,13),(5,12),(6,2),(6,13),(7,4),(7,14),(8,1),(9,6),(10,11),(10,12),(11,3),(11,7),(12,9),(13,15),(14,8),(15,16)],17)
=> ? = 1
[2,4,3,5,1] => [[0,0,0,0,1],[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0]]
=> [[1,1,1,1,5],[2,2,3,5],[3,3,5],[4,5],[5]]
=> ([(0,8),(0,13),(1,19),(2,16),(2,18),(3,21),(4,26),(5,24),(6,16),(6,22),(7,20),(7,23),(8,17),(9,4),(9,18),(10,9),(11,7),(11,30),(12,3),(12,25),(13,14),(13,17),(14,1),(14,15),(15,2),(15,6),(15,19),(16,28),(17,10),(18,26),(18,28),(19,11),(19,22),(20,24),(20,31),(22,30),(23,31),(24,12),(24,27),(25,21),(26,23),(26,29),(27,25),(28,29),(29,31),(30,5),(30,20),(31,27)],32)
=> ? = 0
[2,4,5,1,3] => [[0,0,0,1,0],[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0]]
=> [[1,1,1,1,4],[2,2,4,4],[3,4,5],[4,5],[5]]
=> ([(0,9),(0,10),(1,2),(3,7),(3,23),(4,6),(4,22),(5,15),(6,16),(7,8),(7,24),(8,20),(9,19),(10,4),(10,19),(11,14),(11,18),(12,26),(13,26),(14,25),(15,1),(16,21),(17,13),(17,25),(18,12),(18,25),(19,3),(19,22),(20,12),(20,13),(21,14),(21,17),(22,16),(22,23),(23,11),(23,21),(23,24),(24,17),(24,18),(24,20),(25,5),(25,26),(26,15)],27)
=> ? = 0
[2,4,5,3,1] => [[0,0,0,0,1],[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0]]
=> [[1,1,1,1,5],[2,2,4,5],[3,4,5],[4,5],[5]]
=> ([(0,17),(0,18),(1,11),(1,12),(2,53),(3,50),(4,33),(5,16),(5,65),(6,13),(6,61),(7,14),(7,62),(8,15),(8,51),(9,25),(9,63),(10,24),(10,52),(11,54),(12,22),(12,23),(12,54),(13,36),(14,35),(15,40),(16,59),(17,1),(17,48),(18,7),(18,48),(19,32),(19,45),(20,29),(20,38),(21,55),(21,58),(22,49),(22,60),(23,42),(23,49),(24,31),(24,46),(25,21),(25,60),(25,64),(27,70),(28,70),(29,67),(30,66),(31,68),(32,3),(32,69),(33,8),(34,39),(35,57),(36,39),(37,32),(37,66),(38,19),(38,37),(38,67),(39,26),(40,26),(41,30),(41,67),(42,52),(43,44),(43,68),(44,28),(44,69),(45,27),(45,69),(46,53),(46,68),(47,61),(48,9),(48,62),(49,5),(49,56),(50,34),(51,40),(52,2),(52,46),(53,6),(53,47),(54,10),(54,42),(55,31),(55,43),(56,43),(56,65),(57,29),(57,41),(58,30),(58,37),(59,27),(59,28),(60,55),(60,56),(61,34),(61,36),(62,35),(62,63),(63,20),(63,57),(63,64),(64,38),(64,41),(64,58),(65,44),(65,45),(65,59),(66,33),(67,4),(67,66),(68,47),(69,50),(69,70),(70,51)],71)
=> ? = 1
[2,5,1,3,4] => [[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1],[0,1,0,0,0]]
=> [[1,1,1,1,3],[2,3,3,3],[3,4,4],[4,5],[5]]
=> ([(0,4),(0,8),(1,11),(3,10),(4,9),(5,2),(6,3),(6,12),(7,5),(8,6),(8,9),(9,12),(10,11),(11,7),(12,1),(12,10)],13)
=> ? = 0
[3,1,2,5,4] => [[0,1,0,0,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
=> [[1,1,1,2,2],[2,2,2,3],[3,3,3],[4,5],[5]]
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 0
[3,1,4,2,5] => [[0,1,0,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [[1,1,1,2,2],[2,2,2,4],[3,3,4],[4,4],[5]]
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 1
[3,2,1,5,4] => [[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
=> [[1,1,1,2,3],[2,2,2,3],[3,3,3],[4,5],[5]]
=> ([(0,3),(0,6),(0,7),(1,8),(1,12),(2,8),(2,11),(3,9),(3,10),(4,2),(4,13),(5,1),(5,14),(6,4),(6,9),(7,5),(7,10),(8,15),(9,13),(10,14),(11,15),(12,15),(13,11),(14,12)],16)
=> ? = 0
[3,2,4,1,5] => [[0,0,0,1,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [[1,1,1,2,4],[2,2,2,4],[3,3,4],[4,4],[5]]
=> ([(0,7),(0,8),(1,12),(2,11),(3,10),(4,10),(4,11),(5,3),(6,1),(6,13),(7,9),(8,5),(9,2),(9,4),(10,14),(11,6),(11,14),(13,12),(14,13)],15)
=> ? = 1
[3,4,2,1,5] => [[0,0,0,1,0],[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [[1,1,1,3,4],[2,2,3,4],[3,3,4],[4,4],[5]]
=> ([(0,13),(0,15),(1,17),(2,16),(2,17),(3,19),(4,16),(4,18),(5,22),(6,21),(7,20),(8,23),(8,29),(9,4),(9,28),(10,3),(10,28),(11,6),(12,7),(12,24),(13,14),(14,1),(14,2),(15,9),(15,10),(16,25),(17,12),(17,25),(18,26),(18,29),(19,23),(19,26),(20,27),(22,27),(23,30),(24,20),(24,22),(25,24),(26,30),(27,21),(28,8),(28,18),(28,19),(29,5),(29,30),(30,11)],31)
=> ? = 1
[3,5,2,1,4] => [[0,0,0,1,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0]]
=> [[1,1,1,3,4],[2,3,3,4],[3,4,4],[4,5],[5]]
=> ([(0,15),(0,16),(0,20),(1,9),(2,13),(2,47),(3,38),(4,14),(4,46),(5,40),(6,10),(6,26),(7,18),(7,45),(8,19),(8,39),(9,25),(10,32),(11,31),(12,44),(13,12),(13,48),(14,11),(14,42),(15,8),(15,28),(16,7),(16,37),(17,24),(17,33),(18,21),(18,36),(19,21),(19,35),(20,28),(20,37),(21,51),(22,49),(23,49),(24,3),(24,50),(26,1),(27,25),(28,39),(29,46),(30,27),(31,30),(32,27),(33,23),(33,50),(34,22),(34,50),(35,40),(35,51),(36,41),(36,51),(37,2),(37,45),(38,43),(39,5),(39,35),(40,4),(40,29),(41,24),(41,34),(42,31),(42,43),(43,30),(43,32),(44,22),(44,23),(45,36),(45,47),(46,38),(46,42),(47,17),(47,41),(47,48),(48,33),(48,34),(48,44),(49,26),(50,6),(50,49),(51,29)],52)
=> ? = 1
[3,5,2,4,1] => [[0,0,0,0,1],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0]]
=> [[1,1,1,3,5],[2,3,3,5],[3,4,5],[4,5],[5]]
=> ([(0,16),(0,17),(0,28),(1,9),(2,70),(3,13),(3,85),(4,27),(4,69),(5,83),(6,15),(6,43),(7,26),(7,84),(8,12),(8,29),(8,71),(9,68),(10,77),(11,76),(12,14),(12,78),(13,10),(13,86),(14,11),(14,87),(15,75),(16,8),(16,48),(17,7),(17,67),(18,42),(18,61),(19,25),(19,62),(19,63),(20,22),(20,59),(20,79),(21,24),(21,41),(21,60),(22,23),(22,80),(22,81),(23,64),(23,66),(24,37),(24,65),(25,36),(25,46),(26,50),(26,58),(27,31),(27,32),(28,48),(28,67),(29,57),(29,58),(29,78),(31,103),(32,103),(33,89),(34,89),(35,90),(36,88),(37,92),(38,102),(39,93),(40,101),(41,4),(41,100),(42,5),(42,97),(43,1),(44,53),(45,51),(45,95),(46,41),(46,88),(47,54),(48,71),(49,79),(50,73),(50,98),(51,68),(51,102),(52,31),(52,96),(53,30),(54,30),(55,33),(55,97),(56,35),(56,99),(57,70),(57,98),(58,74),(58,98),(59,81),(59,90),(60,37),(60,100),(61,34),(61,97),(62,36),(62,99),(63,21),(63,46),(63,99),(64,52),(64,91),(65,52),(65,92),(66,45),(66,91),(67,3),(67,84),(68,47),(69,32),(70,20),(70,49),(71,2),(71,57),(72,53),(72,54),(73,42),(73,55),(74,56),(74,62),(75,38),(75,51),(76,35),(76,59),(77,33),(77,34),(78,19),(78,74),(78,87),(79,80),(79,83),(79,90),(80,66),(80,82),(80,94),(81,64),(81,65),(81,94),(82,45),(82,75),(82,93),(83,39),(83,82),(84,50),(84,85),(85,18),(85,73),(85,86),(86,55),(86,61),(86,77),(87,56),(87,63),(87,76),(88,100),(89,43),(90,39),(90,94),(91,95),(91,96),(92,40),(92,96),(93,38),(93,40),(93,95),(94,91),(94,92),(94,93),(95,101),(95,102),(96,101),(96,103),(97,6),(97,89),(98,49),(99,60),(99,88),(100,69),(101,44),(101,72),(102,47),(102,72),(103,44)],104)
=> ? = 2
[3,5,4,1,2] => [[0,0,0,1,0],[0,0,0,0,1],[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0]]
=> [[1,1,1,4,4],[2,3,4,5],[3,4,5],[4,5],[5]]
=> ([(0,12),(0,13),(1,6),(2,61),(3,5),(3,94),(4,81),(5,80),(6,32),(7,4),(7,95),(8,22),(8,87),(9,20),(9,85),(10,19),(10,92),(11,17),(11,18),(11,98),(12,51),(13,11),(13,21),(13,51),(14,46),(14,47),(15,42),(15,89),(16,73),(16,75),(17,27),(17,48),(17,97),(18,48),(18,90),(19,43),(19,91),(20,44),(20,76),(21,25),(21,88),(21,98),(22,26),(22,74),(22,96),(23,24),(23,45),(23,77),(24,66),(24,67),(25,53),(25,93),(26,68),(26,84),(27,74),(27,78),(28,37),(28,60),(28,72),(29,124),(30,124),(31,101),(31,123),(33,117),(33,125),(34,118),(35,99),(36,116),(36,128),(37,101),(37,121),(38,109),(38,125),(39,100),(39,103),(40,109),(40,129),(41,126),(42,119),(43,107),(44,113),(45,9),(45,106),(46,108),(47,2),(47,108),(48,10),(48,122),(49,65),(49,128),(50,64),(51,8),(51,88),(52,39),(52,121),(52,123),(53,79),(54,45),(54,100),(55,32),(56,29),(56,127),(57,30),(57,127),(58,35),(58,120),(59,34),(59,99),(60,63),(60,101),(61,55),(62,56),(62,104),(63,83),(63,111),(64,57),(64,104),(65,44),(65,114),(66,58),(66,110),(67,65),(67,110),(68,43),(68,115),(69,34),(69,105),(70,36),(70,112),(71,33),(71,103),(71,119),(72,23),(72,54),(72,121),(73,50),(74,68),(74,102),(75,3),(75,82),(76,64),(76,113),(77,66),(77,106),(78,39),(78,54),(78,102),(79,42),(79,71),(80,29),(80,30),(81,35),(81,59),(82,62),(82,94),(83,49),(83,67),(83,112),(84,33),(84,38),(84,115),(85,50),(85,76),(86,59),(86,69),(86,120),(87,15),(87,79),(87,96),(88,53),(88,87),(89,38),(89,40),(89,119),(90,31),(90,60),(90,122),(91,36),(91,49),(91,107),(92,70),(92,83),(92,91),(93,31),(93,37),(93,52),(94,56),(94,57),(94,80),(95,58),(95,81),(95,86),(96,71),(96,84),(96,89),(96,102),(97,52),(97,72),(97,78),(97,122),(98,28),(98,90),(98,93),(98,97),(99,46),(99,118),(100,106),(101,7),(101,111),(102,40),(102,103),(102,115),(103,117),(103,129),(104,127),(105,47),(105,118),(106,85),(107,41),(107,116),(108,1),(109,41),(109,130),(110,114),(110,120),(111,95),(111,112),(112,86),(112,110),(112,128),(113,104),(114,105),(114,113),(115,107),(115,109),(115,117),(116,126),(117,116),(117,130),(118,108),(119,16),(119,125),(119,129),(120,14),(120,99),(120,105),(121,77),(121,100),(122,63),(122,92),(122,123),(123,70),(123,111),(124,55),(125,75),(125,130),(126,62),(127,61),(127,124),(128,69),(128,114),(129,73),(129,130),(130,82),(130,126)],131)
=> ? = 0
[4,1,3,2,5] => [[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1]]
=> [[1,1,2,2,2],[2,2,3,4],[3,3,4],[4,4],[5]]
=> ([(0,7),(0,8),(1,12),(2,11),(3,10),(4,10),(4,11),(5,3),(6,1),(6,13),(7,9),(8,5),(9,2),(9,4),(10,14),(11,6),(11,14),(13,12),(14,13)],15)
=> ? = 0
[4,1,5,2,3] => [[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1],[1,0,0,0,0],[0,0,1,0,0]]
=> [[1,1,2,2,2],[2,2,4,4],[3,4,5],[4,5],[5]]
=> ([(0,1),(1,4),(1,5),(2,8),(2,32),(3,6),(3,30),(4,7),(4,33),(5,10),(5,11),(5,33),(6,20),(7,31),(8,27),(9,15),(9,19),(10,18),(10,28),(11,18),(11,25),(13,39),(14,36),(14,39),(15,36),(16,38),(17,38),(18,2),(18,37),(19,26),(19,36),(20,21),(21,12),(22,12),(23,17),(23,35),(24,16),(24,35),(25,13),(25,37),(26,24),(26,34),(27,16),(27,17),(28,14),(28,19),(28,37),(29,21),(29,22),(30,20),(30,29),(31,13),(31,14),(31,15),(32,23),(32,24),(32,27),(33,9),(33,25),(33,28),(33,31),(34,30),(34,35),(35,29),(35,38),(36,3),(36,34),(37,26),(37,32),(37,39),(38,22),(39,23),(39,34)],40)
=> ? = 0
[4,2,1,3,5] => [[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,0,0,0,1]]
=> [[1,1,2,2,3],[2,2,3,3],[3,3,4],[4,4],[5]]
=> ([(0,5),(0,10),(1,16),(2,15),(3,14),(4,13),(5,12),(6,2),(6,13),(7,4),(7,14),(8,1),(9,6),(10,11),(10,12),(11,3),(11,7),(12,9),(13,15),(14,8),(15,16)],17)
=> ? = 1
[4,2,3,1,5] => [[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1]]
=> [[1,1,2,2,4],[2,2,3,4],[3,3,4],[4,4],[5]]
=> ([(0,14),(0,15),(1,19),(2,18),(3,29),(4,30),(5,22),(6,23),(7,24),(7,25),(8,9),(9,7),(9,18),(9,19),(10,5),(11,6),(12,2),(12,29),(13,1),(13,30),(14,16),(14,28),(15,17),(15,28),(16,3),(16,12),(17,4),(17,13),(18,24),(18,27),(19,25),(19,27),(20,26),(21,26),(22,20),(23,21),(24,22),(24,31),(25,23),(25,31),(27,31),(28,8),(29,10),(30,11),(31,20),(31,21)],32)
=> ? = 0
[4,2,5,1,3] => [[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1],[1,0,0,0,0],[0,0,1,0,0]]
=> [[1,1,2,2,4],[2,2,4,4],[3,4,5],[4,5],[5]]
=> ([(0,7),(0,8),(1,2),(1,45),(2,35),(3,37),(4,14),(4,49),(5,9),(5,48),(6,10),(6,12),(6,54),(7,31),(8,6),(8,13),(8,31),(9,27),(9,42),(10,28),(10,41),(11,26),(11,52),(12,17),(12,28),(12,51),(13,15),(13,50),(13,54),(14,16),(14,40),(14,53),(15,33),(15,44),(16,38),(16,47),(17,30),(17,40),(19,64),(19,66),(20,62),(21,65),(22,58),(23,60),(23,66),(24,60),(24,63),(25,67),(26,55),(27,59),(28,5),(28,56),(29,34),(30,22),(30,57),(31,4),(31,50),(32,22),(32,65),(33,43),(34,18),(35,18),(36,20),(37,1),(37,46),(38,27),(38,61),(39,19),(39,55),(39,58),(40,38),(40,57),(41,21),(41,56),(42,20),(42,59),(43,26),(43,39),(44,21),(44,32),(45,34),(45,35),(46,29),(46,45),(47,19),(47,23),(47,61),(48,36),(48,42),(49,11),(49,43),(49,53),(50,33),(50,49),(51,30),(51,32),(51,56),(52,23),(52,24),(52,55),(53,39),(53,47),(53,52),(53,57),(54,41),(54,44),(54,51),(55,3),(55,63),(55,66),(56,48),(56,65),(57,24),(57,58),(57,61),(58,63),(58,64),(59,25),(59,62),(60,25),(60,68),(61,59),(61,60),(61,64),(62,67),(63,68),(64,62),(64,68),(65,36),(66,37),(66,68),(67,29),(68,46),(68,67)],69)
=> ? = 1
[4,3,1,2,5] => [[0,0,1,0,0],[0,0,0,1,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1]]
=> [[1,1,2,3,3],[2,2,3,4],[3,3,4],[4,4],[5]]
=> ([(0,13),(0,15),(1,17),(2,16),(2,17),(3,19),(4,16),(4,18),(5,22),(6,21),(7,20),(8,23),(8,29),(9,4),(9,28),(10,3),(10,28),(11,6),(12,7),(12,24),(13,14),(14,1),(14,2),(15,9),(15,10),(16,25),(17,12),(17,25),(18,26),(18,29),(19,23),(19,26),(20,27),(22,27),(23,30),(24,20),(24,22),(25,24),(26,30),(27,21),(28,8),(28,18),(28,19),(29,5),(29,30),(30,11)],31)
=> ? = 0
[4,3,2,1,5] => [[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1]]
=> [[1,1,2,3,4],[2,2,3,4],[3,3,4],[4,4],[5]]
=> ([(0,5),(0,16),(0,17),(1,23),(2,19),(3,11),(3,21),(4,10),(4,20),(5,12),(5,13),(6,50),(7,51),(8,24),(8,58),(9,25),(9,59),(10,14),(10,52),(11,15),(11,53),(12,26),(12,60),(13,27),(13,60),(14,54),(15,55),(16,4),(16,29),(17,3),(17,29),(18,48),(18,49),(19,32),(19,33),(20,46),(20,52),(21,47),(21,53),(22,34),(22,35),(23,18),(23,54),(23,55),(24,40),(24,42),(25,41),(25,43),(26,46),(26,56),(27,47),(27,57),(28,63),(29,1),(30,62),(31,61),(32,61),(33,61),(34,6),(34,62),(35,7),(35,62),(36,58),(37,59),(38,32),(39,33),(40,44),(41,45),(42,38),(43,39),(44,31),(45,31),(46,36),(47,37),(48,40),(48,63),(49,41),(49,63),(50,38),(51,39),(52,8),(52,36),(53,9),(53,37),(54,28),(54,48),(55,28),(55,49),(56,30),(56,34),(57,30),(57,35),(58,42),(58,50),(59,43),(59,51),(60,22),(60,56),(60,57),(62,2),(63,44),(63,45)],64)
=> ? = 0
[4,3,5,1,2] => [[0,0,0,1,0],[0,0,0,0,1],[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0]]
=> [[1,1,2,4,4],[2,2,4,5],[3,4,5],[4,5],[5]]
=> ([(0,2),(0,3),(1,8),(1,16),(2,1),(3,7),(3,10),(4,13),(4,59),(5,12),(5,81),(6,20),(6,82),(7,11),(7,83),(8,60),(9,23),(9,58),(10,19),(10,22),(10,83),(11,78),(12,64),(13,24),(14,52),(14,72),(15,17),(15,73),(15,80),(16,60),(16,74),(17,39),(17,70),(18,36),(18,44),(19,51),(19,69),(20,33),(20,75),(21,28),(21,38),(21,50),(22,51),(22,71),(22,74),(23,49),(23,56),(23,57),(25,101),(26,113),(27,107),(27,110),(28,107),(28,111),(29,110),(29,111),(30,112),(31,90),(31,98),(32,94),(32,114),(33,96),(34,91),(34,92),(35,89),(35,92),(36,108),(37,94),(37,103),(38,9),(38,111),(39,45),(40,31),(40,102),(40,114),(41,31),(41,104),(42,37),(42,99),(43,34),(43,85),(43,87),(44,30),(44,108),(45,55),(46,33),(46,86),(47,48),(47,86),(48,25),(48,100),(49,42),(49,85),(50,14),(50,76),(50,107),(51,15),(51,61),(51,84),(52,46),(52,109),(53,32),(53,93),(54,26),(54,95),(55,25),(55,91),(56,35),(56,85),(56,97),(57,53),(57,97),(58,57),(59,24),(60,5),(60,63),(61,67),(61,73),(62,34),(62,35),(62,113),(63,67),(63,81),(64,46),(64,47),(65,45),(65,68),(66,47),(66,68),(66,109),(67,65),(67,66),(68,48),(68,55),(68,87),(69,29),(69,38),(69,84),(70,26),(70,62),(71,27),(71,50),(71,84),(72,43),(72,49),(72,109),(73,39),(73,65),(74,61),(74,63),(75,32),(75,40),(75,96),(76,72),(76,79),(76,88),(77,40),(77,41),(77,93),(78,27),(78,28),(78,29),(79,43),(79,56),(79,62),(79,95),(80,54),(80,70),(80,79),(81,52),(81,64),(81,66),(82,53),(82,75),(82,77),(83,21),(83,69),(83,71),(83,78),(84,76),(84,80),(84,110),(85,92),(85,99),(86,37),(86,96),(86,100),(87,91),(87,99),(87,100),(88,82),(88,95),(89,104),(90,108),(90,116),(91,101),(91,106),(92,106),(93,18),(93,104),(93,114),(94,115),(95,77),(95,97),(95,113),(96,94),(96,102),(97,89),(97,93),(98,116),(99,103),(99,106),(100,101),(100,102),(100,103),(101,98),(101,105),(102,98),(102,115),(103,105),(103,115),(104,36),(104,90),(105,116),(106,105),(107,6),(107,88),(108,4),(108,112),(109,42),(109,86),(109,87),(110,54),(110,88),(111,58),(112,59),(113,41),(113,89),(114,44),(114,90),(114,115),(115,30),(115,116),(116,112)],117)
=> ? = 0
[4,3,5,2,1] => [[0,0,0,0,1],[0,0,0,1,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0]]
=> [[1,1,2,4,5],[2,2,4,5],[3,4,5],[4,5],[5]]
=> ([(0,4),(0,15),(0,16),(1,34),(2,7),(2,32),(3,14),(3,33),(4,11),(4,12),(5,147),(6,38),(6,125),(7,5),(7,114),(8,39),(8,161),(9,30),(9,158),(10,31),(10,96),(11,29),(11,159),(12,28),(12,41),(12,159),(13,24),(13,75),(14,20),(14,21),(14,156),(15,2),(15,54),(16,3),(16,54),(17,68),(17,119),(18,115),(18,120),(19,113),(19,149),(20,122),(20,154),(21,122),(21,164),(22,111),(22,145),(23,67),(23,116),(24,65),(24,66),(25,42),(25,117),(25,148),(26,37),(26,152),(26,163),(27,35),(27,150),(27,155),(28,118),(28,153),(29,121),(29,162),(30,110),(30,146),(31,109),(31,112),(32,114),(32,151),(33,121),(33,156),(34,36),(34,147),(34,164),(35,79),(35,81),(36,84),(36,134),(37,80),(37,137),(38,95),(38,106),(38,107),(39,58),(39,94),(39,139),(40,52),(40,64),(40,108),(41,118),(41,132),(41,151),(42,76),(42,77),(42,78),(43,211),(44,202),(45,173),(45,214),(46,168),(47,167),(47,168),(48,217),(49,212),(49,215),(50,174),(50,215),(51,218),(52,6),(52,212),(53,10),(54,1),(55,176),(56,176),(56,211),(57,192),(57,203),(58,173),(58,186),(59,177),(59,187),(60,175),(60,177),(61,214),(62,193),(63,182),(63,200),(64,22),(64,174),(64,212),(65,181),(66,181),(67,180),(68,179),(69,96),(70,57),(70,199),(70,213),(71,60),(71,169),(71,171),(72,100),(72,206),(73,58),(73,172),(74,66),(74,197),(75,65),(76,83),(76,170),(77,91),(77,167),(78,120),(78,167),(78,170),(79,88),(80,87),(81,136),(82,67),(82,216),(83,94),(83,208),(84,110),(84,210),(85,69),(85,208),(86,63),(86,198),(87,105),(88,55),(89,93),(89,172),(90,46),(90,210),(91,45),(91,196),(92,43),(92,209),(93,44),(93,195),(94,101),(94,173),(95,86),(95,169),(96,112),(97,102),(97,166),(97,188),(98,103),(98,188),(99,57),(99,191),(100,109),(100,182),(100,213),(101,97),(101,184),(102,56),(102,183),(102,209),(103,55),(103,183),(104,48),(104,185),(105,44),(105,175),(106,59),(106,169),(106,190),(107,72),(107,190),(108,19),(108,144),(108,174),(109,62),(109,166),(110,135),(111,53),(112,92),(112,166),(113,73),(113,207),(114,9),(114,126),(115,69),(115,178),(116,74),(116,180),(117,18),(117,78),(117,218),(118,26),(118,123),(118,165),(119,23),(119,82),(119,179),(120,27),(120,140),(120,178),(121,133),(122,138),(123,130),(123,152),(124,88),(124,103),(125,53),(125,107),(126,130),(126,158),(127,59),(127,60),(127,217),(128,87),(128,131),(129,89),(129,131),(129,207),(130,128),(130,129),(131,93),(131,105),(131,171),(132,50),(132,108),(132,165),(133,51),(133,148),(134,47),(134,77),(134,210),(135,45),(135,61),(136,43),(136,56),(137,48),(137,127),(138,46),(138,47),(139,70),(139,100),(139,186),(140,143),(140,150),(141,70),(141,99),(141,206),(142,97),(142,157),(143,98),(143,124),(144,149),(144,160),(144,189),(145,83),(145,85),(146,73),(146,89),(147,84),(147,90),(148,76),(148,145),(148,218),(149,71),(149,95),(149,207),(150,79),(150,124),(151,123),(151,126),(152,80),(152,128),(153,49),(153,52),(153,165),(154,51),(154,117),(155,81),(155,157),(156,25),(156,133),(156,154),(157,92),(157,102),(157,136),(158,113),(158,129),(158,146),(159,40),(159,132),(159,153),(159,162),(160,71),(160,106),(160,127),(160,185),(161,72),(161,139),(161,141),(162,49),(162,50),(162,64),(163,104),(163,137),(163,160),(164,90),(164,134),(164,138),(165,144),(165,163),(165,215),(166,193),(166,209),(167,140),(167,196),(168,61),(168,196),(169,177),(169,198),(170,178),(170,208),(171,175),(171,195),(171,198),(172,63),(172,186),(172,195),(173,184),(174,8),(174,189),(175,202),(175,204),(176,194),(177,204),(178,142),(178,155),(179,13),(179,216),(180,197),(182,62),(182,220),(183,176),(183,201),(184,188),(185,141),(185,190),(185,217),(186,182),(186,199),(187,191),(188,183),(188,193),(189,161),(189,185),(190,187),(190,206),(191,68),(191,192),(192,179),(192,219),(193,201),(194,197),(195,199),(195,200),(195,202),(196,143),(196,214),(197,181),(198,200),(198,204),(199,203),(199,220),(200,205),(200,220),(201,180),(201,194),(202,203),(202,205),(203,219),(204,205),(205,219),(206,17),(206,191),(206,213),(207,86),(207,171),(207,172),(208,101),(208,142),(209,116),(209,201),(209,211),(210,91),(210,135),(210,168),(211,74),(211,194),(212,111),(212,125),(213,119),(213,192),(213,220),(214,98),(214,184),(215,104),(215,189),(216,75),(217,99),(217,187),(218,85),(218,115),(218,170),(219,216),(220,82),(220,219)],221)
=> ? = 1
[4,5,3,1,2] => [[0,0,0,1,0],[0,0,0,0,1],[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0]]
=> [[1,1,3,4,4],[2,3,4,5],[3,4,5],[4,5],[5]]
=> ([(0,1),(0,2),(1,12),(1,14),(2,11),(2,13),(3,145),(4,146),(5,31),(5,155),(6,32),(6,156),(7,15),(7,143),(8,16),(8,144),(9,37),(9,114),(10,38),(10,115),(11,17),(11,157),(12,18),(12,158),(13,29),(13,35),(13,157),(14,30),(14,36),(14,158),(15,84),(16,85),(17,147),(18,148),(19,102),(19,133),(20,103),(20,134),(21,23),(21,149),(21,153),(22,24),(22,150),(22,154),(23,118),(23,128),(24,119),(24,129),(25,62),(25,82),(26,63),(26,83),(27,74),(27,139),(28,75),(28,140),(29,100),(29,126),(30,101),(30,127),(31,55),(31,135),(32,56),(32,136),(33,47),(33,72),(33,98),(34,48),(34,73),(34,99),(35,100),(35,130),(35,132),(36,101),(36,131),(36,132),(37,96),(37,110),(37,112),(38,97),(38,111),(38,113),(40,201),(40,202),(41,225),(42,226),(43,221),(43,223),(44,222),(44,224),(45,213),(45,221),(46,214),(46,222),(47,213),(47,223),(48,214),(48,224),(49,161),(50,162),(51,183),(51,227),(52,184),(52,228),(53,173),(53,195),(54,174),(54,196),(55,185),(56,186),(57,179),(57,180),(58,175),(58,177),(59,176),(59,178),(60,171),(60,177),(61,172),(61,178),(62,215),(63,216),(64,220),(65,219),(66,219),(67,220),(68,183),(68,203),(69,184),(69,204),(70,179),(70,199),(71,180),(71,200),(72,9),(72,223),(73,10),(73,224),(74,3),(74,189),(75,4),(75,190),(76,53),(76,205),(76,227),(77,54),(77,206),(77,228),(78,53),(78,207),(79,54),(79,208),(80,58),(80,163),(80,167),(81,59),(81,164),(81,168),(82,49),(82,215),(83,50),(83,216),(84,94),(85,95),(86,68),(86,197),(87,69),(87,198),(88,94),(89,95),(90,55),(90,169),(91,56),(91,170),(92,108),(92,170),(93,109),(93,169),(94,39),(95,39),(96,86),(96,163),(97,87),(97,164),(98,19),(98,137),(98,213),(99,20),(99,138),(99,214),(100,21),(100,116),(100,159),(101,22),(101,117),(101,160),(102,90),(102,217),(103,91),(103,218),(104,51),(104,181),(105,52),(105,182),(106,41),(106,187),(107,42),(107,188),(108,40),(108,175),(108,194),(109,40),(109,176),(109,193),(110,60),(110,163),(110,191),(111,61),(111,164),(111,192),(112,104),(112,191),(113,105),(113,192),(114,112),(115,113),(116,124),(116,149),(117,124),(117,150),(118,91),(118,92),(119,90),(119,93),(120,58),(120,60),(120,225),(121,59),(121,61),(121,226),(122,92),(122,125),(122,218),(123,93),(123,125),(123,217),(124,122),(124,123),(125,108),(125,109),(125,167),(125,168),(126,43),(126,72),(126,159),(127,44),(127,73),(127,160),(128,41),(128,120),(129,42),(129,121),(130,45),(130,98),(130,159),(131,46),(131,99),(131,160),(132,116),(132,117),(133,80),(133,96),(133,217),(134,81),(134,97),(134,218),(135,51),(135,76),(135,185),(136,52),(136,77),(136,186),(137,133),(137,151),(137,165),(138,134),(138,152),(138,166),(139,57),(139,70),(139,189),(140,57),(140,71),(140,190),(141,76),(141,78),(141,181),(142,77),(142,79),(142,182),(143,84),(143,88),(144,85),(144,89),(145,64),(145,67),(146,65),(146,66),(147,43),(147,45),(147,47),(148,44),(148,46),(148,48),(149,103),(149,118),(149,122),(150,102),(150,119),(150,123),(151,80),(151,110),(151,120),(151,187),(152,81),(152,111),(152,121),(152,188),(153,106),(153,128),(153,151),(154,107),(154,129),(154,152),(155,104),(155,135),(155,141),(156,105),(156,136),(156,142),(157,33),(157,126),(157,130),(157,147),(158,34),(158,127),(158,131),(158,148),(159,137),(159,153),(159,221),(160,138),(160,154),(160,222),(161,143),(162,144),(163,27),(163,177),(163,197),(164,28),(164,178),(164,198),(165,155),(165,187),(166,156),(166,188),(167,175),(167,193),(167,197),(168,176),(168,194),(168,198),(169,68),(169,185),(169,193),(170,69),(170,186),(170,194),(171,207),(172,208),(173,215),(173,231),(174,216),(174,232),(175,201),(175,209),(176,202),(176,210),(177,74),(177,209),(178,75),(178,210),(179,66),(179,233),(180,67),(180,233),(181,25),(181,207),(181,227),(182,26),(182,208),(182,228),(183,229),(184,230),(185,183),(185,205),(186,184),(186,206),(187,141),(187,191),(187,225),(188,142),(188,192),(188,226),(189,145),(189,180),(189,199),(190,146),(190,179),(190,200),(191,171),(191,181),(192,172),(192,182),(193,201),(193,203),(193,205),(194,202),(194,204),(194,206),(195,231),(196,232),(197,139),(197,203),(197,209),(198,140),(198,204),(198,210),(199,64),(199,233),(200,65),(200,233),(201,195),(201,211),(202,196),(202,212),(203,70),(203,211),(203,229),(204,71),(204,212),(204,230),(205,195),(205,229),(206,196),(206,230),(207,62),(207,173),(208,63),(208,174),(209,189),(209,211),(210,190),(210,212),(211,199),(211,231),(212,200),(212,232),(213,5),(213,165),(214,6),(214,166),(215,7),(215,161),(216,8),(216,162),(217,86),(217,167),(217,169),(218,87),(218,168),(218,170),(219,88),(220,89),(221,106),(221,165),(222,107),(222,166),(223,114),(224,115),(225,78),(225,171),(226,79),(226,172),(227,82),(227,173),(227,229),(228,83),(228,174),(228,230),(229,49),(229,231),(230,50),(230,232),(231,161),(232,162),(233,219),(233,220)],234)
=> ? = 0
[1,2,3,4,6,5] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,4,4],[5,6],[6]]
=> ([(0,1)],2)
=> 0
[1,2,3,5,4,6] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,4,5],[5,5],[6]]
=> ([(0,1)],2)
=> 0
[1,2,4,3,5,6] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,4],[4,4,4],[5,5],[6]]
=> ([(0,1)],2)
=> 0
[1,2,4,3,6,5] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,4],[4,4,4],[5,6],[6]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[1,3,2,4,5,6] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,3],[4,4,4],[5,5],[6]]
=> ([(0,1)],2)
=> 0
[1,3,2,4,6,5] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,3],[4,4,4],[5,6],[6]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[1,3,2,5,4,6] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,3],[4,4,5],[5,5],[6]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[2,1,3,4,5,6] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,3],[4,4,4],[5,5],[6]]
=> ([(0,1)],2)
=> 0
[2,1,3,4,6,5] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,3],[4,4,4],[5,6],[6]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[2,1,3,5,4,6] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,3],[4,4,5],[5,5],[6]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[2,1,4,3,5,6] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,4],[4,4,4],[5,5],[6]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
Description
The number of potential covers of a poset. A potential cover is a pair of uncomparable elements $(x, y)$ which can be added to the poset without adding any other relations. For example, let $P$ be the disjoint union of a single relation $(1, 2)$ with the one element poset $0$. Then the relation $(0, 1)$ cannot be added without adding also $(0, 2)$, however, the relations $(0, 2)$ and $(1, 0)$ are potential covers.
Matching statistic: St000524
Mp00063: Permutations to alternating sign matrixAlternating sign matrices
Mp00001: Alternating sign matrices to semistandard tableau via monotone trianglesSemistandard tableaux
Mp00214: Semistandard tableaux subcrystalPosets
St000524: Posets ⟶ ℤResult quality: 5% values known / values provided: 5%distinct values known / distinct values provided: 18%
Values
[2,1] => [[0,1],[1,0]]
=> [[1,2],[2]]
=> ([(0,1)],2)
=> 1 = 0 + 1
[1,3,2] => [[1,0,0],[0,0,1],[0,1,0]]
=> [[1,1,1],[2,3],[3]]
=> ([(0,1)],2)
=> 1 = 0 + 1
[2,1,3] => [[0,1,0],[1,0,0],[0,0,1]]
=> [[1,1,2],[2,2],[3]]
=> ([(0,1)],2)
=> 1 = 0 + 1
[1,2,4,3] => [[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
=> [[1,1,1,1],[2,2,2],[3,4],[4]]
=> ([(0,1)],2)
=> 1 = 0 + 1
[1,3,2,4] => [[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,3],[3,3],[4]]
=> ([(0,1)],2)
=> 1 = 0 + 1
[1,4,2,3] => [[1,0,0,0],[0,0,1,0],[0,0,0,1],[0,1,0,0]]
=> [[1,1,1,1],[2,3,3],[3,4],[4]]
=> ([(0,3),(2,1),(3,2)],4)
=> 1 = 0 + 1
[2,1,3,4] => [[0,1,0,0],[1,0,0,0],[0,0,1,0],[0,0,0,1]]
=> [[1,1,1,2],[2,2,2],[3,3],[4]]
=> ([(0,1)],2)
=> 1 = 0 + 1
[2,1,4,3] => [[0,1,0,0],[1,0,0,0],[0,0,0,1],[0,0,1,0]]
=> [[1,1,1,2],[2,2,2],[3,4],[4]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 2 + 1
[2,3,4,1] => [[0,0,0,1],[1,0,0,0],[0,1,0,0],[0,0,1,0]]
=> [[1,1,1,4],[2,2,4],[3,4],[4]]
=> ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
=> ? = 0 + 1
[2,4,1,3] => [[0,0,1,0],[1,0,0,0],[0,0,0,1],[0,1,0,0]]
=> [[1,1,1,3],[2,3,3],[3,4],[4]]
=> ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> ? = 0 + 1
[2,4,3,1] => [[0,0,0,1],[1,0,0,0],[0,0,1,0],[0,1,0,0]]
=> [[1,1,1,4],[2,3,4],[3,4],[4]]
=> ([(0,5),(0,10),(1,16),(2,15),(3,14),(4,13),(5,12),(6,2),(6,13),(7,4),(7,14),(8,1),(9,6),(10,11),(10,12),(11,3),(11,7),(12,9),(13,15),(14,8),(15,16)],17)
=> ? = 1 + 1
[3,1,4,2] => [[0,1,0,0],[0,0,0,1],[1,0,0,0],[0,0,1,0]]
=> [[1,1,2,2],[2,2,4],[3,4],[4]]
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 1 + 1
[3,2,4,1] => [[0,0,0,1],[0,1,0,0],[1,0,0,0],[0,0,1,0]]
=> [[1,1,2,4],[2,2,4],[3,4],[4]]
=> ([(0,7),(0,8),(1,12),(2,11),(3,10),(4,10),(4,11),(5,3),(6,1),(6,13),(7,9),(8,5),(9,2),(9,4),(10,14),(11,6),(11,14),(13,12),(14,13)],15)
=> ? = 1 + 1
[3,4,2,1] => [[0,0,0,1],[0,0,1,0],[1,0,0,0],[0,1,0,0]]
=> [[1,1,3,4],[2,3,4],[3,4],[4]]
=> ([(0,13),(0,15),(1,17),(2,16),(2,17),(3,19),(4,16),(4,18),(5,22),(6,21),(7,20),(8,23),(8,29),(9,4),(9,28),(10,3),(10,28),(11,6),(12,7),(12,24),(13,14),(14,1),(14,2),(15,9),(15,10),(16,25),(17,12),(17,25),(18,26),(18,29),(19,23),(19,26),(20,27),(22,27),(23,30),(24,20),(24,22),(25,24),(26,30),(27,21),(28,8),(28,18),(28,19),(29,5),(29,30),(30,11)],31)
=> ? = 1 + 1
[4,1,3,2] => [[0,1,0,0],[0,0,0,1],[0,0,1,0],[1,0,0,0]]
=> [[1,2,2,2],[2,3,4],[3,4],[4]]
=> ([(0,7),(0,8),(1,12),(2,11),(3,10),(4,10),(4,11),(5,3),(6,1),(6,13),(7,9),(8,5),(9,2),(9,4),(10,14),(11,6),(11,14),(13,12),(14,13)],15)
=> ? = 0 + 1
[4,2,1,3] => [[0,0,1,0],[0,1,0,0],[0,0,0,1],[1,0,0,0]]
=> [[1,2,2,3],[2,3,3],[3,4],[4]]
=> ([(0,5),(0,10),(1,16),(2,15),(3,14),(4,13),(5,12),(6,2),(6,13),(7,4),(7,14),(8,1),(9,6),(10,11),(10,12),(11,3),(11,7),(12,9),(13,15),(14,8),(15,16)],17)
=> ? = 1 + 1
[4,2,3,1] => [[0,0,0,1],[0,1,0,0],[0,0,1,0],[1,0,0,0]]
=> [[1,2,2,4],[2,3,4],[3,4],[4]]
=> ([(0,14),(0,15),(1,19),(2,18),(3,29),(4,30),(5,22),(6,23),(7,24),(7,25),(8,9),(9,7),(9,18),(9,19),(10,5),(11,6),(12,2),(12,29),(13,1),(13,30),(14,16),(14,28),(15,17),(15,28),(16,3),(16,12),(17,4),(17,13),(18,24),(18,27),(19,25),(19,27),(20,26),(21,26),(22,20),(23,21),(24,22),(24,31),(25,23),(25,31),(27,31),(28,8),(29,10),(30,11),(31,20),(31,21)],32)
=> ? = 0 + 1
[4,3,1,2] => [[0,0,1,0],[0,0,0,1],[0,1,0,0],[1,0,0,0]]
=> [[1,2,3,3],[2,3,4],[3,4],[4]]
=> ([(0,13),(0,15),(1,17),(2,16),(2,17),(3,19),(4,16),(4,18),(5,22),(6,21),(7,20),(8,23),(8,29),(9,4),(9,28),(10,3),(10,28),(11,6),(12,7),(12,24),(13,14),(14,1),(14,2),(15,9),(15,10),(16,25),(17,12),(17,25),(18,26),(18,29),(19,23),(19,26),(20,27),(22,27),(23,30),(24,20),(24,22),(25,24),(26,30),(27,21),(28,8),(28,18),(28,19),(29,5),(29,30),(30,11)],31)
=> ? = 0 + 1
[4,3,2,1] => [[0,0,0,1],[0,0,1,0],[0,1,0,0],[1,0,0,0]]
=> [[1,2,3,4],[2,3,4],[3,4],[4]]
=> ([(0,5),(0,16),(0,17),(1,23),(2,19),(3,11),(3,21),(4,10),(4,20),(5,12),(5,13),(6,50),(7,51),(8,24),(8,58),(9,25),(9,59),(10,14),(10,52),(11,15),(11,53),(12,26),(12,60),(13,27),(13,60),(14,54),(15,55),(16,4),(16,29),(17,3),(17,29),(18,48),(18,49),(19,32),(19,33),(20,46),(20,52),(21,47),(21,53),(22,34),(22,35),(23,18),(23,54),(23,55),(24,40),(24,42),(25,41),(25,43),(26,46),(26,56),(27,47),(27,57),(28,63),(29,1),(30,62),(31,61),(32,61),(33,61),(34,6),(34,62),(35,7),(35,62),(36,58),(37,59),(38,32),(39,33),(40,44),(41,45),(42,38),(43,39),(44,31),(45,31),(46,36),(47,37),(48,40),(48,63),(49,41),(49,63),(50,38),(51,39),(52,8),(52,36),(53,9),(53,37),(54,28),(54,48),(55,28),(55,49),(56,30),(56,34),(57,30),(57,35),(58,42),(58,50),(59,43),(59,51),(60,22),(60,56),(60,57),(62,2),(63,44),(63,45)],64)
=> ? = 0 + 1
[1,2,3,5,4] => [[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0]]
=> [[1,1,1,1,1],[2,2,2,2],[3,3,3],[4,5],[5]]
=> ([(0,1)],2)
=> 1 = 0 + 1
[1,2,4,3,5] => [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [[1,1,1,1,1],[2,2,2,2],[3,3,4],[4,4],[5]]
=> ([(0,1)],2)
=> 1 = 0 + 1
[1,2,5,3,4] => [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1],[0,0,1,0,0]]
=> [[1,1,1,1,1],[2,2,2,2],[3,4,4],[4,5],[5]]
=> ([(0,3),(2,1),(3,2)],4)
=> 1 = 0 + 1
[1,3,2,4,5] => [[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
=> [[1,1,1,1,1],[2,2,2,3],[3,3,3],[4,4],[5]]
=> ([(0,1)],2)
=> 1 = 0 + 1
[1,3,2,5,4] => [[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
=> [[1,1,1,1,1],[2,2,2,3],[3,3,3],[4,5],[5]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 2 + 1
[1,3,4,5,2] => [[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0]]
=> [[1,1,1,1,1],[2,2,2,5],[3,3,5],[4,5],[5]]
=> ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
=> ? = 0 + 1
[1,3,5,2,4] => [[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,1,0,0]]
=> [[1,1,1,1,1],[2,2,2,4],[3,4,4],[4,5],[5]]
=> ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> ? = 0 + 1
[1,3,5,4,2] => [[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0]]
=> [[1,1,1,1,1],[2,2,2,5],[3,4,5],[4,5],[5]]
=> ([(0,5),(0,10),(1,16),(2,15),(3,14),(4,13),(5,12),(6,2),(6,13),(7,4),(7,14),(8,1),(9,6),(10,11),(10,12),(11,3),(11,7),(12,9),(13,15),(14,8),(15,16)],17)
=> ? = 1 + 1
[1,4,2,3,5] => [[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [[1,1,1,1,1],[2,2,3,3],[3,3,4],[4,4],[5]]
=> ([(0,3),(2,1),(3,2)],4)
=> 1 = 0 + 1
[1,4,2,5,3] => [[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,0,1,0]]
=> [[1,1,1,1,1],[2,2,3,3],[3,3,5],[4,5],[5]]
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 1 + 1
[1,4,3,5,2] => [[1,0,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0]]
=> [[1,1,1,1,1],[2,2,3,5],[3,3,5],[4,5],[5]]
=> ([(0,7),(0,8),(1,12),(2,11),(3,10),(4,10),(4,11),(5,3),(6,1),(6,13),(7,9),(8,5),(9,2),(9,4),(10,14),(11,6),(11,14),(13,12),(14,13)],15)
=> ? = 1 + 1
[1,4,5,2,3] => [[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0]]
=> [[1,1,1,1,1],[2,2,4,4],[3,4,5],[4,5],[5]]
=> ([(0,8),(2,11),(2,12),(3,10),(4,9),(5,4),(5,14),(6,3),(6,14),(7,1),(8,5),(8,6),(9,11),(9,13),(10,12),(10,13),(11,15),(12,15),(13,15),(14,2),(14,9),(14,10),(15,7)],16)
=> ? = 0 + 1
[1,4,5,3,2] => [[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0]]
=> [[1,1,1,1,1],[2,2,4,5],[3,4,5],[4,5],[5]]
=> ([(0,13),(0,15),(1,17),(2,16),(2,17),(3,19),(4,16),(4,18),(5,22),(6,21),(7,20),(8,23),(8,29),(9,4),(9,28),(10,3),(10,28),(11,6),(12,7),(12,24),(13,14),(14,1),(14,2),(15,9),(15,10),(16,25),(17,12),(17,25),(18,26),(18,29),(19,23),(19,26),(20,27),(22,27),(23,30),(24,20),(24,22),(25,24),(26,30),(27,21),(28,8),(28,18),(28,19),(29,5),(29,30),(30,11)],31)
=> ? = 1 + 1
[1,5,3,2,4] => [[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1],[0,1,0,0,0]]
=> [[1,1,1,1,1],[2,3,3,4],[3,4,4],[4,5],[5]]
=> ([(0,5),(0,10),(1,16),(2,15),(3,14),(4,13),(5,12),(6,2),(6,13),(7,4),(7,14),(8,1),(9,6),(10,11),(10,12),(11,3),(11,7),(12,9),(13,15),(14,8),(15,16)],17)
=> ? = 1 + 1
[1,5,4,3,2] => [[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0]]
=> [[1,1,1,1,1],[2,3,4,5],[3,4,5],[4,5],[5]]
=> ([(0,5),(0,16),(0,17),(1,23),(2,19),(3,11),(3,21),(4,10),(4,20),(5,12),(5,13),(6,50),(7,51),(8,24),(8,58),(9,25),(9,59),(10,14),(10,52),(11,15),(11,53),(12,26),(12,60),(13,27),(13,60),(14,54),(15,55),(16,4),(16,29),(17,3),(17,29),(18,48),(18,49),(19,32),(19,33),(20,46),(20,52),(21,47),(21,53),(22,34),(22,35),(23,18),(23,54),(23,55),(24,40),(24,42),(25,41),(25,43),(26,46),(26,56),(27,47),(27,57),(28,63),(29,1),(30,62),(31,61),(32,61),(33,61),(34,6),(34,62),(35,7),(35,62),(36,58),(37,59),(38,32),(39,33),(40,44),(41,45),(42,38),(43,39),(44,31),(45,31),(46,36),(47,37),(48,40),(48,63),(49,41),(49,63),(50,38),(51,39),(52,8),(52,36),(53,9),(53,37),(54,28),(54,48),(55,28),(55,49),(56,30),(56,34),(57,30),(57,35),(58,42),(58,50),(59,43),(59,51),(60,22),(60,56),(60,57),(62,2),(63,44),(63,45)],64)
=> ? = 0 + 1
[2,1,3,4,5] => [[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]]
=> [[1,1,1,1,2],[2,2,2,2],[3,3,3],[4,4],[5]]
=> ([(0,1)],2)
=> 1 = 0 + 1
[2,1,3,5,4] => [[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0]]
=> [[1,1,1,1,2],[2,2,2,2],[3,3,3],[4,5],[5]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 2 + 1
[2,1,4,3,5] => [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [[1,1,1,1,2],[2,2,2,2],[3,3,4],[4,4],[5]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 2 + 1
[2,1,4,5,3] => [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,0,0,1,0]]
=> [[1,1,1,1,2],[2,2,2,2],[3,3,5],[4,5],[5]]
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 1 + 1
[2,1,5,4,3] => [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0]]
=> [[1,1,1,1,2],[2,2,2,2],[3,4,5],[4,5],[5]]
=> ([(0,3),(0,6),(0,7),(1,8),(1,12),(2,8),(2,11),(3,9),(3,10),(4,2),(4,13),(5,1),(5,14),(6,4),(6,9),(7,5),(7,10),(8,15),(9,13),(10,14),(11,15),(12,15),(13,11),(14,12)],16)
=> ? = 0 + 1
[2,3,1,5,4] => [[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
=> [[1,1,1,1,3],[2,2,2,3],[3,3,3],[4,5],[5]]
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 1 + 1
[2,3,4,1,5] => [[0,0,0,1,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [[1,1,1,1,4],[2,2,2,4],[3,3,4],[4,4],[5]]
=> ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
=> ? = 0 + 1
[2,3,4,5,1] => [[0,0,0,0,1],[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0]]
=> [[1,1,1,1,5],[2,2,2,5],[3,3,5],[4,5],[5]]
=> ([(0,9),(1,13),(2,14),(4,12),(5,11),(6,1),(6,12),(7,3),(8,5),(8,15),(9,10),(10,4),(10,6),(11,14),(12,8),(12,13),(13,15),(14,7),(15,2),(15,11)],16)
=> ? = 0 + 1
[2,4,1,3,5] => [[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [[1,1,1,1,3],[2,2,3,3],[3,3,4],[4,4],[5]]
=> ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> ? = 0 + 1
[2,4,1,5,3] => [[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,0,1,0]]
=> [[1,1,1,1,3],[2,2,3,3],[3,3,5],[4,5],[5]]
=> ([(0,6),(0,7),(1,5),(1,15),(2,4),(2,14),(3,13),(4,12),(5,3),(5,16),(6,9),(7,2),(7,9),(9,1),(9,14),(10,11),(11,8),(12,10),(13,8),(14,12),(14,15),(15,10),(15,16),(16,11),(16,13)],17)
=> ? = 0 + 1
[2,4,3,1,5] => [[0,0,0,1,0],[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [[1,1,1,1,4],[2,2,3,4],[3,3,4],[4,4],[5]]
=> ([(0,5),(0,10),(1,16),(2,15),(3,14),(4,13),(5,12),(6,2),(6,13),(7,4),(7,14),(8,1),(9,6),(10,11),(10,12),(11,3),(11,7),(12,9),(13,15),(14,8),(15,16)],17)
=> ? = 1 + 1
[2,4,3,5,1] => [[0,0,0,0,1],[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0]]
=> [[1,1,1,1,5],[2,2,3,5],[3,3,5],[4,5],[5]]
=> ([(0,8),(0,13),(1,19),(2,16),(2,18),(3,21),(4,26),(5,24),(6,16),(6,22),(7,20),(7,23),(8,17),(9,4),(9,18),(10,9),(11,7),(11,30),(12,3),(12,25),(13,14),(13,17),(14,1),(14,15),(15,2),(15,6),(15,19),(16,28),(17,10),(18,26),(18,28),(19,11),(19,22),(20,24),(20,31),(22,30),(23,31),(24,12),(24,27),(25,21),(26,23),(26,29),(27,25),(28,29),(29,31),(30,5),(30,20),(31,27)],32)
=> ? = 0 + 1
[2,4,5,1,3] => [[0,0,0,1,0],[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0]]
=> [[1,1,1,1,4],[2,2,4,4],[3,4,5],[4,5],[5]]
=> ([(0,9),(0,10),(1,2),(3,7),(3,23),(4,6),(4,22),(5,15),(6,16),(7,8),(7,24),(8,20),(9,19),(10,4),(10,19),(11,14),(11,18),(12,26),(13,26),(14,25),(15,1),(16,21),(17,13),(17,25),(18,12),(18,25),(19,3),(19,22),(20,12),(20,13),(21,14),(21,17),(22,16),(22,23),(23,11),(23,21),(23,24),(24,17),(24,18),(24,20),(25,5),(25,26),(26,15)],27)
=> ? = 0 + 1
[2,4,5,3,1] => [[0,0,0,0,1],[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0]]
=> [[1,1,1,1,5],[2,2,4,5],[3,4,5],[4,5],[5]]
=> ([(0,17),(0,18),(1,11),(1,12),(2,53),(3,50),(4,33),(5,16),(5,65),(6,13),(6,61),(7,14),(7,62),(8,15),(8,51),(9,25),(9,63),(10,24),(10,52),(11,54),(12,22),(12,23),(12,54),(13,36),(14,35),(15,40),(16,59),(17,1),(17,48),(18,7),(18,48),(19,32),(19,45),(20,29),(20,38),(21,55),(21,58),(22,49),(22,60),(23,42),(23,49),(24,31),(24,46),(25,21),(25,60),(25,64),(27,70),(28,70),(29,67),(30,66),(31,68),(32,3),(32,69),(33,8),(34,39),(35,57),(36,39),(37,32),(37,66),(38,19),(38,37),(38,67),(39,26),(40,26),(41,30),(41,67),(42,52),(43,44),(43,68),(44,28),(44,69),(45,27),(45,69),(46,53),(46,68),(47,61),(48,9),(48,62),(49,5),(49,56),(50,34),(51,40),(52,2),(52,46),(53,6),(53,47),(54,10),(54,42),(55,31),(55,43),(56,43),(56,65),(57,29),(57,41),(58,30),(58,37),(59,27),(59,28),(60,55),(60,56),(61,34),(61,36),(62,35),(62,63),(63,20),(63,57),(63,64),(64,38),(64,41),(64,58),(65,44),(65,45),(65,59),(66,33),(67,4),(67,66),(68,47),(69,50),(69,70),(70,51)],71)
=> ? = 1 + 1
[2,5,1,3,4] => [[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1],[0,1,0,0,0]]
=> [[1,1,1,1,3],[2,3,3,3],[3,4,4],[4,5],[5]]
=> ([(0,4),(0,8),(1,11),(3,10),(4,9),(5,2),(6,3),(6,12),(7,5),(8,6),(8,9),(9,12),(10,11),(11,7),(12,1),(12,10)],13)
=> ? = 0 + 1
[3,1,2,5,4] => [[0,1,0,0,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
=> [[1,1,1,2,2],[2,2,2,3],[3,3,3],[4,5],[5]]
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 0 + 1
[3,1,4,2,5] => [[0,1,0,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [[1,1,1,2,2],[2,2,2,4],[3,3,4],[4,4],[5]]
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 1 + 1
[3,2,1,5,4] => [[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
=> [[1,1,1,2,3],[2,2,2,3],[3,3,3],[4,5],[5]]
=> ([(0,3),(0,6),(0,7),(1,8),(1,12),(2,8),(2,11),(3,9),(3,10),(4,2),(4,13),(5,1),(5,14),(6,4),(6,9),(7,5),(7,10),(8,15),(9,13),(10,14),(11,15),(12,15),(13,11),(14,12)],16)
=> ? = 0 + 1
[3,2,4,1,5] => [[0,0,0,1,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [[1,1,1,2,4],[2,2,2,4],[3,3,4],[4,4],[5]]
=> ([(0,7),(0,8),(1,12),(2,11),(3,10),(4,10),(4,11),(5,3),(6,1),(6,13),(7,9),(8,5),(9,2),(9,4),(10,14),(11,6),(11,14),(13,12),(14,13)],15)
=> ? = 1 + 1
[3,4,2,1,5] => [[0,0,0,1,0],[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [[1,1,1,3,4],[2,2,3,4],[3,3,4],[4,4],[5]]
=> ([(0,13),(0,15),(1,17),(2,16),(2,17),(3,19),(4,16),(4,18),(5,22),(6,21),(7,20),(8,23),(8,29),(9,4),(9,28),(10,3),(10,28),(11,6),(12,7),(12,24),(13,14),(14,1),(14,2),(15,9),(15,10),(16,25),(17,12),(17,25),(18,26),(18,29),(19,23),(19,26),(20,27),(22,27),(23,30),(24,20),(24,22),(25,24),(26,30),(27,21),(28,8),(28,18),(28,19),(29,5),(29,30),(30,11)],31)
=> ? = 1 + 1
[3,5,2,1,4] => [[0,0,0,1,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0]]
=> [[1,1,1,3,4],[2,3,3,4],[3,4,4],[4,5],[5]]
=> ([(0,15),(0,16),(0,20),(1,9),(2,13),(2,47),(3,38),(4,14),(4,46),(5,40),(6,10),(6,26),(7,18),(7,45),(8,19),(8,39),(9,25),(10,32),(11,31),(12,44),(13,12),(13,48),(14,11),(14,42),(15,8),(15,28),(16,7),(16,37),(17,24),(17,33),(18,21),(18,36),(19,21),(19,35),(20,28),(20,37),(21,51),(22,49),(23,49),(24,3),(24,50),(26,1),(27,25),(28,39),(29,46),(30,27),(31,30),(32,27),(33,23),(33,50),(34,22),(34,50),(35,40),(35,51),(36,41),(36,51),(37,2),(37,45),(38,43),(39,5),(39,35),(40,4),(40,29),(41,24),(41,34),(42,31),(42,43),(43,30),(43,32),(44,22),(44,23),(45,36),(45,47),(46,38),(46,42),(47,17),(47,41),(47,48),(48,33),(48,34),(48,44),(49,26),(50,6),(50,49),(51,29)],52)
=> ? = 1 + 1
[3,5,2,4,1] => [[0,0,0,0,1],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0]]
=> [[1,1,1,3,5],[2,3,3,5],[3,4,5],[4,5],[5]]
=> ([(0,16),(0,17),(0,28),(1,9),(2,70),(3,13),(3,85),(4,27),(4,69),(5,83),(6,15),(6,43),(7,26),(7,84),(8,12),(8,29),(8,71),(9,68),(10,77),(11,76),(12,14),(12,78),(13,10),(13,86),(14,11),(14,87),(15,75),(16,8),(16,48),(17,7),(17,67),(18,42),(18,61),(19,25),(19,62),(19,63),(20,22),(20,59),(20,79),(21,24),(21,41),(21,60),(22,23),(22,80),(22,81),(23,64),(23,66),(24,37),(24,65),(25,36),(25,46),(26,50),(26,58),(27,31),(27,32),(28,48),(28,67),(29,57),(29,58),(29,78),(31,103),(32,103),(33,89),(34,89),(35,90),(36,88),(37,92),(38,102),(39,93),(40,101),(41,4),(41,100),(42,5),(42,97),(43,1),(44,53),(45,51),(45,95),(46,41),(46,88),(47,54),(48,71),(49,79),(50,73),(50,98),(51,68),(51,102),(52,31),(52,96),(53,30),(54,30),(55,33),(55,97),(56,35),(56,99),(57,70),(57,98),(58,74),(58,98),(59,81),(59,90),(60,37),(60,100),(61,34),(61,97),(62,36),(62,99),(63,21),(63,46),(63,99),(64,52),(64,91),(65,52),(65,92),(66,45),(66,91),(67,3),(67,84),(68,47),(69,32),(70,20),(70,49),(71,2),(71,57),(72,53),(72,54),(73,42),(73,55),(74,56),(74,62),(75,38),(75,51),(76,35),(76,59),(77,33),(77,34),(78,19),(78,74),(78,87),(79,80),(79,83),(79,90),(80,66),(80,82),(80,94),(81,64),(81,65),(81,94),(82,45),(82,75),(82,93),(83,39),(83,82),(84,50),(84,85),(85,18),(85,73),(85,86),(86,55),(86,61),(86,77),(87,56),(87,63),(87,76),(88,100),(89,43),(90,39),(90,94),(91,95),(91,96),(92,40),(92,96),(93,38),(93,40),(93,95),(94,91),(94,92),(94,93),(95,101),(95,102),(96,101),(96,103),(97,6),(97,89),(98,49),(99,60),(99,88),(100,69),(101,44),(101,72),(102,47),(102,72),(103,44)],104)
=> ? = 2 + 1
[3,5,4,1,2] => [[0,0,0,1,0],[0,0,0,0,1],[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0]]
=> [[1,1,1,4,4],[2,3,4,5],[3,4,5],[4,5],[5]]
=> ([(0,12),(0,13),(1,6),(2,61),(3,5),(3,94),(4,81),(5,80),(6,32),(7,4),(7,95),(8,22),(8,87),(9,20),(9,85),(10,19),(10,92),(11,17),(11,18),(11,98),(12,51),(13,11),(13,21),(13,51),(14,46),(14,47),(15,42),(15,89),(16,73),(16,75),(17,27),(17,48),(17,97),(18,48),(18,90),(19,43),(19,91),(20,44),(20,76),(21,25),(21,88),(21,98),(22,26),(22,74),(22,96),(23,24),(23,45),(23,77),(24,66),(24,67),(25,53),(25,93),(26,68),(26,84),(27,74),(27,78),(28,37),(28,60),(28,72),(29,124),(30,124),(31,101),(31,123),(33,117),(33,125),(34,118),(35,99),(36,116),(36,128),(37,101),(37,121),(38,109),(38,125),(39,100),(39,103),(40,109),(40,129),(41,126),(42,119),(43,107),(44,113),(45,9),(45,106),(46,108),(47,2),(47,108),(48,10),(48,122),(49,65),(49,128),(50,64),(51,8),(51,88),(52,39),(52,121),(52,123),(53,79),(54,45),(54,100),(55,32),(56,29),(56,127),(57,30),(57,127),(58,35),(58,120),(59,34),(59,99),(60,63),(60,101),(61,55),(62,56),(62,104),(63,83),(63,111),(64,57),(64,104),(65,44),(65,114),(66,58),(66,110),(67,65),(67,110),(68,43),(68,115),(69,34),(69,105),(70,36),(70,112),(71,33),(71,103),(71,119),(72,23),(72,54),(72,121),(73,50),(74,68),(74,102),(75,3),(75,82),(76,64),(76,113),(77,66),(77,106),(78,39),(78,54),(78,102),(79,42),(79,71),(80,29),(80,30),(81,35),(81,59),(82,62),(82,94),(83,49),(83,67),(83,112),(84,33),(84,38),(84,115),(85,50),(85,76),(86,59),(86,69),(86,120),(87,15),(87,79),(87,96),(88,53),(88,87),(89,38),(89,40),(89,119),(90,31),(90,60),(90,122),(91,36),(91,49),(91,107),(92,70),(92,83),(92,91),(93,31),(93,37),(93,52),(94,56),(94,57),(94,80),(95,58),(95,81),(95,86),(96,71),(96,84),(96,89),(96,102),(97,52),(97,72),(97,78),(97,122),(98,28),(98,90),(98,93),(98,97),(99,46),(99,118),(100,106),(101,7),(101,111),(102,40),(102,103),(102,115),(103,117),(103,129),(104,127),(105,47),(105,118),(106,85),(107,41),(107,116),(108,1),(109,41),(109,130),(110,114),(110,120),(111,95),(111,112),(112,86),(112,110),(112,128),(113,104),(114,105),(114,113),(115,107),(115,109),(115,117),(116,126),(117,116),(117,130),(118,108),(119,16),(119,125),(119,129),(120,14),(120,99),(120,105),(121,77),(121,100),(122,63),(122,92),(122,123),(123,70),(123,111),(124,55),(125,75),(125,130),(126,62),(127,61),(127,124),(128,69),(128,114),(129,73),(129,130),(130,82),(130,126)],131)
=> ? = 0 + 1
[4,1,3,2,5] => [[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1]]
=> [[1,1,2,2,2],[2,2,3,4],[3,3,4],[4,4],[5]]
=> ([(0,7),(0,8),(1,12),(2,11),(3,10),(4,10),(4,11),(5,3),(6,1),(6,13),(7,9),(8,5),(9,2),(9,4),(10,14),(11,6),(11,14),(13,12),(14,13)],15)
=> ? = 0 + 1
[4,1,5,2,3] => [[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1],[1,0,0,0,0],[0,0,1,0,0]]
=> [[1,1,2,2,2],[2,2,4,4],[3,4,5],[4,5],[5]]
=> ([(0,1),(1,4),(1,5),(2,8),(2,32),(3,6),(3,30),(4,7),(4,33),(5,10),(5,11),(5,33),(6,20),(7,31),(8,27),(9,15),(9,19),(10,18),(10,28),(11,18),(11,25),(13,39),(14,36),(14,39),(15,36),(16,38),(17,38),(18,2),(18,37),(19,26),(19,36),(20,21),(21,12),(22,12),(23,17),(23,35),(24,16),(24,35),(25,13),(25,37),(26,24),(26,34),(27,16),(27,17),(28,14),(28,19),(28,37),(29,21),(29,22),(30,20),(30,29),(31,13),(31,14),(31,15),(32,23),(32,24),(32,27),(33,9),(33,25),(33,28),(33,31),(34,30),(34,35),(35,29),(35,38),(36,3),(36,34),(37,26),(37,32),(37,39),(38,22),(39,23),(39,34)],40)
=> ? = 0 + 1
[4,2,1,3,5] => [[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,0,0,0,1]]
=> [[1,1,2,2,3],[2,2,3,3],[3,3,4],[4,4],[5]]
=> ([(0,5),(0,10),(1,16),(2,15),(3,14),(4,13),(5,12),(6,2),(6,13),(7,4),(7,14),(8,1),(9,6),(10,11),(10,12),(11,3),(11,7),(12,9),(13,15),(14,8),(15,16)],17)
=> ? = 1 + 1
[4,2,3,1,5] => [[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1]]
=> [[1,1,2,2,4],[2,2,3,4],[3,3,4],[4,4],[5]]
=> ([(0,14),(0,15),(1,19),(2,18),(3,29),(4,30),(5,22),(6,23),(7,24),(7,25),(8,9),(9,7),(9,18),(9,19),(10,5),(11,6),(12,2),(12,29),(13,1),(13,30),(14,16),(14,28),(15,17),(15,28),(16,3),(16,12),(17,4),(17,13),(18,24),(18,27),(19,25),(19,27),(20,26),(21,26),(22,20),(23,21),(24,22),(24,31),(25,23),(25,31),(27,31),(28,8),(29,10),(30,11),(31,20),(31,21)],32)
=> ? = 0 + 1
[4,2,5,1,3] => [[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1],[1,0,0,0,0],[0,0,1,0,0]]
=> [[1,1,2,2,4],[2,2,4,4],[3,4,5],[4,5],[5]]
=> ([(0,7),(0,8),(1,2),(1,45),(2,35),(3,37),(4,14),(4,49),(5,9),(5,48),(6,10),(6,12),(6,54),(7,31),(8,6),(8,13),(8,31),(9,27),(9,42),(10,28),(10,41),(11,26),(11,52),(12,17),(12,28),(12,51),(13,15),(13,50),(13,54),(14,16),(14,40),(14,53),(15,33),(15,44),(16,38),(16,47),(17,30),(17,40),(19,64),(19,66),(20,62),(21,65),(22,58),(23,60),(23,66),(24,60),(24,63),(25,67),(26,55),(27,59),(28,5),(28,56),(29,34),(30,22),(30,57),(31,4),(31,50),(32,22),(32,65),(33,43),(34,18),(35,18),(36,20),(37,1),(37,46),(38,27),(38,61),(39,19),(39,55),(39,58),(40,38),(40,57),(41,21),(41,56),(42,20),(42,59),(43,26),(43,39),(44,21),(44,32),(45,34),(45,35),(46,29),(46,45),(47,19),(47,23),(47,61),(48,36),(48,42),(49,11),(49,43),(49,53),(50,33),(50,49),(51,30),(51,32),(51,56),(52,23),(52,24),(52,55),(53,39),(53,47),(53,52),(53,57),(54,41),(54,44),(54,51),(55,3),(55,63),(55,66),(56,48),(56,65),(57,24),(57,58),(57,61),(58,63),(58,64),(59,25),(59,62),(60,25),(60,68),(61,59),(61,60),(61,64),(62,67),(63,68),(64,62),(64,68),(65,36),(66,37),(66,68),(67,29),(68,46),(68,67)],69)
=> ? = 1 + 1
[4,3,1,2,5] => [[0,0,1,0,0],[0,0,0,1,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1]]
=> [[1,1,2,3,3],[2,2,3,4],[3,3,4],[4,4],[5]]
=> ([(0,13),(0,15),(1,17),(2,16),(2,17),(3,19),(4,16),(4,18),(5,22),(6,21),(7,20),(8,23),(8,29),(9,4),(9,28),(10,3),(10,28),(11,6),(12,7),(12,24),(13,14),(14,1),(14,2),(15,9),(15,10),(16,25),(17,12),(17,25),(18,26),(18,29),(19,23),(19,26),(20,27),(22,27),(23,30),(24,20),(24,22),(25,24),(26,30),(27,21),(28,8),(28,18),(28,19),(29,5),(29,30),(30,11)],31)
=> ? = 0 + 1
[4,3,2,1,5] => [[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1]]
=> [[1,1,2,3,4],[2,2,3,4],[3,3,4],[4,4],[5]]
=> ([(0,5),(0,16),(0,17),(1,23),(2,19),(3,11),(3,21),(4,10),(4,20),(5,12),(5,13),(6,50),(7,51),(8,24),(8,58),(9,25),(9,59),(10,14),(10,52),(11,15),(11,53),(12,26),(12,60),(13,27),(13,60),(14,54),(15,55),(16,4),(16,29),(17,3),(17,29),(18,48),(18,49),(19,32),(19,33),(20,46),(20,52),(21,47),(21,53),(22,34),(22,35),(23,18),(23,54),(23,55),(24,40),(24,42),(25,41),(25,43),(26,46),(26,56),(27,47),(27,57),(28,63),(29,1),(30,62),(31,61),(32,61),(33,61),(34,6),(34,62),(35,7),(35,62),(36,58),(37,59),(38,32),(39,33),(40,44),(41,45),(42,38),(43,39),(44,31),(45,31),(46,36),(47,37),(48,40),(48,63),(49,41),(49,63),(50,38),(51,39),(52,8),(52,36),(53,9),(53,37),(54,28),(54,48),(55,28),(55,49),(56,30),(56,34),(57,30),(57,35),(58,42),(58,50),(59,43),(59,51),(60,22),(60,56),(60,57),(62,2),(63,44),(63,45)],64)
=> ? = 0 + 1
[4,3,5,1,2] => [[0,0,0,1,0],[0,0,0,0,1],[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0]]
=> [[1,1,2,4,4],[2,2,4,5],[3,4,5],[4,5],[5]]
=> ([(0,2),(0,3),(1,8),(1,16),(2,1),(3,7),(3,10),(4,13),(4,59),(5,12),(5,81),(6,20),(6,82),(7,11),(7,83),(8,60),(9,23),(9,58),(10,19),(10,22),(10,83),(11,78),(12,64),(13,24),(14,52),(14,72),(15,17),(15,73),(15,80),(16,60),(16,74),(17,39),(17,70),(18,36),(18,44),(19,51),(19,69),(20,33),(20,75),(21,28),(21,38),(21,50),(22,51),(22,71),(22,74),(23,49),(23,56),(23,57),(25,101),(26,113),(27,107),(27,110),(28,107),(28,111),(29,110),(29,111),(30,112),(31,90),(31,98),(32,94),(32,114),(33,96),(34,91),(34,92),(35,89),(35,92),(36,108),(37,94),(37,103),(38,9),(38,111),(39,45),(40,31),(40,102),(40,114),(41,31),(41,104),(42,37),(42,99),(43,34),(43,85),(43,87),(44,30),(44,108),(45,55),(46,33),(46,86),(47,48),(47,86),(48,25),(48,100),(49,42),(49,85),(50,14),(50,76),(50,107),(51,15),(51,61),(51,84),(52,46),(52,109),(53,32),(53,93),(54,26),(54,95),(55,25),(55,91),(56,35),(56,85),(56,97),(57,53),(57,97),(58,57),(59,24),(60,5),(60,63),(61,67),(61,73),(62,34),(62,35),(62,113),(63,67),(63,81),(64,46),(64,47),(65,45),(65,68),(66,47),(66,68),(66,109),(67,65),(67,66),(68,48),(68,55),(68,87),(69,29),(69,38),(69,84),(70,26),(70,62),(71,27),(71,50),(71,84),(72,43),(72,49),(72,109),(73,39),(73,65),(74,61),(74,63),(75,32),(75,40),(75,96),(76,72),(76,79),(76,88),(77,40),(77,41),(77,93),(78,27),(78,28),(78,29),(79,43),(79,56),(79,62),(79,95),(80,54),(80,70),(80,79),(81,52),(81,64),(81,66),(82,53),(82,75),(82,77),(83,21),(83,69),(83,71),(83,78),(84,76),(84,80),(84,110),(85,92),(85,99),(86,37),(86,96),(86,100),(87,91),(87,99),(87,100),(88,82),(88,95),(89,104),(90,108),(90,116),(91,101),(91,106),(92,106),(93,18),(93,104),(93,114),(94,115),(95,77),(95,97),(95,113),(96,94),(96,102),(97,89),(97,93),(98,116),(99,103),(99,106),(100,101),(100,102),(100,103),(101,98),(101,105),(102,98),(102,115),(103,105),(103,115),(104,36),(104,90),(105,116),(106,105),(107,6),(107,88),(108,4),(108,112),(109,42),(109,86),(109,87),(110,54),(110,88),(111,58),(112,59),(113,41),(113,89),(114,44),(114,90),(114,115),(115,30),(115,116),(116,112)],117)
=> ? = 0 + 1
[4,3,5,2,1] => [[0,0,0,0,1],[0,0,0,1,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0]]
=> [[1,1,2,4,5],[2,2,4,5],[3,4,5],[4,5],[5]]
=> ([(0,4),(0,15),(0,16),(1,34),(2,7),(2,32),(3,14),(3,33),(4,11),(4,12),(5,147),(6,38),(6,125),(7,5),(7,114),(8,39),(8,161),(9,30),(9,158),(10,31),(10,96),(11,29),(11,159),(12,28),(12,41),(12,159),(13,24),(13,75),(14,20),(14,21),(14,156),(15,2),(15,54),(16,3),(16,54),(17,68),(17,119),(18,115),(18,120),(19,113),(19,149),(20,122),(20,154),(21,122),(21,164),(22,111),(22,145),(23,67),(23,116),(24,65),(24,66),(25,42),(25,117),(25,148),(26,37),(26,152),(26,163),(27,35),(27,150),(27,155),(28,118),(28,153),(29,121),(29,162),(30,110),(30,146),(31,109),(31,112),(32,114),(32,151),(33,121),(33,156),(34,36),(34,147),(34,164),(35,79),(35,81),(36,84),(36,134),(37,80),(37,137),(38,95),(38,106),(38,107),(39,58),(39,94),(39,139),(40,52),(40,64),(40,108),(41,118),(41,132),(41,151),(42,76),(42,77),(42,78),(43,211),(44,202),(45,173),(45,214),(46,168),(47,167),(47,168),(48,217),(49,212),(49,215),(50,174),(50,215),(51,218),(52,6),(52,212),(53,10),(54,1),(55,176),(56,176),(56,211),(57,192),(57,203),(58,173),(58,186),(59,177),(59,187),(60,175),(60,177),(61,214),(62,193),(63,182),(63,200),(64,22),(64,174),(64,212),(65,181),(66,181),(67,180),(68,179),(69,96),(70,57),(70,199),(70,213),(71,60),(71,169),(71,171),(72,100),(72,206),(73,58),(73,172),(74,66),(74,197),(75,65),(76,83),(76,170),(77,91),(77,167),(78,120),(78,167),(78,170),(79,88),(80,87),(81,136),(82,67),(82,216),(83,94),(83,208),(84,110),(84,210),(85,69),(85,208),(86,63),(86,198),(87,105),(88,55),(89,93),(89,172),(90,46),(90,210),(91,45),(91,196),(92,43),(92,209),(93,44),(93,195),(94,101),(94,173),(95,86),(95,169),(96,112),(97,102),(97,166),(97,188),(98,103),(98,188),(99,57),(99,191),(100,109),(100,182),(100,213),(101,97),(101,184),(102,56),(102,183),(102,209),(103,55),(103,183),(104,48),(104,185),(105,44),(105,175),(106,59),(106,169),(106,190),(107,72),(107,190),(108,19),(108,144),(108,174),(109,62),(109,166),(110,135),(111,53),(112,92),(112,166),(113,73),(113,207),(114,9),(114,126),(115,69),(115,178),(116,74),(116,180),(117,18),(117,78),(117,218),(118,26),(118,123),(118,165),(119,23),(119,82),(119,179),(120,27),(120,140),(120,178),(121,133),(122,138),(123,130),(123,152),(124,88),(124,103),(125,53),(125,107),(126,130),(126,158),(127,59),(127,60),(127,217),(128,87),(128,131),(129,89),(129,131),(129,207),(130,128),(130,129),(131,93),(131,105),(131,171),(132,50),(132,108),(132,165),(133,51),(133,148),(134,47),(134,77),(134,210),(135,45),(135,61),(136,43),(136,56),(137,48),(137,127),(138,46),(138,47),(139,70),(139,100),(139,186),(140,143),(140,150),(141,70),(141,99),(141,206),(142,97),(142,157),(143,98),(143,124),(144,149),(144,160),(144,189),(145,83),(145,85),(146,73),(146,89),(147,84),(147,90),(148,76),(148,145),(148,218),(149,71),(149,95),(149,207),(150,79),(150,124),(151,123),(151,126),(152,80),(152,128),(153,49),(153,52),(153,165),(154,51),(154,117),(155,81),(155,157),(156,25),(156,133),(156,154),(157,92),(157,102),(157,136),(158,113),(158,129),(158,146),(159,40),(159,132),(159,153),(159,162),(160,71),(160,106),(160,127),(160,185),(161,72),(161,139),(161,141),(162,49),(162,50),(162,64),(163,104),(163,137),(163,160),(164,90),(164,134),(164,138),(165,144),(165,163),(165,215),(166,193),(166,209),(167,140),(167,196),(168,61),(168,196),(169,177),(169,198),(170,178),(170,208),(171,175),(171,195),(171,198),(172,63),(172,186),(172,195),(173,184),(174,8),(174,189),(175,202),(175,204),(176,194),(177,204),(178,142),(178,155),(179,13),(179,216),(180,197),(182,62),(182,220),(183,176),(183,201),(184,188),(185,141),(185,190),(185,217),(186,182),(186,199),(187,191),(188,183),(188,193),(189,161),(189,185),(190,187),(190,206),(191,68),(191,192),(192,179),(192,219),(193,201),(194,197),(195,199),(195,200),(195,202),(196,143),(196,214),(197,181),(198,200),(198,204),(199,203),(199,220),(200,205),(200,220),(201,180),(201,194),(202,203),(202,205),(203,219),(204,205),(205,219),(206,17),(206,191),(206,213),(207,86),(207,171),(207,172),(208,101),(208,142),(209,116),(209,201),(209,211),(210,91),(210,135),(210,168),(211,74),(211,194),(212,111),(212,125),(213,119),(213,192),(213,220),(214,98),(214,184),(215,104),(215,189),(216,75),(217,99),(217,187),(218,85),(218,115),(218,170),(219,216),(220,82),(220,219)],221)
=> ? = 1 + 1
[4,5,3,1,2] => [[0,0,0,1,0],[0,0,0,0,1],[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0]]
=> [[1,1,3,4,4],[2,3,4,5],[3,4,5],[4,5],[5]]
=> ([(0,1),(0,2),(1,12),(1,14),(2,11),(2,13),(3,145),(4,146),(5,31),(5,155),(6,32),(6,156),(7,15),(7,143),(8,16),(8,144),(9,37),(9,114),(10,38),(10,115),(11,17),(11,157),(12,18),(12,158),(13,29),(13,35),(13,157),(14,30),(14,36),(14,158),(15,84),(16,85),(17,147),(18,148),(19,102),(19,133),(20,103),(20,134),(21,23),(21,149),(21,153),(22,24),(22,150),(22,154),(23,118),(23,128),(24,119),(24,129),(25,62),(25,82),(26,63),(26,83),(27,74),(27,139),(28,75),(28,140),(29,100),(29,126),(30,101),(30,127),(31,55),(31,135),(32,56),(32,136),(33,47),(33,72),(33,98),(34,48),(34,73),(34,99),(35,100),(35,130),(35,132),(36,101),(36,131),(36,132),(37,96),(37,110),(37,112),(38,97),(38,111),(38,113),(40,201),(40,202),(41,225),(42,226),(43,221),(43,223),(44,222),(44,224),(45,213),(45,221),(46,214),(46,222),(47,213),(47,223),(48,214),(48,224),(49,161),(50,162),(51,183),(51,227),(52,184),(52,228),(53,173),(53,195),(54,174),(54,196),(55,185),(56,186),(57,179),(57,180),(58,175),(58,177),(59,176),(59,178),(60,171),(60,177),(61,172),(61,178),(62,215),(63,216),(64,220),(65,219),(66,219),(67,220),(68,183),(68,203),(69,184),(69,204),(70,179),(70,199),(71,180),(71,200),(72,9),(72,223),(73,10),(73,224),(74,3),(74,189),(75,4),(75,190),(76,53),(76,205),(76,227),(77,54),(77,206),(77,228),(78,53),(78,207),(79,54),(79,208),(80,58),(80,163),(80,167),(81,59),(81,164),(81,168),(82,49),(82,215),(83,50),(83,216),(84,94),(85,95),(86,68),(86,197),(87,69),(87,198),(88,94),(89,95),(90,55),(90,169),(91,56),(91,170),(92,108),(92,170),(93,109),(93,169),(94,39),(95,39),(96,86),(96,163),(97,87),(97,164),(98,19),(98,137),(98,213),(99,20),(99,138),(99,214),(100,21),(100,116),(100,159),(101,22),(101,117),(101,160),(102,90),(102,217),(103,91),(103,218),(104,51),(104,181),(105,52),(105,182),(106,41),(106,187),(107,42),(107,188),(108,40),(108,175),(108,194),(109,40),(109,176),(109,193),(110,60),(110,163),(110,191),(111,61),(111,164),(111,192),(112,104),(112,191),(113,105),(113,192),(114,112),(115,113),(116,124),(116,149),(117,124),(117,150),(118,91),(118,92),(119,90),(119,93),(120,58),(120,60),(120,225),(121,59),(121,61),(121,226),(122,92),(122,125),(122,218),(123,93),(123,125),(123,217),(124,122),(124,123),(125,108),(125,109),(125,167),(125,168),(126,43),(126,72),(126,159),(127,44),(127,73),(127,160),(128,41),(128,120),(129,42),(129,121),(130,45),(130,98),(130,159),(131,46),(131,99),(131,160),(132,116),(132,117),(133,80),(133,96),(133,217),(134,81),(134,97),(134,218),(135,51),(135,76),(135,185),(136,52),(136,77),(136,186),(137,133),(137,151),(137,165),(138,134),(138,152),(138,166),(139,57),(139,70),(139,189),(140,57),(140,71),(140,190),(141,76),(141,78),(141,181),(142,77),(142,79),(142,182),(143,84),(143,88),(144,85),(144,89),(145,64),(145,67),(146,65),(146,66),(147,43),(147,45),(147,47),(148,44),(148,46),(148,48),(149,103),(149,118),(149,122),(150,102),(150,119),(150,123),(151,80),(151,110),(151,120),(151,187),(152,81),(152,111),(152,121),(152,188),(153,106),(153,128),(153,151),(154,107),(154,129),(154,152),(155,104),(155,135),(155,141),(156,105),(156,136),(156,142),(157,33),(157,126),(157,130),(157,147),(158,34),(158,127),(158,131),(158,148),(159,137),(159,153),(159,221),(160,138),(160,154),(160,222),(161,143),(162,144),(163,27),(163,177),(163,197),(164,28),(164,178),(164,198),(165,155),(165,187),(166,156),(166,188),(167,175),(167,193),(167,197),(168,176),(168,194),(168,198),(169,68),(169,185),(169,193),(170,69),(170,186),(170,194),(171,207),(172,208),(173,215),(173,231),(174,216),(174,232),(175,201),(175,209),(176,202),(176,210),(177,74),(177,209),(178,75),(178,210),(179,66),(179,233),(180,67),(180,233),(181,25),(181,207),(181,227),(182,26),(182,208),(182,228),(183,229),(184,230),(185,183),(185,205),(186,184),(186,206),(187,141),(187,191),(187,225),(188,142),(188,192),(188,226),(189,145),(189,180),(189,199),(190,146),(190,179),(190,200),(191,171),(191,181),(192,172),(192,182),(193,201),(193,203),(193,205),(194,202),(194,204),(194,206),(195,231),(196,232),(197,139),(197,203),(197,209),(198,140),(198,204),(198,210),(199,64),(199,233),(200,65),(200,233),(201,195),(201,211),(202,196),(202,212),(203,70),(203,211),(203,229),(204,71),(204,212),(204,230),(205,195),(205,229),(206,196),(206,230),(207,62),(207,173),(208,63),(208,174),(209,189),(209,211),(210,190),(210,212),(211,199),(211,231),(212,200),(212,232),(213,5),(213,165),(214,6),(214,166),(215,7),(215,161),(216,8),(216,162),(217,86),(217,167),(217,169),(218,87),(218,168),(218,170),(219,88),(220,89),(221,106),(221,165),(222,107),(222,166),(223,114),(224,115),(225,78),(225,171),(226,79),(226,172),(227,82),(227,173),(227,229),(228,83),(228,174),(228,230),(229,49),(229,231),(230,50),(230,232),(231,161),(232,162),(233,219),(233,220)],234)
=> ? = 0 + 1
[1,2,3,4,6,5] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,4,4],[5,6],[6]]
=> ([(0,1)],2)
=> 1 = 0 + 1
[1,2,3,5,4,6] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,4,5],[5,5],[6]]
=> ([(0,1)],2)
=> 1 = 0 + 1
[1,2,4,3,5,6] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,4],[4,4,4],[5,5],[6]]
=> ([(0,1)],2)
=> 1 = 0 + 1
[1,2,4,3,6,5] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,4],[4,4,4],[5,6],[6]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 2 + 1
[1,3,2,4,5,6] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,3],[4,4,4],[5,5],[6]]
=> ([(0,1)],2)
=> 1 = 0 + 1
[1,3,2,4,6,5] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,3],[4,4,4],[5,6],[6]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 2 + 1
[1,3,2,5,4,6] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,3],[4,4,5],[5,5],[6]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 2 + 1
[2,1,3,4,5,6] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,3],[4,4,4],[5,5],[6]]
=> ([(0,1)],2)
=> 1 = 0 + 1
[2,1,3,4,6,5] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,3],[4,4,4],[5,6],[6]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 2 + 1
[2,1,3,5,4,6] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,3],[4,4,5],[5,5],[6]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 2 + 1
[2,1,4,3,5,6] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,4],[4,4,4],[5,5],[6]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 2 + 1
Description
The number of posets with the same order polynomial. The order polynomial of a poset $P$ is the polynomial $S$ such that $S(m)$ is the number of order-preserving maps from $P$ to $\{1,\dots,m\}$. See sections 3.12 and 3.15 of [1].
Matching statistic: St000525
Mp00063: Permutations to alternating sign matrixAlternating sign matrices
Mp00001: Alternating sign matrices to semistandard tableau via monotone trianglesSemistandard tableaux
Mp00214: Semistandard tableaux subcrystalPosets
St000525: Posets ⟶ ℤResult quality: 5% values known / values provided: 5%distinct values known / distinct values provided: 18%
Values
[2,1] => [[0,1],[1,0]]
=> [[1,2],[2]]
=> ([(0,1)],2)
=> 1 = 0 + 1
[1,3,2] => [[1,0,0],[0,0,1],[0,1,0]]
=> [[1,1,1],[2,3],[3]]
=> ([(0,1)],2)
=> 1 = 0 + 1
[2,1,3] => [[0,1,0],[1,0,0],[0,0,1]]
=> [[1,1,2],[2,2],[3]]
=> ([(0,1)],2)
=> 1 = 0 + 1
[1,2,4,3] => [[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
=> [[1,1,1,1],[2,2,2],[3,4],[4]]
=> ([(0,1)],2)
=> 1 = 0 + 1
[1,3,2,4] => [[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,3],[3,3],[4]]
=> ([(0,1)],2)
=> 1 = 0 + 1
[1,4,2,3] => [[1,0,0,0],[0,0,1,0],[0,0,0,1],[0,1,0,0]]
=> [[1,1,1,1],[2,3,3],[3,4],[4]]
=> ([(0,3),(2,1),(3,2)],4)
=> 1 = 0 + 1
[2,1,3,4] => [[0,1,0,0],[1,0,0,0],[0,0,1,0],[0,0,0,1]]
=> [[1,1,1,2],[2,2,2],[3,3],[4]]
=> ([(0,1)],2)
=> 1 = 0 + 1
[2,1,4,3] => [[0,1,0,0],[1,0,0,0],[0,0,0,1],[0,0,1,0]]
=> [[1,1,1,2],[2,2,2],[3,4],[4]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 2 + 1
[2,3,4,1] => [[0,0,0,1],[1,0,0,0],[0,1,0,0],[0,0,1,0]]
=> [[1,1,1,4],[2,2,4],[3,4],[4]]
=> ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
=> ? = 0 + 1
[2,4,1,3] => [[0,0,1,0],[1,0,0,0],[0,0,0,1],[0,1,0,0]]
=> [[1,1,1,3],[2,3,3],[3,4],[4]]
=> ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> ? = 0 + 1
[2,4,3,1] => [[0,0,0,1],[1,0,0,0],[0,0,1,0],[0,1,0,0]]
=> [[1,1,1,4],[2,3,4],[3,4],[4]]
=> ([(0,5),(0,10),(1,16),(2,15),(3,14),(4,13),(5,12),(6,2),(6,13),(7,4),(7,14),(8,1),(9,6),(10,11),(10,12),(11,3),(11,7),(12,9),(13,15),(14,8),(15,16)],17)
=> ? = 1 + 1
[3,1,4,2] => [[0,1,0,0],[0,0,0,1],[1,0,0,0],[0,0,1,0]]
=> [[1,1,2,2],[2,2,4],[3,4],[4]]
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 1 + 1
[3,2,4,1] => [[0,0,0,1],[0,1,0,0],[1,0,0,0],[0,0,1,0]]
=> [[1,1,2,4],[2,2,4],[3,4],[4]]
=> ([(0,7),(0,8),(1,12),(2,11),(3,10),(4,10),(4,11),(5,3),(6,1),(6,13),(7,9),(8,5),(9,2),(9,4),(10,14),(11,6),(11,14),(13,12),(14,13)],15)
=> ? = 1 + 1
[3,4,2,1] => [[0,0,0,1],[0,0,1,0],[1,0,0,0],[0,1,0,0]]
=> [[1,1,3,4],[2,3,4],[3,4],[4]]
=> ([(0,13),(0,15),(1,17),(2,16),(2,17),(3,19),(4,16),(4,18),(5,22),(6,21),(7,20),(8,23),(8,29),(9,4),(9,28),(10,3),(10,28),(11,6),(12,7),(12,24),(13,14),(14,1),(14,2),(15,9),(15,10),(16,25),(17,12),(17,25),(18,26),(18,29),(19,23),(19,26),(20,27),(22,27),(23,30),(24,20),(24,22),(25,24),(26,30),(27,21),(28,8),(28,18),(28,19),(29,5),(29,30),(30,11)],31)
=> ? = 1 + 1
[4,1,3,2] => [[0,1,0,0],[0,0,0,1],[0,0,1,0],[1,0,0,0]]
=> [[1,2,2,2],[2,3,4],[3,4],[4]]
=> ([(0,7),(0,8),(1,12),(2,11),(3,10),(4,10),(4,11),(5,3),(6,1),(6,13),(7,9),(8,5),(9,2),(9,4),(10,14),(11,6),(11,14),(13,12),(14,13)],15)
=> ? = 0 + 1
[4,2,1,3] => [[0,0,1,0],[0,1,0,0],[0,0,0,1],[1,0,0,0]]
=> [[1,2,2,3],[2,3,3],[3,4],[4]]
=> ([(0,5),(0,10),(1,16),(2,15),(3,14),(4,13),(5,12),(6,2),(6,13),(7,4),(7,14),(8,1),(9,6),(10,11),(10,12),(11,3),(11,7),(12,9),(13,15),(14,8),(15,16)],17)
=> ? = 1 + 1
[4,2,3,1] => [[0,0,0,1],[0,1,0,0],[0,0,1,0],[1,0,0,0]]
=> [[1,2,2,4],[2,3,4],[3,4],[4]]
=> ([(0,14),(0,15),(1,19),(2,18),(3,29),(4,30),(5,22),(6,23),(7,24),(7,25),(8,9),(9,7),(9,18),(9,19),(10,5),(11,6),(12,2),(12,29),(13,1),(13,30),(14,16),(14,28),(15,17),(15,28),(16,3),(16,12),(17,4),(17,13),(18,24),(18,27),(19,25),(19,27),(20,26),(21,26),(22,20),(23,21),(24,22),(24,31),(25,23),(25,31),(27,31),(28,8),(29,10),(30,11),(31,20),(31,21)],32)
=> ? = 0 + 1
[4,3,1,2] => [[0,0,1,0],[0,0,0,1],[0,1,0,0],[1,0,0,0]]
=> [[1,2,3,3],[2,3,4],[3,4],[4]]
=> ([(0,13),(0,15),(1,17),(2,16),(2,17),(3,19),(4,16),(4,18),(5,22),(6,21),(7,20),(8,23),(8,29),(9,4),(9,28),(10,3),(10,28),(11,6),(12,7),(12,24),(13,14),(14,1),(14,2),(15,9),(15,10),(16,25),(17,12),(17,25),(18,26),(18,29),(19,23),(19,26),(20,27),(22,27),(23,30),(24,20),(24,22),(25,24),(26,30),(27,21),(28,8),(28,18),(28,19),(29,5),(29,30),(30,11)],31)
=> ? = 0 + 1
[4,3,2,1] => [[0,0,0,1],[0,0,1,0],[0,1,0,0],[1,0,0,0]]
=> [[1,2,3,4],[2,3,4],[3,4],[4]]
=> ([(0,5),(0,16),(0,17),(1,23),(2,19),(3,11),(3,21),(4,10),(4,20),(5,12),(5,13),(6,50),(7,51),(8,24),(8,58),(9,25),(9,59),(10,14),(10,52),(11,15),(11,53),(12,26),(12,60),(13,27),(13,60),(14,54),(15,55),(16,4),(16,29),(17,3),(17,29),(18,48),(18,49),(19,32),(19,33),(20,46),(20,52),(21,47),(21,53),(22,34),(22,35),(23,18),(23,54),(23,55),(24,40),(24,42),(25,41),(25,43),(26,46),(26,56),(27,47),(27,57),(28,63),(29,1),(30,62),(31,61),(32,61),(33,61),(34,6),(34,62),(35,7),(35,62),(36,58),(37,59),(38,32),(39,33),(40,44),(41,45),(42,38),(43,39),(44,31),(45,31),(46,36),(47,37),(48,40),(48,63),(49,41),(49,63),(50,38),(51,39),(52,8),(52,36),(53,9),(53,37),(54,28),(54,48),(55,28),(55,49),(56,30),(56,34),(57,30),(57,35),(58,42),(58,50),(59,43),(59,51),(60,22),(60,56),(60,57),(62,2),(63,44),(63,45)],64)
=> ? = 0 + 1
[1,2,3,5,4] => [[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0]]
=> [[1,1,1,1,1],[2,2,2,2],[3,3,3],[4,5],[5]]
=> ([(0,1)],2)
=> 1 = 0 + 1
[1,2,4,3,5] => [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [[1,1,1,1,1],[2,2,2,2],[3,3,4],[4,4],[5]]
=> ([(0,1)],2)
=> 1 = 0 + 1
[1,2,5,3,4] => [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1],[0,0,1,0,0]]
=> [[1,1,1,1,1],[2,2,2,2],[3,4,4],[4,5],[5]]
=> ([(0,3),(2,1),(3,2)],4)
=> 1 = 0 + 1
[1,3,2,4,5] => [[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
=> [[1,1,1,1,1],[2,2,2,3],[3,3,3],[4,4],[5]]
=> ([(0,1)],2)
=> 1 = 0 + 1
[1,3,2,5,4] => [[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
=> [[1,1,1,1,1],[2,2,2,3],[3,3,3],[4,5],[5]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 2 + 1
[1,3,4,5,2] => [[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0]]
=> [[1,1,1,1,1],[2,2,2,5],[3,3,5],[4,5],[5]]
=> ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
=> ? = 0 + 1
[1,3,5,2,4] => [[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,1,0,0]]
=> [[1,1,1,1,1],[2,2,2,4],[3,4,4],[4,5],[5]]
=> ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> ? = 0 + 1
[1,3,5,4,2] => [[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0]]
=> [[1,1,1,1,1],[2,2,2,5],[3,4,5],[4,5],[5]]
=> ([(0,5),(0,10),(1,16),(2,15),(3,14),(4,13),(5,12),(6,2),(6,13),(7,4),(7,14),(8,1),(9,6),(10,11),(10,12),(11,3),(11,7),(12,9),(13,15),(14,8),(15,16)],17)
=> ? = 1 + 1
[1,4,2,3,5] => [[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [[1,1,1,1,1],[2,2,3,3],[3,3,4],[4,4],[5]]
=> ([(0,3),(2,1),(3,2)],4)
=> 1 = 0 + 1
[1,4,2,5,3] => [[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,0,1,0]]
=> [[1,1,1,1,1],[2,2,3,3],[3,3,5],[4,5],[5]]
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 1 + 1
[1,4,3,5,2] => [[1,0,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0]]
=> [[1,1,1,1,1],[2,2,3,5],[3,3,5],[4,5],[5]]
=> ([(0,7),(0,8),(1,12),(2,11),(3,10),(4,10),(4,11),(5,3),(6,1),(6,13),(7,9),(8,5),(9,2),(9,4),(10,14),(11,6),(11,14),(13,12),(14,13)],15)
=> ? = 1 + 1
[1,4,5,2,3] => [[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0]]
=> [[1,1,1,1,1],[2,2,4,4],[3,4,5],[4,5],[5]]
=> ([(0,8),(2,11),(2,12),(3,10),(4,9),(5,4),(5,14),(6,3),(6,14),(7,1),(8,5),(8,6),(9,11),(9,13),(10,12),(10,13),(11,15),(12,15),(13,15),(14,2),(14,9),(14,10),(15,7)],16)
=> ? = 0 + 1
[1,4,5,3,2] => [[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0]]
=> [[1,1,1,1,1],[2,2,4,5],[3,4,5],[4,5],[5]]
=> ([(0,13),(0,15),(1,17),(2,16),(2,17),(3,19),(4,16),(4,18),(5,22),(6,21),(7,20),(8,23),(8,29),(9,4),(9,28),(10,3),(10,28),(11,6),(12,7),(12,24),(13,14),(14,1),(14,2),(15,9),(15,10),(16,25),(17,12),(17,25),(18,26),(18,29),(19,23),(19,26),(20,27),(22,27),(23,30),(24,20),(24,22),(25,24),(26,30),(27,21),(28,8),(28,18),(28,19),(29,5),(29,30),(30,11)],31)
=> ? = 1 + 1
[1,5,3,2,4] => [[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1],[0,1,0,0,0]]
=> [[1,1,1,1,1],[2,3,3,4],[3,4,4],[4,5],[5]]
=> ([(0,5),(0,10),(1,16),(2,15),(3,14),(4,13),(5,12),(6,2),(6,13),(7,4),(7,14),(8,1),(9,6),(10,11),(10,12),(11,3),(11,7),(12,9),(13,15),(14,8),(15,16)],17)
=> ? = 1 + 1
[1,5,4,3,2] => [[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0]]
=> [[1,1,1,1,1],[2,3,4,5],[3,4,5],[4,5],[5]]
=> ([(0,5),(0,16),(0,17),(1,23),(2,19),(3,11),(3,21),(4,10),(4,20),(5,12),(5,13),(6,50),(7,51),(8,24),(8,58),(9,25),(9,59),(10,14),(10,52),(11,15),(11,53),(12,26),(12,60),(13,27),(13,60),(14,54),(15,55),(16,4),(16,29),(17,3),(17,29),(18,48),(18,49),(19,32),(19,33),(20,46),(20,52),(21,47),(21,53),(22,34),(22,35),(23,18),(23,54),(23,55),(24,40),(24,42),(25,41),(25,43),(26,46),(26,56),(27,47),(27,57),(28,63),(29,1),(30,62),(31,61),(32,61),(33,61),(34,6),(34,62),(35,7),(35,62),(36,58),(37,59),(38,32),(39,33),(40,44),(41,45),(42,38),(43,39),(44,31),(45,31),(46,36),(47,37),(48,40),(48,63),(49,41),(49,63),(50,38),(51,39),(52,8),(52,36),(53,9),(53,37),(54,28),(54,48),(55,28),(55,49),(56,30),(56,34),(57,30),(57,35),(58,42),(58,50),(59,43),(59,51),(60,22),(60,56),(60,57),(62,2),(63,44),(63,45)],64)
=> ? = 0 + 1
[2,1,3,4,5] => [[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]]
=> [[1,1,1,1,2],[2,2,2,2],[3,3,3],[4,4],[5]]
=> ([(0,1)],2)
=> 1 = 0 + 1
[2,1,3,5,4] => [[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0]]
=> [[1,1,1,1,2],[2,2,2,2],[3,3,3],[4,5],[5]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 2 + 1
[2,1,4,3,5] => [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [[1,1,1,1,2],[2,2,2,2],[3,3,4],[4,4],[5]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 2 + 1
[2,1,4,5,3] => [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,0,0,1,0]]
=> [[1,1,1,1,2],[2,2,2,2],[3,3,5],[4,5],[5]]
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 1 + 1
[2,1,5,4,3] => [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0]]
=> [[1,1,1,1,2],[2,2,2,2],[3,4,5],[4,5],[5]]
=> ([(0,3),(0,6),(0,7),(1,8),(1,12),(2,8),(2,11),(3,9),(3,10),(4,2),(4,13),(5,1),(5,14),(6,4),(6,9),(7,5),(7,10),(8,15),(9,13),(10,14),(11,15),(12,15),(13,11),(14,12)],16)
=> ? = 0 + 1
[2,3,1,5,4] => [[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
=> [[1,1,1,1,3],[2,2,2,3],[3,3,3],[4,5],[5]]
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 1 + 1
[2,3,4,1,5] => [[0,0,0,1,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [[1,1,1,1,4],[2,2,2,4],[3,3,4],[4,4],[5]]
=> ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
=> ? = 0 + 1
[2,3,4,5,1] => [[0,0,0,0,1],[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0]]
=> [[1,1,1,1,5],[2,2,2,5],[3,3,5],[4,5],[5]]
=> ([(0,9),(1,13),(2,14),(4,12),(5,11),(6,1),(6,12),(7,3),(8,5),(8,15),(9,10),(10,4),(10,6),(11,14),(12,8),(12,13),(13,15),(14,7),(15,2),(15,11)],16)
=> ? = 0 + 1
[2,4,1,3,5] => [[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [[1,1,1,1,3],[2,2,3,3],[3,3,4],[4,4],[5]]
=> ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> ? = 0 + 1
[2,4,1,5,3] => [[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,0,1,0]]
=> [[1,1,1,1,3],[2,2,3,3],[3,3,5],[4,5],[5]]
=> ([(0,6),(0,7),(1,5),(1,15),(2,4),(2,14),(3,13),(4,12),(5,3),(5,16),(6,9),(7,2),(7,9),(9,1),(9,14),(10,11),(11,8),(12,10),(13,8),(14,12),(14,15),(15,10),(15,16),(16,11),(16,13)],17)
=> ? = 0 + 1
[2,4,3,1,5] => [[0,0,0,1,0],[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [[1,1,1,1,4],[2,2,3,4],[3,3,4],[4,4],[5]]
=> ([(0,5),(0,10),(1,16),(2,15),(3,14),(4,13),(5,12),(6,2),(6,13),(7,4),(7,14),(8,1),(9,6),(10,11),(10,12),(11,3),(11,7),(12,9),(13,15),(14,8),(15,16)],17)
=> ? = 1 + 1
[2,4,3,5,1] => [[0,0,0,0,1],[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0]]
=> [[1,1,1,1,5],[2,2,3,5],[3,3,5],[4,5],[5]]
=> ([(0,8),(0,13),(1,19),(2,16),(2,18),(3,21),(4,26),(5,24),(6,16),(6,22),(7,20),(7,23),(8,17),(9,4),(9,18),(10,9),(11,7),(11,30),(12,3),(12,25),(13,14),(13,17),(14,1),(14,15),(15,2),(15,6),(15,19),(16,28),(17,10),(18,26),(18,28),(19,11),(19,22),(20,24),(20,31),(22,30),(23,31),(24,12),(24,27),(25,21),(26,23),(26,29),(27,25),(28,29),(29,31),(30,5),(30,20),(31,27)],32)
=> ? = 0 + 1
[2,4,5,1,3] => [[0,0,0,1,0],[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0]]
=> [[1,1,1,1,4],[2,2,4,4],[3,4,5],[4,5],[5]]
=> ([(0,9),(0,10),(1,2),(3,7),(3,23),(4,6),(4,22),(5,15),(6,16),(7,8),(7,24),(8,20),(9,19),(10,4),(10,19),(11,14),(11,18),(12,26),(13,26),(14,25),(15,1),(16,21),(17,13),(17,25),(18,12),(18,25),(19,3),(19,22),(20,12),(20,13),(21,14),(21,17),(22,16),(22,23),(23,11),(23,21),(23,24),(24,17),(24,18),(24,20),(25,5),(25,26),(26,15)],27)
=> ? = 0 + 1
[2,4,5,3,1] => [[0,0,0,0,1],[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0]]
=> [[1,1,1,1,5],[2,2,4,5],[3,4,5],[4,5],[5]]
=> ([(0,17),(0,18),(1,11),(1,12),(2,53),(3,50),(4,33),(5,16),(5,65),(6,13),(6,61),(7,14),(7,62),(8,15),(8,51),(9,25),(9,63),(10,24),(10,52),(11,54),(12,22),(12,23),(12,54),(13,36),(14,35),(15,40),(16,59),(17,1),(17,48),(18,7),(18,48),(19,32),(19,45),(20,29),(20,38),(21,55),(21,58),(22,49),(22,60),(23,42),(23,49),(24,31),(24,46),(25,21),(25,60),(25,64),(27,70),(28,70),(29,67),(30,66),(31,68),(32,3),(32,69),(33,8),(34,39),(35,57),(36,39),(37,32),(37,66),(38,19),(38,37),(38,67),(39,26),(40,26),(41,30),(41,67),(42,52),(43,44),(43,68),(44,28),(44,69),(45,27),(45,69),(46,53),(46,68),(47,61),(48,9),(48,62),(49,5),(49,56),(50,34),(51,40),(52,2),(52,46),(53,6),(53,47),(54,10),(54,42),(55,31),(55,43),(56,43),(56,65),(57,29),(57,41),(58,30),(58,37),(59,27),(59,28),(60,55),(60,56),(61,34),(61,36),(62,35),(62,63),(63,20),(63,57),(63,64),(64,38),(64,41),(64,58),(65,44),(65,45),(65,59),(66,33),(67,4),(67,66),(68,47),(69,50),(69,70),(70,51)],71)
=> ? = 1 + 1
[2,5,1,3,4] => [[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1],[0,1,0,0,0]]
=> [[1,1,1,1,3],[2,3,3,3],[3,4,4],[4,5],[5]]
=> ([(0,4),(0,8),(1,11),(3,10),(4,9),(5,2),(6,3),(6,12),(7,5),(8,6),(8,9),(9,12),(10,11),(11,7),(12,1),(12,10)],13)
=> ? = 0 + 1
[3,1,2,5,4] => [[0,1,0,0,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
=> [[1,1,1,2,2],[2,2,2,3],[3,3,3],[4,5],[5]]
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 0 + 1
[3,1,4,2,5] => [[0,1,0,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [[1,1,1,2,2],[2,2,2,4],[3,3,4],[4,4],[5]]
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 1 + 1
[3,2,1,5,4] => [[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
=> [[1,1,1,2,3],[2,2,2,3],[3,3,3],[4,5],[5]]
=> ([(0,3),(0,6),(0,7),(1,8),(1,12),(2,8),(2,11),(3,9),(3,10),(4,2),(4,13),(5,1),(5,14),(6,4),(6,9),(7,5),(7,10),(8,15),(9,13),(10,14),(11,15),(12,15),(13,11),(14,12)],16)
=> ? = 0 + 1
[3,2,4,1,5] => [[0,0,0,1,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [[1,1,1,2,4],[2,2,2,4],[3,3,4],[4,4],[5]]
=> ([(0,7),(0,8),(1,12),(2,11),(3,10),(4,10),(4,11),(5,3),(6,1),(6,13),(7,9),(8,5),(9,2),(9,4),(10,14),(11,6),(11,14),(13,12),(14,13)],15)
=> ? = 1 + 1
[3,4,2,1,5] => [[0,0,0,1,0],[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [[1,1,1,3,4],[2,2,3,4],[3,3,4],[4,4],[5]]
=> ([(0,13),(0,15),(1,17),(2,16),(2,17),(3,19),(4,16),(4,18),(5,22),(6,21),(7,20),(8,23),(8,29),(9,4),(9,28),(10,3),(10,28),(11,6),(12,7),(12,24),(13,14),(14,1),(14,2),(15,9),(15,10),(16,25),(17,12),(17,25),(18,26),(18,29),(19,23),(19,26),(20,27),(22,27),(23,30),(24,20),(24,22),(25,24),(26,30),(27,21),(28,8),(28,18),(28,19),(29,5),(29,30),(30,11)],31)
=> ? = 1 + 1
[3,5,2,1,4] => [[0,0,0,1,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0]]
=> [[1,1,1,3,4],[2,3,3,4],[3,4,4],[4,5],[5]]
=> ([(0,15),(0,16),(0,20),(1,9),(2,13),(2,47),(3,38),(4,14),(4,46),(5,40),(6,10),(6,26),(7,18),(7,45),(8,19),(8,39),(9,25),(10,32),(11,31),(12,44),(13,12),(13,48),(14,11),(14,42),(15,8),(15,28),(16,7),(16,37),(17,24),(17,33),(18,21),(18,36),(19,21),(19,35),(20,28),(20,37),(21,51),(22,49),(23,49),(24,3),(24,50),(26,1),(27,25),(28,39),(29,46),(30,27),(31,30),(32,27),(33,23),(33,50),(34,22),(34,50),(35,40),(35,51),(36,41),(36,51),(37,2),(37,45),(38,43),(39,5),(39,35),(40,4),(40,29),(41,24),(41,34),(42,31),(42,43),(43,30),(43,32),(44,22),(44,23),(45,36),(45,47),(46,38),(46,42),(47,17),(47,41),(47,48),(48,33),(48,34),(48,44),(49,26),(50,6),(50,49),(51,29)],52)
=> ? = 1 + 1
[3,5,2,4,1] => [[0,0,0,0,1],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0]]
=> [[1,1,1,3,5],[2,3,3,5],[3,4,5],[4,5],[5]]
=> ([(0,16),(0,17),(0,28),(1,9),(2,70),(3,13),(3,85),(4,27),(4,69),(5,83),(6,15),(6,43),(7,26),(7,84),(8,12),(8,29),(8,71),(9,68),(10,77),(11,76),(12,14),(12,78),(13,10),(13,86),(14,11),(14,87),(15,75),(16,8),(16,48),(17,7),(17,67),(18,42),(18,61),(19,25),(19,62),(19,63),(20,22),(20,59),(20,79),(21,24),(21,41),(21,60),(22,23),(22,80),(22,81),(23,64),(23,66),(24,37),(24,65),(25,36),(25,46),(26,50),(26,58),(27,31),(27,32),(28,48),(28,67),(29,57),(29,58),(29,78),(31,103),(32,103),(33,89),(34,89),(35,90),(36,88),(37,92),(38,102),(39,93),(40,101),(41,4),(41,100),(42,5),(42,97),(43,1),(44,53),(45,51),(45,95),(46,41),(46,88),(47,54),(48,71),(49,79),(50,73),(50,98),(51,68),(51,102),(52,31),(52,96),(53,30),(54,30),(55,33),(55,97),(56,35),(56,99),(57,70),(57,98),(58,74),(58,98),(59,81),(59,90),(60,37),(60,100),(61,34),(61,97),(62,36),(62,99),(63,21),(63,46),(63,99),(64,52),(64,91),(65,52),(65,92),(66,45),(66,91),(67,3),(67,84),(68,47),(69,32),(70,20),(70,49),(71,2),(71,57),(72,53),(72,54),(73,42),(73,55),(74,56),(74,62),(75,38),(75,51),(76,35),(76,59),(77,33),(77,34),(78,19),(78,74),(78,87),(79,80),(79,83),(79,90),(80,66),(80,82),(80,94),(81,64),(81,65),(81,94),(82,45),(82,75),(82,93),(83,39),(83,82),(84,50),(84,85),(85,18),(85,73),(85,86),(86,55),(86,61),(86,77),(87,56),(87,63),(87,76),(88,100),(89,43),(90,39),(90,94),(91,95),(91,96),(92,40),(92,96),(93,38),(93,40),(93,95),(94,91),(94,92),(94,93),(95,101),(95,102),(96,101),(96,103),(97,6),(97,89),(98,49),(99,60),(99,88),(100,69),(101,44),(101,72),(102,47),(102,72),(103,44)],104)
=> ? = 2 + 1
[3,5,4,1,2] => [[0,0,0,1,0],[0,0,0,0,1],[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0]]
=> [[1,1,1,4,4],[2,3,4,5],[3,4,5],[4,5],[5]]
=> ([(0,12),(0,13),(1,6),(2,61),(3,5),(3,94),(4,81),(5,80),(6,32),(7,4),(7,95),(8,22),(8,87),(9,20),(9,85),(10,19),(10,92),(11,17),(11,18),(11,98),(12,51),(13,11),(13,21),(13,51),(14,46),(14,47),(15,42),(15,89),(16,73),(16,75),(17,27),(17,48),(17,97),(18,48),(18,90),(19,43),(19,91),(20,44),(20,76),(21,25),(21,88),(21,98),(22,26),(22,74),(22,96),(23,24),(23,45),(23,77),(24,66),(24,67),(25,53),(25,93),(26,68),(26,84),(27,74),(27,78),(28,37),(28,60),(28,72),(29,124),(30,124),(31,101),(31,123),(33,117),(33,125),(34,118),(35,99),(36,116),(36,128),(37,101),(37,121),(38,109),(38,125),(39,100),(39,103),(40,109),(40,129),(41,126),(42,119),(43,107),(44,113),(45,9),(45,106),(46,108),(47,2),(47,108),(48,10),(48,122),(49,65),(49,128),(50,64),(51,8),(51,88),(52,39),(52,121),(52,123),(53,79),(54,45),(54,100),(55,32),(56,29),(56,127),(57,30),(57,127),(58,35),(58,120),(59,34),(59,99),(60,63),(60,101),(61,55),(62,56),(62,104),(63,83),(63,111),(64,57),(64,104),(65,44),(65,114),(66,58),(66,110),(67,65),(67,110),(68,43),(68,115),(69,34),(69,105),(70,36),(70,112),(71,33),(71,103),(71,119),(72,23),(72,54),(72,121),(73,50),(74,68),(74,102),(75,3),(75,82),(76,64),(76,113),(77,66),(77,106),(78,39),(78,54),(78,102),(79,42),(79,71),(80,29),(80,30),(81,35),(81,59),(82,62),(82,94),(83,49),(83,67),(83,112),(84,33),(84,38),(84,115),(85,50),(85,76),(86,59),(86,69),(86,120),(87,15),(87,79),(87,96),(88,53),(88,87),(89,38),(89,40),(89,119),(90,31),(90,60),(90,122),(91,36),(91,49),(91,107),(92,70),(92,83),(92,91),(93,31),(93,37),(93,52),(94,56),(94,57),(94,80),(95,58),(95,81),(95,86),(96,71),(96,84),(96,89),(96,102),(97,52),(97,72),(97,78),(97,122),(98,28),(98,90),(98,93),(98,97),(99,46),(99,118),(100,106),(101,7),(101,111),(102,40),(102,103),(102,115),(103,117),(103,129),(104,127),(105,47),(105,118),(106,85),(107,41),(107,116),(108,1),(109,41),(109,130),(110,114),(110,120),(111,95),(111,112),(112,86),(112,110),(112,128),(113,104),(114,105),(114,113),(115,107),(115,109),(115,117),(116,126),(117,116),(117,130),(118,108),(119,16),(119,125),(119,129),(120,14),(120,99),(120,105),(121,77),(121,100),(122,63),(122,92),(122,123),(123,70),(123,111),(124,55),(125,75),(125,130),(126,62),(127,61),(127,124),(128,69),(128,114),(129,73),(129,130),(130,82),(130,126)],131)
=> ? = 0 + 1
[4,1,3,2,5] => [[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1]]
=> [[1,1,2,2,2],[2,2,3,4],[3,3,4],[4,4],[5]]
=> ([(0,7),(0,8),(1,12),(2,11),(3,10),(4,10),(4,11),(5,3),(6,1),(6,13),(7,9),(8,5),(9,2),(9,4),(10,14),(11,6),(11,14),(13,12),(14,13)],15)
=> ? = 0 + 1
[4,1,5,2,3] => [[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1],[1,0,0,0,0],[0,0,1,0,0]]
=> [[1,1,2,2,2],[2,2,4,4],[3,4,5],[4,5],[5]]
=> ([(0,1),(1,4),(1,5),(2,8),(2,32),(3,6),(3,30),(4,7),(4,33),(5,10),(5,11),(5,33),(6,20),(7,31),(8,27),(9,15),(9,19),(10,18),(10,28),(11,18),(11,25),(13,39),(14,36),(14,39),(15,36),(16,38),(17,38),(18,2),(18,37),(19,26),(19,36),(20,21),(21,12),(22,12),(23,17),(23,35),(24,16),(24,35),(25,13),(25,37),(26,24),(26,34),(27,16),(27,17),(28,14),(28,19),(28,37),(29,21),(29,22),(30,20),(30,29),(31,13),(31,14),(31,15),(32,23),(32,24),(32,27),(33,9),(33,25),(33,28),(33,31),(34,30),(34,35),(35,29),(35,38),(36,3),(36,34),(37,26),(37,32),(37,39),(38,22),(39,23),(39,34)],40)
=> ? = 0 + 1
[4,2,1,3,5] => [[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,0,0,0,1]]
=> [[1,1,2,2,3],[2,2,3,3],[3,3,4],[4,4],[5]]
=> ([(0,5),(0,10),(1,16),(2,15),(3,14),(4,13),(5,12),(6,2),(6,13),(7,4),(7,14),(8,1),(9,6),(10,11),(10,12),(11,3),(11,7),(12,9),(13,15),(14,8),(15,16)],17)
=> ? = 1 + 1
[4,2,3,1,5] => [[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1]]
=> [[1,1,2,2,4],[2,2,3,4],[3,3,4],[4,4],[5]]
=> ([(0,14),(0,15),(1,19),(2,18),(3,29),(4,30),(5,22),(6,23),(7,24),(7,25),(8,9),(9,7),(9,18),(9,19),(10,5),(11,6),(12,2),(12,29),(13,1),(13,30),(14,16),(14,28),(15,17),(15,28),(16,3),(16,12),(17,4),(17,13),(18,24),(18,27),(19,25),(19,27),(20,26),(21,26),(22,20),(23,21),(24,22),(24,31),(25,23),(25,31),(27,31),(28,8),(29,10),(30,11),(31,20),(31,21)],32)
=> ? = 0 + 1
[4,2,5,1,3] => [[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1],[1,0,0,0,0],[0,0,1,0,0]]
=> [[1,1,2,2,4],[2,2,4,4],[3,4,5],[4,5],[5]]
=> ([(0,7),(0,8),(1,2),(1,45),(2,35),(3,37),(4,14),(4,49),(5,9),(5,48),(6,10),(6,12),(6,54),(7,31),(8,6),(8,13),(8,31),(9,27),(9,42),(10,28),(10,41),(11,26),(11,52),(12,17),(12,28),(12,51),(13,15),(13,50),(13,54),(14,16),(14,40),(14,53),(15,33),(15,44),(16,38),(16,47),(17,30),(17,40),(19,64),(19,66),(20,62),(21,65),(22,58),(23,60),(23,66),(24,60),(24,63),(25,67),(26,55),(27,59),(28,5),(28,56),(29,34),(30,22),(30,57),(31,4),(31,50),(32,22),(32,65),(33,43),(34,18),(35,18),(36,20),(37,1),(37,46),(38,27),(38,61),(39,19),(39,55),(39,58),(40,38),(40,57),(41,21),(41,56),(42,20),(42,59),(43,26),(43,39),(44,21),(44,32),(45,34),(45,35),(46,29),(46,45),(47,19),(47,23),(47,61),(48,36),(48,42),(49,11),(49,43),(49,53),(50,33),(50,49),(51,30),(51,32),(51,56),(52,23),(52,24),(52,55),(53,39),(53,47),(53,52),(53,57),(54,41),(54,44),(54,51),(55,3),(55,63),(55,66),(56,48),(56,65),(57,24),(57,58),(57,61),(58,63),(58,64),(59,25),(59,62),(60,25),(60,68),(61,59),(61,60),(61,64),(62,67),(63,68),(64,62),(64,68),(65,36),(66,37),(66,68),(67,29),(68,46),(68,67)],69)
=> ? = 1 + 1
[4,3,1,2,5] => [[0,0,1,0,0],[0,0,0,1,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1]]
=> [[1,1,2,3,3],[2,2,3,4],[3,3,4],[4,4],[5]]
=> ([(0,13),(0,15),(1,17),(2,16),(2,17),(3,19),(4,16),(4,18),(5,22),(6,21),(7,20),(8,23),(8,29),(9,4),(9,28),(10,3),(10,28),(11,6),(12,7),(12,24),(13,14),(14,1),(14,2),(15,9),(15,10),(16,25),(17,12),(17,25),(18,26),(18,29),(19,23),(19,26),(20,27),(22,27),(23,30),(24,20),(24,22),(25,24),(26,30),(27,21),(28,8),(28,18),(28,19),(29,5),(29,30),(30,11)],31)
=> ? = 0 + 1
[4,3,2,1,5] => [[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1]]
=> [[1,1,2,3,4],[2,2,3,4],[3,3,4],[4,4],[5]]
=> ([(0,5),(0,16),(0,17),(1,23),(2,19),(3,11),(3,21),(4,10),(4,20),(5,12),(5,13),(6,50),(7,51),(8,24),(8,58),(9,25),(9,59),(10,14),(10,52),(11,15),(11,53),(12,26),(12,60),(13,27),(13,60),(14,54),(15,55),(16,4),(16,29),(17,3),(17,29),(18,48),(18,49),(19,32),(19,33),(20,46),(20,52),(21,47),(21,53),(22,34),(22,35),(23,18),(23,54),(23,55),(24,40),(24,42),(25,41),(25,43),(26,46),(26,56),(27,47),(27,57),(28,63),(29,1),(30,62),(31,61),(32,61),(33,61),(34,6),(34,62),(35,7),(35,62),(36,58),(37,59),(38,32),(39,33),(40,44),(41,45),(42,38),(43,39),(44,31),(45,31),(46,36),(47,37),(48,40),(48,63),(49,41),(49,63),(50,38),(51,39),(52,8),(52,36),(53,9),(53,37),(54,28),(54,48),(55,28),(55,49),(56,30),(56,34),(57,30),(57,35),(58,42),(58,50),(59,43),(59,51),(60,22),(60,56),(60,57),(62,2),(63,44),(63,45)],64)
=> ? = 0 + 1
[4,3,5,1,2] => [[0,0,0,1,0],[0,0,0,0,1],[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0]]
=> [[1,1,2,4,4],[2,2,4,5],[3,4,5],[4,5],[5]]
=> ([(0,2),(0,3),(1,8),(1,16),(2,1),(3,7),(3,10),(4,13),(4,59),(5,12),(5,81),(6,20),(6,82),(7,11),(7,83),(8,60),(9,23),(9,58),(10,19),(10,22),(10,83),(11,78),(12,64),(13,24),(14,52),(14,72),(15,17),(15,73),(15,80),(16,60),(16,74),(17,39),(17,70),(18,36),(18,44),(19,51),(19,69),(20,33),(20,75),(21,28),(21,38),(21,50),(22,51),(22,71),(22,74),(23,49),(23,56),(23,57),(25,101),(26,113),(27,107),(27,110),(28,107),(28,111),(29,110),(29,111),(30,112),(31,90),(31,98),(32,94),(32,114),(33,96),(34,91),(34,92),(35,89),(35,92),(36,108),(37,94),(37,103),(38,9),(38,111),(39,45),(40,31),(40,102),(40,114),(41,31),(41,104),(42,37),(42,99),(43,34),(43,85),(43,87),(44,30),(44,108),(45,55),(46,33),(46,86),(47,48),(47,86),(48,25),(48,100),(49,42),(49,85),(50,14),(50,76),(50,107),(51,15),(51,61),(51,84),(52,46),(52,109),(53,32),(53,93),(54,26),(54,95),(55,25),(55,91),(56,35),(56,85),(56,97),(57,53),(57,97),(58,57),(59,24),(60,5),(60,63),(61,67),(61,73),(62,34),(62,35),(62,113),(63,67),(63,81),(64,46),(64,47),(65,45),(65,68),(66,47),(66,68),(66,109),(67,65),(67,66),(68,48),(68,55),(68,87),(69,29),(69,38),(69,84),(70,26),(70,62),(71,27),(71,50),(71,84),(72,43),(72,49),(72,109),(73,39),(73,65),(74,61),(74,63),(75,32),(75,40),(75,96),(76,72),(76,79),(76,88),(77,40),(77,41),(77,93),(78,27),(78,28),(78,29),(79,43),(79,56),(79,62),(79,95),(80,54),(80,70),(80,79),(81,52),(81,64),(81,66),(82,53),(82,75),(82,77),(83,21),(83,69),(83,71),(83,78),(84,76),(84,80),(84,110),(85,92),(85,99),(86,37),(86,96),(86,100),(87,91),(87,99),(87,100),(88,82),(88,95),(89,104),(90,108),(90,116),(91,101),(91,106),(92,106),(93,18),(93,104),(93,114),(94,115),(95,77),(95,97),(95,113),(96,94),(96,102),(97,89),(97,93),(98,116),(99,103),(99,106),(100,101),(100,102),(100,103),(101,98),(101,105),(102,98),(102,115),(103,105),(103,115),(104,36),(104,90),(105,116),(106,105),(107,6),(107,88),(108,4),(108,112),(109,42),(109,86),(109,87),(110,54),(110,88),(111,58),(112,59),(113,41),(113,89),(114,44),(114,90),(114,115),(115,30),(115,116),(116,112)],117)
=> ? = 0 + 1
[4,3,5,2,1] => [[0,0,0,0,1],[0,0,0,1,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0]]
=> [[1,1,2,4,5],[2,2,4,5],[3,4,5],[4,5],[5]]
=> ([(0,4),(0,15),(0,16),(1,34),(2,7),(2,32),(3,14),(3,33),(4,11),(4,12),(5,147),(6,38),(6,125),(7,5),(7,114),(8,39),(8,161),(9,30),(9,158),(10,31),(10,96),(11,29),(11,159),(12,28),(12,41),(12,159),(13,24),(13,75),(14,20),(14,21),(14,156),(15,2),(15,54),(16,3),(16,54),(17,68),(17,119),(18,115),(18,120),(19,113),(19,149),(20,122),(20,154),(21,122),(21,164),(22,111),(22,145),(23,67),(23,116),(24,65),(24,66),(25,42),(25,117),(25,148),(26,37),(26,152),(26,163),(27,35),(27,150),(27,155),(28,118),(28,153),(29,121),(29,162),(30,110),(30,146),(31,109),(31,112),(32,114),(32,151),(33,121),(33,156),(34,36),(34,147),(34,164),(35,79),(35,81),(36,84),(36,134),(37,80),(37,137),(38,95),(38,106),(38,107),(39,58),(39,94),(39,139),(40,52),(40,64),(40,108),(41,118),(41,132),(41,151),(42,76),(42,77),(42,78),(43,211),(44,202),(45,173),(45,214),(46,168),(47,167),(47,168),(48,217),(49,212),(49,215),(50,174),(50,215),(51,218),(52,6),(52,212),(53,10),(54,1),(55,176),(56,176),(56,211),(57,192),(57,203),(58,173),(58,186),(59,177),(59,187),(60,175),(60,177),(61,214),(62,193),(63,182),(63,200),(64,22),(64,174),(64,212),(65,181),(66,181),(67,180),(68,179),(69,96),(70,57),(70,199),(70,213),(71,60),(71,169),(71,171),(72,100),(72,206),(73,58),(73,172),(74,66),(74,197),(75,65),(76,83),(76,170),(77,91),(77,167),(78,120),(78,167),(78,170),(79,88),(80,87),(81,136),(82,67),(82,216),(83,94),(83,208),(84,110),(84,210),(85,69),(85,208),(86,63),(86,198),(87,105),(88,55),(89,93),(89,172),(90,46),(90,210),(91,45),(91,196),(92,43),(92,209),(93,44),(93,195),(94,101),(94,173),(95,86),(95,169),(96,112),(97,102),(97,166),(97,188),(98,103),(98,188),(99,57),(99,191),(100,109),(100,182),(100,213),(101,97),(101,184),(102,56),(102,183),(102,209),(103,55),(103,183),(104,48),(104,185),(105,44),(105,175),(106,59),(106,169),(106,190),(107,72),(107,190),(108,19),(108,144),(108,174),(109,62),(109,166),(110,135),(111,53),(112,92),(112,166),(113,73),(113,207),(114,9),(114,126),(115,69),(115,178),(116,74),(116,180),(117,18),(117,78),(117,218),(118,26),(118,123),(118,165),(119,23),(119,82),(119,179),(120,27),(120,140),(120,178),(121,133),(122,138),(123,130),(123,152),(124,88),(124,103),(125,53),(125,107),(126,130),(126,158),(127,59),(127,60),(127,217),(128,87),(128,131),(129,89),(129,131),(129,207),(130,128),(130,129),(131,93),(131,105),(131,171),(132,50),(132,108),(132,165),(133,51),(133,148),(134,47),(134,77),(134,210),(135,45),(135,61),(136,43),(136,56),(137,48),(137,127),(138,46),(138,47),(139,70),(139,100),(139,186),(140,143),(140,150),(141,70),(141,99),(141,206),(142,97),(142,157),(143,98),(143,124),(144,149),(144,160),(144,189),(145,83),(145,85),(146,73),(146,89),(147,84),(147,90),(148,76),(148,145),(148,218),(149,71),(149,95),(149,207),(150,79),(150,124),(151,123),(151,126),(152,80),(152,128),(153,49),(153,52),(153,165),(154,51),(154,117),(155,81),(155,157),(156,25),(156,133),(156,154),(157,92),(157,102),(157,136),(158,113),(158,129),(158,146),(159,40),(159,132),(159,153),(159,162),(160,71),(160,106),(160,127),(160,185),(161,72),(161,139),(161,141),(162,49),(162,50),(162,64),(163,104),(163,137),(163,160),(164,90),(164,134),(164,138),(165,144),(165,163),(165,215),(166,193),(166,209),(167,140),(167,196),(168,61),(168,196),(169,177),(169,198),(170,178),(170,208),(171,175),(171,195),(171,198),(172,63),(172,186),(172,195),(173,184),(174,8),(174,189),(175,202),(175,204),(176,194),(177,204),(178,142),(178,155),(179,13),(179,216),(180,197),(182,62),(182,220),(183,176),(183,201),(184,188),(185,141),(185,190),(185,217),(186,182),(186,199),(187,191),(188,183),(188,193),(189,161),(189,185),(190,187),(190,206),(191,68),(191,192),(192,179),(192,219),(193,201),(194,197),(195,199),(195,200),(195,202),(196,143),(196,214),(197,181),(198,200),(198,204),(199,203),(199,220),(200,205),(200,220),(201,180),(201,194),(202,203),(202,205),(203,219),(204,205),(205,219),(206,17),(206,191),(206,213),(207,86),(207,171),(207,172),(208,101),(208,142),(209,116),(209,201),(209,211),(210,91),(210,135),(210,168),(211,74),(211,194),(212,111),(212,125),(213,119),(213,192),(213,220),(214,98),(214,184),(215,104),(215,189),(216,75),(217,99),(217,187),(218,85),(218,115),(218,170),(219,216),(220,82),(220,219)],221)
=> ? = 1 + 1
[4,5,3,1,2] => [[0,0,0,1,0],[0,0,0,0,1],[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0]]
=> [[1,1,3,4,4],[2,3,4,5],[3,4,5],[4,5],[5]]
=> ([(0,1),(0,2),(1,12),(1,14),(2,11),(2,13),(3,145),(4,146),(5,31),(5,155),(6,32),(6,156),(7,15),(7,143),(8,16),(8,144),(9,37),(9,114),(10,38),(10,115),(11,17),(11,157),(12,18),(12,158),(13,29),(13,35),(13,157),(14,30),(14,36),(14,158),(15,84),(16,85),(17,147),(18,148),(19,102),(19,133),(20,103),(20,134),(21,23),(21,149),(21,153),(22,24),(22,150),(22,154),(23,118),(23,128),(24,119),(24,129),(25,62),(25,82),(26,63),(26,83),(27,74),(27,139),(28,75),(28,140),(29,100),(29,126),(30,101),(30,127),(31,55),(31,135),(32,56),(32,136),(33,47),(33,72),(33,98),(34,48),(34,73),(34,99),(35,100),(35,130),(35,132),(36,101),(36,131),(36,132),(37,96),(37,110),(37,112),(38,97),(38,111),(38,113),(40,201),(40,202),(41,225),(42,226),(43,221),(43,223),(44,222),(44,224),(45,213),(45,221),(46,214),(46,222),(47,213),(47,223),(48,214),(48,224),(49,161),(50,162),(51,183),(51,227),(52,184),(52,228),(53,173),(53,195),(54,174),(54,196),(55,185),(56,186),(57,179),(57,180),(58,175),(58,177),(59,176),(59,178),(60,171),(60,177),(61,172),(61,178),(62,215),(63,216),(64,220),(65,219),(66,219),(67,220),(68,183),(68,203),(69,184),(69,204),(70,179),(70,199),(71,180),(71,200),(72,9),(72,223),(73,10),(73,224),(74,3),(74,189),(75,4),(75,190),(76,53),(76,205),(76,227),(77,54),(77,206),(77,228),(78,53),(78,207),(79,54),(79,208),(80,58),(80,163),(80,167),(81,59),(81,164),(81,168),(82,49),(82,215),(83,50),(83,216),(84,94),(85,95),(86,68),(86,197),(87,69),(87,198),(88,94),(89,95),(90,55),(90,169),(91,56),(91,170),(92,108),(92,170),(93,109),(93,169),(94,39),(95,39),(96,86),(96,163),(97,87),(97,164),(98,19),(98,137),(98,213),(99,20),(99,138),(99,214),(100,21),(100,116),(100,159),(101,22),(101,117),(101,160),(102,90),(102,217),(103,91),(103,218),(104,51),(104,181),(105,52),(105,182),(106,41),(106,187),(107,42),(107,188),(108,40),(108,175),(108,194),(109,40),(109,176),(109,193),(110,60),(110,163),(110,191),(111,61),(111,164),(111,192),(112,104),(112,191),(113,105),(113,192),(114,112),(115,113),(116,124),(116,149),(117,124),(117,150),(118,91),(118,92),(119,90),(119,93),(120,58),(120,60),(120,225),(121,59),(121,61),(121,226),(122,92),(122,125),(122,218),(123,93),(123,125),(123,217),(124,122),(124,123),(125,108),(125,109),(125,167),(125,168),(126,43),(126,72),(126,159),(127,44),(127,73),(127,160),(128,41),(128,120),(129,42),(129,121),(130,45),(130,98),(130,159),(131,46),(131,99),(131,160),(132,116),(132,117),(133,80),(133,96),(133,217),(134,81),(134,97),(134,218),(135,51),(135,76),(135,185),(136,52),(136,77),(136,186),(137,133),(137,151),(137,165),(138,134),(138,152),(138,166),(139,57),(139,70),(139,189),(140,57),(140,71),(140,190),(141,76),(141,78),(141,181),(142,77),(142,79),(142,182),(143,84),(143,88),(144,85),(144,89),(145,64),(145,67),(146,65),(146,66),(147,43),(147,45),(147,47),(148,44),(148,46),(148,48),(149,103),(149,118),(149,122),(150,102),(150,119),(150,123),(151,80),(151,110),(151,120),(151,187),(152,81),(152,111),(152,121),(152,188),(153,106),(153,128),(153,151),(154,107),(154,129),(154,152),(155,104),(155,135),(155,141),(156,105),(156,136),(156,142),(157,33),(157,126),(157,130),(157,147),(158,34),(158,127),(158,131),(158,148),(159,137),(159,153),(159,221),(160,138),(160,154),(160,222),(161,143),(162,144),(163,27),(163,177),(163,197),(164,28),(164,178),(164,198),(165,155),(165,187),(166,156),(166,188),(167,175),(167,193),(167,197),(168,176),(168,194),(168,198),(169,68),(169,185),(169,193),(170,69),(170,186),(170,194),(171,207),(172,208),(173,215),(173,231),(174,216),(174,232),(175,201),(175,209),(176,202),(176,210),(177,74),(177,209),(178,75),(178,210),(179,66),(179,233),(180,67),(180,233),(181,25),(181,207),(181,227),(182,26),(182,208),(182,228),(183,229),(184,230),(185,183),(185,205),(186,184),(186,206),(187,141),(187,191),(187,225),(188,142),(188,192),(188,226),(189,145),(189,180),(189,199),(190,146),(190,179),(190,200),(191,171),(191,181),(192,172),(192,182),(193,201),(193,203),(193,205),(194,202),(194,204),(194,206),(195,231),(196,232),(197,139),(197,203),(197,209),(198,140),(198,204),(198,210),(199,64),(199,233),(200,65),(200,233),(201,195),(201,211),(202,196),(202,212),(203,70),(203,211),(203,229),(204,71),(204,212),(204,230),(205,195),(205,229),(206,196),(206,230),(207,62),(207,173),(208,63),(208,174),(209,189),(209,211),(210,190),(210,212),(211,199),(211,231),(212,200),(212,232),(213,5),(213,165),(214,6),(214,166),(215,7),(215,161),(216,8),(216,162),(217,86),(217,167),(217,169),(218,87),(218,168),(218,170),(219,88),(220,89),(221,106),(221,165),(222,107),(222,166),(223,114),(224,115),(225,78),(225,171),(226,79),(226,172),(227,82),(227,173),(227,229),(228,83),(228,174),(228,230),(229,49),(229,231),(230,50),(230,232),(231,161),(232,162),(233,219),(233,220)],234)
=> ? = 0 + 1
[1,2,3,4,6,5] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,4,4],[5,6],[6]]
=> ([(0,1)],2)
=> 1 = 0 + 1
[1,2,3,5,4,6] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,4,5],[5,5],[6]]
=> ([(0,1)],2)
=> 1 = 0 + 1
[1,2,4,3,5,6] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,4],[4,4,4],[5,5],[6]]
=> ([(0,1)],2)
=> 1 = 0 + 1
[1,2,4,3,6,5] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,4],[4,4,4],[5,6],[6]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 2 + 1
[1,3,2,4,5,6] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,3],[4,4,4],[5,5],[6]]
=> ([(0,1)],2)
=> 1 = 0 + 1
[1,3,2,4,6,5] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,3],[4,4,4],[5,6],[6]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 2 + 1
[1,3,2,5,4,6] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,3],[4,4,5],[5,5],[6]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 2 + 1
[2,1,3,4,5,6] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,3],[4,4,4],[5,5],[6]]
=> ([(0,1)],2)
=> 1 = 0 + 1
[2,1,3,4,6,5] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,3],[4,4,4],[5,6],[6]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 2 + 1
[2,1,3,5,4,6] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,3],[4,4,5],[5,5],[6]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 2 + 1
[2,1,4,3,5,6] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,4],[4,4,4],[5,5],[6]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 2 + 1
Description
The number of posets with the same zeta polynomial. The zeta polynomial $Z$ is the polynomial such that $Z(m)$ is the number of weakly increasing sequences $x_1\leq x_2\leq\dots\leq x_{m−1}$ of elements of the poset. See section 3.12 of [1]. Since $$ Z(q) = \sum_{k\geq 1} \binom{q-2}{k-1} c_k, $$ where $c_k$ is the number of chains of length $k$, this statistic is the same as the number of posets with the same chain polynomial.
Matching statistic: St000526
Mp00063: Permutations to alternating sign matrixAlternating sign matrices
Mp00001: Alternating sign matrices to semistandard tableau via monotone trianglesSemistandard tableaux
Mp00214: Semistandard tableaux subcrystalPosets
St000526: Posets ⟶ ℤResult quality: 5% values known / values provided: 5%distinct values known / distinct values provided: 18%
Values
[2,1] => [[0,1],[1,0]]
=> [[1,2],[2]]
=> ([(0,1)],2)
=> 1 = 0 + 1
[1,3,2] => [[1,0,0],[0,0,1],[0,1,0]]
=> [[1,1,1],[2,3],[3]]
=> ([(0,1)],2)
=> 1 = 0 + 1
[2,1,3] => [[0,1,0],[1,0,0],[0,0,1]]
=> [[1,1,2],[2,2],[3]]
=> ([(0,1)],2)
=> 1 = 0 + 1
[1,2,4,3] => [[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
=> [[1,1,1,1],[2,2,2],[3,4],[4]]
=> ([(0,1)],2)
=> 1 = 0 + 1
[1,3,2,4] => [[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,3],[3,3],[4]]
=> ([(0,1)],2)
=> 1 = 0 + 1
[1,4,2,3] => [[1,0,0,0],[0,0,1,0],[0,0,0,1],[0,1,0,0]]
=> [[1,1,1,1],[2,3,3],[3,4],[4]]
=> ([(0,3),(2,1),(3,2)],4)
=> 1 = 0 + 1
[2,1,3,4] => [[0,1,0,0],[1,0,0,0],[0,0,1,0],[0,0,0,1]]
=> [[1,1,1,2],[2,2,2],[3,3],[4]]
=> ([(0,1)],2)
=> 1 = 0 + 1
[2,1,4,3] => [[0,1,0,0],[1,0,0,0],[0,0,0,1],[0,0,1,0]]
=> [[1,1,1,2],[2,2,2],[3,4],[4]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 2 + 1
[2,3,4,1] => [[0,0,0,1],[1,0,0,0],[0,1,0,0],[0,0,1,0]]
=> [[1,1,1,4],[2,2,4],[3,4],[4]]
=> ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
=> ? = 0 + 1
[2,4,1,3] => [[0,0,1,0],[1,0,0,0],[0,0,0,1],[0,1,0,0]]
=> [[1,1,1,3],[2,3,3],[3,4],[4]]
=> ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> ? = 0 + 1
[2,4,3,1] => [[0,0,0,1],[1,0,0,0],[0,0,1,0],[0,1,0,0]]
=> [[1,1,1,4],[2,3,4],[3,4],[4]]
=> ([(0,5),(0,10),(1,16),(2,15),(3,14),(4,13),(5,12),(6,2),(6,13),(7,4),(7,14),(8,1),(9,6),(10,11),(10,12),(11,3),(11,7),(12,9),(13,15),(14,8),(15,16)],17)
=> ? = 1 + 1
[3,1,4,2] => [[0,1,0,0],[0,0,0,1],[1,0,0,0],[0,0,1,0]]
=> [[1,1,2,2],[2,2,4],[3,4],[4]]
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 1 + 1
[3,2,4,1] => [[0,0,0,1],[0,1,0,0],[1,0,0,0],[0,0,1,0]]
=> [[1,1,2,4],[2,2,4],[3,4],[4]]
=> ([(0,7),(0,8),(1,12),(2,11),(3,10),(4,10),(4,11),(5,3),(6,1),(6,13),(7,9),(8,5),(9,2),(9,4),(10,14),(11,6),(11,14),(13,12),(14,13)],15)
=> ? = 1 + 1
[3,4,2,1] => [[0,0,0,1],[0,0,1,0],[1,0,0,0],[0,1,0,0]]
=> [[1,1,3,4],[2,3,4],[3,4],[4]]
=> ([(0,13),(0,15),(1,17),(2,16),(2,17),(3,19),(4,16),(4,18),(5,22),(6,21),(7,20),(8,23),(8,29),(9,4),(9,28),(10,3),(10,28),(11,6),(12,7),(12,24),(13,14),(14,1),(14,2),(15,9),(15,10),(16,25),(17,12),(17,25),(18,26),(18,29),(19,23),(19,26),(20,27),(22,27),(23,30),(24,20),(24,22),(25,24),(26,30),(27,21),(28,8),(28,18),(28,19),(29,5),(29,30),(30,11)],31)
=> ? = 1 + 1
[4,1,3,2] => [[0,1,0,0],[0,0,0,1],[0,0,1,0],[1,0,0,0]]
=> [[1,2,2,2],[2,3,4],[3,4],[4]]
=> ([(0,7),(0,8),(1,12),(2,11),(3,10),(4,10),(4,11),(5,3),(6,1),(6,13),(7,9),(8,5),(9,2),(9,4),(10,14),(11,6),(11,14),(13,12),(14,13)],15)
=> ? = 0 + 1
[4,2,1,3] => [[0,0,1,0],[0,1,0,0],[0,0,0,1],[1,0,0,0]]
=> [[1,2,2,3],[2,3,3],[3,4],[4]]
=> ([(0,5),(0,10),(1,16),(2,15),(3,14),(4,13),(5,12),(6,2),(6,13),(7,4),(7,14),(8,1),(9,6),(10,11),(10,12),(11,3),(11,7),(12,9),(13,15),(14,8),(15,16)],17)
=> ? = 1 + 1
[4,2,3,1] => [[0,0,0,1],[0,1,0,0],[0,0,1,0],[1,0,0,0]]
=> [[1,2,2,4],[2,3,4],[3,4],[4]]
=> ([(0,14),(0,15),(1,19),(2,18),(3,29),(4,30),(5,22),(6,23),(7,24),(7,25),(8,9),(9,7),(9,18),(9,19),(10,5),(11,6),(12,2),(12,29),(13,1),(13,30),(14,16),(14,28),(15,17),(15,28),(16,3),(16,12),(17,4),(17,13),(18,24),(18,27),(19,25),(19,27),(20,26),(21,26),(22,20),(23,21),(24,22),(24,31),(25,23),(25,31),(27,31),(28,8),(29,10),(30,11),(31,20),(31,21)],32)
=> ? = 0 + 1
[4,3,1,2] => [[0,0,1,0],[0,0,0,1],[0,1,0,0],[1,0,0,0]]
=> [[1,2,3,3],[2,3,4],[3,4],[4]]
=> ([(0,13),(0,15),(1,17),(2,16),(2,17),(3,19),(4,16),(4,18),(5,22),(6,21),(7,20),(8,23),(8,29),(9,4),(9,28),(10,3),(10,28),(11,6),(12,7),(12,24),(13,14),(14,1),(14,2),(15,9),(15,10),(16,25),(17,12),(17,25),(18,26),(18,29),(19,23),(19,26),(20,27),(22,27),(23,30),(24,20),(24,22),(25,24),(26,30),(27,21),(28,8),(28,18),(28,19),(29,5),(29,30),(30,11)],31)
=> ? = 0 + 1
[4,3,2,1] => [[0,0,0,1],[0,0,1,0],[0,1,0,0],[1,0,0,0]]
=> [[1,2,3,4],[2,3,4],[3,4],[4]]
=> ([(0,5),(0,16),(0,17),(1,23),(2,19),(3,11),(3,21),(4,10),(4,20),(5,12),(5,13),(6,50),(7,51),(8,24),(8,58),(9,25),(9,59),(10,14),(10,52),(11,15),(11,53),(12,26),(12,60),(13,27),(13,60),(14,54),(15,55),(16,4),(16,29),(17,3),(17,29),(18,48),(18,49),(19,32),(19,33),(20,46),(20,52),(21,47),(21,53),(22,34),(22,35),(23,18),(23,54),(23,55),(24,40),(24,42),(25,41),(25,43),(26,46),(26,56),(27,47),(27,57),(28,63),(29,1),(30,62),(31,61),(32,61),(33,61),(34,6),(34,62),(35,7),(35,62),(36,58),(37,59),(38,32),(39,33),(40,44),(41,45),(42,38),(43,39),(44,31),(45,31),(46,36),(47,37),(48,40),(48,63),(49,41),(49,63),(50,38),(51,39),(52,8),(52,36),(53,9),(53,37),(54,28),(54,48),(55,28),(55,49),(56,30),(56,34),(57,30),(57,35),(58,42),(58,50),(59,43),(59,51),(60,22),(60,56),(60,57),(62,2),(63,44),(63,45)],64)
=> ? = 0 + 1
[1,2,3,5,4] => [[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0]]
=> [[1,1,1,1,1],[2,2,2,2],[3,3,3],[4,5],[5]]
=> ([(0,1)],2)
=> 1 = 0 + 1
[1,2,4,3,5] => [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [[1,1,1,1,1],[2,2,2,2],[3,3,4],[4,4],[5]]
=> ([(0,1)],2)
=> 1 = 0 + 1
[1,2,5,3,4] => [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1],[0,0,1,0,0]]
=> [[1,1,1,1,1],[2,2,2,2],[3,4,4],[4,5],[5]]
=> ([(0,3),(2,1),(3,2)],4)
=> 1 = 0 + 1
[1,3,2,4,5] => [[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
=> [[1,1,1,1,1],[2,2,2,3],[3,3,3],[4,4],[5]]
=> ([(0,1)],2)
=> 1 = 0 + 1
[1,3,2,5,4] => [[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
=> [[1,1,1,1,1],[2,2,2,3],[3,3,3],[4,5],[5]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 2 + 1
[1,3,4,5,2] => [[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0]]
=> [[1,1,1,1,1],[2,2,2,5],[3,3,5],[4,5],[5]]
=> ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
=> ? = 0 + 1
[1,3,5,2,4] => [[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,1,0,0]]
=> [[1,1,1,1,1],[2,2,2,4],[3,4,4],[4,5],[5]]
=> ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> ? = 0 + 1
[1,3,5,4,2] => [[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0]]
=> [[1,1,1,1,1],[2,2,2,5],[3,4,5],[4,5],[5]]
=> ([(0,5),(0,10),(1,16),(2,15),(3,14),(4,13),(5,12),(6,2),(6,13),(7,4),(7,14),(8,1),(9,6),(10,11),(10,12),(11,3),(11,7),(12,9),(13,15),(14,8),(15,16)],17)
=> ? = 1 + 1
[1,4,2,3,5] => [[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [[1,1,1,1,1],[2,2,3,3],[3,3,4],[4,4],[5]]
=> ([(0,3),(2,1),(3,2)],4)
=> 1 = 0 + 1
[1,4,2,5,3] => [[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,0,1,0]]
=> [[1,1,1,1,1],[2,2,3,3],[3,3,5],[4,5],[5]]
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 1 + 1
[1,4,3,5,2] => [[1,0,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0]]
=> [[1,1,1,1,1],[2,2,3,5],[3,3,5],[4,5],[5]]
=> ([(0,7),(0,8),(1,12),(2,11),(3,10),(4,10),(4,11),(5,3),(6,1),(6,13),(7,9),(8,5),(9,2),(9,4),(10,14),(11,6),(11,14),(13,12),(14,13)],15)
=> ? = 1 + 1
[1,4,5,2,3] => [[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0]]
=> [[1,1,1,1,1],[2,2,4,4],[3,4,5],[4,5],[5]]
=> ([(0,8),(2,11),(2,12),(3,10),(4,9),(5,4),(5,14),(6,3),(6,14),(7,1),(8,5),(8,6),(9,11),(9,13),(10,12),(10,13),(11,15),(12,15),(13,15),(14,2),(14,9),(14,10),(15,7)],16)
=> ? = 0 + 1
[1,4,5,3,2] => [[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0]]
=> [[1,1,1,1,1],[2,2,4,5],[3,4,5],[4,5],[5]]
=> ([(0,13),(0,15),(1,17),(2,16),(2,17),(3,19),(4,16),(4,18),(5,22),(6,21),(7,20),(8,23),(8,29),(9,4),(9,28),(10,3),(10,28),(11,6),(12,7),(12,24),(13,14),(14,1),(14,2),(15,9),(15,10),(16,25),(17,12),(17,25),(18,26),(18,29),(19,23),(19,26),(20,27),(22,27),(23,30),(24,20),(24,22),(25,24),(26,30),(27,21),(28,8),(28,18),(28,19),(29,5),(29,30),(30,11)],31)
=> ? = 1 + 1
[1,5,3,2,4] => [[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1],[0,1,0,0,0]]
=> [[1,1,1,1,1],[2,3,3,4],[3,4,4],[4,5],[5]]
=> ([(0,5),(0,10),(1,16),(2,15),(3,14),(4,13),(5,12),(6,2),(6,13),(7,4),(7,14),(8,1),(9,6),(10,11),(10,12),(11,3),(11,7),(12,9),(13,15),(14,8),(15,16)],17)
=> ? = 1 + 1
[1,5,4,3,2] => [[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0]]
=> [[1,1,1,1,1],[2,3,4,5],[3,4,5],[4,5],[5]]
=> ([(0,5),(0,16),(0,17),(1,23),(2,19),(3,11),(3,21),(4,10),(4,20),(5,12),(5,13),(6,50),(7,51),(8,24),(8,58),(9,25),(9,59),(10,14),(10,52),(11,15),(11,53),(12,26),(12,60),(13,27),(13,60),(14,54),(15,55),(16,4),(16,29),(17,3),(17,29),(18,48),(18,49),(19,32),(19,33),(20,46),(20,52),(21,47),(21,53),(22,34),(22,35),(23,18),(23,54),(23,55),(24,40),(24,42),(25,41),(25,43),(26,46),(26,56),(27,47),(27,57),(28,63),(29,1),(30,62),(31,61),(32,61),(33,61),(34,6),(34,62),(35,7),(35,62),(36,58),(37,59),(38,32),(39,33),(40,44),(41,45),(42,38),(43,39),(44,31),(45,31),(46,36),(47,37),(48,40),(48,63),(49,41),(49,63),(50,38),(51,39),(52,8),(52,36),(53,9),(53,37),(54,28),(54,48),(55,28),(55,49),(56,30),(56,34),(57,30),(57,35),(58,42),(58,50),(59,43),(59,51),(60,22),(60,56),(60,57),(62,2),(63,44),(63,45)],64)
=> ? = 0 + 1
[2,1,3,4,5] => [[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]]
=> [[1,1,1,1,2],[2,2,2,2],[3,3,3],[4,4],[5]]
=> ([(0,1)],2)
=> 1 = 0 + 1
[2,1,3,5,4] => [[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0]]
=> [[1,1,1,1,2],[2,2,2,2],[3,3,3],[4,5],[5]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 2 + 1
[2,1,4,3,5] => [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [[1,1,1,1,2],[2,2,2,2],[3,3,4],[4,4],[5]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 2 + 1
[2,1,4,5,3] => [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,0,0,1,0]]
=> [[1,1,1,1,2],[2,2,2,2],[3,3,5],[4,5],[5]]
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 1 + 1
[2,1,5,4,3] => [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0]]
=> [[1,1,1,1,2],[2,2,2,2],[3,4,5],[4,5],[5]]
=> ([(0,3),(0,6),(0,7),(1,8),(1,12),(2,8),(2,11),(3,9),(3,10),(4,2),(4,13),(5,1),(5,14),(6,4),(6,9),(7,5),(7,10),(8,15),(9,13),(10,14),(11,15),(12,15),(13,11),(14,12)],16)
=> ? = 0 + 1
[2,3,1,5,4] => [[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
=> [[1,1,1,1,3],[2,2,2,3],[3,3,3],[4,5],[5]]
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 1 + 1
[2,3,4,1,5] => [[0,0,0,1,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [[1,1,1,1,4],[2,2,2,4],[3,3,4],[4,4],[5]]
=> ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
=> ? = 0 + 1
[2,3,4,5,1] => [[0,0,0,0,1],[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0]]
=> [[1,1,1,1,5],[2,2,2,5],[3,3,5],[4,5],[5]]
=> ([(0,9),(1,13),(2,14),(4,12),(5,11),(6,1),(6,12),(7,3),(8,5),(8,15),(9,10),(10,4),(10,6),(11,14),(12,8),(12,13),(13,15),(14,7),(15,2),(15,11)],16)
=> ? = 0 + 1
[2,4,1,3,5] => [[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [[1,1,1,1,3],[2,2,3,3],[3,3,4],[4,4],[5]]
=> ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> ? = 0 + 1
[2,4,1,5,3] => [[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,0,1,0]]
=> [[1,1,1,1,3],[2,2,3,3],[3,3,5],[4,5],[5]]
=> ([(0,6),(0,7),(1,5),(1,15),(2,4),(2,14),(3,13),(4,12),(5,3),(5,16),(6,9),(7,2),(7,9),(9,1),(9,14),(10,11),(11,8),(12,10),(13,8),(14,12),(14,15),(15,10),(15,16),(16,11),(16,13)],17)
=> ? = 0 + 1
[2,4,3,1,5] => [[0,0,0,1,0],[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [[1,1,1,1,4],[2,2,3,4],[3,3,4],[4,4],[5]]
=> ([(0,5),(0,10),(1,16),(2,15),(3,14),(4,13),(5,12),(6,2),(6,13),(7,4),(7,14),(8,1),(9,6),(10,11),(10,12),(11,3),(11,7),(12,9),(13,15),(14,8),(15,16)],17)
=> ? = 1 + 1
[2,4,3,5,1] => [[0,0,0,0,1],[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0]]
=> [[1,1,1,1,5],[2,2,3,5],[3,3,5],[4,5],[5]]
=> ([(0,8),(0,13),(1,19),(2,16),(2,18),(3,21),(4,26),(5,24),(6,16),(6,22),(7,20),(7,23),(8,17),(9,4),(9,18),(10,9),(11,7),(11,30),(12,3),(12,25),(13,14),(13,17),(14,1),(14,15),(15,2),(15,6),(15,19),(16,28),(17,10),(18,26),(18,28),(19,11),(19,22),(20,24),(20,31),(22,30),(23,31),(24,12),(24,27),(25,21),(26,23),(26,29),(27,25),(28,29),(29,31),(30,5),(30,20),(31,27)],32)
=> ? = 0 + 1
[2,4,5,1,3] => [[0,0,0,1,0],[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0]]
=> [[1,1,1,1,4],[2,2,4,4],[3,4,5],[4,5],[5]]
=> ([(0,9),(0,10),(1,2),(3,7),(3,23),(4,6),(4,22),(5,15),(6,16),(7,8),(7,24),(8,20),(9,19),(10,4),(10,19),(11,14),(11,18),(12,26),(13,26),(14,25),(15,1),(16,21),(17,13),(17,25),(18,12),(18,25),(19,3),(19,22),(20,12),(20,13),(21,14),(21,17),(22,16),(22,23),(23,11),(23,21),(23,24),(24,17),(24,18),(24,20),(25,5),(25,26),(26,15)],27)
=> ? = 0 + 1
[2,4,5,3,1] => [[0,0,0,0,1],[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0]]
=> [[1,1,1,1,5],[2,2,4,5],[3,4,5],[4,5],[5]]
=> ([(0,17),(0,18),(1,11),(1,12),(2,53),(3,50),(4,33),(5,16),(5,65),(6,13),(6,61),(7,14),(7,62),(8,15),(8,51),(9,25),(9,63),(10,24),(10,52),(11,54),(12,22),(12,23),(12,54),(13,36),(14,35),(15,40),(16,59),(17,1),(17,48),(18,7),(18,48),(19,32),(19,45),(20,29),(20,38),(21,55),(21,58),(22,49),(22,60),(23,42),(23,49),(24,31),(24,46),(25,21),(25,60),(25,64),(27,70),(28,70),(29,67),(30,66),(31,68),(32,3),(32,69),(33,8),(34,39),(35,57),(36,39),(37,32),(37,66),(38,19),(38,37),(38,67),(39,26),(40,26),(41,30),(41,67),(42,52),(43,44),(43,68),(44,28),(44,69),(45,27),(45,69),(46,53),(46,68),(47,61),(48,9),(48,62),(49,5),(49,56),(50,34),(51,40),(52,2),(52,46),(53,6),(53,47),(54,10),(54,42),(55,31),(55,43),(56,43),(56,65),(57,29),(57,41),(58,30),(58,37),(59,27),(59,28),(60,55),(60,56),(61,34),(61,36),(62,35),(62,63),(63,20),(63,57),(63,64),(64,38),(64,41),(64,58),(65,44),(65,45),(65,59),(66,33),(67,4),(67,66),(68,47),(69,50),(69,70),(70,51)],71)
=> ? = 1 + 1
[2,5,1,3,4] => [[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1],[0,1,0,0,0]]
=> [[1,1,1,1,3],[2,3,3,3],[3,4,4],[4,5],[5]]
=> ([(0,4),(0,8),(1,11),(3,10),(4,9),(5,2),(6,3),(6,12),(7,5),(8,6),(8,9),(9,12),(10,11),(11,7),(12,1),(12,10)],13)
=> ? = 0 + 1
[3,1,2,5,4] => [[0,1,0,0,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
=> [[1,1,1,2,2],[2,2,2,3],[3,3,3],[4,5],[5]]
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 0 + 1
[3,1,4,2,5] => [[0,1,0,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [[1,1,1,2,2],[2,2,2,4],[3,3,4],[4,4],[5]]
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 1 + 1
[3,2,1,5,4] => [[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
=> [[1,1,1,2,3],[2,2,2,3],[3,3,3],[4,5],[5]]
=> ([(0,3),(0,6),(0,7),(1,8),(1,12),(2,8),(2,11),(3,9),(3,10),(4,2),(4,13),(5,1),(5,14),(6,4),(6,9),(7,5),(7,10),(8,15),(9,13),(10,14),(11,15),(12,15),(13,11),(14,12)],16)
=> ? = 0 + 1
[3,2,4,1,5] => [[0,0,0,1,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [[1,1,1,2,4],[2,2,2,4],[3,3,4],[4,4],[5]]
=> ([(0,7),(0,8),(1,12),(2,11),(3,10),(4,10),(4,11),(5,3),(6,1),(6,13),(7,9),(8,5),(9,2),(9,4),(10,14),(11,6),(11,14),(13,12),(14,13)],15)
=> ? = 1 + 1
[3,4,2,1,5] => [[0,0,0,1,0],[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [[1,1,1,3,4],[2,2,3,4],[3,3,4],[4,4],[5]]
=> ([(0,13),(0,15),(1,17),(2,16),(2,17),(3,19),(4,16),(4,18),(5,22),(6,21),(7,20),(8,23),(8,29),(9,4),(9,28),(10,3),(10,28),(11,6),(12,7),(12,24),(13,14),(14,1),(14,2),(15,9),(15,10),(16,25),(17,12),(17,25),(18,26),(18,29),(19,23),(19,26),(20,27),(22,27),(23,30),(24,20),(24,22),(25,24),(26,30),(27,21),(28,8),(28,18),(28,19),(29,5),(29,30),(30,11)],31)
=> ? = 1 + 1
[3,5,2,1,4] => [[0,0,0,1,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0]]
=> [[1,1,1,3,4],[2,3,3,4],[3,4,4],[4,5],[5]]
=> ([(0,15),(0,16),(0,20),(1,9),(2,13),(2,47),(3,38),(4,14),(4,46),(5,40),(6,10),(6,26),(7,18),(7,45),(8,19),(8,39),(9,25),(10,32),(11,31),(12,44),(13,12),(13,48),(14,11),(14,42),(15,8),(15,28),(16,7),(16,37),(17,24),(17,33),(18,21),(18,36),(19,21),(19,35),(20,28),(20,37),(21,51),(22,49),(23,49),(24,3),(24,50),(26,1),(27,25),(28,39),(29,46),(30,27),(31,30),(32,27),(33,23),(33,50),(34,22),(34,50),(35,40),(35,51),(36,41),(36,51),(37,2),(37,45),(38,43),(39,5),(39,35),(40,4),(40,29),(41,24),(41,34),(42,31),(42,43),(43,30),(43,32),(44,22),(44,23),(45,36),(45,47),(46,38),(46,42),(47,17),(47,41),(47,48),(48,33),(48,34),(48,44),(49,26),(50,6),(50,49),(51,29)],52)
=> ? = 1 + 1
[3,5,2,4,1] => [[0,0,0,0,1],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0]]
=> [[1,1,1,3,5],[2,3,3,5],[3,4,5],[4,5],[5]]
=> ([(0,16),(0,17),(0,28),(1,9),(2,70),(3,13),(3,85),(4,27),(4,69),(5,83),(6,15),(6,43),(7,26),(7,84),(8,12),(8,29),(8,71),(9,68),(10,77),(11,76),(12,14),(12,78),(13,10),(13,86),(14,11),(14,87),(15,75),(16,8),(16,48),(17,7),(17,67),(18,42),(18,61),(19,25),(19,62),(19,63),(20,22),(20,59),(20,79),(21,24),(21,41),(21,60),(22,23),(22,80),(22,81),(23,64),(23,66),(24,37),(24,65),(25,36),(25,46),(26,50),(26,58),(27,31),(27,32),(28,48),(28,67),(29,57),(29,58),(29,78),(31,103),(32,103),(33,89),(34,89),(35,90),(36,88),(37,92),(38,102),(39,93),(40,101),(41,4),(41,100),(42,5),(42,97),(43,1),(44,53),(45,51),(45,95),(46,41),(46,88),(47,54),(48,71),(49,79),(50,73),(50,98),(51,68),(51,102),(52,31),(52,96),(53,30),(54,30),(55,33),(55,97),(56,35),(56,99),(57,70),(57,98),(58,74),(58,98),(59,81),(59,90),(60,37),(60,100),(61,34),(61,97),(62,36),(62,99),(63,21),(63,46),(63,99),(64,52),(64,91),(65,52),(65,92),(66,45),(66,91),(67,3),(67,84),(68,47),(69,32),(70,20),(70,49),(71,2),(71,57),(72,53),(72,54),(73,42),(73,55),(74,56),(74,62),(75,38),(75,51),(76,35),(76,59),(77,33),(77,34),(78,19),(78,74),(78,87),(79,80),(79,83),(79,90),(80,66),(80,82),(80,94),(81,64),(81,65),(81,94),(82,45),(82,75),(82,93),(83,39),(83,82),(84,50),(84,85),(85,18),(85,73),(85,86),(86,55),(86,61),(86,77),(87,56),(87,63),(87,76),(88,100),(89,43),(90,39),(90,94),(91,95),(91,96),(92,40),(92,96),(93,38),(93,40),(93,95),(94,91),(94,92),(94,93),(95,101),(95,102),(96,101),(96,103),(97,6),(97,89),(98,49),(99,60),(99,88),(100,69),(101,44),(101,72),(102,47),(102,72),(103,44)],104)
=> ? = 2 + 1
[3,5,4,1,2] => [[0,0,0,1,0],[0,0,0,0,1],[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0]]
=> [[1,1,1,4,4],[2,3,4,5],[3,4,5],[4,5],[5]]
=> ([(0,12),(0,13),(1,6),(2,61),(3,5),(3,94),(4,81),(5,80),(6,32),(7,4),(7,95),(8,22),(8,87),(9,20),(9,85),(10,19),(10,92),(11,17),(11,18),(11,98),(12,51),(13,11),(13,21),(13,51),(14,46),(14,47),(15,42),(15,89),(16,73),(16,75),(17,27),(17,48),(17,97),(18,48),(18,90),(19,43),(19,91),(20,44),(20,76),(21,25),(21,88),(21,98),(22,26),(22,74),(22,96),(23,24),(23,45),(23,77),(24,66),(24,67),(25,53),(25,93),(26,68),(26,84),(27,74),(27,78),(28,37),(28,60),(28,72),(29,124),(30,124),(31,101),(31,123),(33,117),(33,125),(34,118),(35,99),(36,116),(36,128),(37,101),(37,121),(38,109),(38,125),(39,100),(39,103),(40,109),(40,129),(41,126),(42,119),(43,107),(44,113),(45,9),(45,106),(46,108),(47,2),(47,108),(48,10),(48,122),(49,65),(49,128),(50,64),(51,8),(51,88),(52,39),(52,121),(52,123),(53,79),(54,45),(54,100),(55,32),(56,29),(56,127),(57,30),(57,127),(58,35),(58,120),(59,34),(59,99),(60,63),(60,101),(61,55),(62,56),(62,104),(63,83),(63,111),(64,57),(64,104),(65,44),(65,114),(66,58),(66,110),(67,65),(67,110),(68,43),(68,115),(69,34),(69,105),(70,36),(70,112),(71,33),(71,103),(71,119),(72,23),(72,54),(72,121),(73,50),(74,68),(74,102),(75,3),(75,82),(76,64),(76,113),(77,66),(77,106),(78,39),(78,54),(78,102),(79,42),(79,71),(80,29),(80,30),(81,35),(81,59),(82,62),(82,94),(83,49),(83,67),(83,112),(84,33),(84,38),(84,115),(85,50),(85,76),(86,59),(86,69),(86,120),(87,15),(87,79),(87,96),(88,53),(88,87),(89,38),(89,40),(89,119),(90,31),(90,60),(90,122),(91,36),(91,49),(91,107),(92,70),(92,83),(92,91),(93,31),(93,37),(93,52),(94,56),(94,57),(94,80),(95,58),(95,81),(95,86),(96,71),(96,84),(96,89),(96,102),(97,52),(97,72),(97,78),(97,122),(98,28),(98,90),(98,93),(98,97),(99,46),(99,118),(100,106),(101,7),(101,111),(102,40),(102,103),(102,115),(103,117),(103,129),(104,127),(105,47),(105,118),(106,85),(107,41),(107,116),(108,1),(109,41),(109,130),(110,114),(110,120),(111,95),(111,112),(112,86),(112,110),(112,128),(113,104),(114,105),(114,113),(115,107),(115,109),(115,117),(116,126),(117,116),(117,130),(118,108),(119,16),(119,125),(119,129),(120,14),(120,99),(120,105),(121,77),(121,100),(122,63),(122,92),(122,123),(123,70),(123,111),(124,55),(125,75),(125,130),(126,62),(127,61),(127,124),(128,69),(128,114),(129,73),(129,130),(130,82),(130,126)],131)
=> ? = 0 + 1
[4,1,3,2,5] => [[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1]]
=> [[1,1,2,2,2],[2,2,3,4],[3,3,4],[4,4],[5]]
=> ([(0,7),(0,8),(1,12),(2,11),(3,10),(4,10),(4,11),(5,3),(6,1),(6,13),(7,9),(8,5),(9,2),(9,4),(10,14),(11,6),(11,14),(13,12),(14,13)],15)
=> ? = 0 + 1
[4,1,5,2,3] => [[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1],[1,0,0,0,0],[0,0,1,0,0]]
=> [[1,1,2,2,2],[2,2,4,4],[3,4,5],[4,5],[5]]
=> ([(0,1),(1,4),(1,5),(2,8),(2,32),(3,6),(3,30),(4,7),(4,33),(5,10),(5,11),(5,33),(6,20),(7,31),(8,27),(9,15),(9,19),(10,18),(10,28),(11,18),(11,25),(13,39),(14,36),(14,39),(15,36),(16,38),(17,38),(18,2),(18,37),(19,26),(19,36),(20,21),(21,12),(22,12),(23,17),(23,35),(24,16),(24,35),(25,13),(25,37),(26,24),(26,34),(27,16),(27,17),(28,14),(28,19),(28,37),(29,21),(29,22),(30,20),(30,29),(31,13),(31,14),(31,15),(32,23),(32,24),(32,27),(33,9),(33,25),(33,28),(33,31),(34,30),(34,35),(35,29),(35,38),(36,3),(36,34),(37,26),(37,32),(37,39),(38,22),(39,23),(39,34)],40)
=> ? = 0 + 1
[4,2,1,3,5] => [[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,0,0,0,1]]
=> [[1,1,2,2,3],[2,2,3,3],[3,3,4],[4,4],[5]]
=> ([(0,5),(0,10),(1,16),(2,15),(3,14),(4,13),(5,12),(6,2),(6,13),(7,4),(7,14),(8,1),(9,6),(10,11),(10,12),(11,3),(11,7),(12,9),(13,15),(14,8),(15,16)],17)
=> ? = 1 + 1
[4,2,3,1,5] => [[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1]]
=> [[1,1,2,2,4],[2,2,3,4],[3,3,4],[4,4],[5]]
=> ([(0,14),(0,15),(1,19),(2,18),(3,29),(4,30),(5,22),(6,23),(7,24),(7,25),(8,9),(9,7),(9,18),(9,19),(10,5),(11,6),(12,2),(12,29),(13,1),(13,30),(14,16),(14,28),(15,17),(15,28),(16,3),(16,12),(17,4),(17,13),(18,24),(18,27),(19,25),(19,27),(20,26),(21,26),(22,20),(23,21),(24,22),(24,31),(25,23),(25,31),(27,31),(28,8),(29,10),(30,11),(31,20),(31,21)],32)
=> ? = 0 + 1
[4,2,5,1,3] => [[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1],[1,0,0,0,0],[0,0,1,0,0]]
=> [[1,1,2,2,4],[2,2,4,4],[3,4,5],[4,5],[5]]
=> ([(0,7),(0,8),(1,2),(1,45),(2,35),(3,37),(4,14),(4,49),(5,9),(5,48),(6,10),(6,12),(6,54),(7,31),(8,6),(8,13),(8,31),(9,27),(9,42),(10,28),(10,41),(11,26),(11,52),(12,17),(12,28),(12,51),(13,15),(13,50),(13,54),(14,16),(14,40),(14,53),(15,33),(15,44),(16,38),(16,47),(17,30),(17,40),(19,64),(19,66),(20,62),(21,65),(22,58),(23,60),(23,66),(24,60),(24,63),(25,67),(26,55),(27,59),(28,5),(28,56),(29,34),(30,22),(30,57),(31,4),(31,50),(32,22),(32,65),(33,43),(34,18),(35,18),(36,20),(37,1),(37,46),(38,27),(38,61),(39,19),(39,55),(39,58),(40,38),(40,57),(41,21),(41,56),(42,20),(42,59),(43,26),(43,39),(44,21),(44,32),(45,34),(45,35),(46,29),(46,45),(47,19),(47,23),(47,61),(48,36),(48,42),(49,11),(49,43),(49,53),(50,33),(50,49),(51,30),(51,32),(51,56),(52,23),(52,24),(52,55),(53,39),(53,47),(53,52),(53,57),(54,41),(54,44),(54,51),(55,3),(55,63),(55,66),(56,48),(56,65),(57,24),(57,58),(57,61),(58,63),(58,64),(59,25),(59,62),(60,25),(60,68),(61,59),(61,60),(61,64),(62,67),(63,68),(64,62),(64,68),(65,36),(66,37),(66,68),(67,29),(68,46),(68,67)],69)
=> ? = 1 + 1
[4,3,1,2,5] => [[0,0,1,0,0],[0,0,0,1,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1]]
=> [[1,1,2,3,3],[2,2,3,4],[3,3,4],[4,4],[5]]
=> ([(0,13),(0,15),(1,17),(2,16),(2,17),(3,19),(4,16),(4,18),(5,22),(6,21),(7,20),(8,23),(8,29),(9,4),(9,28),(10,3),(10,28),(11,6),(12,7),(12,24),(13,14),(14,1),(14,2),(15,9),(15,10),(16,25),(17,12),(17,25),(18,26),(18,29),(19,23),(19,26),(20,27),(22,27),(23,30),(24,20),(24,22),(25,24),(26,30),(27,21),(28,8),(28,18),(28,19),(29,5),(29,30),(30,11)],31)
=> ? = 0 + 1
[4,3,2,1,5] => [[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1]]
=> [[1,1,2,3,4],[2,2,3,4],[3,3,4],[4,4],[5]]
=> ([(0,5),(0,16),(0,17),(1,23),(2,19),(3,11),(3,21),(4,10),(4,20),(5,12),(5,13),(6,50),(7,51),(8,24),(8,58),(9,25),(9,59),(10,14),(10,52),(11,15),(11,53),(12,26),(12,60),(13,27),(13,60),(14,54),(15,55),(16,4),(16,29),(17,3),(17,29),(18,48),(18,49),(19,32),(19,33),(20,46),(20,52),(21,47),(21,53),(22,34),(22,35),(23,18),(23,54),(23,55),(24,40),(24,42),(25,41),(25,43),(26,46),(26,56),(27,47),(27,57),(28,63),(29,1),(30,62),(31,61),(32,61),(33,61),(34,6),(34,62),(35,7),(35,62),(36,58),(37,59),(38,32),(39,33),(40,44),(41,45),(42,38),(43,39),(44,31),(45,31),(46,36),(47,37),(48,40),(48,63),(49,41),(49,63),(50,38),(51,39),(52,8),(52,36),(53,9),(53,37),(54,28),(54,48),(55,28),(55,49),(56,30),(56,34),(57,30),(57,35),(58,42),(58,50),(59,43),(59,51),(60,22),(60,56),(60,57),(62,2),(63,44),(63,45)],64)
=> ? = 0 + 1
[4,3,5,1,2] => [[0,0,0,1,0],[0,0,0,0,1],[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0]]
=> [[1,1,2,4,4],[2,2,4,5],[3,4,5],[4,5],[5]]
=> ([(0,2),(0,3),(1,8),(1,16),(2,1),(3,7),(3,10),(4,13),(4,59),(5,12),(5,81),(6,20),(6,82),(7,11),(7,83),(8,60),(9,23),(9,58),(10,19),(10,22),(10,83),(11,78),(12,64),(13,24),(14,52),(14,72),(15,17),(15,73),(15,80),(16,60),(16,74),(17,39),(17,70),(18,36),(18,44),(19,51),(19,69),(20,33),(20,75),(21,28),(21,38),(21,50),(22,51),(22,71),(22,74),(23,49),(23,56),(23,57),(25,101),(26,113),(27,107),(27,110),(28,107),(28,111),(29,110),(29,111),(30,112),(31,90),(31,98),(32,94),(32,114),(33,96),(34,91),(34,92),(35,89),(35,92),(36,108),(37,94),(37,103),(38,9),(38,111),(39,45),(40,31),(40,102),(40,114),(41,31),(41,104),(42,37),(42,99),(43,34),(43,85),(43,87),(44,30),(44,108),(45,55),(46,33),(46,86),(47,48),(47,86),(48,25),(48,100),(49,42),(49,85),(50,14),(50,76),(50,107),(51,15),(51,61),(51,84),(52,46),(52,109),(53,32),(53,93),(54,26),(54,95),(55,25),(55,91),(56,35),(56,85),(56,97),(57,53),(57,97),(58,57),(59,24),(60,5),(60,63),(61,67),(61,73),(62,34),(62,35),(62,113),(63,67),(63,81),(64,46),(64,47),(65,45),(65,68),(66,47),(66,68),(66,109),(67,65),(67,66),(68,48),(68,55),(68,87),(69,29),(69,38),(69,84),(70,26),(70,62),(71,27),(71,50),(71,84),(72,43),(72,49),(72,109),(73,39),(73,65),(74,61),(74,63),(75,32),(75,40),(75,96),(76,72),(76,79),(76,88),(77,40),(77,41),(77,93),(78,27),(78,28),(78,29),(79,43),(79,56),(79,62),(79,95),(80,54),(80,70),(80,79),(81,52),(81,64),(81,66),(82,53),(82,75),(82,77),(83,21),(83,69),(83,71),(83,78),(84,76),(84,80),(84,110),(85,92),(85,99),(86,37),(86,96),(86,100),(87,91),(87,99),(87,100),(88,82),(88,95),(89,104),(90,108),(90,116),(91,101),(91,106),(92,106),(93,18),(93,104),(93,114),(94,115),(95,77),(95,97),(95,113),(96,94),(96,102),(97,89),(97,93),(98,116),(99,103),(99,106),(100,101),(100,102),(100,103),(101,98),(101,105),(102,98),(102,115),(103,105),(103,115),(104,36),(104,90),(105,116),(106,105),(107,6),(107,88),(108,4),(108,112),(109,42),(109,86),(109,87),(110,54),(110,88),(111,58),(112,59),(113,41),(113,89),(114,44),(114,90),(114,115),(115,30),(115,116),(116,112)],117)
=> ? = 0 + 1
[4,3,5,2,1] => [[0,0,0,0,1],[0,0,0,1,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0]]
=> [[1,1,2,4,5],[2,2,4,5],[3,4,5],[4,5],[5]]
=> ([(0,4),(0,15),(0,16),(1,34),(2,7),(2,32),(3,14),(3,33),(4,11),(4,12),(5,147),(6,38),(6,125),(7,5),(7,114),(8,39),(8,161),(9,30),(9,158),(10,31),(10,96),(11,29),(11,159),(12,28),(12,41),(12,159),(13,24),(13,75),(14,20),(14,21),(14,156),(15,2),(15,54),(16,3),(16,54),(17,68),(17,119),(18,115),(18,120),(19,113),(19,149),(20,122),(20,154),(21,122),(21,164),(22,111),(22,145),(23,67),(23,116),(24,65),(24,66),(25,42),(25,117),(25,148),(26,37),(26,152),(26,163),(27,35),(27,150),(27,155),(28,118),(28,153),(29,121),(29,162),(30,110),(30,146),(31,109),(31,112),(32,114),(32,151),(33,121),(33,156),(34,36),(34,147),(34,164),(35,79),(35,81),(36,84),(36,134),(37,80),(37,137),(38,95),(38,106),(38,107),(39,58),(39,94),(39,139),(40,52),(40,64),(40,108),(41,118),(41,132),(41,151),(42,76),(42,77),(42,78),(43,211),(44,202),(45,173),(45,214),(46,168),(47,167),(47,168),(48,217),(49,212),(49,215),(50,174),(50,215),(51,218),(52,6),(52,212),(53,10),(54,1),(55,176),(56,176),(56,211),(57,192),(57,203),(58,173),(58,186),(59,177),(59,187),(60,175),(60,177),(61,214),(62,193),(63,182),(63,200),(64,22),(64,174),(64,212),(65,181),(66,181),(67,180),(68,179),(69,96),(70,57),(70,199),(70,213),(71,60),(71,169),(71,171),(72,100),(72,206),(73,58),(73,172),(74,66),(74,197),(75,65),(76,83),(76,170),(77,91),(77,167),(78,120),(78,167),(78,170),(79,88),(80,87),(81,136),(82,67),(82,216),(83,94),(83,208),(84,110),(84,210),(85,69),(85,208),(86,63),(86,198),(87,105),(88,55),(89,93),(89,172),(90,46),(90,210),(91,45),(91,196),(92,43),(92,209),(93,44),(93,195),(94,101),(94,173),(95,86),(95,169),(96,112),(97,102),(97,166),(97,188),(98,103),(98,188),(99,57),(99,191),(100,109),(100,182),(100,213),(101,97),(101,184),(102,56),(102,183),(102,209),(103,55),(103,183),(104,48),(104,185),(105,44),(105,175),(106,59),(106,169),(106,190),(107,72),(107,190),(108,19),(108,144),(108,174),(109,62),(109,166),(110,135),(111,53),(112,92),(112,166),(113,73),(113,207),(114,9),(114,126),(115,69),(115,178),(116,74),(116,180),(117,18),(117,78),(117,218),(118,26),(118,123),(118,165),(119,23),(119,82),(119,179),(120,27),(120,140),(120,178),(121,133),(122,138),(123,130),(123,152),(124,88),(124,103),(125,53),(125,107),(126,130),(126,158),(127,59),(127,60),(127,217),(128,87),(128,131),(129,89),(129,131),(129,207),(130,128),(130,129),(131,93),(131,105),(131,171),(132,50),(132,108),(132,165),(133,51),(133,148),(134,47),(134,77),(134,210),(135,45),(135,61),(136,43),(136,56),(137,48),(137,127),(138,46),(138,47),(139,70),(139,100),(139,186),(140,143),(140,150),(141,70),(141,99),(141,206),(142,97),(142,157),(143,98),(143,124),(144,149),(144,160),(144,189),(145,83),(145,85),(146,73),(146,89),(147,84),(147,90),(148,76),(148,145),(148,218),(149,71),(149,95),(149,207),(150,79),(150,124),(151,123),(151,126),(152,80),(152,128),(153,49),(153,52),(153,165),(154,51),(154,117),(155,81),(155,157),(156,25),(156,133),(156,154),(157,92),(157,102),(157,136),(158,113),(158,129),(158,146),(159,40),(159,132),(159,153),(159,162),(160,71),(160,106),(160,127),(160,185),(161,72),(161,139),(161,141),(162,49),(162,50),(162,64),(163,104),(163,137),(163,160),(164,90),(164,134),(164,138),(165,144),(165,163),(165,215),(166,193),(166,209),(167,140),(167,196),(168,61),(168,196),(169,177),(169,198),(170,178),(170,208),(171,175),(171,195),(171,198),(172,63),(172,186),(172,195),(173,184),(174,8),(174,189),(175,202),(175,204),(176,194),(177,204),(178,142),(178,155),(179,13),(179,216),(180,197),(182,62),(182,220),(183,176),(183,201),(184,188),(185,141),(185,190),(185,217),(186,182),(186,199),(187,191),(188,183),(188,193),(189,161),(189,185),(190,187),(190,206),(191,68),(191,192),(192,179),(192,219),(193,201),(194,197),(195,199),(195,200),(195,202),(196,143),(196,214),(197,181),(198,200),(198,204),(199,203),(199,220),(200,205),(200,220),(201,180),(201,194),(202,203),(202,205),(203,219),(204,205),(205,219),(206,17),(206,191),(206,213),(207,86),(207,171),(207,172),(208,101),(208,142),(209,116),(209,201),(209,211),(210,91),(210,135),(210,168),(211,74),(211,194),(212,111),(212,125),(213,119),(213,192),(213,220),(214,98),(214,184),(215,104),(215,189),(216,75),(217,99),(217,187),(218,85),(218,115),(218,170),(219,216),(220,82),(220,219)],221)
=> ? = 1 + 1
[4,5,3,1,2] => [[0,0,0,1,0],[0,0,0,0,1],[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0]]
=> [[1,1,3,4,4],[2,3,4,5],[3,4,5],[4,5],[5]]
=> ([(0,1),(0,2),(1,12),(1,14),(2,11),(2,13),(3,145),(4,146),(5,31),(5,155),(6,32),(6,156),(7,15),(7,143),(8,16),(8,144),(9,37),(9,114),(10,38),(10,115),(11,17),(11,157),(12,18),(12,158),(13,29),(13,35),(13,157),(14,30),(14,36),(14,158),(15,84),(16,85),(17,147),(18,148),(19,102),(19,133),(20,103),(20,134),(21,23),(21,149),(21,153),(22,24),(22,150),(22,154),(23,118),(23,128),(24,119),(24,129),(25,62),(25,82),(26,63),(26,83),(27,74),(27,139),(28,75),(28,140),(29,100),(29,126),(30,101),(30,127),(31,55),(31,135),(32,56),(32,136),(33,47),(33,72),(33,98),(34,48),(34,73),(34,99),(35,100),(35,130),(35,132),(36,101),(36,131),(36,132),(37,96),(37,110),(37,112),(38,97),(38,111),(38,113),(40,201),(40,202),(41,225),(42,226),(43,221),(43,223),(44,222),(44,224),(45,213),(45,221),(46,214),(46,222),(47,213),(47,223),(48,214),(48,224),(49,161),(50,162),(51,183),(51,227),(52,184),(52,228),(53,173),(53,195),(54,174),(54,196),(55,185),(56,186),(57,179),(57,180),(58,175),(58,177),(59,176),(59,178),(60,171),(60,177),(61,172),(61,178),(62,215),(63,216),(64,220),(65,219),(66,219),(67,220),(68,183),(68,203),(69,184),(69,204),(70,179),(70,199),(71,180),(71,200),(72,9),(72,223),(73,10),(73,224),(74,3),(74,189),(75,4),(75,190),(76,53),(76,205),(76,227),(77,54),(77,206),(77,228),(78,53),(78,207),(79,54),(79,208),(80,58),(80,163),(80,167),(81,59),(81,164),(81,168),(82,49),(82,215),(83,50),(83,216),(84,94),(85,95),(86,68),(86,197),(87,69),(87,198),(88,94),(89,95),(90,55),(90,169),(91,56),(91,170),(92,108),(92,170),(93,109),(93,169),(94,39),(95,39),(96,86),(96,163),(97,87),(97,164),(98,19),(98,137),(98,213),(99,20),(99,138),(99,214),(100,21),(100,116),(100,159),(101,22),(101,117),(101,160),(102,90),(102,217),(103,91),(103,218),(104,51),(104,181),(105,52),(105,182),(106,41),(106,187),(107,42),(107,188),(108,40),(108,175),(108,194),(109,40),(109,176),(109,193),(110,60),(110,163),(110,191),(111,61),(111,164),(111,192),(112,104),(112,191),(113,105),(113,192),(114,112),(115,113),(116,124),(116,149),(117,124),(117,150),(118,91),(118,92),(119,90),(119,93),(120,58),(120,60),(120,225),(121,59),(121,61),(121,226),(122,92),(122,125),(122,218),(123,93),(123,125),(123,217),(124,122),(124,123),(125,108),(125,109),(125,167),(125,168),(126,43),(126,72),(126,159),(127,44),(127,73),(127,160),(128,41),(128,120),(129,42),(129,121),(130,45),(130,98),(130,159),(131,46),(131,99),(131,160),(132,116),(132,117),(133,80),(133,96),(133,217),(134,81),(134,97),(134,218),(135,51),(135,76),(135,185),(136,52),(136,77),(136,186),(137,133),(137,151),(137,165),(138,134),(138,152),(138,166),(139,57),(139,70),(139,189),(140,57),(140,71),(140,190),(141,76),(141,78),(141,181),(142,77),(142,79),(142,182),(143,84),(143,88),(144,85),(144,89),(145,64),(145,67),(146,65),(146,66),(147,43),(147,45),(147,47),(148,44),(148,46),(148,48),(149,103),(149,118),(149,122),(150,102),(150,119),(150,123),(151,80),(151,110),(151,120),(151,187),(152,81),(152,111),(152,121),(152,188),(153,106),(153,128),(153,151),(154,107),(154,129),(154,152),(155,104),(155,135),(155,141),(156,105),(156,136),(156,142),(157,33),(157,126),(157,130),(157,147),(158,34),(158,127),(158,131),(158,148),(159,137),(159,153),(159,221),(160,138),(160,154),(160,222),(161,143),(162,144),(163,27),(163,177),(163,197),(164,28),(164,178),(164,198),(165,155),(165,187),(166,156),(166,188),(167,175),(167,193),(167,197),(168,176),(168,194),(168,198),(169,68),(169,185),(169,193),(170,69),(170,186),(170,194),(171,207),(172,208),(173,215),(173,231),(174,216),(174,232),(175,201),(175,209),(176,202),(176,210),(177,74),(177,209),(178,75),(178,210),(179,66),(179,233),(180,67),(180,233),(181,25),(181,207),(181,227),(182,26),(182,208),(182,228),(183,229),(184,230),(185,183),(185,205),(186,184),(186,206),(187,141),(187,191),(187,225),(188,142),(188,192),(188,226),(189,145),(189,180),(189,199),(190,146),(190,179),(190,200),(191,171),(191,181),(192,172),(192,182),(193,201),(193,203),(193,205),(194,202),(194,204),(194,206),(195,231),(196,232),(197,139),(197,203),(197,209),(198,140),(198,204),(198,210),(199,64),(199,233),(200,65),(200,233),(201,195),(201,211),(202,196),(202,212),(203,70),(203,211),(203,229),(204,71),(204,212),(204,230),(205,195),(205,229),(206,196),(206,230),(207,62),(207,173),(208,63),(208,174),(209,189),(209,211),(210,190),(210,212),(211,199),(211,231),(212,200),(212,232),(213,5),(213,165),(214,6),(214,166),(215,7),(215,161),(216,8),(216,162),(217,86),(217,167),(217,169),(218,87),(218,168),(218,170),(219,88),(220,89),(221,106),(221,165),(222,107),(222,166),(223,114),(224,115),(225,78),(225,171),(226,79),(226,172),(227,82),(227,173),(227,229),(228,83),(228,174),(228,230),(229,49),(229,231),(230,50),(230,232),(231,161),(232,162),(233,219),(233,220)],234)
=> ? = 0 + 1
[1,2,3,4,6,5] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,4,4],[5,6],[6]]
=> ([(0,1)],2)
=> 1 = 0 + 1
[1,2,3,5,4,6] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,4,5],[5,5],[6]]
=> ([(0,1)],2)
=> 1 = 0 + 1
[1,2,4,3,5,6] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,4],[4,4,4],[5,5],[6]]
=> ([(0,1)],2)
=> 1 = 0 + 1
[1,2,4,3,6,5] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,4],[4,4,4],[5,6],[6]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 2 + 1
[1,3,2,4,5,6] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,3],[4,4,4],[5,5],[6]]
=> ([(0,1)],2)
=> 1 = 0 + 1
[1,3,2,4,6,5] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,3],[4,4,4],[5,6],[6]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 2 + 1
[1,3,2,5,4,6] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,3],[4,4,5],[5,5],[6]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 2 + 1
[2,1,3,4,5,6] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,3],[4,4,4],[5,5],[6]]
=> ([(0,1)],2)
=> 1 = 0 + 1
[2,1,3,4,6,5] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,3],[4,4,4],[5,6],[6]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 2 + 1
[2,1,3,5,4,6] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,3],[4,4,5],[5,5],[6]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 2 + 1
[2,1,4,3,5,6] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,4],[4,4,4],[5,5],[6]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 2 + 1
Description
The number of posets with combinatorially isomorphic order polytopes.
Matching statistic: St001472
Mp00063: Permutations to alternating sign matrixAlternating sign matrices
Mp00001: Alternating sign matrices to semistandard tableau via monotone trianglesSemistandard tableaux
Mp00214: Semistandard tableaux subcrystalPosets
St001472: Posets ⟶ ℤResult quality: 5% values known / values provided: 5%distinct values known / distinct values provided: 18%
Values
[2,1] => [[0,1],[1,0]]
=> [[1,2],[2]]
=> ([(0,1)],2)
=> -1 = 0 - 1
[1,3,2] => [[1,0,0],[0,0,1],[0,1,0]]
=> [[1,1,1],[2,3],[3]]
=> ([(0,1)],2)
=> -1 = 0 - 1
[2,1,3] => [[0,1,0],[1,0,0],[0,0,1]]
=> [[1,1,2],[2,2],[3]]
=> ([(0,1)],2)
=> -1 = 0 - 1
[1,2,4,3] => [[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
=> [[1,1,1,1],[2,2,2],[3,4],[4]]
=> ([(0,1)],2)
=> -1 = 0 - 1
[1,3,2,4] => [[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,3],[3,3],[4]]
=> ([(0,1)],2)
=> -1 = 0 - 1
[1,4,2,3] => [[1,0,0,0],[0,0,1,0],[0,0,0,1],[0,1,0,0]]
=> [[1,1,1,1],[2,3,3],[3,4],[4]]
=> ([(0,3),(2,1),(3,2)],4)
=> -1 = 0 - 1
[2,1,3,4] => [[0,1,0,0],[1,0,0,0],[0,0,1,0],[0,0,0,1]]
=> [[1,1,1,2],[2,2,2],[3,3],[4]]
=> ([(0,1)],2)
=> -1 = 0 - 1
[2,1,4,3] => [[0,1,0,0],[1,0,0,0],[0,0,0,1],[0,0,1,0]]
=> [[1,1,1,2],[2,2,2],[3,4],[4]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1 = 2 - 1
[2,3,4,1] => [[0,0,0,1],[1,0,0,0],[0,1,0,0],[0,0,1,0]]
=> [[1,1,1,4],[2,2,4],[3,4],[4]]
=> ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
=> ? = 0 - 1
[2,4,1,3] => [[0,0,1,0],[1,0,0,0],[0,0,0,1],[0,1,0,0]]
=> [[1,1,1,3],[2,3,3],[3,4],[4]]
=> ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> ? = 0 - 1
[2,4,3,1] => [[0,0,0,1],[1,0,0,0],[0,0,1,0],[0,1,0,0]]
=> [[1,1,1,4],[2,3,4],[3,4],[4]]
=> ([(0,5),(0,10),(1,16),(2,15),(3,14),(4,13),(5,12),(6,2),(6,13),(7,4),(7,14),(8,1),(9,6),(10,11),(10,12),(11,3),(11,7),(12,9),(13,15),(14,8),(15,16)],17)
=> ? = 1 - 1
[3,1,4,2] => [[0,1,0,0],[0,0,0,1],[1,0,0,0],[0,0,1,0]]
=> [[1,1,2,2],[2,2,4],[3,4],[4]]
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 1 - 1
[3,2,4,1] => [[0,0,0,1],[0,1,0,0],[1,0,0,0],[0,0,1,0]]
=> [[1,1,2,4],[2,2,4],[3,4],[4]]
=> ([(0,7),(0,8),(1,12),(2,11),(3,10),(4,10),(4,11),(5,3),(6,1),(6,13),(7,9),(8,5),(9,2),(9,4),(10,14),(11,6),(11,14),(13,12),(14,13)],15)
=> ? = 1 - 1
[3,4,2,1] => [[0,0,0,1],[0,0,1,0],[1,0,0,0],[0,1,0,0]]
=> [[1,1,3,4],[2,3,4],[3,4],[4]]
=> ([(0,13),(0,15),(1,17),(2,16),(2,17),(3,19),(4,16),(4,18),(5,22),(6,21),(7,20),(8,23),(8,29),(9,4),(9,28),(10,3),(10,28),(11,6),(12,7),(12,24),(13,14),(14,1),(14,2),(15,9),(15,10),(16,25),(17,12),(17,25),(18,26),(18,29),(19,23),(19,26),(20,27),(22,27),(23,30),(24,20),(24,22),(25,24),(26,30),(27,21),(28,8),(28,18),(28,19),(29,5),(29,30),(30,11)],31)
=> ? = 1 - 1
[4,1,3,2] => [[0,1,0,0],[0,0,0,1],[0,0,1,0],[1,0,0,0]]
=> [[1,2,2,2],[2,3,4],[3,4],[4]]
=> ([(0,7),(0,8),(1,12),(2,11),(3,10),(4,10),(4,11),(5,3),(6,1),(6,13),(7,9),(8,5),(9,2),(9,4),(10,14),(11,6),(11,14),(13,12),(14,13)],15)
=> ? = 0 - 1
[4,2,1,3] => [[0,0,1,0],[0,1,0,0],[0,0,0,1],[1,0,0,0]]
=> [[1,2,2,3],[2,3,3],[3,4],[4]]
=> ([(0,5),(0,10),(1,16),(2,15),(3,14),(4,13),(5,12),(6,2),(6,13),(7,4),(7,14),(8,1),(9,6),(10,11),(10,12),(11,3),(11,7),(12,9),(13,15),(14,8),(15,16)],17)
=> ? = 1 - 1
[4,2,3,1] => [[0,0,0,1],[0,1,0,0],[0,0,1,0],[1,0,0,0]]
=> [[1,2,2,4],[2,3,4],[3,4],[4]]
=> ([(0,14),(0,15),(1,19),(2,18),(3,29),(4,30),(5,22),(6,23),(7,24),(7,25),(8,9),(9,7),(9,18),(9,19),(10,5),(11,6),(12,2),(12,29),(13,1),(13,30),(14,16),(14,28),(15,17),(15,28),(16,3),(16,12),(17,4),(17,13),(18,24),(18,27),(19,25),(19,27),(20,26),(21,26),(22,20),(23,21),(24,22),(24,31),(25,23),(25,31),(27,31),(28,8),(29,10),(30,11),(31,20),(31,21)],32)
=> ? = 0 - 1
[4,3,1,2] => [[0,0,1,0],[0,0,0,1],[0,1,0,0],[1,0,0,0]]
=> [[1,2,3,3],[2,3,4],[3,4],[4]]
=> ([(0,13),(0,15),(1,17),(2,16),(2,17),(3,19),(4,16),(4,18),(5,22),(6,21),(7,20),(8,23),(8,29),(9,4),(9,28),(10,3),(10,28),(11,6),(12,7),(12,24),(13,14),(14,1),(14,2),(15,9),(15,10),(16,25),(17,12),(17,25),(18,26),(18,29),(19,23),(19,26),(20,27),(22,27),(23,30),(24,20),(24,22),(25,24),(26,30),(27,21),(28,8),(28,18),(28,19),(29,5),(29,30),(30,11)],31)
=> ? = 0 - 1
[4,3,2,1] => [[0,0,0,1],[0,0,1,0],[0,1,0,0],[1,0,0,0]]
=> [[1,2,3,4],[2,3,4],[3,4],[4]]
=> ([(0,5),(0,16),(0,17),(1,23),(2,19),(3,11),(3,21),(4,10),(4,20),(5,12),(5,13),(6,50),(7,51),(8,24),(8,58),(9,25),(9,59),(10,14),(10,52),(11,15),(11,53),(12,26),(12,60),(13,27),(13,60),(14,54),(15,55),(16,4),(16,29),(17,3),(17,29),(18,48),(18,49),(19,32),(19,33),(20,46),(20,52),(21,47),(21,53),(22,34),(22,35),(23,18),(23,54),(23,55),(24,40),(24,42),(25,41),(25,43),(26,46),(26,56),(27,47),(27,57),(28,63),(29,1),(30,62),(31,61),(32,61),(33,61),(34,6),(34,62),(35,7),(35,62),(36,58),(37,59),(38,32),(39,33),(40,44),(41,45),(42,38),(43,39),(44,31),(45,31),(46,36),(47,37),(48,40),(48,63),(49,41),(49,63),(50,38),(51,39),(52,8),(52,36),(53,9),(53,37),(54,28),(54,48),(55,28),(55,49),(56,30),(56,34),(57,30),(57,35),(58,42),(58,50),(59,43),(59,51),(60,22),(60,56),(60,57),(62,2),(63,44),(63,45)],64)
=> ? = 0 - 1
[1,2,3,5,4] => [[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0]]
=> [[1,1,1,1,1],[2,2,2,2],[3,3,3],[4,5],[5]]
=> ([(0,1)],2)
=> -1 = 0 - 1
[1,2,4,3,5] => [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [[1,1,1,1,1],[2,2,2,2],[3,3,4],[4,4],[5]]
=> ([(0,1)],2)
=> -1 = 0 - 1
[1,2,5,3,4] => [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1],[0,0,1,0,0]]
=> [[1,1,1,1,1],[2,2,2,2],[3,4,4],[4,5],[5]]
=> ([(0,3),(2,1),(3,2)],4)
=> -1 = 0 - 1
[1,3,2,4,5] => [[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
=> [[1,1,1,1,1],[2,2,2,3],[3,3,3],[4,4],[5]]
=> ([(0,1)],2)
=> -1 = 0 - 1
[1,3,2,5,4] => [[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
=> [[1,1,1,1,1],[2,2,2,3],[3,3,3],[4,5],[5]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1 = 2 - 1
[1,3,4,5,2] => [[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0]]
=> [[1,1,1,1,1],[2,2,2,5],[3,3,5],[4,5],[5]]
=> ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
=> ? = 0 - 1
[1,3,5,2,4] => [[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,1,0,0]]
=> [[1,1,1,1,1],[2,2,2,4],[3,4,4],[4,5],[5]]
=> ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> ? = 0 - 1
[1,3,5,4,2] => [[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0]]
=> [[1,1,1,1,1],[2,2,2,5],[3,4,5],[4,5],[5]]
=> ([(0,5),(0,10),(1,16),(2,15),(3,14),(4,13),(5,12),(6,2),(6,13),(7,4),(7,14),(8,1),(9,6),(10,11),(10,12),(11,3),(11,7),(12,9),(13,15),(14,8),(15,16)],17)
=> ? = 1 - 1
[1,4,2,3,5] => [[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [[1,1,1,1,1],[2,2,3,3],[3,3,4],[4,4],[5]]
=> ([(0,3),(2,1),(3,2)],4)
=> -1 = 0 - 1
[1,4,2,5,3] => [[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,0,1,0]]
=> [[1,1,1,1,1],[2,2,3,3],[3,3,5],[4,5],[5]]
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 1 - 1
[1,4,3,5,2] => [[1,0,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0]]
=> [[1,1,1,1,1],[2,2,3,5],[3,3,5],[4,5],[5]]
=> ([(0,7),(0,8),(1,12),(2,11),(3,10),(4,10),(4,11),(5,3),(6,1),(6,13),(7,9),(8,5),(9,2),(9,4),(10,14),(11,6),(11,14),(13,12),(14,13)],15)
=> ? = 1 - 1
[1,4,5,2,3] => [[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0]]
=> [[1,1,1,1,1],[2,2,4,4],[3,4,5],[4,5],[5]]
=> ([(0,8),(2,11),(2,12),(3,10),(4,9),(5,4),(5,14),(6,3),(6,14),(7,1),(8,5),(8,6),(9,11),(9,13),(10,12),(10,13),(11,15),(12,15),(13,15),(14,2),(14,9),(14,10),(15,7)],16)
=> ? = 0 - 1
[1,4,5,3,2] => [[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0]]
=> [[1,1,1,1,1],[2,2,4,5],[3,4,5],[4,5],[5]]
=> ([(0,13),(0,15),(1,17),(2,16),(2,17),(3,19),(4,16),(4,18),(5,22),(6,21),(7,20),(8,23),(8,29),(9,4),(9,28),(10,3),(10,28),(11,6),(12,7),(12,24),(13,14),(14,1),(14,2),(15,9),(15,10),(16,25),(17,12),(17,25),(18,26),(18,29),(19,23),(19,26),(20,27),(22,27),(23,30),(24,20),(24,22),(25,24),(26,30),(27,21),(28,8),(28,18),(28,19),(29,5),(29,30),(30,11)],31)
=> ? = 1 - 1
[1,5,3,2,4] => [[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1],[0,1,0,0,0]]
=> [[1,1,1,1,1],[2,3,3,4],[3,4,4],[4,5],[5]]
=> ([(0,5),(0,10),(1,16),(2,15),(3,14),(4,13),(5,12),(6,2),(6,13),(7,4),(7,14),(8,1),(9,6),(10,11),(10,12),(11,3),(11,7),(12,9),(13,15),(14,8),(15,16)],17)
=> ? = 1 - 1
[1,5,4,3,2] => [[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0]]
=> [[1,1,1,1,1],[2,3,4,5],[3,4,5],[4,5],[5]]
=> ([(0,5),(0,16),(0,17),(1,23),(2,19),(3,11),(3,21),(4,10),(4,20),(5,12),(5,13),(6,50),(7,51),(8,24),(8,58),(9,25),(9,59),(10,14),(10,52),(11,15),(11,53),(12,26),(12,60),(13,27),(13,60),(14,54),(15,55),(16,4),(16,29),(17,3),(17,29),(18,48),(18,49),(19,32),(19,33),(20,46),(20,52),(21,47),(21,53),(22,34),(22,35),(23,18),(23,54),(23,55),(24,40),(24,42),(25,41),(25,43),(26,46),(26,56),(27,47),(27,57),(28,63),(29,1),(30,62),(31,61),(32,61),(33,61),(34,6),(34,62),(35,7),(35,62),(36,58),(37,59),(38,32),(39,33),(40,44),(41,45),(42,38),(43,39),(44,31),(45,31),(46,36),(47,37),(48,40),(48,63),(49,41),(49,63),(50,38),(51,39),(52,8),(52,36),(53,9),(53,37),(54,28),(54,48),(55,28),(55,49),(56,30),(56,34),(57,30),(57,35),(58,42),(58,50),(59,43),(59,51),(60,22),(60,56),(60,57),(62,2),(63,44),(63,45)],64)
=> ? = 0 - 1
[2,1,3,4,5] => [[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]]
=> [[1,1,1,1,2],[2,2,2,2],[3,3,3],[4,4],[5]]
=> ([(0,1)],2)
=> -1 = 0 - 1
[2,1,3,5,4] => [[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0]]
=> [[1,1,1,1,2],[2,2,2,2],[3,3,3],[4,5],[5]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1 = 2 - 1
[2,1,4,3,5] => [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [[1,1,1,1,2],[2,2,2,2],[3,3,4],[4,4],[5]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1 = 2 - 1
[2,1,4,5,3] => [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,0,0,1,0]]
=> [[1,1,1,1,2],[2,2,2,2],[3,3,5],[4,5],[5]]
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 1 - 1
[2,1,5,4,3] => [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0]]
=> [[1,1,1,1,2],[2,2,2,2],[3,4,5],[4,5],[5]]
=> ([(0,3),(0,6),(0,7),(1,8),(1,12),(2,8),(2,11),(3,9),(3,10),(4,2),(4,13),(5,1),(5,14),(6,4),(6,9),(7,5),(7,10),(8,15),(9,13),(10,14),(11,15),(12,15),(13,11),(14,12)],16)
=> ? = 0 - 1
[2,3,1,5,4] => [[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
=> [[1,1,1,1,3],[2,2,2,3],[3,3,3],[4,5],[5]]
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 1 - 1
[2,3,4,1,5] => [[0,0,0,1,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [[1,1,1,1,4],[2,2,2,4],[3,3,4],[4,4],[5]]
=> ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
=> ? = 0 - 1
[2,3,4,5,1] => [[0,0,0,0,1],[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0]]
=> [[1,1,1,1,5],[2,2,2,5],[3,3,5],[4,5],[5]]
=> ([(0,9),(1,13),(2,14),(4,12),(5,11),(6,1),(6,12),(7,3),(8,5),(8,15),(9,10),(10,4),(10,6),(11,14),(12,8),(12,13),(13,15),(14,7),(15,2),(15,11)],16)
=> ? = 0 - 1
[2,4,1,3,5] => [[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [[1,1,1,1,3],[2,2,3,3],[3,3,4],[4,4],[5]]
=> ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> ? = 0 - 1
[2,4,1,5,3] => [[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,0,1,0]]
=> [[1,1,1,1,3],[2,2,3,3],[3,3,5],[4,5],[5]]
=> ([(0,6),(0,7),(1,5),(1,15),(2,4),(2,14),(3,13),(4,12),(5,3),(5,16),(6,9),(7,2),(7,9),(9,1),(9,14),(10,11),(11,8),(12,10),(13,8),(14,12),(14,15),(15,10),(15,16),(16,11),(16,13)],17)
=> ? = 0 - 1
[2,4,3,1,5] => [[0,0,0,1,0],[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [[1,1,1,1,4],[2,2,3,4],[3,3,4],[4,4],[5]]
=> ([(0,5),(0,10),(1,16),(2,15),(3,14),(4,13),(5,12),(6,2),(6,13),(7,4),(7,14),(8,1),(9,6),(10,11),(10,12),(11,3),(11,7),(12,9),(13,15),(14,8),(15,16)],17)
=> ? = 1 - 1
[2,4,3,5,1] => [[0,0,0,0,1],[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0]]
=> [[1,1,1,1,5],[2,2,3,5],[3,3,5],[4,5],[5]]
=> ([(0,8),(0,13),(1,19),(2,16),(2,18),(3,21),(4,26),(5,24),(6,16),(6,22),(7,20),(7,23),(8,17),(9,4),(9,18),(10,9),(11,7),(11,30),(12,3),(12,25),(13,14),(13,17),(14,1),(14,15),(15,2),(15,6),(15,19),(16,28),(17,10),(18,26),(18,28),(19,11),(19,22),(20,24),(20,31),(22,30),(23,31),(24,12),(24,27),(25,21),(26,23),(26,29),(27,25),(28,29),(29,31),(30,5),(30,20),(31,27)],32)
=> ? = 0 - 1
[2,4,5,1,3] => [[0,0,0,1,0],[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0]]
=> [[1,1,1,1,4],[2,2,4,4],[3,4,5],[4,5],[5]]
=> ([(0,9),(0,10),(1,2),(3,7),(3,23),(4,6),(4,22),(5,15),(6,16),(7,8),(7,24),(8,20),(9,19),(10,4),(10,19),(11,14),(11,18),(12,26),(13,26),(14,25),(15,1),(16,21),(17,13),(17,25),(18,12),(18,25),(19,3),(19,22),(20,12),(20,13),(21,14),(21,17),(22,16),(22,23),(23,11),(23,21),(23,24),(24,17),(24,18),(24,20),(25,5),(25,26),(26,15)],27)
=> ? = 0 - 1
[2,4,5,3,1] => [[0,0,0,0,1],[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0]]
=> [[1,1,1,1,5],[2,2,4,5],[3,4,5],[4,5],[5]]
=> ([(0,17),(0,18),(1,11),(1,12),(2,53),(3,50),(4,33),(5,16),(5,65),(6,13),(6,61),(7,14),(7,62),(8,15),(8,51),(9,25),(9,63),(10,24),(10,52),(11,54),(12,22),(12,23),(12,54),(13,36),(14,35),(15,40),(16,59),(17,1),(17,48),(18,7),(18,48),(19,32),(19,45),(20,29),(20,38),(21,55),(21,58),(22,49),(22,60),(23,42),(23,49),(24,31),(24,46),(25,21),(25,60),(25,64),(27,70),(28,70),(29,67),(30,66),(31,68),(32,3),(32,69),(33,8),(34,39),(35,57),(36,39),(37,32),(37,66),(38,19),(38,37),(38,67),(39,26),(40,26),(41,30),(41,67),(42,52),(43,44),(43,68),(44,28),(44,69),(45,27),(45,69),(46,53),(46,68),(47,61),(48,9),(48,62),(49,5),(49,56),(50,34),(51,40),(52,2),(52,46),(53,6),(53,47),(54,10),(54,42),(55,31),(55,43),(56,43),(56,65),(57,29),(57,41),(58,30),(58,37),(59,27),(59,28),(60,55),(60,56),(61,34),(61,36),(62,35),(62,63),(63,20),(63,57),(63,64),(64,38),(64,41),(64,58),(65,44),(65,45),(65,59),(66,33),(67,4),(67,66),(68,47),(69,50),(69,70),(70,51)],71)
=> ? = 1 - 1
[2,5,1,3,4] => [[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1],[0,1,0,0,0]]
=> [[1,1,1,1,3],[2,3,3,3],[3,4,4],[4,5],[5]]
=> ([(0,4),(0,8),(1,11),(3,10),(4,9),(5,2),(6,3),(6,12),(7,5),(8,6),(8,9),(9,12),(10,11),(11,7),(12,1),(12,10)],13)
=> ? = 0 - 1
[3,1,2,5,4] => [[0,1,0,0,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
=> [[1,1,1,2,2],[2,2,2,3],[3,3,3],[4,5],[5]]
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 0 - 1
[3,1,4,2,5] => [[0,1,0,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [[1,1,1,2,2],[2,2,2,4],[3,3,4],[4,4],[5]]
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 1 - 1
[3,2,1,5,4] => [[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
=> [[1,1,1,2,3],[2,2,2,3],[3,3,3],[4,5],[5]]
=> ([(0,3),(0,6),(0,7),(1,8),(1,12),(2,8),(2,11),(3,9),(3,10),(4,2),(4,13),(5,1),(5,14),(6,4),(6,9),(7,5),(7,10),(8,15),(9,13),(10,14),(11,15),(12,15),(13,11),(14,12)],16)
=> ? = 0 - 1
[3,2,4,1,5] => [[0,0,0,1,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [[1,1,1,2,4],[2,2,2,4],[3,3,4],[4,4],[5]]
=> ([(0,7),(0,8),(1,12),(2,11),(3,10),(4,10),(4,11),(5,3),(6,1),(6,13),(7,9),(8,5),(9,2),(9,4),(10,14),(11,6),(11,14),(13,12),(14,13)],15)
=> ? = 1 - 1
[3,4,2,1,5] => [[0,0,0,1,0],[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [[1,1,1,3,4],[2,2,3,4],[3,3,4],[4,4],[5]]
=> ([(0,13),(0,15),(1,17),(2,16),(2,17),(3,19),(4,16),(4,18),(5,22),(6,21),(7,20),(8,23),(8,29),(9,4),(9,28),(10,3),(10,28),(11,6),(12,7),(12,24),(13,14),(14,1),(14,2),(15,9),(15,10),(16,25),(17,12),(17,25),(18,26),(18,29),(19,23),(19,26),(20,27),(22,27),(23,30),(24,20),(24,22),(25,24),(26,30),(27,21),(28,8),(28,18),(28,19),(29,5),(29,30),(30,11)],31)
=> ? = 1 - 1
[3,5,2,1,4] => [[0,0,0,1,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0]]
=> [[1,1,1,3,4],[2,3,3,4],[3,4,4],[4,5],[5]]
=> ([(0,15),(0,16),(0,20),(1,9),(2,13),(2,47),(3,38),(4,14),(4,46),(5,40),(6,10),(6,26),(7,18),(7,45),(8,19),(8,39),(9,25),(10,32),(11,31),(12,44),(13,12),(13,48),(14,11),(14,42),(15,8),(15,28),(16,7),(16,37),(17,24),(17,33),(18,21),(18,36),(19,21),(19,35),(20,28),(20,37),(21,51),(22,49),(23,49),(24,3),(24,50),(26,1),(27,25),(28,39),(29,46),(30,27),(31,30),(32,27),(33,23),(33,50),(34,22),(34,50),(35,40),(35,51),(36,41),(36,51),(37,2),(37,45),(38,43),(39,5),(39,35),(40,4),(40,29),(41,24),(41,34),(42,31),(42,43),(43,30),(43,32),(44,22),(44,23),(45,36),(45,47),(46,38),(46,42),(47,17),(47,41),(47,48),(48,33),(48,34),(48,44),(49,26),(50,6),(50,49),(51,29)],52)
=> ? = 1 - 1
[3,5,2,4,1] => [[0,0,0,0,1],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0]]
=> [[1,1,1,3,5],[2,3,3,5],[3,4,5],[4,5],[5]]
=> ([(0,16),(0,17),(0,28),(1,9),(2,70),(3,13),(3,85),(4,27),(4,69),(5,83),(6,15),(6,43),(7,26),(7,84),(8,12),(8,29),(8,71),(9,68),(10,77),(11,76),(12,14),(12,78),(13,10),(13,86),(14,11),(14,87),(15,75),(16,8),(16,48),(17,7),(17,67),(18,42),(18,61),(19,25),(19,62),(19,63),(20,22),(20,59),(20,79),(21,24),(21,41),(21,60),(22,23),(22,80),(22,81),(23,64),(23,66),(24,37),(24,65),(25,36),(25,46),(26,50),(26,58),(27,31),(27,32),(28,48),(28,67),(29,57),(29,58),(29,78),(31,103),(32,103),(33,89),(34,89),(35,90),(36,88),(37,92),(38,102),(39,93),(40,101),(41,4),(41,100),(42,5),(42,97),(43,1),(44,53),(45,51),(45,95),(46,41),(46,88),(47,54),(48,71),(49,79),(50,73),(50,98),(51,68),(51,102),(52,31),(52,96),(53,30),(54,30),(55,33),(55,97),(56,35),(56,99),(57,70),(57,98),(58,74),(58,98),(59,81),(59,90),(60,37),(60,100),(61,34),(61,97),(62,36),(62,99),(63,21),(63,46),(63,99),(64,52),(64,91),(65,52),(65,92),(66,45),(66,91),(67,3),(67,84),(68,47),(69,32),(70,20),(70,49),(71,2),(71,57),(72,53),(72,54),(73,42),(73,55),(74,56),(74,62),(75,38),(75,51),(76,35),(76,59),(77,33),(77,34),(78,19),(78,74),(78,87),(79,80),(79,83),(79,90),(80,66),(80,82),(80,94),(81,64),(81,65),(81,94),(82,45),(82,75),(82,93),(83,39),(83,82),(84,50),(84,85),(85,18),(85,73),(85,86),(86,55),(86,61),(86,77),(87,56),(87,63),(87,76),(88,100),(89,43),(90,39),(90,94),(91,95),(91,96),(92,40),(92,96),(93,38),(93,40),(93,95),(94,91),(94,92),(94,93),(95,101),(95,102),(96,101),(96,103),(97,6),(97,89),(98,49),(99,60),(99,88),(100,69),(101,44),(101,72),(102,47),(102,72),(103,44)],104)
=> ? = 2 - 1
[3,5,4,1,2] => [[0,0,0,1,0],[0,0,0,0,1],[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0]]
=> [[1,1,1,4,4],[2,3,4,5],[3,4,5],[4,5],[5]]
=> ([(0,12),(0,13),(1,6),(2,61),(3,5),(3,94),(4,81),(5,80),(6,32),(7,4),(7,95),(8,22),(8,87),(9,20),(9,85),(10,19),(10,92),(11,17),(11,18),(11,98),(12,51),(13,11),(13,21),(13,51),(14,46),(14,47),(15,42),(15,89),(16,73),(16,75),(17,27),(17,48),(17,97),(18,48),(18,90),(19,43),(19,91),(20,44),(20,76),(21,25),(21,88),(21,98),(22,26),(22,74),(22,96),(23,24),(23,45),(23,77),(24,66),(24,67),(25,53),(25,93),(26,68),(26,84),(27,74),(27,78),(28,37),(28,60),(28,72),(29,124),(30,124),(31,101),(31,123),(33,117),(33,125),(34,118),(35,99),(36,116),(36,128),(37,101),(37,121),(38,109),(38,125),(39,100),(39,103),(40,109),(40,129),(41,126),(42,119),(43,107),(44,113),(45,9),(45,106),(46,108),(47,2),(47,108),(48,10),(48,122),(49,65),(49,128),(50,64),(51,8),(51,88),(52,39),(52,121),(52,123),(53,79),(54,45),(54,100),(55,32),(56,29),(56,127),(57,30),(57,127),(58,35),(58,120),(59,34),(59,99),(60,63),(60,101),(61,55),(62,56),(62,104),(63,83),(63,111),(64,57),(64,104),(65,44),(65,114),(66,58),(66,110),(67,65),(67,110),(68,43),(68,115),(69,34),(69,105),(70,36),(70,112),(71,33),(71,103),(71,119),(72,23),(72,54),(72,121),(73,50),(74,68),(74,102),(75,3),(75,82),(76,64),(76,113),(77,66),(77,106),(78,39),(78,54),(78,102),(79,42),(79,71),(80,29),(80,30),(81,35),(81,59),(82,62),(82,94),(83,49),(83,67),(83,112),(84,33),(84,38),(84,115),(85,50),(85,76),(86,59),(86,69),(86,120),(87,15),(87,79),(87,96),(88,53),(88,87),(89,38),(89,40),(89,119),(90,31),(90,60),(90,122),(91,36),(91,49),(91,107),(92,70),(92,83),(92,91),(93,31),(93,37),(93,52),(94,56),(94,57),(94,80),(95,58),(95,81),(95,86),(96,71),(96,84),(96,89),(96,102),(97,52),(97,72),(97,78),(97,122),(98,28),(98,90),(98,93),(98,97),(99,46),(99,118),(100,106),(101,7),(101,111),(102,40),(102,103),(102,115),(103,117),(103,129),(104,127),(105,47),(105,118),(106,85),(107,41),(107,116),(108,1),(109,41),(109,130),(110,114),(110,120),(111,95),(111,112),(112,86),(112,110),(112,128),(113,104),(114,105),(114,113),(115,107),(115,109),(115,117),(116,126),(117,116),(117,130),(118,108),(119,16),(119,125),(119,129),(120,14),(120,99),(120,105),(121,77),(121,100),(122,63),(122,92),(122,123),(123,70),(123,111),(124,55),(125,75),(125,130),(126,62),(127,61),(127,124),(128,69),(128,114),(129,73),(129,130),(130,82),(130,126)],131)
=> ? = 0 - 1
[4,1,3,2,5] => [[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1]]
=> [[1,1,2,2,2],[2,2,3,4],[3,3,4],[4,4],[5]]
=> ([(0,7),(0,8),(1,12),(2,11),(3,10),(4,10),(4,11),(5,3),(6,1),(6,13),(7,9),(8,5),(9,2),(9,4),(10,14),(11,6),(11,14),(13,12),(14,13)],15)
=> ? = 0 - 1
[4,1,5,2,3] => [[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1],[1,0,0,0,0],[0,0,1,0,0]]
=> [[1,1,2,2,2],[2,2,4,4],[3,4,5],[4,5],[5]]
=> ([(0,1),(1,4),(1,5),(2,8),(2,32),(3,6),(3,30),(4,7),(4,33),(5,10),(5,11),(5,33),(6,20),(7,31),(8,27),(9,15),(9,19),(10,18),(10,28),(11,18),(11,25),(13,39),(14,36),(14,39),(15,36),(16,38),(17,38),(18,2),(18,37),(19,26),(19,36),(20,21),(21,12),(22,12),(23,17),(23,35),(24,16),(24,35),(25,13),(25,37),(26,24),(26,34),(27,16),(27,17),(28,14),(28,19),(28,37),(29,21),(29,22),(30,20),(30,29),(31,13),(31,14),(31,15),(32,23),(32,24),(32,27),(33,9),(33,25),(33,28),(33,31),(34,30),(34,35),(35,29),(35,38),(36,3),(36,34),(37,26),(37,32),(37,39),(38,22),(39,23),(39,34)],40)
=> ? = 0 - 1
[4,2,1,3,5] => [[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,0,0,0,1]]
=> [[1,1,2,2,3],[2,2,3,3],[3,3,4],[4,4],[5]]
=> ([(0,5),(0,10),(1,16),(2,15),(3,14),(4,13),(5,12),(6,2),(6,13),(7,4),(7,14),(8,1),(9,6),(10,11),(10,12),(11,3),(11,7),(12,9),(13,15),(14,8),(15,16)],17)
=> ? = 1 - 1
[4,2,3,1,5] => [[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1]]
=> [[1,1,2,2,4],[2,2,3,4],[3,3,4],[4,4],[5]]
=> ([(0,14),(0,15),(1,19),(2,18),(3,29),(4,30),(5,22),(6,23),(7,24),(7,25),(8,9),(9,7),(9,18),(9,19),(10,5),(11,6),(12,2),(12,29),(13,1),(13,30),(14,16),(14,28),(15,17),(15,28),(16,3),(16,12),(17,4),(17,13),(18,24),(18,27),(19,25),(19,27),(20,26),(21,26),(22,20),(23,21),(24,22),(24,31),(25,23),(25,31),(27,31),(28,8),(29,10),(30,11),(31,20),(31,21)],32)
=> ? = 0 - 1
[4,2,5,1,3] => [[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1],[1,0,0,0,0],[0,0,1,0,0]]
=> [[1,1,2,2,4],[2,2,4,4],[3,4,5],[4,5],[5]]
=> ([(0,7),(0,8),(1,2),(1,45),(2,35),(3,37),(4,14),(4,49),(5,9),(5,48),(6,10),(6,12),(6,54),(7,31),(8,6),(8,13),(8,31),(9,27),(9,42),(10,28),(10,41),(11,26),(11,52),(12,17),(12,28),(12,51),(13,15),(13,50),(13,54),(14,16),(14,40),(14,53),(15,33),(15,44),(16,38),(16,47),(17,30),(17,40),(19,64),(19,66),(20,62),(21,65),(22,58),(23,60),(23,66),(24,60),(24,63),(25,67),(26,55),(27,59),(28,5),(28,56),(29,34),(30,22),(30,57),(31,4),(31,50),(32,22),(32,65),(33,43),(34,18),(35,18),(36,20),(37,1),(37,46),(38,27),(38,61),(39,19),(39,55),(39,58),(40,38),(40,57),(41,21),(41,56),(42,20),(42,59),(43,26),(43,39),(44,21),(44,32),(45,34),(45,35),(46,29),(46,45),(47,19),(47,23),(47,61),(48,36),(48,42),(49,11),(49,43),(49,53),(50,33),(50,49),(51,30),(51,32),(51,56),(52,23),(52,24),(52,55),(53,39),(53,47),(53,52),(53,57),(54,41),(54,44),(54,51),(55,3),(55,63),(55,66),(56,48),(56,65),(57,24),(57,58),(57,61),(58,63),(58,64),(59,25),(59,62),(60,25),(60,68),(61,59),(61,60),(61,64),(62,67),(63,68),(64,62),(64,68),(65,36),(66,37),(66,68),(67,29),(68,46),(68,67)],69)
=> ? = 1 - 1
[4,3,1,2,5] => [[0,0,1,0,0],[0,0,0,1,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1]]
=> [[1,1,2,3,3],[2,2,3,4],[3,3,4],[4,4],[5]]
=> ([(0,13),(0,15),(1,17),(2,16),(2,17),(3,19),(4,16),(4,18),(5,22),(6,21),(7,20),(8,23),(8,29),(9,4),(9,28),(10,3),(10,28),(11,6),(12,7),(12,24),(13,14),(14,1),(14,2),(15,9),(15,10),(16,25),(17,12),(17,25),(18,26),(18,29),(19,23),(19,26),(20,27),(22,27),(23,30),(24,20),(24,22),(25,24),(26,30),(27,21),(28,8),(28,18),(28,19),(29,5),(29,30),(30,11)],31)
=> ? = 0 - 1
[4,3,2,1,5] => [[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1]]
=> [[1,1,2,3,4],[2,2,3,4],[3,3,4],[4,4],[5]]
=> ([(0,5),(0,16),(0,17),(1,23),(2,19),(3,11),(3,21),(4,10),(4,20),(5,12),(5,13),(6,50),(7,51),(8,24),(8,58),(9,25),(9,59),(10,14),(10,52),(11,15),(11,53),(12,26),(12,60),(13,27),(13,60),(14,54),(15,55),(16,4),(16,29),(17,3),(17,29),(18,48),(18,49),(19,32),(19,33),(20,46),(20,52),(21,47),(21,53),(22,34),(22,35),(23,18),(23,54),(23,55),(24,40),(24,42),(25,41),(25,43),(26,46),(26,56),(27,47),(27,57),(28,63),(29,1),(30,62),(31,61),(32,61),(33,61),(34,6),(34,62),(35,7),(35,62),(36,58),(37,59),(38,32),(39,33),(40,44),(41,45),(42,38),(43,39),(44,31),(45,31),(46,36),(47,37),(48,40),(48,63),(49,41),(49,63),(50,38),(51,39),(52,8),(52,36),(53,9),(53,37),(54,28),(54,48),(55,28),(55,49),(56,30),(56,34),(57,30),(57,35),(58,42),(58,50),(59,43),(59,51),(60,22),(60,56),(60,57),(62,2),(63,44),(63,45)],64)
=> ? = 0 - 1
[4,3,5,1,2] => [[0,0,0,1,0],[0,0,0,0,1],[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0]]
=> [[1,1,2,4,4],[2,2,4,5],[3,4,5],[4,5],[5]]
=> ([(0,2),(0,3),(1,8),(1,16),(2,1),(3,7),(3,10),(4,13),(4,59),(5,12),(5,81),(6,20),(6,82),(7,11),(7,83),(8,60),(9,23),(9,58),(10,19),(10,22),(10,83),(11,78),(12,64),(13,24),(14,52),(14,72),(15,17),(15,73),(15,80),(16,60),(16,74),(17,39),(17,70),(18,36),(18,44),(19,51),(19,69),(20,33),(20,75),(21,28),(21,38),(21,50),(22,51),(22,71),(22,74),(23,49),(23,56),(23,57),(25,101),(26,113),(27,107),(27,110),(28,107),(28,111),(29,110),(29,111),(30,112),(31,90),(31,98),(32,94),(32,114),(33,96),(34,91),(34,92),(35,89),(35,92),(36,108),(37,94),(37,103),(38,9),(38,111),(39,45),(40,31),(40,102),(40,114),(41,31),(41,104),(42,37),(42,99),(43,34),(43,85),(43,87),(44,30),(44,108),(45,55),(46,33),(46,86),(47,48),(47,86),(48,25),(48,100),(49,42),(49,85),(50,14),(50,76),(50,107),(51,15),(51,61),(51,84),(52,46),(52,109),(53,32),(53,93),(54,26),(54,95),(55,25),(55,91),(56,35),(56,85),(56,97),(57,53),(57,97),(58,57),(59,24),(60,5),(60,63),(61,67),(61,73),(62,34),(62,35),(62,113),(63,67),(63,81),(64,46),(64,47),(65,45),(65,68),(66,47),(66,68),(66,109),(67,65),(67,66),(68,48),(68,55),(68,87),(69,29),(69,38),(69,84),(70,26),(70,62),(71,27),(71,50),(71,84),(72,43),(72,49),(72,109),(73,39),(73,65),(74,61),(74,63),(75,32),(75,40),(75,96),(76,72),(76,79),(76,88),(77,40),(77,41),(77,93),(78,27),(78,28),(78,29),(79,43),(79,56),(79,62),(79,95),(80,54),(80,70),(80,79),(81,52),(81,64),(81,66),(82,53),(82,75),(82,77),(83,21),(83,69),(83,71),(83,78),(84,76),(84,80),(84,110),(85,92),(85,99),(86,37),(86,96),(86,100),(87,91),(87,99),(87,100),(88,82),(88,95),(89,104),(90,108),(90,116),(91,101),(91,106),(92,106),(93,18),(93,104),(93,114),(94,115),(95,77),(95,97),(95,113),(96,94),(96,102),(97,89),(97,93),(98,116),(99,103),(99,106),(100,101),(100,102),(100,103),(101,98),(101,105),(102,98),(102,115),(103,105),(103,115),(104,36),(104,90),(105,116),(106,105),(107,6),(107,88),(108,4),(108,112),(109,42),(109,86),(109,87),(110,54),(110,88),(111,58),(112,59),(113,41),(113,89),(114,44),(114,90),(114,115),(115,30),(115,116),(116,112)],117)
=> ? = 0 - 1
[4,3,5,2,1] => [[0,0,0,0,1],[0,0,0,1,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0]]
=> [[1,1,2,4,5],[2,2,4,5],[3,4,5],[4,5],[5]]
=> ([(0,4),(0,15),(0,16),(1,34),(2,7),(2,32),(3,14),(3,33),(4,11),(4,12),(5,147),(6,38),(6,125),(7,5),(7,114),(8,39),(8,161),(9,30),(9,158),(10,31),(10,96),(11,29),(11,159),(12,28),(12,41),(12,159),(13,24),(13,75),(14,20),(14,21),(14,156),(15,2),(15,54),(16,3),(16,54),(17,68),(17,119),(18,115),(18,120),(19,113),(19,149),(20,122),(20,154),(21,122),(21,164),(22,111),(22,145),(23,67),(23,116),(24,65),(24,66),(25,42),(25,117),(25,148),(26,37),(26,152),(26,163),(27,35),(27,150),(27,155),(28,118),(28,153),(29,121),(29,162),(30,110),(30,146),(31,109),(31,112),(32,114),(32,151),(33,121),(33,156),(34,36),(34,147),(34,164),(35,79),(35,81),(36,84),(36,134),(37,80),(37,137),(38,95),(38,106),(38,107),(39,58),(39,94),(39,139),(40,52),(40,64),(40,108),(41,118),(41,132),(41,151),(42,76),(42,77),(42,78),(43,211),(44,202),(45,173),(45,214),(46,168),(47,167),(47,168),(48,217),(49,212),(49,215),(50,174),(50,215),(51,218),(52,6),(52,212),(53,10),(54,1),(55,176),(56,176),(56,211),(57,192),(57,203),(58,173),(58,186),(59,177),(59,187),(60,175),(60,177),(61,214),(62,193),(63,182),(63,200),(64,22),(64,174),(64,212),(65,181),(66,181),(67,180),(68,179),(69,96),(70,57),(70,199),(70,213),(71,60),(71,169),(71,171),(72,100),(72,206),(73,58),(73,172),(74,66),(74,197),(75,65),(76,83),(76,170),(77,91),(77,167),(78,120),(78,167),(78,170),(79,88),(80,87),(81,136),(82,67),(82,216),(83,94),(83,208),(84,110),(84,210),(85,69),(85,208),(86,63),(86,198),(87,105),(88,55),(89,93),(89,172),(90,46),(90,210),(91,45),(91,196),(92,43),(92,209),(93,44),(93,195),(94,101),(94,173),(95,86),(95,169),(96,112),(97,102),(97,166),(97,188),(98,103),(98,188),(99,57),(99,191),(100,109),(100,182),(100,213),(101,97),(101,184),(102,56),(102,183),(102,209),(103,55),(103,183),(104,48),(104,185),(105,44),(105,175),(106,59),(106,169),(106,190),(107,72),(107,190),(108,19),(108,144),(108,174),(109,62),(109,166),(110,135),(111,53),(112,92),(112,166),(113,73),(113,207),(114,9),(114,126),(115,69),(115,178),(116,74),(116,180),(117,18),(117,78),(117,218),(118,26),(118,123),(118,165),(119,23),(119,82),(119,179),(120,27),(120,140),(120,178),(121,133),(122,138),(123,130),(123,152),(124,88),(124,103),(125,53),(125,107),(126,130),(126,158),(127,59),(127,60),(127,217),(128,87),(128,131),(129,89),(129,131),(129,207),(130,128),(130,129),(131,93),(131,105),(131,171),(132,50),(132,108),(132,165),(133,51),(133,148),(134,47),(134,77),(134,210),(135,45),(135,61),(136,43),(136,56),(137,48),(137,127),(138,46),(138,47),(139,70),(139,100),(139,186),(140,143),(140,150),(141,70),(141,99),(141,206),(142,97),(142,157),(143,98),(143,124),(144,149),(144,160),(144,189),(145,83),(145,85),(146,73),(146,89),(147,84),(147,90),(148,76),(148,145),(148,218),(149,71),(149,95),(149,207),(150,79),(150,124),(151,123),(151,126),(152,80),(152,128),(153,49),(153,52),(153,165),(154,51),(154,117),(155,81),(155,157),(156,25),(156,133),(156,154),(157,92),(157,102),(157,136),(158,113),(158,129),(158,146),(159,40),(159,132),(159,153),(159,162),(160,71),(160,106),(160,127),(160,185),(161,72),(161,139),(161,141),(162,49),(162,50),(162,64),(163,104),(163,137),(163,160),(164,90),(164,134),(164,138),(165,144),(165,163),(165,215),(166,193),(166,209),(167,140),(167,196),(168,61),(168,196),(169,177),(169,198),(170,178),(170,208),(171,175),(171,195),(171,198),(172,63),(172,186),(172,195),(173,184),(174,8),(174,189),(175,202),(175,204),(176,194),(177,204),(178,142),(178,155),(179,13),(179,216),(180,197),(182,62),(182,220),(183,176),(183,201),(184,188),(185,141),(185,190),(185,217),(186,182),(186,199),(187,191),(188,183),(188,193),(189,161),(189,185),(190,187),(190,206),(191,68),(191,192),(192,179),(192,219),(193,201),(194,197),(195,199),(195,200),(195,202),(196,143),(196,214),(197,181),(198,200),(198,204),(199,203),(199,220),(200,205),(200,220),(201,180),(201,194),(202,203),(202,205),(203,219),(204,205),(205,219),(206,17),(206,191),(206,213),(207,86),(207,171),(207,172),(208,101),(208,142),(209,116),(209,201),(209,211),(210,91),(210,135),(210,168),(211,74),(211,194),(212,111),(212,125),(213,119),(213,192),(213,220),(214,98),(214,184),(215,104),(215,189),(216,75),(217,99),(217,187),(218,85),(218,115),(218,170),(219,216),(220,82),(220,219)],221)
=> ? = 1 - 1
[4,5,3,1,2] => [[0,0,0,1,0],[0,0,0,0,1],[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0]]
=> [[1,1,3,4,4],[2,3,4,5],[3,4,5],[4,5],[5]]
=> ([(0,1),(0,2),(1,12),(1,14),(2,11),(2,13),(3,145),(4,146),(5,31),(5,155),(6,32),(6,156),(7,15),(7,143),(8,16),(8,144),(9,37),(9,114),(10,38),(10,115),(11,17),(11,157),(12,18),(12,158),(13,29),(13,35),(13,157),(14,30),(14,36),(14,158),(15,84),(16,85),(17,147),(18,148),(19,102),(19,133),(20,103),(20,134),(21,23),(21,149),(21,153),(22,24),(22,150),(22,154),(23,118),(23,128),(24,119),(24,129),(25,62),(25,82),(26,63),(26,83),(27,74),(27,139),(28,75),(28,140),(29,100),(29,126),(30,101),(30,127),(31,55),(31,135),(32,56),(32,136),(33,47),(33,72),(33,98),(34,48),(34,73),(34,99),(35,100),(35,130),(35,132),(36,101),(36,131),(36,132),(37,96),(37,110),(37,112),(38,97),(38,111),(38,113),(40,201),(40,202),(41,225),(42,226),(43,221),(43,223),(44,222),(44,224),(45,213),(45,221),(46,214),(46,222),(47,213),(47,223),(48,214),(48,224),(49,161),(50,162),(51,183),(51,227),(52,184),(52,228),(53,173),(53,195),(54,174),(54,196),(55,185),(56,186),(57,179),(57,180),(58,175),(58,177),(59,176),(59,178),(60,171),(60,177),(61,172),(61,178),(62,215),(63,216),(64,220),(65,219),(66,219),(67,220),(68,183),(68,203),(69,184),(69,204),(70,179),(70,199),(71,180),(71,200),(72,9),(72,223),(73,10),(73,224),(74,3),(74,189),(75,4),(75,190),(76,53),(76,205),(76,227),(77,54),(77,206),(77,228),(78,53),(78,207),(79,54),(79,208),(80,58),(80,163),(80,167),(81,59),(81,164),(81,168),(82,49),(82,215),(83,50),(83,216),(84,94),(85,95),(86,68),(86,197),(87,69),(87,198),(88,94),(89,95),(90,55),(90,169),(91,56),(91,170),(92,108),(92,170),(93,109),(93,169),(94,39),(95,39),(96,86),(96,163),(97,87),(97,164),(98,19),(98,137),(98,213),(99,20),(99,138),(99,214),(100,21),(100,116),(100,159),(101,22),(101,117),(101,160),(102,90),(102,217),(103,91),(103,218),(104,51),(104,181),(105,52),(105,182),(106,41),(106,187),(107,42),(107,188),(108,40),(108,175),(108,194),(109,40),(109,176),(109,193),(110,60),(110,163),(110,191),(111,61),(111,164),(111,192),(112,104),(112,191),(113,105),(113,192),(114,112),(115,113),(116,124),(116,149),(117,124),(117,150),(118,91),(118,92),(119,90),(119,93),(120,58),(120,60),(120,225),(121,59),(121,61),(121,226),(122,92),(122,125),(122,218),(123,93),(123,125),(123,217),(124,122),(124,123),(125,108),(125,109),(125,167),(125,168),(126,43),(126,72),(126,159),(127,44),(127,73),(127,160),(128,41),(128,120),(129,42),(129,121),(130,45),(130,98),(130,159),(131,46),(131,99),(131,160),(132,116),(132,117),(133,80),(133,96),(133,217),(134,81),(134,97),(134,218),(135,51),(135,76),(135,185),(136,52),(136,77),(136,186),(137,133),(137,151),(137,165),(138,134),(138,152),(138,166),(139,57),(139,70),(139,189),(140,57),(140,71),(140,190),(141,76),(141,78),(141,181),(142,77),(142,79),(142,182),(143,84),(143,88),(144,85),(144,89),(145,64),(145,67),(146,65),(146,66),(147,43),(147,45),(147,47),(148,44),(148,46),(148,48),(149,103),(149,118),(149,122),(150,102),(150,119),(150,123),(151,80),(151,110),(151,120),(151,187),(152,81),(152,111),(152,121),(152,188),(153,106),(153,128),(153,151),(154,107),(154,129),(154,152),(155,104),(155,135),(155,141),(156,105),(156,136),(156,142),(157,33),(157,126),(157,130),(157,147),(158,34),(158,127),(158,131),(158,148),(159,137),(159,153),(159,221),(160,138),(160,154),(160,222),(161,143),(162,144),(163,27),(163,177),(163,197),(164,28),(164,178),(164,198),(165,155),(165,187),(166,156),(166,188),(167,175),(167,193),(167,197),(168,176),(168,194),(168,198),(169,68),(169,185),(169,193),(170,69),(170,186),(170,194),(171,207),(172,208),(173,215),(173,231),(174,216),(174,232),(175,201),(175,209),(176,202),(176,210),(177,74),(177,209),(178,75),(178,210),(179,66),(179,233),(180,67),(180,233),(181,25),(181,207),(181,227),(182,26),(182,208),(182,228),(183,229),(184,230),(185,183),(185,205),(186,184),(186,206),(187,141),(187,191),(187,225),(188,142),(188,192),(188,226),(189,145),(189,180),(189,199),(190,146),(190,179),(190,200),(191,171),(191,181),(192,172),(192,182),(193,201),(193,203),(193,205),(194,202),(194,204),(194,206),(195,231),(196,232),(197,139),(197,203),(197,209),(198,140),(198,204),(198,210),(199,64),(199,233),(200,65),(200,233),(201,195),(201,211),(202,196),(202,212),(203,70),(203,211),(203,229),(204,71),(204,212),(204,230),(205,195),(205,229),(206,196),(206,230),(207,62),(207,173),(208,63),(208,174),(209,189),(209,211),(210,190),(210,212),(211,199),(211,231),(212,200),(212,232),(213,5),(213,165),(214,6),(214,166),(215,7),(215,161),(216,8),(216,162),(217,86),(217,167),(217,169),(218,87),(218,168),(218,170),(219,88),(220,89),(221,106),(221,165),(222,107),(222,166),(223,114),(224,115),(225,78),(225,171),(226,79),(226,172),(227,82),(227,173),(227,229),(228,83),(228,174),(228,230),(229,49),(229,231),(230,50),(230,232),(231,161),(232,162),(233,219),(233,220)],234)
=> ? = 0 - 1
[1,2,3,4,6,5] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,4,4],[5,6],[6]]
=> ([(0,1)],2)
=> -1 = 0 - 1
[1,2,3,5,4,6] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,4,5],[5,5],[6]]
=> ([(0,1)],2)
=> -1 = 0 - 1
[1,2,4,3,5,6] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,4],[4,4,4],[5,5],[6]]
=> ([(0,1)],2)
=> -1 = 0 - 1
[1,2,4,3,6,5] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,4],[4,4,4],[5,6],[6]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1 = 2 - 1
[1,3,2,4,5,6] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,3],[4,4,4],[5,5],[6]]
=> ([(0,1)],2)
=> -1 = 0 - 1
[1,3,2,4,6,5] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,3],[4,4,4],[5,6],[6]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1 = 2 - 1
[1,3,2,5,4,6] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,3],[4,4,5],[5,5],[6]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1 = 2 - 1
[2,1,3,4,5,6] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,3],[4,4,4],[5,5],[6]]
=> ([(0,1)],2)
=> -1 = 0 - 1
[2,1,3,4,6,5] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,3],[4,4,4],[5,6],[6]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1 = 2 - 1
[2,1,3,5,4,6] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,3],[4,4,5],[5,5],[6]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1 = 2 - 1
[2,1,4,3,5,6] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,4],[4,4,4],[5,5],[6]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1 = 2 - 1
Description
The permanent of the Coxeter matrix of the poset.
Matching statistic: St001635
Mp00063: Permutations to alternating sign matrixAlternating sign matrices
Mp00001: Alternating sign matrices to semistandard tableau via monotone trianglesSemistandard tableaux
Mp00214: Semistandard tableaux subcrystalPosets
St001635: Posets ⟶ ℤResult quality: 5% values known / values provided: 5%distinct values known / distinct values provided: 18%
Values
[2,1] => [[0,1],[1,0]]
=> [[1,2],[2]]
=> ([(0,1)],2)
=> -1 = 0 - 1
[1,3,2] => [[1,0,0],[0,0,1],[0,1,0]]
=> [[1,1,1],[2,3],[3]]
=> ([(0,1)],2)
=> -1 = 0 - 1
[2,1,3] => [[0,1,0],[1,0,0],[0,0,1]]
=> [[1,1,2],[2,2],[3]]
=> ([(0,1)],2)
=> -1 = 0 - 1
[1,2,4,3] => [[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
=> [[1,1,1,1],[2,2,2],[3,4],[4]]
=> ([(0,1)],2)
=> -1 = 0 - 1
[1,3,2,4] => [[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,3],[3,3],[4]]
=> ([(0,1)],2)
=> -1 = 0 - 1
[1,4,2,3] => [[1,0,0,0],[0,0,1,0],[0,0,0,1],[0,1,0,0]]
=> [[1,1,1,1],[2,3,3],[3,4],[4]]
=> ([(0,3),(2,1),(3,2)],4)
=> -1 = 0 - 1
[2,1,3,4] => [[0,1,0,0],[1,0,0,0],[0,0,1,0],[0,0,0,1]]
=> [[1,1,1,2],[2,2,2],[3,3],[4]]
=> ([(0,1)],2)
=> -1 = 0 - 1
[2,1,4,3] => [[0,1,0,0],[1,0,0,0],[0,0,0,1],[0,0,1,0]]
=> [[1,1,1,2],[2,2,2],[3,4],[4]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1 = 2 - 1
[2,3,4,1] => [[0,0,0,1],[1,0,0,0],[0,1,0,0],[0,0,1,0]]
=> [[1,1,1,4],[2,2,4],[3,4],[4]]
=> ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
=> ? = 0 - 1
[2,4,1,3] => [[0,0,1,0],[1,0,0,0],[0,0,0,1],[0,1,0,0]]
=> [[1,1,1,3],[2,3,3],[3,4],[4]]
=> ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> ? = 0 - 1
[2,4,3,1] => [[0,0,0,1],[1,0,0,0],[0,0,1,0],[0,1,0,0]]
=> [[1,1,1,4],[2,3,4],[3,4],[4]]
=> ([(0,5),(0,10),(1,16),(2,15),(3,14),(4,13),(5,12),(6,2),(6,13),(7,4),(7,14),(8,1),(9,6),(10,11),(10,12),(11,3),(11,7),(12,9),(13,15),(14,8),(15,16)],17)
=> ? = 1 - 1
[3,1,4,2] => [[0,1,0,0],[0,0,0,1],[1,0,0,0],[0,0,1,0]]
=> [[1,1,2,2],[2,2,4],[3,4],[4]]
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 1 - 1
[3,2,4,1] => [[0,0,0,1],[0,1,0,0],[1,0,0,0],[0,0,1,0]]
=> [[1,1,2,4],[2,2,4],[3,4],[4]]
=> ([(0,7),(0,8),(1,12),(2,11),(3,10),(4,10),(4,11),(5,3),(6,1),(6,13),(7,9),(8,5),(9,2),(9,4),(10,14),(11,6),(11,14),(13,12),(14,13)],15)
=> ? = 1 - 1
[3,4,2,1] => [[0,0,0,1],[0,0,1,0],[1,0,0,0],[0,1,0,0]]
=> [[1,1,3,4],[2,3,4],[3,4],[4]]
=> ([(0,13),(0,15),(1,17),(2,16),(2,17),(3,19),(4,16),(4,18),(5,22),(6,21),(7,20),(8,23),(8,29),(9,4),(9,28),(10,3),(10,28),(11,6),(12,7),(12,24),(13,14),(14,1),(14,2),(15,9),(15,10),(16,25),(17,12),(17,25),(18,26),(18,29),(19,23),(19,26),(20,27),(22,27),(23,30),(24,20),(24,22),(25,24),(26,30),(27,21),(28,8),(28,18),(28,19),(29,5),(29,30),(30,11)],31)
=> ? = 1 - 1
[4,1,3,2] => [[0,1,0,0],[0,0,0,1],[0,0,1,0],[1,0,0,0]]
=> [[1,2,2,2],[2,3,4],[3,4],[4]]
=> ([(0,7),(0,8),(1,12),(2,11),(3,10),(4,10),(4,11),(5,3),(6,1),(6,13),(7,9),(8,5),(9,2),(9,4),(10,14),(11,6),(11,14),(13,12),(14,13)],15)
=> ? = 0 - 1
[4,2,1,3] => [[0,0,1,0],[0,1,0,0],[0,0,0,1],[1,0,0,0]]
=> [[1,2,2,3],[2,3,3],[3,4],[4]]
=> ([(0,5),(0,10),(1,16),(2,15),(3,14),(4,13),(5,12),(6,2),(6,13),(7,4),(7,14),(8,1),(9,6),(10,11),(10,12),(11,3),(11,7),(12,9),(13,15),(14,8),(15,16)],17)
=> ? = 1 - 1
[4,2,3,1] => [[0,0,0,1],[0,1,0,0],[0,0,1,0],[1,0,0,0]]
=> [[1,2,2,4],[2,3,4],[3,4],[4]]
=> ([(0,14),(0,15),(1,19),(2,18),(3,29),(4,30),(5,22),(6,23),(7,24),(7,25),(8,9),(9,7),(9,18),(9,19),(10,5),(11,6),(12,2),(12,29),(13,1),(13,30),(14,16),(14,28),(15,17),(15,28),(16,3),(16,12),(17,4),(17,13),(18,24),(18,27),(19,25),(19,27),(20,26),(21,26),(22,20),(23,21),(24,22),(24,31),(25,23),(25,31),(27,31),(28,8),(29,10),(30,11),(31,20),(31,21)],32)
=> ? = 0 - 1
[4,3,1,2] => [[0,0,1,0],[0,0,0,1],[0,1,0,0],[1,0,0,0]]
=> [[1,2,3,3],[2,3,4],[3,4],[4]]
=> ([(0,13),(0,15),(1,17),(2,16),(2,17),(3,19),(4,16),(4,18),(5,22),(6,21),(7,20),(8,23),(8,29),(9,4),(9,28),(10,3),(10,28),(11,6),(12,7),(12,24),(13,14),(14,1),(14,2),(15,9),(15,10),(16,25),(17,12),(17,25),(18,26),(18,29),(19,23),(19,26),(20,27),(22,27),(23,30),(24,20),(24,22),(25,24),(26,30),(27,21),(28,8),(28,18),(28,19),(29,5),(29,30),(30,11)],31)
=> ? = 0 - 1
[4,3,2,1] => [[0,0,0,1],[0,0,1,0],[0,1,0,0],[1,0,0,0]]
=> [[1,2,3,4],[2,3,4],[3,4],[4]]
=> ([(0,5),(0,16),(0,17),(1,23),(2,19),(3,11),(3,21),(4,10),(4,20),(5,12),(5,13),(6,50),(7,51),(8,24),(8,58),(9,25),(9,59),(10,14),(10,52),(11,15),(11,53),(12,26),(12,60),(13,27),(13,60),(14,54),(15,55),(16,4),(16,29),(17,3),(17,29),(18,48),(18,49),(19,32),(19,33),(20,46),(20,52),(21,47),(21,53),(22,34),(22,35),(23,18),(23,54),(23,55),(24,40),(24,42),(25,41),(25,43),(26,46),(26,56),(27,47),(27,57),(28,63),(29,1),(30,62),(31,61),(32,61),(33,61),(34,6),(34,62),(35,7),(35,62),(36,58),(37,59),(38,32),(39,33),(40,44),(41,45),(42,38),(43,39),(44,31),(45,31),(46,36),(47,37),(48,40),(48,63),(49,41),(49,63),(50,38),(51,39),(52,8),(52,36),(53,9),(53,37),(54,28),(54,48),(55,28),(55,49),(56,30),(56,34),(57,30),(57,35),(58,42),(58,50),(59,43),(59,51),(60,22),(60,56),(60,57),(62,2),(63,44),(63,45)],64)
=> ? = 0 - 1
[1,2,3,5,4] => [[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0]]
=> [[1,1,1,1,1],[2,2,2,2],[3,3,3],[4,5],[5]]
=> ([(0,1)],2)
=> -1 = 0 - 1
[1,2,4,3,5] => [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [[1,1,1,1,1],[2,2,2,2],[3,3,4],[4,4],[5]]
=> ([(0,1)],2)
=> -1 = 0 - 1
[1,2,5,3,4] => [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1],[0,0,1,0,0]]
=> [[1,1,1,1,1],[2,2,2,2],[3,4,4],[4,5],[5]]
=> ([(0,3),(2,1),(3,2)],4)
=> -1 = 0 - 1
[1,3,2,4,5] => [[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
=> [[1,1,1,1,1],[2,2,2,3],[3,3,3],[4,4],[5]]
=> ([(0,1)],2)
=> -1 = 0 - 1
[1,3,2,5,4] => [[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
=> [[1,1,1,1,1],[2,2,2,3],[3,3,3],[4,5],[5]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1 = 2 - 1
[1,3,4,5,2] => [[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0]]
=> [[1,1,1,1,1],[2,2,2,5],[3,3,5],[4,5],[5]]
=> ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
=> ? = 0 - 1
[1,3,5,2,4] => [[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,1,0,0]]
=> [[1,1,1,1,1],[2,2,2,4],[3,4,4],[4,5],[5]]
=> ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> ? = 0 - 1
[1,3,5,4,2] => [[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0]]
=> [[1,1,1,1,1],[2,2,2,5],[3,4,5],[4,5],[5]]
=> ([(0,5),(0,10),(1,16),(2,15),(3,14),(4,13),(5,12),(6,2),(6,13),(7,4),(7,14),(8,1),(9,6),(10,11),(10,12),(11,3),(11,7),(12,9),(13,15),(14,8),(15,16)],17)
=> ? = 1 - 1
[1,4,2,3,5] => [[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [[1,1,1,1,1],[2,2,3,3],[3,3,4],[4,4],[5]]
=> ([(0,3),(2,1),(3,2)],4)
=> -1 = 0 - 1
[1,4,2,5,3] => [[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,0,1,0]]
=> [[1,1,1,1,1],[2,2,3,3],[3,3,5],[4,5],[5]]
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 1 - 1
[1,4,3,5,2] => [[1,0,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0]]
=> [[1,1,1,1,1],[2,2,3,5],[3,3,5],[4,5],[5]]
=> ([(0,7),(0,8),(1,12),(2,11),(3,10),(4,10),(4,11),(5,3),(6,1),(6,13),(7,9),(8,5),(9,2),(9,4),(10,14),(11,6),(11,14),(13,12),(14,13)],15)
=> ? = 1 - 1
[1,4,5,2,3] => [[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0]]
=> [[1,1,1,1,1],[2,2,4,4],[3,4,5],[4,5],[5]]
=> ([(0,8),(2,11),(2,12),(3,10),(4,9),(5,4),(5,14),(6,3),(6,14),(7,1),(8,5),(8,6),(9,11),(9,13),(10,12),(10,13),(11,15),(12,15),(13,15),(14,2),(14,9),(14,10),(15,7)],16)
=> ? = 0 - 1
[1,4,5,3,2] => [[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0]]
=> [[1,1,1,1,1],[2,2,4,5],[3,4,5],[4,5],[5]]
=> ([(0,13),(0,15),(1,17),(2,16),(2,17),(3,19),(4,16),(4,18),(5,22),(6,21),(7,20),(8,23),(8,29),(9,4),(9,28),(10,3),(10,28),(11,6),(12,7),(12,24),(13,14),(14,1),(14,2),(15,9),(15,10),(16,25),(17,12),(17,25),(18,26),(18,29),(19,23),(19,26),(20,27),(22,27),(23,30),(24,20),(24,22),(25,24),(26,30),(27,21),(28,8),(28,18),(28,19),(29,5),(29,30),(30,11)],31)
=> ? = 1 - 1
[1,5,3,2,4] => [[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1],[0,1,0,0,0]]
=> [[1,1,1,1,1],[2,3,3,4],[3,4,4],[4,5],[5]]
=> ([(0,5),(0,10),(1,16),(2,15),(3,14),(4,13),(5,12),(6,2),(6,13),(7,4),(7,14),(8,1),(9,6),(10,11),(10,12),(11,3),(11,7),(12,9),(13,15),(14,8),(15,16)],17)
=> ? = 1 - 1
[1,5,4,3,2] => [[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0]]
=> [[1,1,1,1,1],[2,3,4,5],[3,4,5],[4,5],[5]]
=> ([(0,5),(0,16),(0,17),(1,23),(2,19),(3,11),(3,21),(4,10),(4,20),(5,12),(5,13),(6,50),(7,51),(8,24),(8,58),(9,25),(9,59),(10,14),(10,52),(11,15),(11,53),(12,26),(12,60),(13,27),(13,60),(14,54),(15,55),(16,4),(16,29),(17,3),(17,29),(18,48),(18,49),(19,32),(19,33),(20,46),(20,52),(21,47),(21,53),(22,34),(22,35),(23,18),(23,54),(23,55),(24,40),(24,42),(25,41),(25,43),(26,46),(26,56),(27,47),(27,57),(28,63),(29,1),(30,62),(31,61),(32,61),(33,61),(34,6),(34,62),(35,7),(35,62),(36,58),(37,59),(38,32),(39,33),(40,44),(41,45),(42,38),(43,39),(44,31),(45,31),(46,36),(47,37),(48,40),(48,63),(49,41),(49,63),(50,38),(51,39),(52,8),(52,36),(53,9),(53,37),(54,28),(54,48),(55,28),(55,49),(56,30),(56,34),(57,30),(57,35),(58,42),(58,50),(59,43),(59,51),(60,22),(60,56),(60,57),(62,2),(63,44),(63,45)],64)
=> ? = 0 - 1
[2,1,3,4,5] => [[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]]
=> [[1,1,1,1,2],[2,2,2,2],[3,3,3],[4,4],[5]]
=> ([(0,1)],2)
=> -1 = 0 - 1
[2,1,3,5,4] => [[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0]]
=> [[1,1,1,1,2],[2,2,2,2],[3,3,3],[4,5],[5]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1 = 2 - 1
[2,1,4,3,5] => [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [[1,1,1,1,2],[2,2,2,2],[3,3,4],[4,4],[5]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1 = 2 - 1
[2,1,4,5,3] => [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,0,0,1,0]]
=> [[1,1,1,1,2],[2,2,2,2],[3,3,5],[4,5],[5]]
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 1 - 1
[2,1,5,4,3] => [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0]]
=> [[1,1,1,1,2],[2,2,2,2],[3,4,5],[4,5],[5]]
=> ([(0,3),(0,6),(0,7),(1,8),(1,12),(2,8),(2,11),(3,9),(3,10),(4,2),(4,13),(5,1),(5,14),(6,4),(6,9),(7,5),(7,10),(8,15),(9,13),(10,14),(11,15),(12,15),(13,11),(14,12)],16)
=> ? = 0 - 1
[2,3,1,5,4] => [[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
=> [[1,1,1,1,3],[2,2,2,3],[3,3,3],[4,5],[5]]
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 1 - 1
[2,3,4,1,5] => [[0,0,0,1,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [[1,1,1,1,4],[2,2,2,4],[3,3,4],[4,4],[5]]
=> ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
=> ? = 0 - 1
[2,3,4,5,1] => [[0,0,0,0,1],[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0]]
=> [[1,1,1,1,5],[2,2,2,5],[3,3,5],[4,5],[5]]
=> ([(0,9),(1,13),(2,14),(4,12),(5,11),(6,1),(6,12),(7,3),(8,5),(8,15),(9,10),(10,4),(10,6),(11,14),(12,8),(12,13),(13,15),(14,7),(15,2),(15,11)],16)
=> ? = 0 - 1
[2,4,1,3,5] => [[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [[1,1,1,1,3],[2,2,3,3],[3,3,4],[4,4],[5]]
=> ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> ? = 0 - 1
[2,4,1,5,3] => [[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,0,1,0]]
=> [[1,1,1,1,3],[2,2,3,3],[3,3,5],[4,5],[5]]
=> ([(0,6),(0,7),(1,5),(1,15),(2,4),(2,14),(3,13),(4,12),(5,3),(5,16),(6,9),(7,2),(7,9),(9,1),(9,14),(10,11),(11,8),(12,10),(13,8),(14,12),(14,15),(15,10),(15,16),(16,11),(16,13)],17)
=> ? = 0 - 1
[2,4,3,1,5] => [[0,0,0,1,0],[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [[1,1,1,1,4],[2,2,3,4],[3,3,4],[4,4],[5]]
=> ([(0,5),(0,10),(1,16),(2,15),(3,14),(4,13),(5,12),(6,2),(6,13),(7,4),(7,14),(8,1),(9,6),(10,11),(10,12),(11,3),(11,7),(12,9),(13,15),(14,8),(15,16)],17)
=> ? = 1 - 1
[2,4,3,5,1] => [[0,0,0,0,1],[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0]]
=> [[1,1,1,1,5],[2,2,3,5],[3,3,5],[4,5],[5]]
=> ([(0,8),(0,13),(1,19),(2,16),(2,18),(3,21),(4,26),(5,24),(6,16),(6,22),(7,20),(7,23),(8,17),(9,4),(9,18),(10,9),(11,7),(11,30),(12,3),(12,25),(13,14),(13,17),(14,1),(14,15),(15,2),(15,6),(15,19),(16,28),(17,10),(18,26),(18,28),(19,11),(19,22),(20,24),(20,31),(22,30),(23,31),(24,12),(24,27),(25,21),(26,23),(26,29),(27,25),(28,29),(29,31),(30,5),(30,20),(31,27)],32)
=> ? = 0 - 1
[2,4,5,1,3] => [[0,0,0,1,0],[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0]]
=> [[1,1,1,1,4],[2,2,4,4],[3,4,5],[4,5],[5]]
=> ([(0,9),(0,10),(1,2),(3,7),(3,23),(4,6),(4,22),(5,15),(6,16),(7,8),(7,24),(8,20),(9,19),(10,4),(10,19),(11,14),(11,18),(12,26),(13,26),(14,25),(15,1),(16,21),(17,13),(17,25),(18,12),(18,25),(19,3),(19,22),(20,12),(20,13),(21,14),(21,17),(22,16),(22,23),(23,11),(23,21),(23,24),(24,17),(24,18),(24,20),(25,5),(25,26),(26,15)],27)
=> ? = 0 - 1
[2,4,5,3,1] => [[0,0,0,0,1],[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0]]
=> [[1,1,1,1,5],[2,2,4,5],[3,4,5],[4,5],[5]]
=> ([(0,17),(0,18),(1,11),(1,12),(2,53),(3,50),(4,33),(5,16),(5,65),(6,13),(6,61),(7,14),(7,62),(8,15),(8,51),(9,25),(9,63),(10,24),(10,52),(11,54),(12,22),(12,23),(12,54),(13,36),(14,35),(15,40),(16,59),(17,1),(17,48),(18,7),(18,48),(19,32),(19,45),(20,29),(20,38),(21,55),(21,58),(22,49),(22,60),(23,42),(23,49),(24,31),(24,46),(25,21),(25,60),(25,64),(27,70),(28,70),(29,67),(30,66),(31,68),(32,3),(32,69),(33,8),(34,39),(35,57),(36,39),(37,32),(37,66),(38,19),(38,37),(38,67),(39,26),(40,26),(41,30),(41,67),(42,52),(43,44),(43,68),(44,28),(44,69),(45,27),(45,69),(46,53),(46,68),(47,61),(48,9),(48,62),(49,5),(49,56),(50,34),(51,40),(52,2),(52,46),(53,6),(53,47),(54,10),(54,42),(55,31),(55,43),(56,43),(56,65),(57,29),(57,41),(58,30),(58,37),(59,27),(59,28),(60,55),(60,56),(61,34),(61,36),(62,35),(62,63),(63,20),(63,57),(63,64),(64,38),(64,41),(64,58),(65,44),(65,45),(65,59),(66,33),(67,4),(67,66),(68,47),(69,50),(69,70),(70,51)],71)
=> ? = 1 - 1
[2,5,1,3,4] => [[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1],[0,1,0,0,0]]
=> [[1,1,1,1,3],[2,3,3,3],[3,4,4],[4,5],[5]]
=> ([(0,4),(0,8),(1,11),(3,10),(4,9),(5,2),(6,3),(6,12),(7,5),(8,6),(8,9),(9,12),(10,11),(11,7),(12,1),(12,10)],13)
=> ? = 0 - 1
[3,1,2,5,4] => [[0,1,0,0,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
=> [[1,1,1,2,2],[2,2,2,3],[3,3,3],[4,5],[5]]
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 0 - 1
[3,1,4,2,5] => [[0,1,0,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [[1,1,1,2,2],[2,2,2,4],[3,3,4],[4,4],[5]]
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 1 - 1
[3,2,1,5,4] => [[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
=> [[1,1,1,2,3],[2,2,2,3],[3,3,3],[4,5],[5]]
=> ([(0,3),(0,6),(0,7),(1,8),(1,12),(2,8),(2,11),(3,9),(3,10),(4,2),(4,13),(5,1),(5,14),(6,4),(6,9),(7,5),(7,10),(8,15),(9,13),(10,14),(11,15),(12,15),(13,11),(14,12)],16)
=> ? = 0 - 1
[3,2,4,1,5] => [[0,0,0,1,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [[1,1,1,2,4],[2,2,2,4],[3,3,4],[4,4],[5]]
=> ([(0,7),(0,8),(1,12),(2,11),(3,10),(4,10),(4,11),(5,3),(6,1),(6,13),(7,9),(8,5),(9,2),(9,4),(10,14),(11,6),(11,14),(13,12),(14,13)],15)
=> ? = 1 - 1
[3,4,2,1,5] => [[0,0,0,1,0],[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [[1,1,1,3,4],[2,2,3,4],[3,3,4],[4,4],[5]]
=> ([(0,13),(0,15),(1,17),(2,16),(2,17),(3,19),(4,16),(4,18),(5,22),(6,21),(7,20),(8,23),(8,29),(9,4),(9,28),(10,3),(10,28),(11,6),(12,7),(12,24),(13,14),(14,1),(14,2),(15,9),(15,10),(16,25),(17,12),(17,25),(18,26),(18,29),(19,23),(19,26),(20,27),(22,27),(23,30),(24,20),(24,22),(25,24),(26,30),(27,21),(28,8),(28,18),(28,19),(29,5),(29,30),(30,11)],31)
=> ? = 1 - 1
[3,5,2,1,4] => [[0,0,0,1,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0]]
=> [[1,1,1,3,4],[2,3,3,4],[3,4,4],[4,5],[5]]
=> ([(0,15),(0,16),(0,20),(1,9),(2,13),(2,47),(3,38),(4,14),(4,46),(5,40),(6,10),(6,26),(7,18),(7,45),(8,19),(8,39),(9,25),(10,32),(11,31),(12,44),(13,12),(13,48),(14,11),(14,42),(15,8),(15,28),(16,7),(16,37),(17,24),(17,33),(18,21),(18,36),(19,21),(19,35),(20,28),(20,37),(21,51),(22,49),(23,49),(24,3),(24,50),(26,1),(27,25),(28,39),(29,46),(30,27),(31,30),(32,27),(33,23),(33,50),(34,22),(34,50),(35,40),(35,51),(36,41),(36,51),(37,2),(37,45),(38,43),(39,5),(39,35),(40,4),(40,29),(41,24),(41,34),(42,31),(42,43),(43,30),(43,32),(44,22),(44,23),(45,36),(45,47),(46,38),(46,42),(47,17),(47,41),(47,48),(48,33),(48,34),(48,44),(49,26),(50,6),(50,49),(51,29)],52)
=> ? = 1 - 1
[3,5,2,4,1] => [[0,0,0,0,1],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0]]
=> [[1,1,1,3,5],[2,3,3,5],[3,4,5],[4,5],[5]]
=> ([(0,16),(0,17),(0,28),(1,9),(2,70),(3,13),(3,85),(4,27),(4,69),(5,83),(6,15),(6,43),(7,26),(7,84),(8,12),(8,29),(8,71),(9,68),(10,77),(11,76),(12,14),(12,78),(13,10),(13,86),(14,11),(14,87),(15,75),(16,8),(16,48),(17,7),(17,67),(18,42),(18,61),(19,25),(19,62),(19,63),(20,22),(20,59),(20,79),(21,24),(21,41),(21,60),(22,23),(22,80),(22,81),(23,64),(23,66),(24,37),(24,65),(25,36),(25,46),(26,50),(26,58),(27,31),(27,32),(28,48),(28,67),(29,57),(29,58),(29,78),(31,103),(32,103),(33,89),(34,89),(35,90),(36,88),(37,92),(38,102),(39,93),(40,101),(41,4),(41,100),(42,5),(42,97),(43,1),(44,53),(45,51),(45,95),(46,41),(46,88),(47,54),(48,71),(49,79),(50,73),(50,98),(51,68),(51,102),(52,31),(52,96),(53,30),(54,30),(55,33),(55,97),(56,35),(56,99),(57,70),(57,98),(58,74),(58,98),(59,81),(59,90),(60,37),(60,100),(61,34),(61,97),(62,36),(62,99),(63,21),(63,46),(63,99),(64,52),(64,91),(65,52),(65,92),(66,45),(66,91),(67,3),(67,84),(68,47),(69,32),(70,20),(70,49),(71,2),(71,57),(72,53),(72,54),(73,42),(73,55),(74,56),(74,62),(75,38),(75,51),(76,35),(76,59),(77,33),(77,34),(78,19),(78,74),(78,87),(79,80),(79,83),(79,90),(80,66),(80,82),(80,94),(81,64),(81,65),(81,94),(82,45),(82,75),(82,93),(83,39),(83,82),(84,50),(84,85),(85,18),(85,73),(85,86),(86,55),(86,61),(86,77),(87,56),(87,63),(87,76),(88,100),(89,43),(90,39),(90,94),(91,95),(91,96),(92,40),(92,96),(93,38),(93,40),(93,95),(94,91),(94,92),(94,93),(95,101),(95,102),(96,101),(96,103),(97,6),(97,89),(98,49),(99,60),(99,88),(100,69),(101,44),(101,72),(102,47),(102,72),(103,44)],104)
=> ? = 2 - 1
[3,5,4,1,2] => [[0,0,0,1,0],[0,0,0,0,1],[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0]]
=> [[1,1,1,4,4],[2,3,4,5],[3,4,5],[4,5],[5]]
=> ([(0,12),(0,13),(1,6),(2,61),(3,5),(3,94),(4,81),(5,80),(6,32),(7,4),(7,95),(8,22),(8,87),(9,20),(9,85),(10,19),(10,92),(11,17),(11,18),(11,98),(12,51),(13,11),(13,21),(13,51),(14,46),(14,47),(15,42),(15,89),(16,73),(16,75),(17,27),(17,48),(17,97),(18,48),(18,90),(19,43),(19,91),(20,44),(20,76),(21,25),(21,88),(21,98),(22,26),(22,74),(22,96),(23,24),(23,45),(23,77),(24,66),(24,67),(25,53),(25,93),(26,68),(26,84),(27,74),(27,78),(28,37),(28,60),(28,72),(29,124),(30,124),(31,101),(31,123),(33,117),(33,125),(34,118),(35,99),(36,116),(36,128),(37,101),(37,121),(38,109),(38,125),(39,100),(39,103),(40,109),(40,129),(41,126),(42,119),(43,107),(44,113),(45,9),(45,106),(46,108),(47,2),(47,108),(48,10),(48,122),(49,65),(49,128),(50,64),(51,8),(51,88),(52,39),(52,121),(52,123),(53,79),(54,45),(54,100),(55,32),(56,29),(56,127),(57,30),(57,127),(58,35),(58,120),(59,34),(59,99),(60,63),(60,101),(61,55),(62,56),(62,104),(63,83),(63,111),(64,57),(64,104),(65,44),(65,114),(66,58),(66,110),(67,65),(67,110),(68,43),(68,115),(69,34),(69,105),(70,36),(70,112),(71,33),(71,103),(71,119),(72,23),(72,54),(72,121),(73,50),(74,68),(74,102),(75,3),(75,82),(76,64),(76,113),(77,66),(77,106),(78,39),(78,54),(78,102),(79,42),(79,71),(80,29),(80,30),(81,35),(81,59),(82,62),(82,94),(83,49),(83,67),(83,112),(84,33),(84,38),(84,115),(85,50),(85,76),(86,59),(86,69),(86,120),(87,15),(87,79),(87,96),(88,53),(88,87),(89,38),(89,40),(89,119),(90,31),(90,60),(90,122),(91,36),(91,49),(91,107),(92,70),(92,83),(92,91),(93,31),(93,37),(93,52),(94,56),(94,57),(94,80),(95,58),(95,81),(95,86),(96,71),(96,84),(96,89),(96,102),(97,52),(97,72),(97,78),(97,122),(98,28),(98,90),(98,93),(98,97),(99,46),(99,118),(100,106),(101,7),(101,111),(102,40),(102,103),(102,115),(103,117),(103,129),(104,127),(105,47),(105,118),(106,85),(107,41),(107,116),(108,1),(109,41),(109,130),(110,114),(110,120),(111,95),(111,112),(112,86),(112,110),(112,128),(113,104),(114,105),(114,113),(115,107),(115,109),(115,117),(116,126),(117,116),(117,130),(118,108),(119,16),(119,125),(119,129),(120,14),(120,99),(120,105),(121,77),(121,100),(122,63),(122,92),(122,123),(123,70),(123,111),(124,55),(125,75),(125,130),(126,62),(127,61),(127,124),(128,69),(128,114),(129,73),(129,130),(130,82),(130,126)],131)
=> ? = 0 - 1
[4,1,3,2,5] => [[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1]]
=> [[1,1,2,2,2],[2,2,3,4],[3,3,4],[4,4],[5]]
=> ([(0,7),(0,8),(1,12),(2,11),(3,10),(4,10),(4,11),(5,3),(6,1),(6,13),(7,9),(8,5),(9,2),(9,4),(10,14),(11,6),(11,14),(13,12),(14,13)],15)
=> ? = 0 - 1
[4,1,5,2,3] => [[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1],[1,0,0,0,0],[0,0,1,0,0]]
=> [[1,1,2,2,2],[2,2,4,4],[3,4,5],[4,5],[5]]
=> ([(0,1),(1,4),(1,5),(2,8),(2,32),(3,6),(3,30),(4,7),(4,33),(5,10),(5,11),(5,33),(6,20),(7,31),(8,27),(9,15),(9,19),(10,18),(10,28),(11,18),(11,25),(13,39),(14,36),(14,39),(15,36),(16,38),(17,38),(18,2),(18,37),(19,26),(19,36),(20,21),(21,12),(22,12),(23,17),(23,35),(24,16),(24,35),(25,13),(25,37),(26,24),(26,34),(27,16),(27,17),(28,14),(28,19),(28,37),(29,21),(29,22),(30,20),(30,29),(31,13),(31,14),(31,15),(32,23),(32,24),(32,27),(33,9),(33,25),(33,28),(33,31),(34,30),(34,35),(35,29),(35,38),(36,3),(36,34),(37,26),(37,32),(37,39),(38,22),(39,23),(39,34)],40)
=> ? = 0 - 1
[4,2,1,3,5] => [[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,0,0,0,1]]
=> [[1,1,2,2,3],[2,2,3,3],[3,3,4],[4,4],[5]]
=> ([(0,5),(0,10),(1,16),(2,15),(3,14),(4,13),(5,12),(6,2),(6,13),(7,4),(7,14),(8,1),(9,6),(10,11),(10,12),(11,3),(11,7),(12,9),(13,15),(14,8),(15,16)],17)
=> ? = 1 - 1
[4,2,3,1,5] => [[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1]]
=> [[1,1,2,2,4],[2,2,3,4],[3,3,4],[4,4],[5]]
=> ([(0,14),(0,15),(1,19),(2,18),(3,29),(4,30),(5,22),(6,23),(7,24),(7,25),(8,9),(9,7),(9,18),(9,19),(10,5),(11,6),(12,2),(12,29),(13,1),(13,30),(14,16),(14,28),(15,17),(15,28),(16,3),(16,12),(17,4),(17,13),(18,24),(18,27),(19,25),(19,27),(20,26),(21,26),(22,20),(23,21),(24,22),(24,31),(25,23),(25,31),(27,31),(28,8),(29,10),(30,11),(31,20),(31,21)],32)
=> ? = 0 - 1
[4,2,5,1,3] => [[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1],[1,0,0,0,0],[0,0,1,0,0]]
=> [[1,1,2,2,4],[2,2,4,4],[3,4,5],[4,5],[5]]
=> ([(0,7),(0,8),(1,2),(1,45),(2,35),(3,37),(4,14),(4,49),(5,9),(5,48),(6,10),(6,12),(6,54),(7,31),(8,6),(8,13),(8,31),(9,27),(9,42),(10,28),(10,41),(11,26),(11,52),(12,17),(12,28),(12,51),(13,15),(13,50),(13,54),(14,16),(14,40),(14,53),(15,33),(15,44),(16,38),(16,47),(17,30),(17,40),(19,64),(19,66),(20,62),(21,65),(22,58),(23,60),(23,66),(24,60),(24,63),(25,67),(26,55),(27,59),(28,5),(28,56),(29,34),(30,22),(30,57),(31,4),(31,50),(32,22),(32,65),(33,43),(34,18),(35,18),(36,20),(37,1),(37,46),(38,27),(38,61),(39,19),(39,55),(39,58),(40,38),(40,57),(41,21),(41,56),(42,20),(42,59),(43,26),(43,39),(44,21),(44,32),(45,34),(45,35),(46,29),(46,45),(47,19),(47,23),(47,61),(48,36),(48,42),(49,11),(49,43),(49,53),(50,33),(50,49),(51,30),(51,32),(51,56),(52,23),(52,24),(52,55),(53,39),(53,47),(53,52),(53,57),(54,41),(54,44),(54,51),(55,3),(55,63),(55,66),(56,48),(56,65),(57,24),(57,58),(57,61),(58,63),(58,64),(59,25),(59,62),(60,25),(60,68),(61,59),(61,60),(61,64),(62,67),(63,68),(64,62),(64,68),(65,36),(66,37),(66,68),(67,29),(68,46),(68,67)],69)
=> ? = 1 - 1
[4,3,1,2,5] => [[0,0,1,0,0],[0,0,0,1,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1]]
=> [[1,1,2,3,3],[2,2,3,4],[3,3,4],[4,4],[5]]
=> ([(0,13),(0,15),(1,17),(2,16),(2,17),(3,19),(4,16),(4,18),(5,22),(6,21),(7,20),(8,23),(8,29),(9,4),(9,28),(10,3),(10,28),(11,6),(12,7),(12,24),(13,14),(14,1),(14,2),(15,9),(15,10),(16,25),(17,12),(17,25),(18,26),(18,29),(19,23),(19,26),(20,27),(22,27),(23,30),(24,20),(24,22),(25,24),(26,30),(27,21),(28,8),(28,18),(28,19),(29,5),(29,30),(30,11)],31)
=> ? = 0 - 1
[4,3,2,1,5] => [[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1]]
=> [[1,1,2,3,4],[2,2,3,4],[3,3,4],[4,4],[5]]
=> ([(0,5),(0,16),(0,17),(1,23),(2,19),(3,11),(3,21),(4,10),(4,20),(5,12),(5,13),(6,50),(7,51),(8,24),(8,58),(9,25),(9,59),(10,14),(10,52),(11,15),(11,53),(12,26),(12,60),(13,27),(13,60),(14,54),(15,55),(16,4),(16,29),(17,3),(17,29),(18,48),(18,49),(19,32),(19,33),(20,46),(20,52),(21,47),(21,53),(22,34),(22,35),(23,18),(23,54),(23,55),(24,40),(24,42),(25,41),(25,43),(26,46),(26,56),(27,47),(27,57),(28,63),(29,1),(30,62),(31,61),(32,61),(33,61),(34,6),(34,62),(35,7),(35,62),(36,58),(37,59),(38,32),(39,33),(40,44),(41,45),(42,38),(43,39),(44,31),(45,31),(46,36),(47,37),(48,40),(48,63),(49,41),(49,63),(50,38),(51,39),(52,8),(52,36),(53,9),(53,37),(54,28),(54,48),(55,28),(55,49),(56,30),(56,34),(57,30),(57,35),(58,42),(58,50),(59,43),(59,51),(60,22),(60,56),(60,57),(62,2),(63,44),(63,45)],64)
=> ? = 0 - 1
[4,3,5,1,2] => [[0,0,0,1,0],[0,0,0,0,1],[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0]]
=> [[1,1,2,4,4],[2,2,4,5],[3,4,5],[4,5],[5]]
=> ([(0,2),(0,3),(1,8),(1,16),(2,1),(3,7),(3,10),(4,13),(4,59),(5,12),(5,81),(6,20),(6,82),(7,11),(7,83),(8,60),(9,23),(9,58),(10,19),(10,22),(10,83),(11,78),(12,64),(13,24),(14,52),(14,72),(15,17),(15,73),(15,80),(16,60),(16,74),(17,39),(17,70),(18,36),(18,44),(19,51),(19,69),(20,33),(20,75),(21,28),(21,38),(21,50),(22,51),(22,71),(22,74),(23,49),(23,56),(23,57),(25,101),(26,113),(27,107),(27,110),(28,107),(28,111),(29,110),(29,111),(30,112),(31,90),(31,98),(32,94),(32,114),(33,96),(34,91),(34,92),(35,89),(35,92),(36,108),(37,94),(37,103),(38,9),(38,111),(39,45),(40,31),(40,102),(40,114),(41,31),(41,104),(42,37),(42,99),(43,34),(43,85),(43,87),(44,30),(44,108),(45,55),(46,33),(46,86),(47,48),(47,86),(48,25),(48,100),(49,42),(49,85),(50,14),(50,76),(50,107),(51,15),(51,61),(51,84),(52,46),(52,109),(53,32),(53,93),(54,26),(54,95),(55,25),(55,91),(56,35),(56,85),(56,97),(57,53),(57,97),(58,57),(59,24),(60,5),(60,63),(61,67),(61,73),(62,34),(62,35),(62,113),(63,67),(63,81),(64,46),(64,47),(65,45),(65,68),(66,47),(66,68),(66,109),(67,65),(67,66),(68,48),(68,55),(68,87),(69,29),(69,38),(69,84),(70,26),(70,62),(71,27),(71,50),(71,84),(72,43),(72,49),(72,109),(73,39),(73,65),(74,61),(74,63),(75,32),(75,40),(75,96),(76,72),(76,79),(76,88),(77,40),(77,41),(77,93),(78,27),(78,28),(78,29),(79,43),(79,56),(79,62),(79,95),(80,54),(80,70),(80,79),(81,52),(81,64),(81,66),(82,53),(82,75),(82,77),(83,21),(83,69),(83,71),(83,78),(84,76),(84,80),(84,110),(85,92),(85,99),(86,37),(86,96),(86,100),(87,91),(87,99),(87,100),(88,82),(88,95),(89,104),(90,108),(90,116),(91,101),(91,106),(92,106),(93,18),(93,104),(93,114),(94,115),(95,77),(95,97),(95,113),(96,94),(96,102),(97,89),(97,93),(98,116),(99,103),(99,106),(100,101),(100,102),(100,103),(101,98),(101,105),(102,98),(102,115),(103,105),(103,115),(104,36),(104,90),(105,116),(106,105),(107,6),(107,88),(108,4),(108,112),(109,42),(109,86),(109,87),(110,54),(110,88),(111,58),(112,59),(113,41),(113,89),(114,44),(114,90),(114,115),(115,30),(115,116),(116,112)],117)
=> ? = 0 - 1
[4,3,5,2,1] => [[0,0,0,0,1],[0,0,0,1,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0]]
=> [[1,1,2,4,5],[2,2,4,5],[3,4,5],[4,5],[5]]
=> ([(0,4),(0,15),(0,16),(1,34),(2,7),(2,32),(3,14),(3,33),(4,11),(4,12),(5,147),(6,38),(6,125),(7,5),(7,114),(8,39),(8,161),(9,30),(9,158),(10,31),(10,96),(11,29),(11,159),(12,28),(12,41),(12,159),(13,24),(13,75),(14,20),(14,21),(14,156),(15,2),(15,54),(16,3),(16,54),(17,68),(17,119),(18,115),(18,120),(19,113),(19,149),(20,122),(20,154),(21,122),(21,164),(22,111),(22,145),(23,67),(23,116),(24,65),(24,66),(25,42),(25,117),(25,148),(26,37),(26,152),(26,163),(27,35),(27,150),(27,155),(28,118),(28,153),(29,121),(29,162),(30,110),(30,146),(31,109),(31,112),(32,114),(32,151),(33,121),(33,156),(34,36),(34,147),(34,164),(35,79),(35,81),(36,84),(36,134),(37,80),(37,137),(38,95),(38,106),(38,107),(39,58),(39,94),(39,139),(40,52),(40,64),(40,108),(41,118),(41,132),(41,151),(42,76),(42,77),(42,78),(43,211),(44,202),(45,173),(45,214),(46,168),(47,167),(47,168),(48,217),(49,212),(49,215),(50,174),(50,215),(51,218),(52,6),(52,212),(53,10),(54,1),(55,176),(56,176),(56,211),(57,192),(57,203),(58,173),(58,186),(59,177),(59,187),(60,175),(60,177),(61,214),(62,193),(63,182),(63,200),(64,22),(64,174),(64,212),(65,181),(66,181),(67,180),(68,179),(69,96),(70,57),(70,199),(70,213),(71,60),(71,169),(71,171),(72,100),(72,206),(73,58),(73,172),(74,66),(74,197),(75,65),(76,83),(76,170),(77,91),(77,167),(78,120),(78,167),(78,170),(79,88),(80,87),(81,136),(82,67),(82,216),(83,94),(83,208),(84,110),(84,210),(85,69),(85,208),(86,63),(86,198),(87,105),(88,55),(89,93),(89,172),(90,46),(90,210),(91,45),(91,196),(92,43),(92,209),(93,44),(93,195),(94,101),(94,173),(95,86),(95,169),(96,112),(97,102),(97,166),(97,188),(98,103),(98,188),(99,57),(99,191),(100,109),(100,182),(100,213),(101,97),(101,184),(102,56),(102,183),(102,209),(103,55),(103,183),(104,48),(104,185),(105,44),(105,175),(106,59),(106,169),(106,190),(107,72),(107,190),(108,19),(108,144),(108,174),(109,62),(109,166),(110,135),(111,53),(112,92),(112,166),(113,73),(113,207),(114,9),(114,126),(115,69),(115,178),(116,74),(116,180),(117,18),(117,78),(117,218),(118,26),(118,123),(118,165),(119,23),(119,82),(119,179),(120,27),(120,140),(120,178),(121,133),(122,138),(123,130),(123,152),(124,88),(124,103),(125,53),(125,107),(126,130),(126,158),(127,59),(127,60),(127,217),(128,87),(128,131),(129,89),(129,131),(129,207),(130,128),(130,129),(131,93),(131,105),(131,171),(132,50),(132,108),(132,165),(133,51),(133,148),(134,47),(134,77),(134,210),(135,45),(135,61),(136,43),(136,56),(137,48),(137,127),(138,46),(138,47),(139,70),(139,100),(139,186),(140,143),(140,150),(141,70),(141,99),(141,206),(142,97),(142,157),(143,98),(143,124),(144,149),(144,160),(144,189),(145,83),(145,85),(146,73),(146,89),(147,84),(147,90),(148,76),(148,145),(148,218),(149,71),(149,95),(149,207),(150,79),(150,124),(151,123),(151,126),(152,80),(152,128),(153,49),(153,52),(153,165),(154,51),(154,117),(155,81),(155,157),(156,25),(156,133),(156,154),(157,92),(157,102),(157,136),(158,113),(158,129),(158,146),(159,40),(159,132),(159,153),(159,162),(160,71),(160,106),(160,127),(160,185),(161,72),(161,139),(161,141),(162,49),(162,50),(162,64),(163,104),(163,137),(163,160),(164,90),(164,134),(164,138),(165,144),(165,163),(165,215),(166,193),(166,209),(167,140),(167,196),(168,61),(168,196),(169,177),(169,198),(170,178),(170,208),(171,175),(171,195),(171,198),(172,63),(172,186),(172,195),(173,184),(174,8),(174,189),(175,202),(175,204),(176,194),(177,204),(178,142),(178,155),(179,13),(179,216),(180,197),(182,62),(182,220),(183,176),(183,201),(184,188),(185,141),(185,190),(185,217),(186,182),(186,199),(187,191),(188,183),(188,193),(189,161),(189,185),(190,187),(190,206),(191,68),(191,192),(192,179),(192,219),(193,201),(194,197),(195,199),(195,200),(195,202),(196,143),(196,214),(197,181),(198,200),(198,204),(199,203),(199,220),(200,205),(200,220),(201,180),(201,194),(202,203),(202,205),(203,219),(204,205),(205,219),(206,17),(206,191),(206,213),(207,86),(207,171),(207,172),(208,101),(208,142),(209,116),(209,201),(209,211),(210,91),(210,135),(210,168),(211,74),(211,194),(212,111),(212,125),(213,119),(213,192),(213,220),(214,98),(214,184),(215,104),(215,189),(216,75),(217,99),(217,187),(218,85),(218,115),(218,170),(219,216),(220,82),(220,219)],221)
=> ? = 1 - 1
[4,5,3,1,2] => [[0,0,0,1,0],[0,0,0,0,1],[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0]]
=> [[1,1,3,4,4],[2,3,4,5],[3,4,5],[4,5],[5]]
=> ([(0,1),(0,2),(1,12),(1,14),(2,11),(2,13),(3,145),(4,146),(5,31),(5,155),(6,32),(6,156),(7,15),(7,143),(8,16),(8,144),(9,37),(9,114),(10,38),(10,115),(11,17),(11,157),(12,18),(12,158),(13,29),(13,35),(13,157),(14,30),(14,36),(14,158),(15,84),(16,85),(17,147),(18,148),(19,102),(19,133),(20,103),(20,134),(21,23),(21,149),(21,153),(22,24),(22,150),(22,154),(23,118),(23,128),(24,119),(24,129),(25,62),(25,82),(26,63),(26,83),(27,74),(27,139),(28,75),(28,140),(29,100),(29,126),(30,101),(30,127),(31,55),(31,135),(32,56),(32,136),(33,47),(33,72),(33,98),(34,48),(34,73),(34,99),(35,100),(35,130),(35,132),(36,101),(36,131),(36,132),(37,96),(37,110),(37,112),(38,97),(38,111),(38,113),(40,201),(40,202),(41,225),(42,226),(43,221),(43,223),(44,222),(44,224),(45,213),(45,221),(46,214),(46,222),(47,213),(47,223),(48,214),(48,224),(49,161),(50,162),(51,183),(51,227),(52,184),(52,228),(53,173),(53,195),(54,174),(54,196),(55,185),(56,186),(57,179),(57,180),(58,175),(58,177),(59,176),(59,178),(60,171),(60,177),(61,172),(61,178),(62,215),(63,216),(64,220),(65,219),(66,219),(67,220),(68,183),(68,203),(69,184),(69,204),(70,179),(70,199),(71,180),(71,200),(72,9),(72,223),(73,10),(73,224),(74,3),(74,189),(75,4),(75,190),(76,53),(76,205),(76,227),(77,54),(77,206),(77,228),(78,53),(78,207),(79,54),(79,208),(80,58),(80,163),(80,167),(81,59),(81,164),(81,168),(82,49),(82,215),(83,50),(83,216),(84,94),(85,95),(86,68),(86,197),(87,69),(87,198),(88,94),(89,95),(90,55),(90,169),(91,56),(91,170),(92,108),(92,170),(93,109),(93,169),(94,39),(95,39),(96,86),(96,163),(97,87),(97,164),(98,19),(98,137),(98,213),(99,20),(99,138),(99,214),(100,21),(100,116),(100,159),(101,22),(101,117),(101,160),(102,90),(102,217),(103,91),(103,218),(104,51),(104,181),(105,52),(105,182),(106,41),(106,187),(107,42),(107,188),(108,40),(108,175),(108,194),(109,40),(109,176),(109,193),(110,60),(110,163),(110,191),(111,61),(111,164),(111,192),(112,104),(112,191),(113,105),(113,192),(114,112),(115,113),(116,124),(116,149),(117,124),(117,150),(118,91),(118,92),(119,90),(119,93),(120,58),(120,60),(120,225),(121,59),(121,61),(121,226),(122,92),(122,125),(122,218),(123,93),(123,125),(123,217),(124,122),(124,123),(125,108),(125,109),(125,167),(125,168),(126,43),(126,72),(126,159),(127,44),(127,73),(127,160),(128,41),(128,120),(129,42),(129,121),(130,45),(130,98),(130,159),(131,46),(131,99),(131,160),(132,116),(132,117),(133,80),(133,96),(133,217),(134,81),(134,97),(134,218),(135,51),(135,76),(135,185),(136,52),(136,77),(136,186),(137,133),(137,151),(137,165),(138,134),(138,152),(138,166),(139,57),(139,70),(139,189),(140,57),(140,71),(140,190),(141,76),(141,78),(141,181),(142,77),(142,79),(142,182),(143,84),(143,88),(144,85),(144,89),(145,64),(145,67),(146,65),(146,66),(147,43),(147,45),(147,47),(148,44),(148,46),(148,48),(149,103),(149,118),(149,122),(150,102),(150,119),(150,123),(151,80),(151,110),(151,120),(151,187),(152,81),(152,111),(152,121),(152,188),(153,106),(153,128),(153,151),(154,107),(154,129),(154,152),(155,104),(155,135),(155,141),(156,105),(156,136),(156,142),(157,33),(157,126),(157,130),(157,147),(158,34),(158,127),(158,131),(158,148),(159,137),(159,153),(159,221),(160,138),(160,154),(160,222),(161,143),(162,144),(163,27),(163,177),(163,197),(164,28),(164,178),(164,198),(165,155),(165,187),(166,156),(166,188),(167,175),(167,193),(167,197),(168,176),(168,194),(168,198),(169,68),(169,185),(169,193),(170,69),(170,186),(170,194),(171,207),(172,208),(173,215),(173,231),(174,216),(174,232),(175,201),(175,209),(176,202),(176,210),(177,74),(177,209),(178,75),(178,210),(179,66),(179,233),(180,67),(180,233),(181,25),(181,207),(181,227),(182,26),(182,208),(182,228),(183,229),(184,230),(185,183),(185,205),(186,184),(186,206),(187,141),(187,191),(187,225),(188,142),(188,192),(188,226),(189,145),(189,180),(189,199),(190,146),(190,179),(190,200),(191,171),(191,181),(192,172),(192,182),(193,201),(193,203),(193,205),(194,202),(194,204),(194,206),(195,231),(196,232),(197,139),(197,203),(197,209),(198,140),(198,204),(198,210),(199,64),(199,233),(200,65),(200,233),(201,195),(201,211),(202,196),(202,212),(203,70),(203,211),(203,229),(204,71),(204,212),(204,230),(205,195),(205,229),(206,196),(206,230),(207,62),(207,173),(208,63),(208,174),(209,189),(209,211),(210,190),(210,212),(211,199),(211,231),(212,200),(212,232),(213,5),(213,165),(214,6),(214,166),(215,7),(215,161),(216,8),(216,162),(217,86),(217,167),(217,169),(218,87),(218,168),(218,170),(219,88),(220,89),(221,106),(221,165),(222,107),(222,166),(223,114),(224,115),(225,78),(225,171),(226,79),(226,172),(227,82),(227,173),(227,229),(228,83),(228,174),(228,230),(229,49),(229,231),(230,50),(230,232),(231,161),(232,162),(233,219),(233,220)],234)
=> ? = 0 - 1
[1,2,3,4,6,5] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,4,4],[5,6],[6]]
=> ([(0,1)],2)
=> -1 = 0 - 1
[1,2,3,5,4,6] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,4,5],[5,5],[6]]
=> ([(0,1)],2)
=> -1 = 0 - 1
[1,2,4,3,5,6] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,4],[4,4,4],[5,5],[6]]
=> ([(0,1)],2)
=> -1 = 0 - 1
[1,2,4,3,6,5] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,4],[4,4,4],[5,6],[6]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1 = 2 - 1
[1,3,2,4,5,6] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,3],[4,4,4],[5,5],[6]]
=> ([(0,1)],2)
=> -1 = 0 - 1
[1,3,2,4,6,5] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,3],[4,4,4],[5,6],[6]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1 = 2 - 1
[1,3,2,5,4,6] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,3],[4,4,5],[5,5],[6]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1 = 2 - 1
[2,1,3,4,5,6] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,3],[4,4,4],[5,5],[6]]
=> ([(0,1)],2)
=> -1 = 0 - 1
[2,1,3,4,6,5] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,3],[4,4,4],[5,6],[6]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1 = 2 - 1
[2,1,3,5,4,6] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,3],[4,4,5],[5,5],[6]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1 = 2 - 1
[2,1,4,3,5,6] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,4],[4,4,4],[5,5],[6]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1 = 2 - 1
Description
The trace of the square of the Coxeter matrix of the incidence algebra of a poset.
Matching statistic: St001964
Mp00067: Permutations Foata bijectionPermutations
Mp00090: Permutations cycle-as-one-line notationPermutations
Mp00209: Permutations pattern posetPosets
St001964: Posets ⟶ ℤResult quality: 4% values known / values provided: 4%distinct values known / distinct values provided: 9%
Values
[2,1] => [2,1] => [1,2] => ([(0,1)],2)
=> 0
[1,3,2] => [3,1,2] => [1,3,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 0
[2,1,3] => [2,1,3] => [1,2,3] => ([(0,2),(2,1)],3)
=> 0
[1,2,4,3] => [4,1,2,3] => [1,4,3,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 0
[1,3,2,4] => [3,1,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 0
[1,4,2,3] => [1,4,2,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 0
[2,1,3,4] => [2,1,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 0
[2,1,4,3] => [4,2,1,3] => [1,4,3,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[2,3,4,1] => [2,3,4,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 0
[2,4,1,3] => [2,1,4,3] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 0
[2,4,3,1] => [4,2,3,1] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 1
[3,1,4,2] => [3,4,1,2] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 1
[3,2,4,1] => [3,2,4,1] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 1
[3,4,2,1] => [3,4,2,1] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 1
[4,1,3,2] => [4,1,3,2] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 0
[4,2,1,3] => [2,4,1,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 1
[4,2,3,1] => [2,4,3,1] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 0
[4,3,1,2] => [1,4,3,2] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 0
[4,3,2,1] => [4,3,2,1] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 0
[1,2,3,5,4] => [5,1,2,3,4] => [1,5,4,3,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 0
[1,2,4,3,5] => [4,1,2,3,5] => [1,4,3,2,5] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 0
[1,2,5,3,4] => [1,5,2,3,4] => [1,2,5,4,3] => ([(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)
=> ? = 0
[1,3,2,4,5] => [3,1,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 0
[1,3,2,5,4] => [5,3,1,2,4] => [1,5,4,2,3] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 2
[1,3,4,5,2] => [3,1,4,5,2] => [1,3,4,5,2] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 0
[1,3,5,2,4] => [3,1,2,5,4] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 0
[1,3,5,4,2] => [5,3,1,4,2] => [1,5,2,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 1
[1,4,2,3,5] => [1,4,2,3,5] => [1,2,4,3,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 0
[1,4,2,5,3] => [4,5,1,2,3] => [1,4,2,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> ? = 1
[1,4,3,5,2] => [4,3,1,5,2] => [1,4,5,2,3] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(5,9),(5,10),(6,9),(6,10),(7,10),(8,9),(8,10),(9,4),(10,4)],11)
=> ? = 1
[1,4,5,2,3] => [1,4,2,5,3] => [1,2,4,5,3] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 0
[1,4,5,3,2] => [4,5,1,3,2] => [1,4,3,2,5] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 1
[1,5,3,2,4] => [3,5,1,2,4] => [1,3,2,5,4] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ? = 1
[1,5,4,3,2] => [5,4,3,1,2] => [1,5,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ? = 0
[2,1,3,4,5] => [2,1,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0
[2,1,3,5,4] => [5,2,1,3,4] => [1,5,4,3,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 2
[2,1,4,3,5] => [4,2,1,3,5] => [1,4,3,2,5] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 2
[2,1,4,5,3] => [4,2,1,5,3] => [1,4,5,3,2] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 1
[2,1,5,4,3] => [5,4,2,1,3] => [1,5,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ? = 0
[2,3,1,5,4] => [5,2,3,1,4] => [1,5,4,2,3] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 1
[2,3,4,1,5] => [2,3,4,1,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0
[2,3,4,5,1] => [2,3,4,5,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0
[2,4,1,3,5] => [2,1,4,3,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0
[2,4,1,5,3] => [4,2,5,1,3] => [1,4,2,3,5] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> ? = 0
[2,4,3,1,5] => [4,2,3,1,5] => [1,4,2,3,5] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> ? = 1
[2,4,3,5,1] => [4,2,3,5,1] => [1,4,5,2,3] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(5,9),(5,10),(6,9),(6,10),(7,10),(8,9),(8,10),(9,4),(10,4)],11)
=> ? = 0
[2,4,5,1,3] => [2,1,4,5,3] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0
[2,4,5,3,1] => [4,2,5,3,1] => [1,4,3,5,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ? = 1
[2,5,1,3,4] => [2,1,3,5,4] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0
[3,1,2,5,4] => [5,1,3,2,4] => [1,5,4,2,3] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 0
[3,1,4,2,5] => [3,4,1,2,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 1
[3,2,1,5,4] => [5,3,2,1,4] => [1,5,4,2,3] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 0
[3,2,4,1,5] => [3,2,4,1,5] => [1,3,4,2,5] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> ? = 1
[3,4,2,1,5] => [3,4,2,1,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 1
[3,5,2,1,4] => [3,2,5,1,4] => [1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ? = 1
[3,5,2,4,1] => [3,2,5,4,1] => [1,3,5,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> ? = 2
[3,5,4,1,2] => [1,5,3,4,2] => [1,2,5,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 0
[4,1,3,2,5] => [4,1,3,2,5] => [1,4,2,3,5] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> ? = 0
[4,1,5,2,3] => [1,4,5,2,3] => [1,2,4,3,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 0
[4,2,1,3,5] => [2,4,1,3,5] => [1,2,4,3,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 1
[4,2,3,1,5] => [2,4,3,1,5] => [1,2,4,3,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 0
[4,2,5,1,3] => [2,4,1,5,3] => [1,2,4,5,3] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 1
[2,1,3,4,5,6] => [2,1,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[2,3,4,1,5,6] => [2,3,4,1,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[2,3,4,5,1,6] => [2,3,4,5,1,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[2,3,4,5,6,1] => [2,3,4,5,6,1] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[2,3,4,6,1,5] => [2,3,4,1,6,5] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[2,4,1,3,5,6] => [2,1,4,3,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[2,4,5,1,3,6] => [2,1,4,5,3,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[2,4,5,6,1,3] => [2,1,4,5,6,3] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[2,4,6,1,3,5] => [2,1,4,3,6,5] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[2,5,1,3,4,6] => [2,1,3,5,4,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[2,5,6,1,3,4] => [2,1,3,5,6,4] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[2,6,1,3,4,5] => [2,1,3,4,6,5] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
Description
The interval resolution global dimension of a poset. This is the cardinality of the longest chain of right minimal approximations by interval modules of an indecomposable module over the incidence algebra.