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Your data matches 7 different statistics following compositions of up to 3 maps.
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(click to perform a complete search on your data)
Matching statistic: St000032
(load all 6 compositions to match this statistic)
(load all 6 compositions to match this statistic)
St000032: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0]
=> 1
[1,0,1,0]
=> 1
[1,1,0,0]
=> 2
[1,0,1,0,1,0]
=> 1
[1,0,1,1,0,0]
=> 2
[1,1,0,0,1,0]
=> 2
[1,1,0,1,0,0]
=> 3
[1,1,1,0,0,0]
=> 5
[1,0,1,0,1,0,1,0]
=> 1
[1,0,1,0,1,1,0,0]
=> 2
[1,0,1,1,0,0,1,0]
=> 2
[1,0,1,1,0,1,0,0]
=> 3
[1,0,1,1,1,0,0,0]
=> 5
[1,1,0,0,1,0,1,0]
=> 2
[1,1,0,0,1,1,0,0]
=> 4
[1,1,0,1,0,0,1,0]
=> 3
[1,1,0,1,0,1,0,0]
=> 4
[1,1,0,1,1,0,0,0]
=> 7
[1,1,1,0,0,0,1,0]
=> 5
[1,1,1,0,0,1,0,0]
=> 7
[1,1,1,0,1,0,0,0]
=> 9
[1,1,1,1,0,0,0,0]
=> 14
[1,0,1,0,1,0,1,0,1,0]
=> 1
[1,0,1,0,1,0,1,1,0,0]
=> 2
[1,0,1,0,1,1,0,0,1,0]
=> 2
[1,0,1,0,1,1,0,1,0,0]
=> 3
[1,0,1,0,1,1,1,0,0,0]
=> 5
[1,0,1,1,0,0,1,0,1,0]
=> 2
[1,0,1,1,0,0,1,1,0,0]
=> 4
[1,0,1,1,0,1,0,0,1,0]
=> 3
[1,0,1,1,0,1,0,1,0,0]
=> 4
[1,0,1,1,0,1,1,0,0,0]
=> 7
[1,0,1,1,1,0,0,0,1,0]
=> 5
[1,0,1,1,1,0,0,1,0,0]
=> 7
[1,0,1,1,1,0,1,0,0,0]
=> 9
[1,0,1,1,1,1,0,0,0,0]
=> 14
[1,1,0,0,1,0,1,0,1,0]
=> 2
[1,1,0,0,1,0,1,1,0,0]
=> 4
[1,1,0,0,1,1,0,0,1,0]
=> 4
[1,1,0,0,1,1,0,1,0,0]
=> 6
[1,1,0,0,1,1,1,0,0,0]
=> 10
[1,1,0,1,0,0,1,0,1,0]
=> 3
[1,1,0,1,0,0,1,1,0,0]
=> 6
[1,1,0,1,0,1,0,0,1,0]
=> 4
[1,1,0,1,0,1,0,1,0,0]
=> 5
[1,1,0,1,0,1,1,0,0,0]
=> 9
[1,1,0,1,1,0,0,0,1,0]
=> 7
[1,1,0,1,1,0,0,1,0,0]
=> 9
[1,1,0,1,1,0,1,0,0,0]
=> 12
[1,1,0,1,1,1,0,0,0,0]
=> 19
Description
The number of elements smaller than the given Dyck path in the Tamari Order.
Matching statistic: St000082
(load all 5 compositions to match this statistic)
(load all 5 compositions to match this statistic)
Mp00029: Dyck paths —to binary tree: left tree, up step, right tree, down step⟶ Binary trees
St000082: Binary trees ⟶ ℤResult quality: 19% ●values known / values provided: 19%●distinct values known / distinct values provided: 44%
St000082: Binary trees ⟶ ℤResult quality: 19% ●values known / values provided: 19%●distinct values known / distinct values provided: 44%
Values
[1,0]
=> [.,.]
=> ? = 1
[1,0,1,0]
=> [[.,.],.]
=> 1
[1,1,0,0]
=> [.,[.,.]]
=> 2
[1,0,1,0,1,0]
=> [[[.,.],.],.]
=> 1
[1,0,1,1,0,0]
=> [[.,.],[.,.]]
=> 2
[1,1,0,0,1,0]
=> [[.,[.,.]],.]
=> 2
[1,1,0,1,0,0]
=> [.,[[.,.],.]]
=> 3
[1,1,1,0,0,0]
=> [.,[.,[.,.]]]
=> 5
[1,0,1,0,1,0,1,0]
=> [[[[.,.],.],.],.]
=> 1
[1,0,1,0,1,1,0,0]
=> [[[.,.],.],[.,.]]
=> 2
[1,0,1,1,0,0,1,0]
=> [[[.,.],[.,.]],.]
=> 2
[1,0,1,1,0,1,0,0]
=> [[.,.],[[.,.],.]]
=> 3
[1,0,1,1,1,0,0,0]
=> [[.,.],[.,[.,.]]]
=> 5
[1,1,0,0,1,0,1,0]
=> [[[.,[.,.]],.],.]
=> 2
[1,1,0,0,1,1,0,0]
=> [[.,[.,.]],[.,.]]
=> 4
[1,1,0,1,0,0,1,0]
=> [[.,[[.,.],.]],.]
=> 3
[1,1,0,1,0,1,0,0]
=> [.,[[[.,.],.],.]]
=> 4
[1,1,0,1,1,0,0,0]
=> [.,[[.,.],[.,.]]]
=> 7
[1,1,1,0,0,0,1,0]
=> [[.,[.,[.,.]]],.]
=> 5
[1,1,1,0,0,1,0,0]
=> [.,[[.,[.,.]],.]]
=> 7
[1,1,1,0,1,0,0,0]
=> [.,[.,[[.,.],.]]]
=> 9
[1,1,1,1,0,0,0,0]
=> [.,[.,[.,[.,.]]]]
=> 14
[1,0,1,0,1,0,1,0,1,0]
=> [[[[[.,.],.],.],.],.]
=> 1
[1,0,1,0,1,0,1,1,0,0]
=> [[[[.,.],.],.],[.,.]]
=> 2
[1,0,1,0,1,1,0,0,1,0]
=> [[[[.,.],.],[.,.]],.]
=> 2
[1,0,1,0,1,1,0,1,0,0]
=> [[[.,.],.],[[.,.],.]]
=> 3
[1,0,1,0,1,1,1,0,0,0]
=> [[[.,.],.],[.,[.,.]]]
=> 5
[1,0,1,1,0,0,1,0,1,0]
=> [[[[.,.],[.,.]],.],.]
=> 2
[1,0,1,1,0,0,1,1,0,0]
=> [[[.,.],[.,.]],[.,.]]
=> 4
[1,0,1,1,0,1,0,0,1,0]
=> [[[.,.],[[.,.],.]],.]
=> 3
[1,0,1,1,0,1,0,1,0,0]
=> [[.,.],[[[.,.],.],.]]
=> 4
[1,0,1,1,0,1,1,0,0,0]
=> [[.,.],[[.,.],[.,.]]]
=> 7
[1,0,1,1,1,0,0,0,1,0]
=> [[[.,.],[.,[.,.]]],.]
=> 5
[1,0,1,1,1,0,0,1,0,0]
=> [[.,.],[[.,[.,.]],.]]
=> 7
[1,0,1,1,1,0,1,0,0,0]
=> [[.,.],[.,[[.,.],.]]]
=> 9
[1,0,1,1,1,1,0,0,0,0]
=> [[.,.],[.,[.,[.,.]]]]
=> 14
[1,1,0,0,1,0,1,0,1,0]
=> [[[[.,[.,.]],.],.],.]
=> 2
[1,1,0,0,1,0,1,1,0,0]
=> [[[.,[.,.]],.],[.,.]]
=> 4
[1,1,0,0,1,1,0,0,1,0]
=> [[[.,[.,.]],[.,.]],.]
=> 4
[1,1,0,0,1,1,0,1,0,0]
=> [[.,[.,.]],[[.,.],.]]
=> 6
[1,1,0,0,1,1,1,0,0,0]
=> [[.,[.,.]],[.,[.,.]]]
=> 10
[1,1,0,1,0,0,1,0,1,0]
=> [[[.,[[.,.],.]],.],.]
=> 3
[1,1,0,1,0,0,1,1,0,0]
=> [[.,[[.,.],.]],[.,.]]
=> 6
[1,1,0,1,0,1,0,0,1,0]
=> [[.,[[[.,.],.],.]],.]
=> 4
[1,1,0,1,0,1,0,1,0,0]
=> [.,[[[[.,.],.],.],.]]
=> 5
[1,1,0,1,0,1,1,0,0,0]
=> [.,[[[.,.],.],[.,.]]]
=> 9
[1,1,0,1,1,0,0,0,1,0]
=> [[.,[[.,.],[.,.]]],.]
=> 7
[1,1,0,1,1,0,0,1,0,0]
=> [.,[[[.,.],[.,.]],.]]
=> 9
[1,1,0,1,1,0,1,0,0,0]
=> [.,[[.,.],[[.,.],.]]]
=> 12
[1,1,0,1,1,1,0,0,0,0]
=> [.,[[.,.],[.,[.,.]]]]
=> 19
[1,1,1,0,0,0,1,0,1,0]
=> [[[.,[.,[.,.]]],.],.]
=> 5
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [[[[[[[.,.],.],.],.],.],.],.]
=> ? = 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> [[[[[[.,.],.],.],.],.],[.,.]]
=> ? = 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [[[[[[.,.],.],.],.],[.,.]],.]
=> ? = 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]
=> [[[[[.,.],.],.],.],[[.,.],.]]
=> ? = 3
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
=> [[[[[.,.],.],.],.],[.,[.,.]]]
=> ? = 5
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [[[[[[.,.],.],.],[.,.]],.],.]
=> ? = 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
=> [[[[[.,.],.],.],[.,.]],[.,.]]
=> ? = 4
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]
=> [[[[[.,.],.],.],[[.,.],.]],.]
=> ? = 3
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]
=> [[[[.,.],.],.],[[[.,.],.],.]]
=> ? = 4
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]
=> [[[[.,.],.],.],[[.,.],[.,.]]]
=> ? = 7
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
=> [[[[[.,.],.],.],[.,[.,.]]],.]
=> ? = 5
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]
=> [[[[.,.],.],.],[[.,[.,.]],.]]
=> ? = 7
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]
=> [[[[.,.],.],.],[.,[[.,.],.]]]
=> ? = 9
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [[[[.,.],.],.],[.,[.,[.,.]]]]
=> ? = 14
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> [[[[[[.,.],.],[.,.]],.],.],.]
=> ? = 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
=> [[[[[.,.],.],[.,.]],.],[.,.]]
=> ? = 4
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [[[[[.,.],.],[.,.]],[.,.]],.]
=> ? = 4
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]
=> [[[[.,.],.],[.,.]],[[.,.],.]]
=> ? = 6
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
=> [[[[.,.],.],[.,.]],[.,[.,.]]]
=> ? = 10
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
=> [[[[[.,.],.],[[.,.],.]],.],.]
=> ? = 3
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]
=> [[[[.,.],.],[[.,.],.]],[.,.]]
=> ? = 6
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]
=> [[[[.,.],.],[[[.,.],.],.]],.]
=> ? = 4
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]
=> [[[.,.],.],[[[[.,.],.],.],.]]
=> ? = 5
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]
=> [[[.,.],.],[[[.,.],.],[.,.]]]
=> ? = 9
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]
=> [[[[.,.],.],[[.,.],[.,.]]],.]
=> ? = 7
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]
=> [[[.,.],.],[[[.,.],[.,.]],.]]
=> ? = 9
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]
=> [[[.,.],.],[[.,.],[[.,.],.]]]
=> ? = 12
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
=> [[[.,.],.],[[.,.],[.,[.,.]]]]
=> ? = 19
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
=> [[[[[.,.],.],[.,[.,.]]],.],.]
=> ? = 5
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
=> [[[[.,.],.],[.,[.,.]]],[.,.]]
=> ? = 10
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]
=> [[[[.,.],.],[[.,[.,.]],.]],.]
=> ? = 7
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]
=> [[[.,.],.],[[[.,[.,.]],.],.]]
=> ? = 9
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]
=> [[[.,.],.],[[.,[.,.]],[.,.]]]
=> ? = 16
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]
=> [[[[.,.],.],[.,[[.,.],.]]],.]
=> ? = 9
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]
=> [[[.,.],.],[[.,[[.,.],.]],.]]
=> ? = 12
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]
=> [[[.,.],.],[.,[[[.,.],.],.]]]
=> ? = 14
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
=> [[[.,.],.],[.,[[.,.],[.,.]]]]
=> ? = 23
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
=> [[[[.,.],.],[.,[.,[.,.]]]],.]
=> ? = 14
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]
=> [[[.,.],.],[[.,[.,[.,.]]],.]]
=> ? = 19
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
=> [[[.,.],.],[.,[[.,[.,.]],.]]]
=> ? = 23
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
=> [[[.,.],.],[.,[.,[[.,.],.]]]]
=> ? = 28
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> [[[.,.],.],[.,[.,[.,[.,.]]]]]
=> ? = 42
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
=> [[[[[[.,.],[.,.]],.],.],.],.]
=> ? = 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
=> [[[[[.,.],[.,.]],.],.],[.,.]]
=> ? = 4
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
=> [[[[[.,.],[.,.]],.],[.,.]],.]
=> ? = 4
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]
=> [[[[.,.],[.,.]],.],[[.,.],.]]
=> ? = 6
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
=> [[[[.,.],[.,.]],.],[.,[.,.]]]
=> ? = 10
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
=> [[[[[.,.],[.,.]],[.,.]],.],.]
=> ? = 4
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
=> [[[[.,.],[.,.]],[.,.]],[.,.]]
=> ? = 8
Description
The number of elements smaller than a binary tree in Tamari order.
Matching statistic: St000189
Mp00137: Dyck paths —to symmetric ASM⟶ Alternating sign matrices
Mp00001: Alternating sign matrices —to semistandard tableau via monotone triangles⟶ Semistandard tableaux
Mp00214: Semistandard tableaux —subcrystal⟶ Posets
St000189: Posets ⟶ ℤResult quality: 6% ●values known / values provided: 6%●distinct values known / distinct values provided: 8%
Mp00001: Alternating sign matrices —to semistandard tableau via monotone triangles⟶ Semistandard tableaux
Mp00214: Semistandard tableaux —subcrystal⟶ Posets
St000189: Posets ⟶ ℤResult quality: 6% ●values known / values provided: 6%●distinct values known / distinct values provided: 8%
Values
[1,0]
=> [[1]]
=> [[1]]
=> ([],1)
=> 1
[1,0,1,0]
=> [[1,0],[0,1]]
=> [[1,1],[2]]
=> ([],1)
=> 1
[1,1,0,0]
=> [[0,1],[1,0]]
=> [[1,2],[2]]
=> ([(0,1)],2)
=> 2
[1,0,1,0,1,0]
=> [[1,0,0],[0,1,0],[0,0,1]]
=> [[1,1,1],[2,2],[3]]
=> ([],1)
=> 1
[1,0,1,1,0,0]
=> [[1,0,0],[0,0,1],[0,1,0]]
=> [[1,1,1],[2,3],[3]]
=> ([(0,1)],2)
=> 2
[1,1,0,0,1,0]
=> [[0,1,0],[1,0,0],[0,0,1]]
=> [[1,1,2],[2,2],[3]]
=> ([(0,1)],2)
=> 2
[1,1,0,1,0,0]
=> [[0,1,0],[1,-1,1],[0,1,0]]
=> [[1,1,2],[2,3],[3]]
=> ([(0,2),(2,1)],3)
=> 3
[1,1,1,0,0,0]
=> [[0,0,1],[0,1,0],[1,0,0]]
=> [[1,2,3],[2,3],[3]]
=> ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8)
=> ? = 5
[1,0,1,0,1,0,1,0]
=> [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,2],[3,3],[4]]
=> ([],1)
=> 1
[1,0,1,0,1,1,0,0]
=> [[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)
=> 2
[1,0,1,1,0,0,1,0]
=> [[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)
=> 2
[1,0,1,1,0,1,0,0]
=> [[1,0,0,0],[0,0,1,0],[0,1,-1,1],[0,0,1,0]]
=> [[1,1,1,1],[2,2,3],[3,4],[4]]
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,1,1,0,0,0]
=> [[1,0,0,0],[0,0,0,1],[0,0,1,0],[0,1,0,0]]
=> [[1,1,1,1],[2,3,4],[3,4],[4]]
=> ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8)
=> ? = 5
[1,1,0,0,1,0,1,0]
=> [[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)
=> 2
[1,1,0,0,1,1,0,0]
=> [[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)
=> 4
[1,1,0,1,0,0,1,0]
=> [[0,1,0,0],[1,-1,1,0],[0,1,0,0],[0,0,0,1]]
=> [[1,1,1,2],[2,2,3],[3,3],[4]]
=> ([(0,2),(2,1)],3)
=> 3
[1,1,0,1,0,1,0,0]
=> [[0,1,0,0],[1,-1,1,0],[0,1,-1,1],[0,0,1,0]]
=> [[1,1,1,2],[2,2,3],[3,4],[4]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[1,1,0,1,1,0,0,0]
=> [[0,1,0,0],[1,-1,0,1],[0,0,1,0],[0,1,0,0]]
=> [[1,1,1,2],[2,3,4],[3,4],[4]]
=> ([(0,5),(0,6),(1,8),(2,9),(3,8),(3,9),(4,1),(5,4),(6,7),(7,2),(7,3),(8,10),(9,10)],11)
=> ? = 7
[1,1,1,0,0,0,1,0]
=> [[0,0,1,0],[0,1,0,0],[1,0,0,0],[0,0,0,1]]
=> [[1,1,2,3],[2,2,3],[3,3],[4]]
=> ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8)
=> ? = 5
[1,1,1,0,0,1,0,0]
=> [[0,0,1,0],[0,1,0,0],[1,0,-1,1],[0,0,1,0]]
=> [[1,1,2,3],[2,2,3],[3,4],[4]]
=> ([(0,3),(0,7),(1,8),(2,8),(3,9),(4,5),(5,1),(6,2),(7,4),(7,9),(9,6)],10)
=> ? = 7
[1,1,1,0,1,0,0,0]
=> [[0,0,1,0],[0,1,-1,1],[1,-1,1,0],[0,1,0,0]]
=> [[1,1,2,3],[2,3,4],[3,4],[4]]
=> ([(0,9),(0,11),(1,18),(2,17),(3,19),(4,13),(4,19),(5,12),(5,13),(6,16),(7,14),(8,5),(8,18),(9,10),(10,3),(10,4),(11,1),(11,8),(12,17),(13,15),(15,16),(16,14),(17,7),(18,2),(18,12),(19,6),(19,15)],20)
=> ? = 9
[1,1,1,1,0,0,0,0]
=> [[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)
=> ? = 14
[1,0,1,0,1,0,1,0,1,0]
=> [[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]]
=> [[1,1,1,1,1],[2,2,2,2],[3,3,3],[4,4],[5]]
=> ([],1)
=> 1
[1,0,1,0,1,0,1,1,0,0]
=> [[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)
=> 2
[1,0,1,0,1,1,0,0,1,0]
=> [[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)
=> 2
[1,0,1,0,1,1,0,1,0,0]
=> [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
=> [[1,1,1,1,1],[2,2,2,2],[3,3,4],[4,5],[5]]
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,0,1,1,1,0,0,0]
=> [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0]]
=> [[1,1,1,1,1],[2,2,2,2],[3,4,5],[4,5],[5]]
=> ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8)
=> ? = 5
[1,0,1,1,0,0,1,0,1,0]
=> [[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)
=> 2
[1,0,1,1,0,0,1,1,0,0]
=> [[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)
=> 4
[1,0,1,1,0,1,0,0,1,0]
=> [[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [[1,1,1,1,1],[2,2,2,3],[3,3,4],[4,4],[5]]
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,1,0,1,0,1,0,0]
=> [[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
=> [[1,1,1,1,1],[2,2,2,3],[3,3,4],[4,5],[5]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[1,0,1,1,0,1,1,0,0,0]
=> [[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,0,1],[0,0,0,1,0],[0,0,1,0,0]]
=> [[1,1,1,1,1],[2,2,2,3],[3,4,5],[4,5],[5]]
=> ([(0,5),(0,6),(1,8),(2,9),(3,8),(3,9),(4,1),(5,4),(6,7),(7,2),(7,3),(8,10),(9,10)],11)
=> ? = 7
[1,0,1,1,1,0,0,0,1,0]
=> [[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [[1,1,1,1,1],[2,2,3,4],[3,3,4],[4,4],[5]]
=> ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8)
=> ? = 5
[1,0,1,1,1,0,0,1,0,0]
=> [[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,-1,1],[0,0,0,1,0]]
=> [[1,1,1,1,1],[2,2,3,4],[3,3,4],[4,5],[5]]
=> ([(0,3),(0,7),(1,8),(2,8),(3,9),(4,5),(5,1),(6,2),(7,4),(7,9),(9,6)],10)
=> ? = 7
[1,0,1,1,1,0,1,0,0,0]
=> [[1,0,0,0,0],[0,0,0,1,0],[0,0,1,-1,1],[0,1,-1,1,0],[0,0,1,0,0]]
=> [[1,1,1,1,1],[2,2,3,4],[3,4,5],[4,5],[5]]
=> ([(0,9),(0,11),(1,18),(2,17),(3,19),(4,13),(4,19),(5,12),(5,13),(6,16),(7,14),(8,5),(8,18),(9,10),(10,3),(10,4),(11,1),(11,8),(12,17),(13,15),(15,16),(16,14),(17,7),(18,2),(18,12),(19,6),(19,15)],20)
=> ? = 9
[1,0,1,1,1,1,0,0,0,0]
=> [[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)
=> ? = 14
[1,1,0,0,1,0,1,0,1,0]
=> [[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)
=> 2
[1,1,0,0,1,0,1,1,0,0]
=> [[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)
=> 4
[1,1,0,0,1,1,0,0,1,0]
=> [[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)
=> 4
[1,1,0,0,1,1,0,1,0,0]
=> [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
=> [[1,1,1,1,2],[2,2,2,2],[3,3,4],[4,5],[5]]
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 6
[1,1,0,0,1,1,1,0,0,0]
=> [[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)
=> ? = 10
[1,1,0,1,0,0,1,0,1,0]
=> [[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
=> [[1,1,1,1,2],[2,2,2,3],[3,3,3],[4,4],[5]]
=> ([(0,2),(2,1)],3)
=> 3
[1,1,0,1,0,0,1,1,0,0]
=> [[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
=> [[1,1,1,1,2],[2,2,2,3],[3,3,3],[4,5],[5]]
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 6
[1,1,0,1,0,1,0,0,1,0]
=> [[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [[1,1,1,1,2],[2,2,2,3],[3,3,4],[4,4],[5]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[1,1,0,1,0,1,0,1,0,0]
=> [[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
=> [[1,1,1,1,2],[2,2,2,3],[3,3,4],[4,5],[5]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[1,1,0,1,0,1,1,0,0,0]
=> [[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,0,1],[0,0,0,1,0],[0,0,1,0,0]]
=> [[1,1,1,1,2],[2,2,2,3],[3,4,5],[4,5],[5]]
=> ([(0,6),(0,7),(1,11),(2,9),(3,9),(3,10),(4,2),(5,1),(5,10),(6,4),(7,8),(8,3),(8,5),(9,12),(10,11),(10,12),(11,13),(12,13)],14)
=> ? = 9
[1,1,0,1,1,0,0,0,1,0]
=> [[0,1,0,0,0],[1,-1,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [[1,1,1,1,2],[2,2,3,4],[3,3,4],[4,4],[5]]
=> ([(0,5),(0,6),(1,8),(2,9),(3,8),(3,9),(4,1),(5,4),(6,7),(7,2),(7,3),(8,10),(9,10)],11)
=> ? = 7
[1,1,0,1,1,0,0,1,0,0]
=> [[0,1,0,0,0],[1,-1,0,1,0],[0,0,1,0,0],[0,1,0,-1,1],[0,0,0,1,0]]
=> [[1,1,1,1,2],[2,2,3,4],[3,3,4],[4,5],[5]]
=> ([(0,4),(0,7),(1,9),(2,10),(3,9),(3,10),(4,11),(5,8),(6,1),(7,5),(7,11),(8,2),(8,3),(9,12),(10,12),(11,6)],13)
=> ? = 9
[1,1,0,1,1,0,1,0,0,0]
=> [[0,1,0,0,0],[1,-1,0,1,0],[0,0,1,-1,1],[0,1,-1,1,0],[0,0,1,0,0]]
=> [[1,1,1,1,2],[2,2,3,4],[3,4,5],[4,5],[5]]
=> ([(0,10),(0,12),(1,23),(2,22),(3,14),(3,24),(4,15),(5,13),(5,14),(6,18),(7,16),(7,20),(8,5),(8,23),(9,4),(9,24),(10,11),(11,3),(11,9),(12,1),(12,8),(13,22),(14,19),(15,16),(15,21),(16,25),(18,17),(19,20),(19,21),(20,18),(20,25),(21,25),(22,6),(23,2),(23,13),(24,7),(24,15),(24,19),(25,17)],26)
=> ? = 12
[1,1,0,1,1,1,0,0,0,0]
=> [[0,1,0,0,0],[1,-1,0,0,1],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0]]
=> [[1,1,1,1,2],[2,3,4,5],[3,4,5],[4,5],[5]]
=> ([(0,5),(0,14),(0,15),(1,26),(2,9),(2,25),(3,13),(3,24),(4,16),(5,11),(5,12),(6,69),(7,64),(8,49),(9,6),(9,52),(10,20),(10,59),(11,19),(11,65),(12,17),(12,65),(13,18),(13,22),(13,71),(14,2),(14,29),(15,3),(15,29),(16,39),(16,55),(17,56),(17,68),(18,57),(18,66),(19,58),(19,67),(20,51),(20,53),(21,40),(21,41),(22,57),(22,72),(23,28),(23,54),(23,70),(24,58),(24,71),(25,52),(25,56),(26,27),(26,69),(26,72),(27,45),(27,60),(28,34),(28,48),(28,50),(29,1),(30,76),(31,75),(32,77),(33,74),(33,80),(34,73),(34,78),(35,73),(35,77),(36,82),(37,79),(38,80),(39,74),(40,7),(40,76),(41,8),(41,76),(42,55),(42,79),(43,59),(44,39),(45,53),(45,83),(46,33),(46,81),(47,32),(47,83),(48,42),(48,78),(49,44),(50,46),(50,73),(51,44),(52,10),(52,43),(53,62),(54,34),(54,75),(55,36),(55,74),(56,43),(57,63),(58,61),(59,49),(59,51),(60,35),(60,50),(60,83),(61,31),(61,70),(62,33),(62,38),(63,32),(63,35),(64,37),(64,42),(65,21),(65,67),(65,68),(66,31),(66,54),(67,30),(67,40),(68,30),(68,41),(69,45),(69,47),(70,48),(70,64),(70,75),(71,23),(71,61),(71,66),(72,47),(72,60),(72,63),(73,81),(74,82),(75,37),(75,78),(76,4),(77,38),(77,81),(78,79),(79,36),(80,82),(81,80),(83,46),(83,62),(83,77)],84)
=> ? = 19
[1,1,1,0,0,0,1,0,1,0]
=> [[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
=> [[1,1,1,2,3],[2,2,2,3],[3,3,3],[4,4],[5]]
=> ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8)
=> ? = 5
[1,1,1,0,0,0,1,1,0,0]
=> [[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)
=> ? = 10
[1,1,1,0,0,1,0,0,1,0]
=> [[0,0,1,0,0],[0,1,0,0,0],[1,0,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [[1,1,1,2,3],[2,2,2,3],[3,3,4],[4,4],[5]]
=> ([(0,3),(0,7),(1,8),(2,8),(3,9),(4,5),(5,1),(6,2),(7,4),(7,9),(9,6)],10)
=> ? = 7
[1,1,1,0,0,1,0,1,0,0]
=> [[0,0,1,0,0],[0,1,0,0,0],[1,0,-1,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
=> [[1,1,1,2,3],[2,2,2,3],[3,3,4],[4,5],[5]]
=> ([(0,3),(0,8),(1,10),(2,10),(3,9),(4,6),(5,4),(5,11),(6,2),(7,1),(8,5),(8,9),(9,11),(11,7)],12)
=> ? = 9
[1,1,1,0,0,1,1,0,0,0]
=> [[0,0,1,0,0],[0,1,0,0,0],[1,0,-1,0,1],[0,0,0,1,0],[0,0,1,0,0]]
=> [[1,1,1,2,3],[2,2,2,3],[3,4,5],[4,5],[5]]
=> ([(0,7),(0,8),(0,11),(1,25),(2,10),(2,24),(3,5),(3,12),(3,26),(4,28),(5,6),(5,29),(6,4),(6,27),(7,2),(7,19),(8,3),(8,18),(9,15),(9,16),(10,13),(10,23),(11,18),(11,19),(12,22),(12,23),(12,29),(13,31),(14,30),(15,30),(16,30),(17,20),(18,26),(19,24),(20,14),(21,16),(22,25),(22,31),(23,17),(23,31),(24,13),(25,9),(25,21),(26,1),(26,22),(27,20),(27,28),(28,14),(28,15),(29,17),(29,27),(31,21)],32)
=> ? = 16
[1,1,1,0,1,0,0,0,1,0]
=> [[0,0,1,0,0],[0,1,-1,1,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [[1,1,1,2,3],[2,2,3,4],[3,3,4],[4,4],[5]]
=> ([(0,9),(0,11),(1,18),(2,17),(3,19),(4,13),(4,19),(5,12),(5,13),(6,16),(7,14),(8,5),(8,18),(9,10),(10,3),(10,4),(11,1),(11,8),(12,17),(13,15),(15,16),(16,14),(17,7),(18,2),(18,12),(19,6),(19,15)],20)
=> ? = 9
[1,1,1,0,1,0,0,1,0,0]
=> [[0,0,1,0,0],[0,1,-1,1,0],[1,-1,1,0,0],[0,1,0,-1,1],[0,0,0,1,0]]
=> [[1,1,1,2,3],[2,2,3,4],[3,3,4],[4,5],[5]]
=> ([(0,10),(0,11),(1,13),(1,14),(2,21),(3,20),(4,14),(4,20),(5,17),(6,16),(7,18),(8,12),(9,1),(9,22),(10,5),(10,15),(11,8),(11,15),(12,3),(12,4),(13,21),(14,19),(15,9),(15,17),(17,22),(18,16),(19,18),(20,7),(20,19),(21,6),(22,2),(22,13)],23)
=> ? = 12
[1,1,1,0,1,0,1,0,0,0]
=> [[0,0,1,0,0],[0,1,-1,1,0],[1,-1,1,-1,1],[0,1,-1,1,0],[0,0,1,0,0]]
=> [[1,1,1,2,3],[2,2,3,4],[3,4,5],[4,5],[5]]
=> ([(0,2),(0,3),(1,9),(1,15),(2,1),(3,7),(3,8),(4,30),(5,31),(6,23),(7,16),(7,37),(8,10),(8,37),(9,11),(9,36),(10,34),(11,35),(12,25),(12,29),(13,19),(13,22),(14,21),(14,27),(15,26),(15,36),(16,26),(16,33),(17,39),(18,38),(19,12),(19,38),(20,6),(21,4),(21,39),(22,5),(22,38),(24,23),(25,28),(26,32),(27,25),(27,39),(28,24),(29,20),(30,24),(31,20),(32,17),(32,27),(33,18),(33,19),(34,18),(34,22),(35,17),(35,21),(36,14),(36,32),(36,35),(37,13),(37,33),(37,34),(38,29),(38,31),(39,28),(39,30)],40)
=> ? = 14
[1,1,1,0,1,1,0,0,0,0]
=> [[0,0,1,0,0],[0,1,-1,0,1],[1,-1,0,1,0],[0,0,1,0,0],[0,1,0,0,0]]
=> [[1,1,1,2,3],[2,3,4,5],[3,4,5],[4,5],[5]]
=> ([(0,4),(0,14),(0,15),(1,29),(2,6),(2,27),(3,13),(3,28),(4,10),(4,11),(5,102),(6,5),(6,87),(7,31),(7,99),(8,25),(8,98),(9,26),(9,72),(10,23),(10,109),(11,24),(11,33),(11,109),(12,22),(12,108),(13,17),(13,18),(13,107),(14,2),(14,38),(15,3),(15,38),(16,84),(16,85),(17,90),(17,111),(18,90),(18,101),(19,82),(19,83),(20,81),(20,100),(21,34),(21,89),(21,104),(22,86),(22,106),(23,91),(23,110),(24,80),(24,105),(25,78),(25,79),(26,52),(26,88),(27,87),(27,103),(28,91),(28,107),(29,30),(29,102),(29,111),(30,63),(30,96),(31,44),(31,71),(31,76),(32,37),(32,51),(32,77),(33,80),(33,94),(33,103),(34,62),(34,74),(34,75),(35,133),(36,9),(37,8),(37,127),(38,1),(39,118),(40,117),(40,122),(41,119),(42,119),(42,126),(43,116),(43,127),(44,112),(44,120),(45,112),(45,113),(46,114),(46,116),(47,121),(48,122),(49,125),(50,113),(51,20),(51,114),(51,127),(52,117),(53,72),(54,88),(54,121),(55,45),(55,132),(56,48),(57,84),(57,124),(58,76),(58,134),(59,66),(60,56),(61,54),(62,55),(62,126),(63,86),(63,129),(64,53),(64,134),(65,47),(66,70),(67,40),(68,40),(68,123),(69,41),(69,129),(70,39),(70,128),(71,54),(71,120),(72,52),(73,44),(73,118),(74,58),(74,115),(75,82),(75,115),(75,126),(76,68),(76,112),(77,16),(77,57),(77,114),(78,65),(79,61),(80,59),(80,130),(81,36),(82,60),(82,131),(83,53),(83,131),(84,78),(84,128),(85,73),(85,128),(86,92),(87,12),(87,95),(88,49),(88,117),(89,19),(89,75),(89,133),(90,97),(91,93),(92,45),(92,50),(93,35),(93,104),(94,46),(94,77),(94,130),(95,66),(95,108),(96,42),(96,62),(96,129),(97,41),(97,42),(98,36),(98,79),(99,61),(99,71),(100,58),(100,64),(101,35),(101,89),(102,63),(102,69),(103,59),(103,95),(104,74),(104,100),(104,133),(105,37),(105,43),(105,130),(106,39),(106,73),(107,21),(107,93),(107,101),(108,70),(108,85),(108,106),(109,32),(109,94),(109,105),(109,110),(110,43),(110,46),(110,51),(111,69),(111,96),(111,97),(112,123),(113,48),(113,123),(114,7),(114,124),(115,131),(115,134),(116,124),(117,125),(118,47),(118,120),(119,50),(119,132),(120,121),(121,49),(122,125),(123,122),(124,99),(126,60),(126,132),(127,81),(127,98),(128,65),(128,118),(129,55),(129,92),(129,119),(130,57),(130,116),(131,67),(132,56),(132,113),(133,64),(133,83),(133,115),(134,67),(134,68)],135)
=> ? = 23
[1,1,1,1,0,0,0,0,1,0]
=> [[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)
=> ? = 14
[1,1,1,1,0,0,0,1,0,0]
=> [[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[1,0,0,-1,1],[0,0,0,1,0]]
=> [[1,1,2,3,4],[2,2,3,4],[3,3,4],[4,5],[5]]
=> ([(0,16),(0,17),(0,28),(1,22),(2,19),(3,11),(3,21),(4,54),(5,55),(6,26),(6,57),(7,25),(7,67),(8,23),(8,64),(9,24),(9,65),(10,14),(10,56),(11,15),(11,58),(12,3),(12,37),(13,27),(13,66),(14,59),(15,60),(16,13),(16,53),(17,6),(17,61),(18,51),(18,52),(19,33),(19,34),(20,35),(20,36),(21,50),(21,58),(22,18),(22,59),(22,60),(23,41),(23,43),(24,42),(24,44),(25,50),(25,63),(26,29),(26,46),(27,29),(27,45),(28,12),(28,53),(28,61),(29,70),(30,71),(31,69),(32,68),(33,68),(34,68),(35,4),(35,69),(36,5),(36,69),(37,1),(38,33),(39,34),(40,64),(41,48),(42,49),(43,38),(44,39),(45,62),(45,70),(46,56),(46,70),(47,65),(48,32),(49,32),(50,40),(51,42),(51,71),(52,41),(52,71),(53,7),(53,66),(54,38),(55,39),(56,9),(56,47),(57,10),(57,46),(58,8),(58,40),(59,30),(59,51),(60,30),(60,52),(61,37),(61,57),(62,31),(62,36),(63,31),(63,35),(64,43),(64,54),(65,44),(65,55),(66,45),(66,67),(67,20),(67,62),(67,63),(69,2),(70,47),(71,48),(71,49)],72)
=> ? = 19
[1,1,1,1,0,0,1,0,0,0]
=> [[0,0,0,1,0],[0,0,1,0,0],[0,1,0,-1,1],[1,0,-1,1,0],[0,0,1,0,0]]
=> [[1,1,2,3,4],[2,2,3,4],[3,4,5],[4,5],[5]]
=> ([(0,15),(0,16),(0,30),(1,26),(2,14),(2,95),(3,78),(4,79),(5,92),(6,77),(7,29),(7,93),(8,27),(8,96),(9,28),(9,94),(10,12),(10,32),(10,80),(11,84),(12,13),(12,86),(13,11),(13,97),(14,19),(14,98),(15,10),(15,54),(16,2),(16,24),(16,76),(17,47),(17,71),(18,46),(18,72),(19,41),(19,91),(20,35),(20,73),(21,69),(21,87),(22,25),(22,75),(22,90),(23,45),(23,70),(24,31),(24,88),(24,95),(25,49),(25,50),(26,39),(26,40),(27,52),(27,53),(28,41),(28,89),(29,33),(29,57),(30,54),(30,76),(31,67),(31,68),(31,85),(32,56),(32,68),(32,86),(33,110),(34,106),(34,107),(35,21),(35,111),(36,100),(37,101),(37,106),(38,102),(39,102),(40,102),(41,99),(42,104),(43,113),(44,103),(45,6),(45,112),(46,7),(46,108),(47,5),(47,107),(48,3),(48,103),(49,55),(49,105),(50,33),(50,105),(51,61),(52,63),(53,61),(54,80),(55,52),(55,113),(56,79),(56,109),(57,60),(57,110),(58,90),(59,81),(60,62),(61,39),(62,40),(63,38),(64,38),(65,37),(65,111),(66,36),(66,108),(67,82),(67,109),(68,83),(68,109),(69,59),(70,48),(70,112),(71,42),(71,107),(72,69),(72,108),(73,23),(73,74),(73,111),(74,45),(74,101),(75,50),(75,100),(76,9),(76,88),(77,51),(78,62),(79,22),(79,58),(80,4),(80,56),(81,60),(81,78),(82,34),(82,47),(83,66),(83,72),(84,36),(84,75),(85,35),(85,65),(86,18),(86,83),(86,97),(87,44),(87,48),(88,67),(88,94),(89,34),(89,71),(89,99),(90,49),(90,92),(90,100),(91,37),(91,74),(91,99),(92,43),(92,55),(93,57),(93,81),(94,17),(94,82),(94,89),(95,20),(95,85),(95,98),(96,51),(96,53),(97,46),(97,66),(97,84),(98,65),(98,73),(98,91),(99,42),(99,106),(100,43),(100,105),(101,44),(101,112),(103,1),(104,96),(105,110),(105,113),(106,104),(107,8),(107,104),(108,59),(108,93),(109,58),(110,64),(111,70),(111,87),(111,101),(112,77),(112,103),(113,63),(113,64)],114)
=> ? = 23
[1,1,1,1,0,1,0,0,0,0]
=> [[0,0,0,1,0],[0,0,1,-1,1],[0,1,-1,1,0],[1,-1,1,0,0],[0,1,0,0,0]]
=> [[1,1,2,3,4],[2,3,4,5],[3,4,5],[4,5],[5]]
=> ([(0,2),(0,17),(0,18),(1,16),(1,41),(2,10),(2,15),(3,207),(4,50),(4,125),(5,181),(6,49),(6,180),(7,188),(8,138),(9,46),(9,208),(10,30),(10,206),(11,35),(11,54),(12,36),(12,97),(13,37),(13,163),(14,40),(14,44),(14,202),(15,28),(15,45),(15,206),(16,26),(16,27),(16,203),(17,1),(17,124),(18,14),(18,33),(18,124),(19,52),(19,201),(19,211),(20,196),(20,200),(21,89),(21,155),(22,149),(22,156),(23,150),(23,198),(24,154),(24,199),(25,90),(25,152),(26,162),(26,210),(27,162),(27,197),(28,159),(28,191),(29,153),(29,190),(30,161),(30,209),(31,144),(31,157),(32,141),(32,151),(33,145),(33,202),(34,143),(34,189),(35,147),(35,148),(36,142),(36,146),(37,88),(37,195),(38,87),(38,192),(39,51),(39,158),(39,194),(40,42),(40,160),(40,193),(41,161),(41,203),(42,102),(42,170),(43,122),(43,123),(43,178),(44,120),(44,160),(44,179),(45,159),(45,177),(45,179),(46,76),(46,119),(46,183),(47,64),(47,121),(47,140),(48,65),(48,86),(48,139),(49,60),(49,92),(49,93),(50,43),(50,169),(50,170),(50,210),(51,99),(51,100),(51,101),(52,104),(52,109),(52,165),(53,272),(54,13),(55,225),(55,275),(56,218),(56,219),(57,227),(57,270),(58,227),(58,269),(59,12),(60,219),(60,226),(61,255),(61,276),(62,253),(62,271),(63,277),(64,269),(64,270),(65,6),(65,265),(66,230),(67,231),(67,256),(68,236),(68,271),(69,236),(69,249),(70,229),(70,247),(71,214),(71,228),(72,235),(73,228),(73,265),(74,213),(74,229),(75,234),(76,225),(76,241),(77,231),(77,234),(78,272),(79,250),(80,274),(81,260),(82,230),(83,232),(84,239),(84,254),(85,237),(86,29),(86,214),(86,265),(87,223),(88,215),(89,244),(90,32),(90,264),(91,97),(92,107),(92,219),(93,128),(93,226),(94,83),(94,275),(95,66),(96,119),(96,266),(97,142),(98,82),(99,96),(99,216),(100,136),(100,220),(101,156),(101,216),(101,220),(102,116),(102,268),(103,91),(103,266),(104,175),(104,259),(105,121),(105,263),(106,140),(106,263),(107,84),(107,248),(108,135),(109,166),(109,259),(110,133),(110,223),(111,69),(112,76),(112,224),(113,88),(113,213),(114,117),(114,262),(115,70),(115,224),(116,54),(117,58),(117,273),(118,57),(118,220),(118,273),(119,127),(119,225),(120,157),(120,212),(121,163),(121,269),(122,106),(122,217),(123,104),(123,217),(123,262),(124,4),(124,145),(125,5),(125,169),(126,155),(127,134),(127,242),(128,132),(128,238),(129,67),(129,240),(130,74),(130,243),(130,258),(131,67),(131,235),(132,146),(132,239),(132,276),(133,70),(133,218),(133,243),(134,77),(134,222),(134,240),(135,62),(135,215),(135,232),(136,55),(136,233),(137,61),(137,238),(138,21),(138,126),(139,23),(139,186),(139,214),(140,24),(140,182),(140,270),(141,98),(142,75),(142,222),(143,171),(144,11),(144,116),(145,125),(146,79),(146,222),(147,113),(147,258),(148,80),(148,258),(149,91),(149,267),(150,112),(150,261),(151,95),(152,53),(152,264),(153,59),(154,72),(154,246),(155,66),(155,244),(156,34),(156,187),(156,267),(157,38),(157,185),(158,22),(158,101),(158,277),(159,20),(159,168),(159,221),(160,19),(160,167),(160,212),(161,174),(162,3),(162,204),(163,111),(163,195),(164,134),(164,171),(165,112),(165,115),(166,74),(166,113),(167,173),(167,211),(168,173),(168,196),(169,122),(169,181),(169,268),(170,114),(170,123),(170,268),(171,75),(171,77),(172,115),(172,133),(172,261),(173,110),(173,172),(174,63),(174,194),(175,55),(175,94),(176,56),(176,60),(176,260),(177,71),(177,139),(177,221),(178,100),(178,118),(178,262),(179,167),(179,168),(180,59),(180,93),(181,47),(181,105),(181,106),(182,135),(182,199),(182,245),(183,61),(183,132),(183,241),(184,129),(184,131),(185,192),(185,205),(186,176),(186,198),(186,252),(187,184),(187,189),(188,53),(188,78),(189,72),(189,131),(190,96),(190,103),(191,65),(191,73),(191,221),(192,130),(192,148),(192,223),(193,102),(193,144),(193,212),(194,99),(194,190),(194,277),(195,68),(195,69),(195,215),(196,87),(196,110),(197,63),(197,158),(198,56),(198,92),(198,261),(199,62),(199,68),(199,246),(200,81),(200,176),(201,109),(201,205),(202,31),(202,120),(202,193),(203,39),(203,174),(203,197),(204,117),(204,118),(204,207),(205,130),(205,147),(205,166),(206,48),(206,177),(206,191),(206,209),(207,57),(207,58),(207,64),(208,128),(208,137),(208,183),(209,71),(209,73),(209,86),(210,114),(210,178),(210,204),(211,150),(211,165),(211,172),(212,185),(212,201),(213,90),(213,251),(214,9),(214,252),(215,249),(215,271),(216,266),(216,267),(217,259),(217,263),(218,247),(218,248),(219,7),(219,248),(220,187),(220,233),(221,186),(221,200),(221,228),(222,234),(222,250),(223,80),(223,243),(224,84),(224,241),(224,247),(225,242),(226,238),(227,83),(227,245),(228,81),(228,252),(229,251),(231,257),(232,249),(232,253),(233,184),(233,275),(234,89),(234,257),(235,85),(235,256),(236,85),(236,279),(237,82),(238,8),(238,276),(239,79),(239,278),(240,231),(240,250),(241,239),(241,255),(242,240),(243,229),(243,274),(244,230),(245,232),(245,246),(246,235),(246,236),(246,253),(247,254),(247,255),(248,188),(248,254),(249,279),(250,257),(251,264),(252,208),(252,260),(253,256),(253,279),(254,78),(254,278),(255,278),(256,237),(257,244),(258,25),(258,213),(258,274),(259,108),(260,137),(260,226),(261,107),(261,218),(261,224),(262,136),(262,175),(262,273),(263,108),(263,182),(264,151),(264,272),(265,153),(265,180),(266,127),(266,164),(267,143),(267,164),(268,105),(268,217),(269,111),(270,154),(270,245),(271,141),(271,279),(272,95),(273,94),(273,227),(273,233),(274,152),(274,251),(275,129),(275,242),(276,138),(276,278),(277,103),(277,149),(277,216),(278,126),(279,98),(279,237)],280)
=> ? = 28
[1,1,1,1,1,0,0,0,0,0]
=> [[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0]]
=> [[1,2,3,4,5],[2,3,4,5],[3,4,5],[4,5],[5]]
=> 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=> ? = 42
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,4,4],[5,5],[6]]
=> ([],1)
=> 1
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [[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)
=> 2
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[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)
=> 2
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [[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,-1,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,4,5],[5,6],[6]]
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,5,6],[5,6],[6]]
=> ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8)
=> ? = 5
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[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)
=> 2
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[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)
=> 4
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,4],[4,4,5],[5,5],[6]]
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,4],[4,4,5],[5,6],[6]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,4],[4,5,6],[5,6],[6]]
=> ([(0,5),(0,6),(1,8),(2,9),(3,8),(3,9),(4,1),(5,4),(6,7),(7,2),(7,3),(8,10),(9,10)],11)
=> ? = 7
[1,0,1,0,1,1,1,0,0,0,1,0]
=> [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,4,5],[4,4,5],[5,5],[6]]
=> ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8)
=> ? = 5
[1,0,1,0,1,1,1,0,0,1,0,0]
=> [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,4,5],[4,4,5],[5,6],[6]]
=> ([(0,3),(0,7),(1,8),(2,8),(3,9),(4,5),(5,1),(6,2),(7,4),(7,9),(9,6)],10)
=> ? = 7
[1,0,1,0,1,1,1,0,1,0,0,0]
=> [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,4,5],[4,5,6],[5,6],[6]]
=> ([(0,9),(0,11),(1,18),(2,17),(3,19),(4,13),(4,19),(5,12),(5,13),(6,16),(7,14),(8,5),(8,18),(9,10),(10,3),(10,4),(11,1),(11,8),(12,17),(13,15),(15,16),(16,14),(17,7),(18,2),(18,12),(19,6),(19,15)],20)
=> ? = 9
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,4,5,6],[4,5,6],[5,6],[6]]
=> ([(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)
=> ? = 14
[1,0,1,1,0,0,1,0,1,0,1,0]
=> [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[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)
=> 2
[1,0,1,1,0,0,1,0,1,1,0,0]
=> [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[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)
=> 4
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[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)
=> 4
[1,0,1,1,0,0,1,1,0,1,0,0]
=> [[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,-1,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,3],[4,4,5],[5,6],[6]]
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 6
[1,0,1,1,0,0,1,1,1,0,0,0]
=> [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,3],[4,5,6],[5,6],[6]]
=> ([(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)
=> ? = 10
[1,0,1,1,0,1,0,0,1,0,1,0]
=> [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,4],[4,4,4],[5,5],[6]]
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,1,0,1,0,0,1,1,0,0]
=> [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,4],[4,4,4],[5,6],[6]]
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 6
[1,0,1,1,0,1,0,1,0,0,1,0]
=> [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,4],[4,4,5],[5,5],[6]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[1,0,1,1,0,1,0,1,0,1,0,0]
=> [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,4],[4,4,5],[5,6],[6]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[1,0,1,1,0,1,0,1,1,0,0,0]
=> [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,4],[4,5,6],[5,6],[6]]
=> ([(0,6),(0,7),(1,11),(2,9),(3,9),(3,10),(4,2),(5,1),(5,10),(6,4),(7,8),(8,3),(8,5),(9,12),(10,11),(10,12),(11,13),(12,13)],14)
=> ? = 9
[1,0,1,1,0,1,1,0,0,0,1,0]
=> [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,4,5],[4,4,5],[5,5],[6]]
=> ([(0,5),(0,6),(1,8),(2,9),(3,8),(3,9),(4,1),(5,4),(6,7),(7,2),(7,3),(8,10),(9,10)],11)
=> ? = 7
[1,0,1,1,0,1,1,0,0,1,0,0]
=> [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,4,5],[4,4,5],[5,6],[6]]
=> ([(0,4),(0,7),(1,9),(2,10),(3,9),(3,10),(4,11),(5,8),(6,1),(7,5),(7,11),(8,2),(8,3),(9,12),(10,12),(11,6)],13)
=> ? = 9
[1,0,1,1,0,1,1,0,1,0,0,0]
=> [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,0,1,0],[0,0,0,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,4,5],[4,5,6],[5,6],[6]]
=> ([(0,10),(0,12),(1,23),(2,22),(3,14),(3,24),(4,15),(5,13),(5,14),(6,18),(7,16),(7,20),(8,5),(8,23),(9,4),(9,24),(10,11),(11,3),(11,9),(12,1),(12,8),(13,22),(14,19),(15,16),(15,21),(16,25),(18,17),(19,20),(19,21),(20,18),(20,25),(21,25),(22,6),(23,2),(23,13),(24,7),(24,15),(24,19),(25,17)],26)
=> ? = 12
[1,0,1,1,0,1,1,1,0,0,0,0]
=> [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,4,5,6],[4,5,6],[5,6],[6]]
=> ([(0,5),(0,14),(0,15),(1,26),(2,9),(2,25),(3,13),(3,24),(4,16),(5,11),(5,12),(6,69),(7,64),(8,49),(9,6),(9,52),(10,20),(10,59),(11,19),(11,65),(12,17),(12,65),(13,18),(13,22),(13,71),(14,2),(14,29),(15,3),(15,29),(16,39),(16,55),(17,56),(17,68),(18,57),(18,66),(19,58),(19,67),(20,51),(20,53),(21,40),(21,41),(22,57),(22,72),(23,28),(23,54),(23,70),(24,58),(24,71),(25,52),(25,56),(26,27),(26,69),(26,72),(27,45),(27,60),(28,34),(28,48),(28,50),(29,1),(30,76),(31,75),(32,77),(33,74),(33,80),(34,73),(34,78),(35,73),(35,77),(36,82),(37,79),(38,80),(39,74),(40,7),(40,76),(41,8),(41,76),(42,55),(42,79),(43,59),(44,39),(45,53),(45,83),(46,33),(46,81),(47,32),(47,83),(48,42),(48,78),(49,44),(50,46),(50,73),(51,44),(52,10),(52,43),(53,62),(54,34),(54,75),(55,36),(55,74),(56,43),(57,63),(58,61),(59,49),(59,51),(60,35),(60,50),(60,83),(61,31),(61,70),(62,33),(62,38),(63,32),(63,35),(64,37),(64,42),(65,21),(65,67),(65,68),(66,31),(66,54),(67,30),(67,40),(68,30),(68,41),(69,45),(69,47),(70,48),(70,64),(70,75),(71,23),(71,61),(71,66),(72,47),(72,60),(72,63),(73,81),(74,82),(75,37),(75,78),(76,4),(77,38),(77,81),(78,79),(79,36),(80,82),(81,80),(83,46),(83,62),(83,77)],84)
=> ? = 19
[1,0,1,1,1,0,0,0,1,0,1,0]
=> [[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,3,4],[3,3,3,4],[4,4,4],[5,5],[6]]
=> ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8)
=> ? = 5
[1,0,1,1,1,0,0,0,1,1,0,0]
=> [[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,1],[2,2,2,3,4],[3,3,3,4],[4,4,4],[5,6],[6]]
=> ([(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)
=> ? = 10
[1,0,1,1,1,0,0,1,0,0,1,0]
=> [[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,3,4],[3,3,3,4],[4,4,5],[5,5],[6]]
=> ([(0,3),(0,7),(1,8),(2,8),(3,9),(4,5),(5,1),(6,2),(7,4),(7,9),(9,6)],10)
=> ? = 7
[1,0,1,1,1,0,0,1,0,1,0,0]
=> [[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,1],[2,2,2,3,4],[3,3,3,4],[4,4,5],[5,6],[6]]
=> ([(0,3),(0,8),(1,10),(2,10),(3,9),(4,6),(5,4),(5,11),(6,2),(7,1),(8,5),(8,9),(9,11),(11,7)],12)
=> ? = 9
[1,0,1,1,1,0,0,1,1,0,0,0]
=> [[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]]
=> [[1,1,1,1,1,1],[2,2,2,3,4],[3,3,3,4],[4,5,6],[5,6],[6]]
=> ([(0,7),(0,8),(0,11),(1,25),(2,10),(2,24),(3,5),(3,12),(3,26),(4,28),(5,6),(5,29),(6,4),(6,27),(7,2),(7,19),(8,3),(8,18),(9,15),(9,16),(10,13),(10,23),(11,18),(11,19),(12,22),(12,23),(12,29),(13,31),(14,30),(15,30),(16,30),(17,20),(18,26),(19,24),(20,14),(21,16),(22,25),(22,31),(23,17),(23,31),(24,13),(25,9),(25,21),(26,1),(26,22),(27,20),(27,28),(28,14),(28,15),(29,17),(29,27),(31,21)],32)
=> ? = 16
[1,1,0,0,1,0,1,0,1,0,1,0]
=> [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[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)
=> 2
[1,1,0,0,1,0,1,0,1,1,0,0]
=> [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[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)
=> 4
[1,1,0,0,1,0,1,1,0,0,1,0]
=> [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[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)
=> 4
Description
The number of elements in the poset.
Matching statistic: St001717
Mp00137: Dyck paths —to symmetric ASM⟶ Alternating sign matrices
Mp00001: Alternating sign matrices —to semistandard tableau via monotone triangles⟶ Semistandard tableaux
Mp00214: Semistandard tableaux —subcrystal⟶ Posets
St001717: Posets ⟶ ℤResult quality: 6% ●values known / values provided: 6%●distinct values known / distinct values provided: 8%
Mp00001: Alternating sign matrices —to semistandard tableau via monotone triangles⟶ Semistandard tableaux
Mp00214: Semistandard tableaux —subcrystal⟶ Posets
St001717: Posets ⟶ ℤResult quality: 6% ●values known / values provided: 6%●distinct values known / distinct values provided: 8%
Values
[1,0]
=> [[1]]
=> [[1]]
=> ([],1)
=> 1
[1,0,1,0]
=> [[1,0],[0,1]]
=> [[1,1],[2]]
=> ([],1)
=> 1
[1,1,0,0]
=> [[0,1],[1,0]]
=> [[1,2],[2]]
=> ([(0,1)],2)
=> 2
[1,0,1,0,1,0]
=> [[1,0,0],[0,1,0],[0,0,1]]
=> [[1,1,1],[2,2],[3]]
=> ([],1)
=> 1
[1,0,1,1,0,0]
=> [[1,0,0],[0,0,1],[0,1,0]]
=> [[1,1,1],[2,3],[3]]
=> ([(0,1)],2)
=> 2
[1,1,0,0,1,0]
=> [[0,1,0],[1,0,0],[0,0,1]]
=> [[1,1,2],[2,2],[3]]
=> ([(0,1)],2)
=> 2
[1,1,0,1,0,0]
=> [[0,1,0],[1,-1,1],[0,1,0]]
=> [[1,1,2],[2,3],[3]]
=> ([(0,2),(2,1)],3)
=> 3
[1,1,1,0,0,0]
=> [[0,0,1],[0,1,0],[1,0,0]]
=> [[1,2,3],[2,3],[3]]
=> ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8)
=> ? = 5
[1,0,1,0,1,0,1,0]
=> [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,2],[3,3],[4]]
=> ([],1)
=> 1
[1,0,1,0,1,1,0,0]
=> [[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)
=> 2
[1,0,1,1,0,0,1,0]
=> [[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)
=> 2
[1,0,1,1,0,1,0,0]
=> [[1,0,0,0],[0,0,1,0],[0,1,-1,1],[0,0,1,0]]
=> [[1,1,1,1],[2,2,3],[3,4],[4]]
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,1,1,0,0,0]
=> [[1,0,0,0],[0,0,0,1],[0,0,1,0],[0,1,0,0]]
=> [[1,1,1,1],[2,3,4],[3,4],[4]]
=> ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8)
=> ? = 5
[1,1,0,0,1,0,1,0]
=> [[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)
=> 2
[1,1,0,0,1,1,0,0]
=> [[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)
=> 4
[1,1,0,1,0,0,1,0]
=> [[0,1,0,0],[1,-1,1,0],[0,1,0,0],[0,0,0,1]]
=> [[1,1,1,2],[2,2,3],[3,3],[4]]
=> ([(0,2),(2,1)],3)
=> 3
[1,1,0,1,0,1,0,0]
=> [[0,1,0,0],[1,-1,1,0],[0,1,-1,1],[0,0,1,0]]
=> [[1,1,1,2],[2,2,3],[3,4],[4]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[1,1,0,1,1,0,0,0]
=> [[0,1,0,0],[1,-1,0,1],[0,0,1,0],[0,1,0,0]]
=> [[1,1,1,2],[2,3,4],[3,4],[4]]
=> ([(0,5),(0,6),(1,8),(2,9),(3,8),(3,9),(4,1),(5,4),(6,7),(7,2),(7,3),(8,10),(9,10)],11)
=> ? = 7
[1,1,1,0,0,0,1,0]
=> [[0,0,1,0],[0,1,0,0],[1,0,0,0],[0,0,0,1]]
=> [[1,1,2,3],[2,2,3],[3,3],[4]]
=> ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8)
=> ? = 5
[1,1,1,0,0,1,0,0]
=> [[0,0,1,0],[0,1,0,0],[1,0,-1,1],[0,0,1,0]]
=> [[1,1,2,3],[2,2,3],[3,4],[4]]
=> ([(0,3),(0,7),(1,8),(2,8),(3,9),(4,5),(5,1),(6,2),(7,4),(7,9),(9,6)],10)
=> ? = 7
[1,1,1,0,1,0,0,0]
=> [[0,0,1,0],[0,1,-1,1],[1,-1,1,0],[0,1,0,0]]
=> [[1,1,2,3],[2,3,4],[3,4],[4]]
=> ([(0,9),(0,11),(1,18),(2,17),(3,19),(4,13),(4,19),(5,12),(5,13),(6,16),(7,14),(8,5),(8,18),(9,10),(10,3),(10,4),(11,1),(11,8),(12,17),(13,15),(15,16),(16,14),(17,7),(18,2),(18,12),(19,6),(19,15)],20)
=> ? = 9
[1,1,1,1,0,0,0,0]
=> [[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)
=> ? = 14
[1,0,1,0,1,0,1,0,1,0]
=> [[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]]
=> [[1,1,1,1,1],[2,2,2,2],[3,3,3],[4,4],[5]]
=> ([],1)
=> 1
[1,0,1,0,1,0,1,1,0,0]
=> [[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)
=> 2
[1,0,1,0,1,1,0,0,1,0]
=> [[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)
=> 2
[1,0,1,0,1,1,0,1,0,0]
=> [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
=> [[1,1,1,1,1],[2,2,2,2],[3,3,4],[4,5],[5]]
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,0,1,1,1,0,0,0]
=> [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0]]
=> [[1,1,1,1,1],[2,2,2,2],[3,4,5],[4,5],[5]]
=> ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8)
=> ? = 5
[1,0,1,1,0,0,1,0,1,0]
=> [[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)
=> 2
[1,0,1,1,0,0,1,1,0,0]
=> [[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)
=> 4
[1,0,1,1,0,1,0,0,1,0]
=> [[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [[1,1,1,1,1],[2,2,2,3],[3,3,4],[4,4],[5]]
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,1,0,1,0,1,0,0]
=> [[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
=> [[1,1,1,1,1],[2,2,2,3],[3,3,4],[4,5],[5]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[1,0,1,1,0,1,1,0,0,0]
=> [[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,0,1],[0,0,0,1,0],[0,0,1,0,0]]
=> [[1,1,1,1,1],[2,2,2,3],[3,4,5],[4,5],[5]]
=> ([(0,5),(0,6),(1,8),(2,9),(3,8),(3,9),(4,1),(5,4),(6,7),(7,2),(7,3),(8,10),(9,10)],11)
=> ? = 7
[1,0,1,1,1,0,0,0,1,0]
=> [[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [[1,1,1,1,1],[2,2,3,4],[3,3,4],[4,4],[5]]
=> ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8)
=> ? = 5
[1,0,1,1,1,0,0,1,0,0]
=> [[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,-1,1],[0,0,0,1,0]]
=> [[1,1,1,1,1],[2,2,3,4],[3,3,4],[4,5],[5]]
=> ([(0,3),(0,7),(1,8),(2,8),(3,9),(4,5),(5,1),(6,2),(7,4),(7,9),(9,6)],10)
=> ? = 7
[1,0,1,1,1,0,1,0,0,0]
=> [[1,0,0,0,0],[0,0,0,1,0],[0,0,1,-1,1],[0,1,-1,1,0],[0,0,1,0,0]]
=> [[1,1,1,1,1],[2,2,3,4],[3,4,5],[4,5],[5]]
=> ([(0,9),(0,11),(1,18),(2,17),(3,19),(4,13),(4,19),(5,12),(5,13),(6,16),(7,14),(8,5),(8,18),(9,10),(10,3),(10,4),(11,1),(11,8),(12,17),(13,15),(15,16),(16,14),(17,7),(18,2),(18,12),(19,6),(19,15)],20)
=> ? = 9
[1,0,1,1,1,1,0,0,0,0]
=> [[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)
=> ? = 14
[1,1,0,0,1,0,1,0,1,0]
=> [[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)
=> 2
[1,1,0,0,1,0,1,1,0,0]
=> [[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)
=> 4
[1,1,0,0,1,1,0,0,1,0]
=> [[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)
=> 4
[1,1,0,0,1,1,0,1,0,0]
=> [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
=> [[1,1,1,1,2],[2,2,2,2],[3,3,4],[4,5],[5]]
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 6
[1,1,0,0,1,1,1,0,0,0]
=> [[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)
=> ? = 10
[1,1,0,1,0,0,1,0,1,0]
=> [[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
=> [[1,1,1,1,2],[2,2,2,3],[3,3,3],[4,4],[5]]
=> ([(0,2),(2,1)],3)
=> 3
[1,1,0,1,0,0,1,1,0,0]
=> [[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
=> [[1,1,1,1,2],[2,2,2,3],[3,3,3],[4,5],[5]]
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 6
[1,1,0,1,0,1,0,0,1,0]
=> [[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [[1,1,1,1,2],[2,2,2,3],[3,3,4],[4,4],[5]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[1,1,0,1,0,1,0,1,0,0]
=> [[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
=> [[1,1,1,1,2],[2,2,2,3],[3,3,4],[4,5],[5]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[1,1,0,1,0,1,1,0,0,0]
=> [[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,0,1],[0,0,0,1,0],[0,0,1,0,0]]
=> [[1,1,1,1,2],[2,2,2,3],[3,4,5],[4,5],[5]]
=> ([(0,6),(0,7),(1,11),(2,9),(3,9),(3,10),(4,2),(5,1),(5,10),(6,4),(7,8),(8,3),(8,5),(9,12),(10,11),(10,12),(11,13),(12,13)],14)
=> ? = 9
[1,1,0,1,1,0,0,0,1,0]
=> [[0,1,0,0,0],[1,-1,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [[1,1,1,1,2],[2,2,3,4],[3,3,4],[4,4],[5]]
=> ([(0,5),(0,6),(1,8),(2,9),(3,8),(3,9),(4,1),(5,4),(6,7),(7,2),(7,3),(8,10),(9,10)],11)
=> ? = 7
[1,1,0,1,1,0,0,1,0,0]
=> [[0,1,0,0,0],[1,-1,0,1,0],[0,0,1,0,0],[0,1,0,-1,1],[0,0,0,1,0]]
=> [[1,1,1,1,2],[2,2,3,4],[3,3,4],[4,5],[5]]
=> ([(0,4),(0,7),(1,9),(2,10),(3,9),(3,10),(4,11),(5,8),(6,1),(7,5),(7,11),(8,2),(8,3),(9,12),(10,12),(11,6)],13)
=> ? = 9
[1,1,0,1,1,0,1,0,0,0]
=> [[0,1,0,0,0],[1,-1,0,1,0],[0,0,1,-1,1],[0,1,-1,1,0],[0,0,1,0,0]]
=> [[1,1,1,1,2],[2,2,3,4],[3,4,5],[4,5],[5]]
=> ([(0,10),(0,12),(1,23),(2,22),(3,14),(3,24),(4,15),(5,13),(5,14),(6,18),(7,16),(7,20),(8,5),(8,23),(9,4),(9,24),(10,11),(11,3),(11,9),(12,1),(12,8),(13,22),(14,19),(15,16),(15,21),(16,25),(18,17),(19,20),(19,21),(20,18),(20,25),(21,25),(22,6),(23,2),(23,13),(24,7),(24,15),(24,19),(25,17)],26)
=> ? = 12
[1,1,0,1,1,1,0,0,0,0]
=> [[0,1,0,0,0],[1,-1,0,0,1],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0]]
=> [[1,1,1,1,2],[2,3,4,5],[3,4,5],[4,5],[5]]
=> ([(0,5),(0,14),(0,15),(1,26),(2,9),(2,25),(3,13),(3,24),(4,16),(5,11),(5,12),(6,69),(7,64),(8,49),(9,6),(9,52),(10,20),(10,59),(11,19),(11,65),(12,17),(12,65),(13,18),(13,22),(13,71),(14,2),(14,29),(15,3),(15,29),(16,39),(16,55),(17,56),(17,68),(18,57),(18,66),(19,58),(19,67),(20,51),(20,53),(21,40),(21,41),(22,57),(22,72),(23,28),(23,54),(23,70),(24,58),(24,71),(25,52),(25,56),(26,27),(26,69),(26,72),(27,45),(27,60),(28,34),(28,48),(28,50),(29,1),(30,76),(31,75),(32,77),(33,74),(33,80),(34,73),(34,78),(35,73),(35,77),(36,82),(37,79),(38,80),(39,74),(40,7),(40,76),(41,8),(41,76),(42,55),(42,79),(43,59),(44,39),(45,53),(45,83),(46,33),(46,81),(47,32),(47,83),(48,42),(48,78),(49,44),(50,46),(50,73),(51,44),(52,10),(52,43),(53,62),(54,34),(54,75),(55,36),(55,74),(56,43),(57,63),(58,61),(59,49),(59,51),(60,35),(60,50),(60,83),(61,31),(61,70),(62,33),(62,38),(63,32),(63,35),(64,37),(64,42),(65,21),(65,67),(65,68),(66,31),(66,54),(67,30),(67,40),(68,30),(68,41),(69,45),(69,47),(70,48),(70,64),(70,75),(71,23),(71,61),(71,66),(72,47),(72,60),(72,63),(73,81),(74,82),(75,37),(75,78),(76,4),(77,38),(77,81),(78,79),(79,36),(80,82),(81,80),(83,46),(83,62),(83,77)],84)
=> ? = 19
[1,1,1,0,0,0,1,0,1,0]
=> [[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
=> [[1,1,1,2,3],[2,2,2,3],[3,3,3],[4,4],[5]]
=> ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8)
=> ? = 5
[1,1,1,0,0,0,1,1,0,0]
=> [[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)
=> ? = 10
[1,1,1,0,0,1,0,0,1,0]
=> [[0,0,1,0,0],[0,1,0,0,0],[1,0,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [[1,1,1,2,3],[2,2,2,3],[3,3,4],[4,4],[5]]
=> ([(0,3),(0,7),(1,8),(2,8),(3,9),(4,5),(5,1),(6,2),(7,4),(7,9),(9,6)],10)
=> ? = 7
[1,1,1,0,0,1,0,1,0,0]
=> [[0,0,1,0,0],[0,1,0,0,0],[1,0,-1,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
=> [[1,1,1,2,3],[2,2,2,3],[3,3,4],[4,5],[5]]
=> ([(0,3),(0,8),(1,10),(2,10),(3,9),(4,6),(5,4),(5,11),(6,2),(7,1),(8,5),(8,9),(9,11),(11,7)],12)
=> ? = 9
[1,1,1,0,0,1,1,0,0,0]
=> [[0,0,1,0,0],[0,1,0,0,0],[1,0,-1,0,1],[0,0,0,1,0],[0,0,1,0,0]]
=> [[1,1,1,2,3],[2,2,2,3],[3,4,5],[4,5],[5]]
=> ([(0,7),(0,8),(0,11),(1,25),(2,10),(2,24),(3,5),(3,12),(3,26),(4,28),(5,6),(5,29),(6,4),(6,27),(7,2),(7,19),(8,3),(8,18),(9,15),(9,16),(10,13),(10,23),(11,18),(11,19),(12,22),(12,23),(12,29),(13,31),(14,30),(15,30),(16,30),(17,20),(18,26),(19,24),(20,14),(21,16),(22,25),(22,31),(23,17),(23,31),(24,13),(25,9),(25,21),(26,1),(26,22),(27,20),(27,28),(28,14),(28,15),(29,17),(29,27),(31,21)],32)
=> ? = 16
[1,1,1,0,1,0,0,0,1,0]
=> [[0,0,1,0,0],[0,1,-1,1,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [[1,1,1,2,3],[2,2,3,4],[3,3,4],[4,4],[5]]
=> ([(0,9),(0,11),(1,18),(2,17),(3,19),(4,13),(4,19),(5,12),(5,13),(6,16),(7,14),(8,5),(8,18),(9,10),(10,3),(10,4),(11,1),(11,8),(12,17),(13,15),(15,16),(16,14),(17,7),(18,2),(18,12),(19,6),(19,15)],20)
=> ? = 9
[1,1,1,0,1,0,0,1,0,0]
=> [[0,0,1,0,0],[0,1,-1,1,0],[1,-1,1,0,0],[0,1,0,-1,1],[0,0,0,1,0]]
=> [[1,1,1,2,3],[2,2,3,4],[3,3,4],[4,5],[5]]
=> ([(0,10),(0,11),(1,13),(1,14),(2,21),(3,20),(4,14),(4,20),(5,17),(6,16),(7,18),(8,12),(9,1),(9,22),(10,5),(10,15),(11,8),(11,15),(12,3),(12,4),(13,21),(14,19),(15,9),(15,17),(17,22),(18,16),(19,18),(20,7),(20,19),(21,6),(22,2),(22,13)],23)
=> ? = 12
[1,1,1,0,1,0,1,0,0,0]
=> [[0,0,1,0,0],[0,1,-1,1,0],[1,-1,1,-1,1],[0,1,-1,1,0],[0,0,1,0,0]]
=> [[1,1,1,2,3],[2,2,3,4],[3,4,5],[4,5],[5]]
=> ([(0,2),(0,3),(1,9),(1,15),(2,1),(3,7),(3,8),(4,30),(5,31),(6,23),(7,16),(7,37),(8,10),(8,37),(9,11),(9,36),(10,34),(11,35),(12,25),(12,29),(13,19),(13,22),(14,21),(14,27),(15,26),(15,36),(16,26),(16,33),(17,39),(18,38),(19,12),(19,38),(20,6),(21,4),(21,39),(22,5),(22,38),(24,23),(25,28),(26,32),(27,25),(27,39),(28,24),(29,20),(30,24),(31,20),(32,17),(32,27),(33,18),(33,19),(34,18),(34,22),(35,17),(35,21),(36,14),(36,32),(36,35),(37,13),(37,33),(37,34),(38,29),(38,31),(39,28),(39,30)],40)
=> ? = 14
[1,1,1,0,1,1,0,0,0,0]
=> [[0,0,1,0,0],[0,1,-1,0,1],[1,-1,0,1,0],[0,0,1,0,0],[0,1,0,0,0]]
=> [[1,1,1,2,3],[2,3,4,5],[3,4,5],[4,5],[5]]
=> ([(0,4),(0,14),(0,15),(1,29),(2,6),(2,27),(3,13),(3,28),(4,10),(4,11),(5,102),(6,5),(6,87),(7,31),(7,99),(8,25),(8,98),(9,26),(9,72),(10,23),(10,109),(11,24),(11,33),(11,109),(12,22),(12,108),(13,17),(13,18),(13,107),(14,2),(14,38),(15,3),(15,38),(16,84),(16,85),(17,90),(17,111),(18,90),(18,101),(19,82),(19,83),(20,81),(20,100),(21,34),(21,89),(21,104),(22,86),(22,106),(23,91),(23,110),(24,80),(24,105),(25,78),(25,79),(26,52),(26,88),(27,87),(27,103),(28,91),(28,107),(29,30),(29,102),(29,111),(30,63),(30,96),(31,44),(31,71),(31,76),(32,37),(32,51),(32,77),(33,80),(33,94),(33,103),(34,62),(34,74),(34,75),(35,133),(36,9),(37,8),(37,127),(38,1),(39,118),(40,117),(40,122),(41,119),(42,119),(42,126),(43,116),(43,127),(44,112),(44,120),(45,112),(45,113),(46,114),(46,116),(47,121),(48,122),(49,125),(50,113),(51,20),(51,114),(51,127),(52,117),(53,72),(54,88),(54,121),(55,45),(55,132),(56,48),(57,84),(57,124),(58,76),(58,134),(59,66),(60,56),(61,54),(62,55),(62,126),(63,86),(63,129),(64,53),(64,134),(65,47),(66,70),(67,40),(68,40),(68,123),(69,41),(69,129),(70,39),(70,128),(71,54),(71,120),(72,52),(73,44),(73,118),(74,58),(74,115),(75,82),(75,115),(75,126),(76,68),(76,112),(77,16),(77,57),(77,114),(78,65),(79,61),(80,59),(80,130),(81,36),(82,60),(82,131),(83,53),(83,131),(84,78),(84,128),(85,73),(85,128),(86,92),(87,12),(87,95),(88,49),(88,117),(89,19),(89,75),(89,133),(90,97),(91,93),(92,45),(92,50),(93,35),(93,104),(94,46),(94,77),(94,130),(95,66),(95,108),(96,42),(96,62),(96,129),(97,41),(97,42),(98,36),(98,79),(99,61),(99,71),(100,58),(100,64),(101,35),(101,89),(102,63),(102,69),(103,59),(103,95),(104,74),(104,100),(104,133),(105,37),(105,43),(105,130),(106,39),(106,73),(107,21),(107,93),(107,101),(108,70),(108,85),(108,106),(109,32),(109,94),(109,105),(109,110),(110,43),(110,46),(110,51),(111,69),(111,96),(111,97),(112,123),(113,48),(113,123),(114,7),(114,124),(115,131),(115,134),(116,124),(117,125),(118,47),(118,120),(119,50),(119,132),(120,121),(121,49),(122,125),(123,122),(124,99),(126,60),(126,132),(127,81),(127,98),(128,65),(128,118),(129,55),(129,92),(129,119),(130,57),(130,116),(131,67),(132,56),(132,113),(133,64),(133,83),(133,115),(134,67),(134,68)],135)
=> ? = 23
[1,1,1,1,0,0,0,0,1,0]
=> [[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)
=> ? = 14
[1,1,1,1,0,0,0,1,0,0]
=> [[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[1,0,0,-1,1],[0,0,0,1,0]]
=> [[1,1,2,3,4],[2,2,3,4],[3,3,4],[4,5],[5]]
=> ([(0,16),(0,17),(0,28),(1,22),(2,19),(3,11),(3,21),(4,54),(5,55),(6,26),(6,57),(7,25),(7,67),(8,23),(8,64),(9,24),(9,65),(10,14),(10,56),(11,15),(11,58),(12,3),(12,37),(13,27),(13,66),(14,59),(15,60),(16,13),(16,53),(17,6),(17,61),(18,51),(18,52),(19,33),(19,34),(20,35),(20,36),(21,50),(21,58),(22,18),(22,59),(22,60),(23,41),(23,43),(24,42),(24,44),(25,50),(25,63),(26,29),(26,46),(27,29),(27,45),(28,12),(28,53),(28,61),(29,70),(30,71),(31,69),(32,68),(33,68),(34,68),(35,4),(35,69),(36,5),(36,69),(37,1),(38,33),(39,34),(40,64),(41,48),(42,49),(43,38),(44,39),(45,62),(45,70),(46,56),(46,70),(47,65),(48,32),(49,32),(50,40),(51,42),(51,71),(52,41),(52,71),(53,7),(53,66),(54,38),(55,39),(56,9),(56,47),(57,10),(57,46),(58,8),(58,40),(59,30),(59,51),(60,30),(60,52),(61,37),(61,57),(62,31),(62,36),(63,31),(63,35),(64,43),(64,54),(65,44),(65,55),(66,45),(66,67),(67,20),(67,62),(67,63),(69,2),(70,47),(71,48),(71,49)],72)
=> ? = 19
[1,1,1,1,0,0,1,0,0,0]
=> [[0,0,0,1,0],[0,0,1,0,0],[0,1,0,-1,1],[1,0,-1,1,0],[0,0,1,0,0]]
=> [[1,1,2,3,4],[2,2,3,4],[3,4,5],[4,5],[5]]
=> ([(0,15),(0,16),(0,30),(1,26),(2,14),(2,95),(3,78),(4,79),(5,92),(6,77),(7,29),(7,93),(8,27),(8,96),(9,28),(9,94),(10,12),(10,32),(10,80),(11,84),(12,13),(12,86),(13,11),(13,97),(14,19),(14,98),(15,10),(15,54),(16,2),(16,24),(16,76),(17,47),(17,71),(18,46),(18,72),(19,41),(19,91),(20,35),(20,73),(21,69),(21,87),(22,25),(22,75),(22,90),(23,45),(23,70),(24,31),(24,88),(24,95),(25,49),(25,50),(26,39),(26,40),(27,52),(27,53),(28,41),(28,89),(29,33),(29,57),(30,54),(30,76),(31,67),(31,68),(31,85),(32,56),(32,68),(32,86),(33,110),(34,106),(34,107),(35,21),(35,111),(36,100),(37,101),(37,106),(38,102),(39,102),(40,102),(41,99),(42,104),(43,113),(44,103),(45,6),(45,112),(46,7),(46,108),(47,5),(47,107),(48,3),(48,103),(49,55),(49,105),(50,33),(50,105),(51,61),(52,63),(53,61),(54,80),(55,52),(55,113),(56,79),(56,109),(57,60),(57,110),(58,90),(59,81),(60,62),(61,39),(62,40),(63,38),(64,38),(65,37),(65,111),(66,36),(66,108),(67,82),(67,109),(68,83),(68,109),(69,59),(70,48),(70,112),(71,42),(71,107),(72,69),(72,108),(73,23),(73,74),(73,111),(74,45),(74,101),(75,50),(75,100),(76,9),(76,88),(77,51),(78,62),(79,22),(79,58),(80,4),(80,56),(81,60),(81,78),(82,34),(82,47),(83,66),(83,72),(84,36),(84,75),(85,35),(85,65),(86,18),(86,83),(86,97),(87,44),(87,48),(88,67),(88,94),(89,34),(89,71),(89,99),(90,49),(90,92),(90,100),(91,37),(91,74),(91,99),(92,43),(92,55),(93,57),(93,81),(94,17),(94,82),(94,89),(95,20),(95,85),(95,98),(96,51),(96,53),(97,46),(97,66),(97,84),(98,65),(98,73),(98,91),(99,42),(99,106),(100,43),(100,105),(101,44),(101,112),(103,1),(104,96),(105,110),(105,113),(106,104),(107,8),(107,104),(108,59),(108,93),(109,58),(110,64),(111,70),(111,87),(111,101),(112,77),(112,103),(113,63),(113,64)],114)
=> ? = 23
[1,1,1,1,0,1,0,0,0,0]
=> [[0,0,0,1,0],[0,0,1,-1,1],[0,1,-1,1,0],[1,-1,1,0,0],[0,1,0,0,0]]
=> [[1,1,2,3,4],[2,3,4,5],[3,4,5],[4,5],[5]]
=> ([(0,2),(0,17),(0,18),(1,16),(1,41),(2,10),(2,15),(3,207),(4,50),(4,125),(5,181),(6,49),(6,180),(7,188),(8,138),(9,46),(9,208),(10,30),(10,206),(11,35),(11,54),(12,36),(12,97),(13,37),(13,163),(14,40),(14,44),(14,202),(15,28),(15,45),(15,206),(16,26),(16,27),(16,203),(17,1),(17,124),(18,14),(18,33),(18,124),(19,52),(19,201),(19,211),(20,196),(20,200),(21,89),(21,155),(22,149),(22,156),(23,150),(23,198),(24,154),(24,199),(25,90),(25,152),(26,162),(26,210),(27,162),(27,197),(28,159),(28,191),(29,153),(29,190),(30,161),(30,209),(31,144),(31,157),(32,141),(32,151),(33,145),(33,202),(34,143),(34,189),(35,147),(35,148),(36,142),(36,146),(37,88),(37,195),(38,87),(38,192),(39,51),(39,158),(39,194),(40,42),(40,160),(40,193),(41,161),(41,203),(42,102),(42,170),(43,122),(43,123),(43,178),(44,120),(44,160),(44,179),(45,159),(45,177),(45,179),(46,76),(46,119),(46,183),(47,64),(47,121),(47,140),(48,65),(48,86),(48,139),(49,60),(49,92),(49,93),(50,43),(50,169),(50,170),(50,210),(51,99),(51,100),(51,101),(52,104),(52,109),(52,165),(53,272),(54,13),(55,225),(55,275),(56,218),(56,219),(57,227),(57,270),(58,227),(58,269),(59,12),(60,219),(60,226),(61,255),(61,276),(62,253),(62,271),(63,277),(64,269),(64,270),(65,6),(65,265),(66,230),(67,231),(67,256),(68,236),(68,271),(69,236),(69,249),(70,229),(70,247),(71,214),(71,228),(72,235),(73,228),(73,265),(74,213),(74,229),(75,234),(76,225),(76,241),(77,231),(77,234),(78,272),(79,250),(80,274),(81,260),(82,230),(83,232),(84,239),(84,254),(85,237),(86,29),(86,214),(86,265),(87,223),(88,215),(89,244),(90,32),(90,264),(91,97),(92,107),(92,219),(93,128),(93,226),(94,83),(94,275),(95,66),(96,119),(96,266),(97,142),(98,82),(99,96),(99,216),(100,136),(100,220),(101,156),(101,216),(101,220),(102,116),(102,268),(103,91),(103,266),(104,175),(104,259),(105,121),(105,263),(106,140),(106,263),(107,84),(107,248),(108,135),(109,166),(109,259),(110,133),(110,223),(111,69),(112,76),(112,224),(113,88),(113,213),(114,117),(114,262),(115,70),(115,224),(116,54),(117,58),(117,273),(118,57),(118,220),(118,273),(119,127),(119,225),(120,157),(120,212),(121,163),(121,269),(122,106),(122,217),(123,104),(123,217),(123,262),(124,4),(124,145),(125,5),(125,169),(126,155),(127,134),(127,242),(128,132),(128,238),(129,67),(129,240),(130,74),(130,243),(130,258),(131,67),(131,235),(132,146),(132,239),(132,276),(133,70),(133,218),(133,243),(134,77),(134,222),(134,240),(135,62),(135,215),(135,232),(136,55),(136,233),(137,61),(137,238),(138,21),(138,126),(139,23),(139,186),(139,214),(140,24),(140,182),(140,270),(141,98),(142,75),(142,222),(143,171),(144,11),(144,116),(145,125),(146,79),(146,222),(147,113),(147,258),(148,80),(148,258),(149,91),(149,267),(150,112),(150,261),(151,95),(152,53),(152,264),(153,59),(154,72),(154,246),(155,66),(155,244),(156,34),(156,187),(156,267),(157,38),(157,185),(158,22),(158,101),(158,277),(159,20),(159,168),(159,221),(160,19),(160,167),(160,212),(161,174),(162,3),(162,204),(163,111),(163,195),(164,134),(164,171),(165,112),(165,115),(166,74),(166,113),(167,173),(167,211),(168,173),(168,196),(169,122),(169,181),(169,268),(170,114),(170,123),(170,268),(171,75),(171,77),(172,115),(172,133),(172,261),(173,110),(173,172),(174,63),(174,194),(175,55),(175,94),(176,56),(176,60),(176,260),(177,71),(177,139),(177,221),(178,100),(178,118),(178,262),(179,167),(179,168),(180,59),(180,93),(181,47),(181,105),(181,106),(182,135),(182,199),(182,245),(183,61),(183,132),(183,241),(184,129),(184,131),(185,192),(185,205),(186,176),(186,198),(186,252),(187,184),(187,189),(188,53),(188,78),(189,72),(189,131),(190,96),(190,103),(191,65),(191,73),(191,221),(192,130),(192,148),(192,223),(193,102),(193,144),(193,212),(194,99),(194,190),(194,277),(195,68),(195,69),(195,215),(196,87),(196,110),(197,63),(197,158),(198,56),(198,92),(198,261),(199,62),(199,68),(199,246),(200,81),(200,176),(201,109),(201,205),(202,31),(202,120),(202,193),(203,39),(203,174),(203,197),(204,117),(204,118),(204,207),(205,130),(205,147),(205,166),(206,48),(206,177),(206,191),(206,209),(207,57),(207,58),(207,64),(208,128),(208,137),(208,183),(209,71),(209,73),(209,86),(210,114),(210,178),(210,204),(211,150),(211,165),(211,172),(212,185),(212,201),(213,90),(213,251),(214,9),(214,252),(215,249),(215,271),(216,266),(216,267),(217,259),(217,263),(218,247),(218,248),(219,7),(219,248),(220,187),(220,233),(221,186),(221,200),(221,228),(222,234),(222,250),(223,80),(223,243),(224,84),(224,241),(224,247),(225,242),(226,238),(227,83),(227,245),(228,81),(228,252),(229,251),(231,257),(232,249),(232,253),(233,184),(233,275),(234,89),(234,257),(235,85),(235,256),(236,85),(236,279),(237,82),(238,8),(238,276),(239,79),(239,278),(240,231),(240,250),(241,239),(241,255),(242,240),(243,229),(243,274),(244,230),(245,232),(245,246),(246,235),(246,236),(246,253),(247,254),(247,255),(248,188),(248,254),(249,279),(250,257),(251,264),(252,208),(252,260),(253,256),(253,279),(254,78),(254,278),(255,278),(256,237),(257,244),(258,25),(258,213),(258,274),(259,108),(260,137),(260,226),(261,107),(261,218),(261,224),(262,136),(262,175),(262,273),(263,108),(263,182),(264,151),(264,272),(265,153),(265,180),(266,127),(266,164),(267,143),(267,164),(268,105),(268,217),(269,111),(270,154),(270,245),(271,141),(271,279),(272,95),(273,94),(273,227),(273,233),(274,152),(274,251),(275,129),(275,242),(276,138),(276,278),(277,103),(277,149),(277,216),(278,126),(279,98),(279,237)],280)
=> ? = 28
[1,1,1,1,1,0,0,0,0,0]
=> [[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0]]
=> [[1,2,3,4,5],[2,3,4,5],[3,4,5],[4,5],[5]]
=> 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=> ? = 42
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,4,4],[5,5],[6]]
=> ([],1)
=> 1
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [[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)
=> 2
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[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)
=> 2
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [[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,-1,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,4,5],[5,6],[6]]
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,5,6],[5,6],[6]]
=> ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8)
=> ? = 5
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[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)
=> 2
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[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)
=> 4
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,4],[4,4,5],[5,5],[6]]
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,4],[4,4,5],[5,6],[6]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,4],[4,5,6],[5,6],[6]]
=> ([(0,5),(0,6),(1,8),(2,9),(3,8),(3,9),(4,1),(5,4),(6,7),(7,2),(7,3),(8,10),(9,10)],11)
=> ? = 7
[1,0,1,0,1,1,1,0,0,0,1,0]
=> [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,4,5],[4,4,5],[5,5],[6]]
=> ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8)
=> ? = 5
[1,0,1,0,1,1,1,0,0,1,0,0]
=> [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,4,5],[4,4,5],[5,6],[6]]
=> ([(0,3),(0,7),(1,8),(2,8),(3,9),(4,5),(5,1),(6,2),(7,4),(7,9),(9,6)],10)
=> ? = 7
[1,0,1,0,1,1,1,0,1,0,0,0]
=> [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,4,5],[4,5,6],[5,6],[6]]
=> ([(0,9),(0,11),(1,18),(2,17),(3,19),(4,13),(4,19),(5,12),(5,13),(6,16),(7,14),(8,5),(8,18),(9,10),(10,3),(10,4),(11,1),(11,8),(12,17),(13,15),(15,16),(16,14),(17,7),(18,2),(18,12),(19,6),(19,15)],20)
=> ? = 9
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,4,5,6],[4,5,6],[5,6],[6]]
=> ([(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)
=> ? = 14
[1,0,1,1,0,0,1,0,1,0,1,0]
=> [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[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)
=> 2
[1,0,1,1,0,0,1,0,1,1,0,0]
=> [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[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)
=> 4
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[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)
=> 4
[1,0,1,1,0,0,1,1,0,1,0,0]
=> [[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,-1,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,3],[4,4,5],[5,6],[6]]
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 6
[1,0,1,1,0,0,1,1,1,0,0,0]
=> [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,3],[4,5,6],[5,6],[6]]
=> ([(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)
=> ? = 10
[1,0,1,1,0,1,0,0,1,0,1,0]
=> [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,4],[4,4,4],[5,5],[6]]
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,1,0,1,0,0,1,1,0,0]
=> [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,4],[4,4,4],[5,6],[6]]
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 6
[1,0,1,1,0,1,0,1,0,0,1,0]
=> [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,4],[4,4,5],[5,5],[6]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[1,0,1,1,0,1,0,1,0,1,0,0]
=> [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,4],[4,4,5],[5,6],[6]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[1,0,1,1,0,1,0,1,1,0,0,0]
=> [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,4],[4,5,6],[5,6],[6]]
=> ([(0,6),(0,7),(1,11),(2,9),(3,9),(3,10),(4,2),(5,1),(5,10),(6,4),(7,8),(8,3),(8,5),(9,12),(10,11),(10,12),(11,13),(12,13)],14)
=> ? = 9
[1,0,1,1,0,1,1,0,0,0,1,0]
=> [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,4,5],[4,4,5],[5,5],[6]]
=> ([(0,5),(0,6),(1,8),(2,9),(3,8),(3,9),(4,1),(5,4),(6,7),(7,2),(7,3),(8,10),(9,10)],11)
=> ? = 7
[1,0,1,1,0,1,1,0,0,1,0,0]
=> [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,4,5],[4,4,5],[5,6],[6]]
=> ([(0,4),(0,7),(1,9),(2,10),(3,9),(3,10),(4,11),(5,8),(6,1),(7,5),(7,11),(8,2),(8,3),(9,12),(10,12),(11,6)],13)
=> ? = 9
[1,0,1,1,0,1,1,0,1,0,0,0]
=> [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,0,1,0],[0,0,0,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,4,5],[4,5,6],[5,6],[6]]
=> ([(0,10),(0,12),(1,23),(2,22),(3,14),(3,24),(4,15),(5,13),(5,14),(6,18),(7,16),(7,20),(8,5),(8,23),(9,4),(9,24),(10,11),(11,3),(11,9),(12,1),(12,8),(13,22),(14,19),(15,16),(15,21),(16,25),(18,17),(19,20),(19,21),(20,18),(20,25),(21,25),(22,6),(23,2),(23,13),(24,7),(24,15),(24,19),(25,17)],26)
=> ? = 12
[1,0,1,1,0,1,1,1,0,0,0,0]
=> [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,4,5,6],[4,5,6],[5,6],[6]]
=> ([(0,5),(0,14),(0,15),(1,26),(2,9),(2,25),(3,13),(3,24),(4,16),(5,11),(5,12),(6,69),(7,64),(8,49),(9,6),(9,52),(10,20),(10,59),(11,19),(11,65),(12,17),(12,65),(13,18),(13,22),(13,71),(14,2),(14,29),(15,3),(15,29),(16,39),(16,55),(17,56),(17,68),(18,57),(18,66),(19,58),(19,67),(20,51),(20,53),(21,40),(21,41),(22,57),(22,72),(23,28),(23,54),(23,70),(24,58),(24,71),(25,52),(25,56),(26,27),(26,69),(26,72),(27,45),(27,60),(28,34),(28,48),(28,50),(29,1),(30,76),(31,75),(32,77),(33,74),(33,80),(34,73),(34,78),(35,73),(35,77),(36,82),(37,79),(38,80),(39,74),(40,7),(40,76),(41,8),(41,76),(42,55),(42,79),(43,59),(44,39),(45,53),(45,83),(46,33),(46,81),(47,32),(47,83),(48,42),(48,78),(49,44),(50,46),(50,73),(51,44),(52,10),(52,43),(53,62),(54,34),(54,75),(55,36),(55,74),(56,43),(57,63),(58,61),(59,49),(59,51),(60,35),(60,50),(60,83),(61,31),(61,70),(62,33),(62,38),(63,32),(63,35),(64,37),(64,42),(65,21),(65,67),(65,68),(66,31),(66,54),(67,30),(67,40),(68,30),(68,41),(69,45),(69,47),(70,48),(70,64),(70,75),(71,23),(71,61),(71,66),(72,47),(72,60),(72,63),(73,81),(74,82),(75,37),(75,78),(76,4),(77,38),(77,81),(78,79),(79,36),(80,82),(81,80),(83,46),(83,62),(83,77)],84)
=> ? = 19
[1,0,1,1,1,0,0,0,1,0,1,0]
=> [[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,3,4],[3,3,3,4],[4,4,4],[5,5],[6]]
=> ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8)
=> ? = 5
[1,0,1,1,1,0,0,0,1,1,0,0]
=> [[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,1],[2,2,2,3,4],[3,3,3,4],[4,4,4],[5,6],[6]]
=> ([(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)
=> ? = 10
[1,0,1,1,1,0,0,1,0,0,1,0]
=> [[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,3,4],[3,3,3,4],[4,4,5],[5,5],[6]]
=> ([(0,3),(0,7),(1,8),(2,8),(3,9),(4,5),(5,1),(6,2),(7,4),(7,9),(9,6)],10)
=> ? = 7
[1,0,1,1,1,0,0,1,0,1,0,0]
=> [[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,1],[2,2,2,3,4],[3,3,3,4],[4,4,5],[5,6],[6]]
=> ([(0,3),(0,8),(1,10),(2,10),(3,9),(4,6),(5,4),(5,11),(6,2),(7,1),(8,5),(8,9),(9,11),(11,7)],12)
=> ? = 9
[1,0,1,1,1,0,0,1,1,0,0,0]
=> [[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]]
=> [[1,1,1,1,1,1],[2,2,2,3,4],[3,3,3,4],[4,5,6],[5,6],[6]]
=> ([(0,7),(0,8),(0,11),(1,25),(2,10),(2,24),(3,5),(3,12),(3,26),(4,28),(5,6),(5,29),(6,4),(6,27),(7,2),(7,19),(8,3),(8,18),(9,15),(9,16),(10,13),(10,23),(11,18),(11,19),(12,22),(12,23),(12,29),(13,31),(14,30),(15,30),(16,30),(17,20),(18,26),(19,24),(20,14),(21,16),(22,25),(22,31),(23,17),(23,31),(24,13),(25,9),(25,21),(26,1),(26,22),(27,20),(27,28),(28,14),(28,15),(29,17),(29,27),(31,21)],32)
=> ? = 16
[1,1,0,0,1,0,1,0,1,0,1,0]
=> [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[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)
=> 2
[1,1,0,0,1,0,1,0,1,1,0,0]
=> [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[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)
=> 4
[1,1,0,0,1,0,1,1,0,0,1,0]
=> [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[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)
=> 4
Description
The largest size of an interval in a poset.
Matching statistic: St001300
Mp00137: Dyck paths —to symmetric ASM⟶ Alternating sign matrices
Mp00001: Alternating sign matrices —to semistandard tableau via monotone triangles⟶ Semistandard tableaux
Mp00214: Semistandard tableaux —subcrystal⟶ Posets
St001300: Posets ⟶ ℤResult quality: 6% ●values known / values provided: 6%●distinct values known / distinct values provided: 8%
Mp00001: Alternating sign matrices —to semistandard tableau via monotone triangles⟶ Semistandard tableaux
Mp00214: Semistandard tableaux —subcrystal⟶ Posets
St001300: Posets ⟶ ℤResult quality: 6% ●values known / values provided: 6%●distinct values known / distinct values provided: 8%
Values
[1,0]
=> [[1]]
=> [[1]]
=> ([],1)
=> 0 = 1 - 1
[1,0,1,0]
=> [[1,0],[0,1]]
=> [[1,1],[2]]
=> ([],1)
=> 0 = 1 - 1
[1,1,0,0]
=> [[0,1],[1,0]]
=> [[1,2],[2]]
=> ([(0,1)],2)
=> 1 = 2 - 1
[1,0,1,0,1,0]
=> [[1,0,0],[0,1,0],[0,0,1]]
=> [[1,1,1],[2,2],[3]]
=> ([],1)
=> 0 = 1 - 1
[1,0,1,1,0,0]
=> [[1,0,0],[0,0,1],[0,1,0]]
=> [[1,1,1],[2,3],[3]]
=> ([(0,1)],2)
=> 1 = 2 - 1
[1,1,0,0,1,0]
=> [[0,1,0],[1,0,0],[0,0,1]]
=> [[1,1,2],[2,2],[3]]
=> ([(0,1)],2)
=> 1 = 2 - 1
[1,1,0,1,0,0]
=> [[0,1,0],[1,-1,1],[0,1,0]]
=> [[1,1,2],[2,3],[3]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
[1,1,1,0,0,0]
=> [[0,0,1],[0,1,0],[1,0,0]]
=> [[1,2,3],[2,3],[3]]
=> ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8)
=> ? = 5 - 1
[1,0,1,0,1,0,1,0]
=> [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,2],[3,3],[4]]
=> ([],1)
=> 0 = 1 - 1
[1,0,1,0,1,1,0,0]
=> [[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 = 2 - 1
[1,0,1,1,0,0,1,0]
=> [[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 = 2 - 1
[1,0,1,1,0,1,0,0]
=> [[1,0,0,0],[0,0,1,0],[0,1,-1,1],[0,0,1,0]]
=> [[1,1,1,1],[2,2,3],[3,4],[4]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
[1,0,1,1,1,0,0,0]
=> [[1,0,0,0],[0,0,0,1],[0,0,1,0],[0,1,0,0]]
=> [[1,1,1,1],[2,3,4],[3,4],[4]]
=> ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8)
=> ? = 5 - 1
[1,1,0,0,1,0,1,0]
=> [[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 = 2 - 1
[1,1,0,0,1,1,0,0]
=> [[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 = 4 - 1
[1,1,0,1,0,0,1,0]
=> [[0,1,0,0],[1,-1,1,0],[0,1,0,0],[0,0,0,1]]
=> [[1,1,1,2],[2,2,3],[3,3],[4]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
[1,1,0,1,0,1,0,0]
=> [[0,1,0,0],[1,-1,1,0],[0,1,-1,1],[0,0,1,0]]
=> [[1,1,1,2],[2,2,3],[3,4],[4]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3 = 4 - 1
[1,1,0,1,1,0,0,0]
=> [[0,1,0,0],[1,-1,0,1],[0,0,1,0],[0,1,0,0]]
=> [[1,1,1,2],[2,3,4],[3,4],[4]]
=> ([(0,5),(0,6),(1,8),(2,9),(3,8),(3,9),(4,1),(5,4),(6,7),(7,2),(7,3),(8,10),(9,10)],11)
=> ? = 7 - 1
[1,1,1,0,0,0,1,0]
=> [[0,0,1,0],[0,1,0,0],[1,0,0,0],[0,0,0,1]]
=> [[1,1,2,3],[2,2,3],[3,3],[4]]
=> ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8)
=> ? = 5 - 1
[1,1,1,0,0,1,0,0]
=> [[0,0,1,0],[0,1,0,0],[1,0,-1,1],[0,0,1,0]]
=> [[1,1,2,3],[2,2,3],[3,4],[4]]
=> ([(0,3),(0,7),(1,8),(2,8),(3,9),(4,5),(5,1),(6,2),(7,4),(7,9),(9,6)],10)
=> ? = 7 - 1
[1,1,1,0,1,0,0,0]
=> [[0,0,1,0],[0,1,-1,1],[1,-1,1,0],[0,1,0,0]]
=> [[1,1,2,3],[2,3,4],[3,4],[4]]
=> ([(0,9),(0,11),(1,18),(2,17),(3,19),(4,13),(4,19),(5,12),(5,13),(6,16),(7,14),(8,5),(8,18),(9,10),(10,3),(10,4),(11,1),(11,8),(12,17),(13,15),(15,16),(16,14),(17,7),(18,2),(18,12),(19,6),(19,15)],20)
=> ? = 9 - 1
[1,1,1,1,0,0,0,0]
=> [[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)
=> ? = 14 - 1
[1,0,1,0,1,0,1,0,1,0]
=> [[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]]
=> [[1,1,1,1,1],[2,2,2,2],[3,3,3],[4,4],[5]]
=> ([],1)
=> 0 = 1 - 1
[1,0,1,0,1,0,1,1,0,0]
=> [[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 = 2 - 1
[1,0,1,0,1,1,0,0,1,0]
=> [[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 = 2 - 1
[1,0,1,0,1,1,0,1,0,0]
=> [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
=> [[1,1,1,1,1],[2,2,2,2],[3,3,4],[4,5],[5]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
[1,0,1,0,1,1,1,0,0,0]
=> [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0]]
=> [[1,1,1,1,1],[2,2,2,2],[3,4,5],[4,5],[5]]
=> ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8)
=> ? = 5 - 1
[1,0,1,1,0,0,1,0,1,0]
=> [[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 = 2 - 1
[1,0,1,1,0,0,1,1,0,0]
=> [[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 = 4 - 1
[1,0,1,1,0,1,0,0,1,0]
=> [[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [[1,1,1,1,1],[2,2,2,3],[3,3,4],[4,4],[5]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
[1,0,1,1,0,1,0,1,0,0]
=> [[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
=> [[1,1,1,1,1],[2,2,2,3],[3,3,4],[4,5],[5]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3 = 4 - 1
[1,0,1,1,0,1,1,0,0,0]
=> [[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,0,1],[0,0,0,1,0],[0,0,1,0,0]]
=> [[1,1,1,1,1],[2,2,2,3],[3,4,5],[4,5],[5]]
=> ([(0,5),(0,6),(1,8),(2,9),(3,8),(3,9),(4,1),(5,4),(6,7),(7,2),(7,3),(8,10),(9,10)],11)
=> ? = 7 - 1
[1,0,1,1,1,0,0,0,1,0]
=> [[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [[1,1,1,1,1],[2,2,3,4],[3,3,4],[4,4],[5]]
=> ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8)
=> ? = 5 - 1
[1,0,1,1,1,0,0,1,0,0]
=> [[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,-1,1],[0,0,0,1,0]]
=> [[1,1,1,1,1],[2,2,3,4],[3,3,4],[4,5],[5]]
=> ([(0,3),(0,7),(1,8),(2,8),(3,9),(4,5),(5,1),(6,2),(7,4),(7,9),(9,6)],10)
=> ? = 7 - 1
[1,0,1,1,1,0,1,0,0,0]
=> [[1,0,0,0,0],[0,0,0,1,0],[0,0,1,-1,1],[0,1,-1,1,0],[0,0,1,0,0]]
=> [[1,1,1,1,1],[2,2,3,4],[3,4,5],[4,5],[5]]
=> ([(0,9),(0,11),(1,18),(2,17),(3,19),(4,13),(4,19),(5,12),(5,13),(6,16),(7,14),(8,5),(8,18),(9,10),(10,3),(10,4),(11,1),(11,8),(12,17),(13,15),(15,16),(16,14),(17,7),(18,2),(18,12),(19,6),(19,15)],20)
=> ? = 9 - 1
[1,0,1,1,1,1,0,0,0,0]
=> [[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)
=> ? = 14 - 1
[1,1,0,0,1,0,1,0,1,0]
=> [[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 = 2 - 1
[1,1,0,0,1,0,1,1,0,0]
=> [[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 = 4 - 1
[1,1,0,0,1,1,0,0,1,0]
=> [[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 = 4 - 1
[1,1,0,0,1,1,0,1,0,0]
=> [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
=> [[1,1,1,1,2],[2,2,2,2],[3,3,4],[4,5],[5]]
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 5 = 6 - 1
[1,1,0,0,1,1,1,0,0,0]
=> [[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)
=> ? = 10 - 1
[1,1,0,1,0,0,1,0,1,0]
=> [[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
=> [[1,1,1,1,2],[2,2,2,3],[3,3,3],[4,4],[5]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
[1,1,0,1,0,0,1,1,0,0]
=> [[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
=> [[1,1,1,1,2],[2,2,2,3],[3,3,3],[4,5],[5]]
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 5 = 6 - 1
[1,1,0,1,0,1,0,0,1,0]
=> [[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [[1,1,1,1,2],[2,2,2,3],[3,3,4],[4,4],[5]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3 = 4 - 1
[1,1,0,1,0,1,0,1,0,0]
=> [[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
=> [[1,1,1,1,2],[2,2,2,3],[3,3,4],[4,5],[5]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4 = 5 - 1
[1,1,0,1,0,1,1,0,0,0]
=> [[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,0,1],[0,0,0,1,0],[0,0,1,0,0]]
=> [[1,1,1,1,2],[2,2,2,3],[3,4,5],[4,5],[5]]
=> ([(0,6),(0,7),(1,11),(2,9),(3,9),(3,10),(4,2),(5,1),(5,10),(6,4),(7,8),(8,3),(8,5),(9,12),(10,11),(10,12),(11,13),(12,13)],14)
=> ? = 9 - 1
[1,1,0,1,1,0,0,0,1,0]
=> [[0,1,0,0,0],[1,-1,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [[1,1,1,1,2],[2,2,3,4],[3,3,4],[4,4],[5]]
=> ([(0,5),(0,6),(1,8),(2,9),(3,8),(3,9),(4,1),(5,4),(6,7),(7,2),(7,3),(8,10),(9,10)],11)
=> ? = 7 - 1
[1,1,0,1,1,0,0,1,0,0]
=> [[0,1,0,0,0],[1,-1,0,1,0],[0,0,1,0,0],[0,1,0,-1,1],[0,0,0,1,0]]
=> [[1,1,1,1,2],[2,2,3,4],[3,3,4],[4,5],[5]]
=> ([(0,4),(0,7),(1,9),(2,10),(3,9),(3,10),(4,11),(5,8),(6,1),(7,5),(7,11),(8,2),(8,3),(9,12),(10,12),(11,6)],13)
=> ? = 9 - 1
[1,1,0,1,1,0,1,0,0,0]
=> [[0,1,0,0,0],[1,-1,0,1,0],[0,0,1,-1,1],[0,1,-1,1,0],[0,0,1,0,0]]
=> [[1,1,1,1,2],[2,2,3,4],[3,4,5],[4,5],[5]]
=> ([(0,10),(0,12),(1,23),(2,22),(3,14),(3,24),(4,15),(5,13),(5,14),(6,18),(7,16),(7,20),(8,5),(8,23),(9,4),(9,24),(10,11),(11,3),(11,9),(12,1),(12,8),(13,22),(14,19),(15,16),(15,21),(16,25),(18,17),(19,20),(19,21),(20,18),(20,25),(21,25),(22,6),(23,2),(23,13),(24,7),(24,15),(24,19),(25,17)],26)
=> ? = 12 - 1
[1,1,0,1,1,1,0,0,0,0]
=> [[0,1,0,0,0],[1,-1,0,0,1],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0]]
=> [[1,1,1,1,2],[2,3,4,5],[3,4,5],[4,5],[5]]
=> ([(0,5),(0,14),(0,15),(1,26),(2,9),(2,25),(3,13),(3,24),(4,16),(5,11),(5,12),(6,69),(7,64),(8,49),(9,6),(9,52),(10,20),(10,59),(11,19),(11,65),(12,17),(12,65),(13,18),(13,22),(13,71),(14,2),(14,29),(15,3),(15,29),(16,39),(16,55),(17,56),(17,68),(18,57),(18,66),(19,58),(19,67),(20,51),(20,53),(21,40),(21,41),(22,57),(22,72),(23,28),(23,54),(23,70),(24,58),(24,71),(25,52),(25,56),(26,27),(26,69),(26,72),(27,45),(27,60),(28,34),(28,48),(28,50),(29,1),(30,76),(31,75),(32,77),(33,74),(33,80),(34,73),(34,78),(35,73),(35,77),(36,82),(37,79),(38,80),(39,74),(40,7),(40,76),(41,8),(41,76),(42,55),(42,79),(43,59),(44,39),(45,53),(45,83),(46,33),(46,81),(47,32),(47,83),(48,42),(48,78),(49,44),(50,46),(50,73),(51,44),(52,10),(52,43),(53,62),(54,34),(54,75),(55,36),(55,74),(56,43),(57,63),(58,61),(59,49),(59,51),(60,35),(60,50),(60,83),(61,31),(61,70),(62,33),(62,38),(63,32),(63,35),(64,37),(64,42),(65,21),(65,67),(65,68),(66,31),(66,54),(67,30),(67,40),(68,30),(68,41),(69,45),(69,47),(70,48),(70,64),(70,75),(71,23),(71,61),(71,66),(72,47),(72,60),(72,63),(73,81),(74,82),(75,37),(75,78),(76,4),(77,38),(77,81),(78,79),(79,36),(80,82),(81,80),(83,46),(83,62),(83,77)],84)
=> ? = 19 - 1
[1,1,1,0,0,0,1,0,1,0]
=> [[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
=> [[1,1,1,2,3],[2,2,2,3],[3,3,3],[4,4],[5]]
=> ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8)
=> ? = 5 - 1
[1,1,1,0,0,0,1,1,0,0]
=> [[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)
=> ? = 10 - 1
[1,1,1,0,0,1,0,0,1,0]
=> [[0,0,1,0,0],[0,1,0,0,0],[1,0,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [[1,1,1,2,3],[2,2,2,3],[3,3,4],[4,4],[5]]
=> ([(0,3),(0,7),(1,8),(2,8),(3,9),(4,5),(5,1),(6,2),(7,4),(7,9),(9,6)],10)
=> ? = 7 - 1
[1,1,1,0,0,1,0,1,0,0]
=> [[0,0,1,0,0],[0,1,0,0,0],[1,0,-1,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
=> [[1,1,1,2,3],[2,2,2,3],[3,3,4],[4,5],[5]]
=> ([(0,3),(0,8),(1,10),(2,10),(3,9),(4,6),(5,4),(5,11),(6,2),(7,1),(8,5),(8,9),(9,11),(11,7)],12)
=> ? = 9 - 1
[1,1,1,0,0,1,1,0,0,0]
=> [[0,0,1,0,0],[0,1,0,0,0],[1,0,-1,0,1],[0,0,0,1,0],[0,0,1,0,0]]
=> [[1,1,1,2,3],[2,2,2,3],[3,4,5],[4,5],[5]]
=> ([(0,7),(0,8),(0,11),(1,25),(2,10),(2,24),(3,5),(3,12),(3,26),(4,28),(5,6),(5,29),(6,4),(6,27),(7,2),(7,19),(8,3),(8,18),(9,15),(9,16),(10,13),(10,23),(11,18),(11,19),(12,22),(12,23),(12,29),(13,31),(14,30),(15,30),(16,30),(17,20),(18,26),(19,24),(20,14),(21,16),(22,25),(22,31),(23,17),(23,31),(24,13),(25,9),(25,21),(26,1),(26,22),(27,20),(27,28),(28,14),(28,15),(29,17),(29,27),(31,21)],32)
=> ? = 16 - 1
[1,1,1,0,1,0,0,0,1,0]
=> [[0,0,1,0,0],[0,1,-1,1,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [[1,1,1,2,3],[2,2,3,4],[3,3,4],[4,4],[5]]
=> ([(0,9),(0,11),(1,18),(2,17),(3,19),(4,13),(4,19),(5,12),(5,13),(6,16),(7,14),(8,5),(8,18),(9,10),(10,3),(10,4),(11,1),(11,8),(12,17),(13,15),(15,16),(16,14),(17,7),(18,2),(18,12),(19,6),(19,15)],20)
=> ? = 9 - 1
[1,1,1,0,1,0,0,1,0,0]
=> [[0,0,1,0,0],[0,1,-1,1,0],[1,-1,1,0,0],[0,1,0,-1,1],[0,0,0,1,0]]
=> [[1,1,1,2,3],[2,2,3,4],[3,3,4],[4,5],[5]]
=> ([(0,10),(0,11),(1,13),(1,14),(2,21),(3,20),(4,14),(4,20),(5,17),(6,16),(7,18),(8,12),(9,1),(9,22),(10,5),(10,15),(11,8),(11,15),(12,3),(12,4),(13,21),(14,19),(15,9),(15,17),(17,22),(18,16),(19,18),(20,7),(20,19),(21,6),(22,2),(22,13)],23)
=> ? = 12 - 1
[1,1,1,0,1,0,1,0,0,0]
=> [[0,0,1,0,0],[0,1,-1,1,0],[1,-1,1,-1,1],[0,1,-1,1,0],[0,0,1,0,0]]
=> [[1,1,1,2,3],[2,2,3,4],[3,4,5],[4,5],[5]]
=> ([(0,2),(0,3),(1,9),(1,15),(2,1),(3,7),(3,8),(4,30),(5,31),(6,23),(7,16),(7,37),(8,10),(8,37),(9,11),(9,36),(10,34),(11,35),(12,25),(12,29),(13,19),(13,22),(14,21),(14,27),(15,26),(15,36),(16,26),(16,33),(17,39),(18,38),(19,12),(19,38),(20,6),(21,4),(21,39),(22,5),(22,38),(24,23),(25,28),(26,32),(27,25),(27,39),(28,24),(29,20),(30,24),(31,20),(32,17),(32,27),(33,18),(33,19),(34,18),(34,22),(35,17),(35,21),(36,14),(36,32),(36,35),(37,13),(37,33),(37,34),(38,29),(38,31),(39,28),(39,30)],40)
=> ? = 14 - 1
[1,1,1,0,1,1,0,0,0,0]
=> [[0,0,1,0,0],[0,1,-1,0,1],[1,-1,0,1,0],[0,0,1,0,0],[0,1,0,0,0]]
=> [[1,1,1,2,3],[2,3,4,5],[3,4,5],[4,5],[5]]
=> ([(0,4),(0,14),(0,15),(1,29),(2,6),(2,27),(3,13),(3,28),(4,10),(4,11),(5,102),(6,5),(6,87),(7,31),(7,99),(8,25),(8,98),(9,26),(9,72),(10,23),(10,109),(11,24),(11,33),(11,109),(12,22),(12,108),(13,17),(13,18),(13,107),(14,2),(14,38),(15,3),(15,38),(16,84),(16,85),(17,90),(17,111),(18,90),(18,101),(19,82),(19,83),(20,81),(20,100),(21,34),(21,89),(21,104),(22,86),(22,106),(23,91),(23,110),(24,80),(24,105),(25,78),(25,79),(26,52),(26,88),(27,87),(27,103),(28,91),(28,107),(29,30),(29,102),(29,111),(30,63),(30,96),(31,44),(31,71),(31,76),(32,37),(32,51),(32,77),(33,80),(33,94),(33,103),(34,62),(34,74),(34,75),(35,133),(36,9),(37,8),(37,127),(38,1),(39,118),(40,117),(40,122),(41,119),(42,119),(42,126),(43,116),(43,127),(44,112),(44,120),(45,112),(45,113),(46,114),(46,116),(47,121),(48,122),(49,125),(50,113),(51,20),(51,114),(51,127),(52,117),(53,72),(54,88),(54,121),(55,45),(55,132),(56,48),(57,84),(57,124),(58,76),(58,134),(59,66),(60,56),(61,54),(62,55),(62,126),(63,86),(63,129),(64,53),(64,134),(65,47),(66,70),(67,40),(68,40),(68,123),(69,41),(69,129),(70,39),(70,128),(71,54),(71,120),(72,52),(73,44),(73,118),(74,58),(74,115),(75,82),(75,115),(75,126),(76,68),(76,112),(77,16),(77,57),(77,114),(78,65),(79,61),(80,59),(80,130),(81,36),(82,60),(82,131),(83,53),(83,131),(84,78),(84,128),(85,73),(85,128),(86,92),(87,12),(87,95),(88,49),(88,117),(89,19),(89,75),(89,133),(90,97),(91,93),(92,45),(92,50),(93,35),(93,104),(94,46),(94,77),(94,130),(95,66),(95,108),(96,42),(96,62),(96,129),(97,41),(97,42),(98,36),(98,79),(99,61),(99,71),(100,58),(100,64),(101,35),(101,89),(102,63),(102,69),(103,59),(103,95),(104,74),(104,100),(104,133),(105,37),(105,43),(105,130),(106,39),(106,73),(107,21),(107,93),(107,101),(108,70),(108,85),(108,106),(109,32),(109,94),(109,105),(109,110),(110,43),(110,46),(110,51),(111,69),(111,96),(111,97),(112,123),(113,48),(113,123),(114,7),(114,124),(115,131),(115,134),(116,124),(117,125),(118,47),(118,120),(119,50),(119,132),(120,121),(121,49),(122,125),(123,122),(124,99),(126,60),(126,132),(127,81),(127,98),(128,65),(128,118),(129,55),(129,92),(129,119),(130,57),(130,116),(131,67),(132,56),(132,113),(133,64),(133,83),(133,115),(134,67),(134,68)],135)
=> ? = 23 - 1
[1,1,1,1,0,0,0,0,1,0]
=> [[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)
=> ? = 14 - 1
[1,1,1,1,0,0,0,1,0,0]
=> [[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[1,0,0,-1,1],[0,0,0,1,0]]
=> [[1,1,2,3,4],[2,2,3,4],[3,3,4],[4,5],[5]]
=> ([(0,16),(0,17),(0,28),(1,22),(2,19),(3,11),(3,21),(4,54),(5,55),(6,26),(6,57),(7,25),(7,67),(8,23),(8,64),(9,24),(9,65),(10,14),(10,56),(11,15),(11,58),(12,3),(12,37),(13,27),(13,66),(14,59),(15,60),(16,13),(16,53),(17,6),(17,61),(18,51),(18,52),(19,33),(19,34),(20,35),(20,36),(21,50),(21,58),(22,18),(22,59),(22,60),(23,41),(23,43),(24,42),(24,44),(25,50),(25,63),(26,29),(26,46),(27,29),(27,45),(28,12),(28,53),(28,61),(29,70),(30,71),(31,69),(32,68),(33,68),(34,68),(35,4),(35,69),(36,5),(36,69),(37,1),(38,33),(39,34),(40,64),(41,48),(42,49),(43,38),(44,39),(45,62),(45,70),(46,56),(46,70),(47,65),(48,32),(49,32),(50,40),(51,42),(51,71),(52,41),(52,71),(53,7),(53,66),(54,38),(55,39),(56,9),(56,47),(57,10),(57,46),(58,8),(58,40),(59,30),(59,51),(60,30),(60,52),(61,37),(61,57),(62,31),(62,36),(63,31),(63,35),(64,43),(64,54),(65,44),(65,55),(66,45),(66,67),(67,20),(67,62),(67,63),(69,2),(70,47),(71,48),(71,49)],72)
=> ? = 19 - 1
[1,1,1,1,0,0,1,0,0,0]
=> [[0,0,0,1,0],[0,0,1,0,0],[0,1,0,-1,1],[1,0,-1,1,0],[0,0,1,0,0]]
=> [[1,1,2,3,4],[2,2,3,4],[3,4,5],[4,5],[5]]
=> ([(0,15),(0,16),(0,30),(1,26),(2,14),(2,95),(3,78),(4,79),(5,92),(6,77),(7,29),(7,93),(8,27),(8,96),(9,28),(9,94),(10,12),(10,32),(10,80),(11,84),(12,13),(12,86),(13,11),(13,97),(14,19),(14,98),(15,10),(15,54),(16,2),(16,24),(16,76),(17,47),(17,71),(18,46),(18,72),(19,41),(19,91),(20,35),(20,73),(21,69),(21,87),(22,25),(22,75),(22,90),(23,45),(23,70),(24,31),(24,88),(24,95),(25,49),(25,50),(26,39),(26,40),(27,52),(27,53),(28,41),(28,89),(29,33),(29,57),(30,54),(30,76),(31,67),(31,68),(31,85),(32,56),(32,68),(32,86),(33,110),(34,106),(34,107),(35,21),(35,111),(36,100),(37,101),(37,106),(38,102),(39,102),(40,102),(41,99),(42,104),(43,113),(44,103),(45,6),(45,112),(46,7),(46,108),(47,5),(47,107),(48,3),(48,103),(49,55),(49,105),(50,33),(50,105),(51,61),(52,63),(53,61),(54,80),(55,52),(55,113),(56,79),(56,109),(57,60),(57,110),(58,90),(59,81),(60,62),(61,39),(62,40),(63,38),(64,38),(65,37),(65,111),(66,36),(66,108),(67,82),(67,109),(68,83),(68,109),(69,59),(70,48),(70,112),(71,42),(71,107),(72,69),(72,108),(73,23),(73,74),(73,111),(74,45),(74,101),(75,50),(75,100),(76,9),(76,88),(77,51),(78,62),(79,22),(79,58),(80,4),(80,56),(81,60),(81,78),(82,34),(82,47),(83,66),(83,72),(84,36),(84,75),(85,35),(85,65),(86,18),(86,83),(86,97),(87,44),(87,48),(88,67),(88,94),(89,34),(89,71),(89,99),(90,49),(90,92),(90,100),(91,37),(91,74),(91,99),(92,43),(92,55),(93,57),(93,81),(94,17),(94,82),(94,89),(95,20),(95,85),(95,98),(96,51),(96,53),(97,46),(97,66),(97,84),(98,65),(98,73),(98,91),(99,42),(99,106),(100,43),(100,105),(101,44),(101,112),(103,1),(104,96),(105,110),(105,113),(106,104),(107,8),(107,104),(108,59),(108,93),(109,58),(110,64),(111,70),(111,87),(111,101),(112,77),(112,103),(113,63),(113,64)],114)
=> ? = 23 - 1
[1,1,1,1,0,1,0,0,0,0]
=> [[0,0,0,1,0],[0,0,1,-1,1],[0,1,-1,1,0],[1,-1,1,0,0],[0,1,0,0,0]]
=> [[1,1,2,3,4],[2,3,4,5],[3,4,5],[4,5],[5]]
=> ([(0,2),(0,17),(0,18),(1,16),(1,41),(2,10),(2,15),(3,207),(4,50),(4,125),(5,181),(6,49),(6,180),(7,188),(8,138),(9,46),(9,208),(10,30),(10,206),(11,35),(11,54),(12,36),(12,97),(13,37),(13,163),(14,40),(14,44),(14,202),(15,28),(15,45),(15,206),(16,26),(16,27),(16,203),(17,1),(17,124),(18,14),(18,33),(18,124),(19,52),(19,201),(19,211),(20,196),(20,200),(21,89),(21,155),(22,149),(22,156),(23,150),(23,198),(24,154),(24,199),(25,90),(25,152),(26,162),(26,210),(27,162),(27,197),(28,159),(28,191),(29,153),(29,190),(30,161),(30,209),(31,144),(31,157),(32,141),(32,151),(33,145),(33,202),(34,143),(34,189),(35,147),(35,148),(36,142),(36,146),(37,88),(37,195),(38,87),(38,192),(39,51),(39,158),(39,194),(40,42),(40,160),(40,193),(41,161),(41,203),(42,102),(42,170),(43,122),(43,123),(43,178),(44,120),(44,160),(44,179),(45,159),(45,177),(45,179),(46,76),(46,119),(46,183),(47,64),(47,121),(47,140),(48,65),(48,86),(48,139),(49,60),(49,92),(49,93),(50,43),(50,169),(50,170),(50,210),(51,99),(51,100),(51,101),(52,104),(52,109),(52,165),(53,272),(54,13),(55,225),(55,275),(56,218),(56,219),(57,227),(57,270),(58,227),(58,269),(59,12),(60,219),(60,226),(61,255),(61,276),(62,253),(62,271),(63,277),(64,269),(64,270),(65,6),(65,265),(66,230),(67,231),(67,256),(68,236),(68,271),(69,236),(69,249),(70,229),(70,247),(71,214),(71,228),(72,235),(73,228),(73,265),(74,213),(74,229),(75,234),(76,225),(76,241),(77,231),(77,234),(78,272),(79,250),(80,274),(81,260),(82,230),(83,232),(84,239),(84,254),(85,237),(86,29),(86,214),(86,265),(87,223),(88,215),(89,244),(90,32),(90,264),(91,97),(92,107),(92,219),(93,128),(93,226),(94,83),(94,275),(95,66),(96,119),(96,266),(97,142),(98,82),(99,96),(99,216),(100,136),(100,220),(101,156),(101,216),(101,220),(102,116),(102,268),(103,91),(103,266),(104,175),(104,259),(105,121),(105,263),(106,140),(106,263),(107,84),(107,248),(108,135),(109,166),(109,259),(110,133),(110,223),(111,69),(112,76),(112,224),(113,88),(113,213),(114,117),(114,262),(115,70),(115,224),(116,54),(117,58),(117,273),(118,57),(118,220),(118,273),(119,127),(119,225),(120,157),(120,212),(121,163),(121,269),(122,106),(122,217),(123,104),(123,217),(123,262),(124,4),(124,145),(125,5),(125,169),(126,155),(127,134),(127,242),(128,132),(128,238),(129,67),(129,240),(130,74),(130,243),(130,258),(131,67),(131,235),(132,146),(132,239),(132,276),(133,70),(133,218),(133,243),(134,77),(134,222),(134,240),(135,62),(135,215),(135,232),(136,55),(136,233),(137,61),(137,238),(138,21),(138,126),(139,23),(139,186),(139,214),(140,24),(140,182),(140,270),(141,98),(142,75),(142,222),(143,171),(144,11),(144,116),(145,125),(146,79),(146,222),(147,113),(147,258),(148,80),(148,258),(149,91),(149,267),(150,112),(150,261),(151,95),(152,53),(152,264),(153,59),(154,72),(154,246),(155,66),(155,244),(156,34),(156,187),(156,267),(157,38),(157,185),(158,22),(158,101),(158,277),(159,20),(159,168),(159,221),(160,19),(160,167),(160,212),(161,174),(162,3),(162,204),(163,111),(163,195),(164,134),(164,171),(165,112),(165,115),(166,74),(166,113),(167,173),(167,211),(168,173),(168,196),(169,122),(169,181),(169,268),(170,114),(170,123),(170,268),(171,75),(171,77),(172,115),(172,133),(172,261),(173,110),(173,172),(174,63),(174,194),(175,55),(175,94),(176,56),(176,60),(176,260),(177,71),(177,139),(177,221),(178,100),(178,118),(178,262),(179,167),(179,168),(180,59),(180,93),(181,47),(181,105),(181,106),(182,135),(182,199),(182,245),(183,61),(183,132),(183,241),(184,129),(184,131),(185,192),(185,205),(186,176),(186,198),(186,252),(187,184),(187,189),(188,53),(188,78),(189,72),(189,131),(190,96),(190,103),(191,65),(191,73),(191,221),(192,130),(192,148),(192,223),(193,102),(193,144),(193,212),(194,99),(194,190),(194,277),(195,68),(195,69),(195,215),(196,87),(196,110),(197,63),(197,158),(198,56),(198,92),(198,261),(199,62),(199,68),(199,246),(200,81),(200,176),(201,109),(201,205),(202,31),(202,120),(202,193),(203,39),(203,174),(203,197),(204,117),(204,118),(204,207),(205,130),(205,147),(205,166),(206,48),(206,177),(206,191),(206,209),(207,57),(207,58),(207,64),(208,128),(208,137),(208,183),(209,71),(209,73),(209,86),(210,114),(210,178),(210,204),(211,150),(211,165),(211,172),(212,185),(212,201),(213,90),(213,251),(214,9),(214,252),(215,249),(215,271),(216,266),(216,267),(217,259),(217,263),(218,247),(218,248),(219,7),(219,248),(220,187),(220,233),(221,186),(221,200),(221,228),(222,234),(222,250),(223,80),(223,243),(224,84),(224,241),(224,247),(225,242),(226,238),(227,83),(227,245),(228,81),(228,252),(229,251),(231,257),(232,249),(232,253),(233,184),(233,275),(234,89),(234,257),(235,85),(235,256),(236,85),(236,279),(237,82),(238,8),(238,276),(239,79),(239,278),(240,231),(240,250),(241,239),(241,255),(242,240),(243,229),(243,274),(244,230),(245,232),(245,246),(246,235),(246,236),(246,253),(247,254),(247,255),(248,188),(248,254),(249,279),(250,257),(251,264),(252,208),(252,260),(253,256),(253,279),(254,78),(254,278),(255,278),(256,237),(257,244),(258,25),(258,213),(258,274),(259,108),(260,137),(260,226),(261,107),(261,218),(261,224),(262,136),(262,175),(262,273),(263,108),(263,182),(264,151),(264,272),(265,153),(265,180),(266,127),(266,164),(267,143),(267,164),(268,105),(268,217),(269,111),(270,154),(270,245),(271,141),(271,279),(272,95),(273,94),(273,227),(273,233),(274,152),(274,251),(275,129),(275,242),(276,138),(276,278),(277,103),(277,149),(277,216),(278,126),(279,98),(279,237)],280)
=> ? = 28 - 1
[1,1,1,1,1,0,0,0,0,0]
=> [[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0]]
=> [[1,2,3,4,5],[2,3,4,5],[3,4,5],[4,5],[5]]
=> 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=> ? = 42 - 1
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,4,4],[5,5],[6]]
=> ([],1)
=> 0 = 1 - 1
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [[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 = 2 - 1
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[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 = 2 - 1
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [[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,-1,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,4,5],[5,6],[6]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,5,6],[5,6],[6]]
=> ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8)
=> ? = 5 - 1
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[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 = 2 - 1
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[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 = 4 - 1
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,4],[4,4,5],[5,5],[6]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,4],[4,4,5],[5,6],[6]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3 = 4 - 1
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,4],[4,5,6],[5,6],[6]]
=> ([(0,5),(0,6),(1,8),(2,9),(3,8),(3,9),(4,1),(5,4),(6,7),(7,2),(7,3),(8,10),(9,10)],11)
=> ? = 7 - 1
[1,0,1,0,1,1,1,0,0,0,1,0]
=> [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,4,5],[4,4,5],[5,5],[6]]
=> ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8)
=> ? = 5 - 1
[1,0,1,0,1,1,1,0,0,1,0,0]
=> [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,4,5],[4,4,5],[5,6],[6]]
=> ([(0,3),(0,7),(1,8),(2,8),(3,9),(4,5),(5,1),(6,2),(7,4),(7,9),(9,6)],10)
=> ? = 7 - 1
[1,0,1,0,1,1,1,0,1,0,0,0]
=> [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,4,5],[4,5,6],[5,6],[6]]
=> ([(0,9),(0,11),(1,18),(2,17),(3,19),(4,13),(4,19),(5,12),(5,13),(6,16),(7,14),(8,5),(8,18),(9,10),(10,3),(10,4),(11,1),(11,8),(12,17),(13,15),(15,16),(16,14),(17,7),(18,2),(18,12),(19,6),(19,15)],20)
=> ? = 9 - 1
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,4,5,6],[4,5,6],[5,6],[6]]
=> ([(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)
=> ? = 14 - 1
[1,0,1,1,0,0,1,0,1,0,1,0]
=> [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[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 = 2 - 1
[1,0,1,1,0,0,1,0,1,1,0,0]
=> [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[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 = 4 - 1
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[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 = 4 - 1
[1,0,1,1,0,0,1,1,0,1,0,0]
=> [[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,-1,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,3],[4,4,5],[5,6],[6]]
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 5 = 6 - 1
[1,0,1,1,0,0,1,1,1,0,0,0]
=> [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,3],[4,5,6],[5,6],[6]]
=> ([(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)
=> ? = 10 - 1
[1,0,1,1,0,1,0,0,1,0,1,0]
=> [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,4],[4,4,4],[5,5],[6]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
[1,0,1,1,0,1,0,0,1,1,0,0]
=> [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,4],[4,4,4],[5,6],[6]]
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 5 = 6 - 1
[1,0,1,1,0,1,0,1,0,0,1,0]
=> [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,4],[4,4,5],[5,5],[6]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3 = 4 - 1
[1,0,1,1,0,1,0,1,0,1,0,0]
=> [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,4],[4,4,5],[5,6],[6]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4 = 5 - 1
[1,0,1,1,0,1,0,1,1,0,0,0]
=> [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,4],[4,5,6],[5,6],[6]]
=> ([(0,6),(0,7),(1,11),(2,9),(3,9),(3,10),(4,2),(5,1),(5,10),(6,4),(7,8),(8,3),(8,5),(9,12),(10,11),(10,12),(11,13),(12,13)],14)
=> ? = 9 - 1
[1,0,1,1,0,1,1,0,0,0,1,0]
=> [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,4,5],[4,4,5],[5,5],[6]]
=> ([(0,5),(0,6),(1,8),(2,9),(3,8),(3,9),(4,1),(5,4),(6,7),(7,2),(7,3),(8,10),(9,10)],11)
=> ? = 7 - 1
[1,0,1,1,0,1,1,0,0,1,0,0]
=> [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,4,5],[4,4,5],[5,6],[6]]
=> ([(0,4),(0,7),(1,9),(2,10),(3,9),(3,10),(4,11),(5,8),(6,1),(7,5),(7,11),(8,2),(8,3),(9,12),(10,12),(11,6)],13)
=> ? = 9 - 1
[1,0,1,1,0,1,1,0,1,0,0,0]
=> [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,0,1,0],[0,0,0,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,4,5],[4,5,6],[5,6],[6]]
=> ([(0,10),(0,12),(1,23),(2,22),(3,14),(3,24),(4,15),(5,13),(5,14),(6,18),(7,16),(7,20),(8,5),(8,23),(9,4),(9,24),(10,11),(11,3),(11,9),(12,1),(12,8),(13,22),(14,19),(15,16),(15,21),(16,25),(18,17),(19,20),(19,21),(20,18),(20,25),(21,25),(22,6),(23,2),(23,13),(24,7),(24,15),(24,19),(25,17)],26)
=> ? = 12 - 1
[1,0,1,1,0,1,1,1,0,0,0,0]
=> [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,4,5,6],[4,5,6],[5,6],[6]]
=> ([(0,5),(0,14),(0,15),(1,26),(2,9),(2,25),(3,13),(3,24),(4,16),(5,11),(5,12),(6,69),(7,64),(8,49),(9,6),(9,52),(10,20),(10,59),(11,19),(11,65),(12,17),(12,65),(13,18),(13,22),(13,71),(14,2),(14,29),(15,3),(15,29),(16,39),(16,55),(17,56),(17,68),(18,57),(18,66),(19,58),(19,67),(20,51),(20,53),(21,40),(21,41),(22,57),(22,72),(23,28),(23,54),(23,70),(24,58),(24,71),(25,52),(25,56),(26,27),(26,69),(26,72),(27,45),(27,60),(28,34),(28,48),(28,50),(29,1),(30,76),(31,75),(32,77),(33,74),(33,80),(34,73),(34,78),(35,73),(35,77),(36,82),(37,79),(38,80),(39,74),(40,7),(40,76),(41,8),(41,76),(42,55),(42,79),(43,59),(44,39),(45,53),(45,83),(46,33),(46,81),(47,32),(47,83),(48,42),(48,78),(49,44),(50,46),(50,73),(51,44),(52,10),(52,43),(53,62),(54,34),(54,75),(55,36),(55,74),(56,43),(57,63),(58,61),(59,49),(59,51),(60,35),(60,50),(60,83),(61,31),(61,70),(62,33),(62,38),(63,32),(63,35),(64,37),(64,42),(65,21),(65,67),(65,68),(66,31),(66,54),(67,30),(67,40),(68,30),(68,41),(69,45),(69,47),(70,48),(70,64),(70,75),(71,23),(71,61),(71,66),(72,47),(72,60),(72,63),(73,81),(74,82),(75,37),(75,78),(76,4),(77,38),(77,81),(78,79),(79,36),(80,82),(81,80),(83,46),(83,62),(83,77)],84)
=> ? = 19 - 1
[1,0,1,1,1,0,0,0,1,0,1,0]
=> [[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,3,4],[3,3,3,4],[4,4,4],[5,5],[6]]
=> ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8)
=> ? = 5 - 1
[1,0,1,1,1,0,0,0,1,1,0,0]
=> [[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,1],[2,2,2,3,4],[3,3,3,4],[4,4,4],[5,6],[6]]
=> ([(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)
=> ? = 10 - 1
[1,0,1,1,1,0,0,1,0,0,1,0]
=> [[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,3,4],[3,3,3,4],[4,4,5],[5,5],[6]]
=> ([(0,3),(0,7),(1,8),(2,8),(3,9),(4,5),(5,1),(6,2),(7,4),(7,9),(9,6)],10)
=> ? = 7 - 1
[1,0,1,1,1,0,0,1,0,1,0,0]
=> [[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,1],[2,2,2,3,4],[3,3,3,4],[4,4,5],[5,6],[6]]
=> ([(0,3),(0,8),(1,10),(2,10),(3,9),(4,6),(5,4),(5,11),(6,2),(7,1),(8,5),(8,9),(9,11),(11,7)],12)
=> ? = 9 - 1
[1,0,1,1,1,0,0,1,1,0,0,0]
=> [[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]]
=> [[1,1,1,1,1,1],[2,2,2,3,4],[3,3,3,4],[4,5,6],[5,6],[6]]
=> ([(0,7),(0,8),(0,11),(1,25),(2,10),(2,24),(3,5),(3,12),(3,26),(4,28),(5,6),(5,29),(6,4),(6,27),(7,2),(7,19),(8,3),(8,18),(9,15),(9,16),(10,13),(10,23),(11,18),(11,19),(12,22),(12,23),(12,29),(13,31),(14,30),(15,30),(16,30),(17,20),(18,26),(19,24),(20,14),(21,16),(22,25),(22,31),(23,17),(23,31),(24,13),(25,9),(25,21),(26,1),(26,22),(27,20),(27,28),(28,14),(28,15),(29,17),(29,27),(31,21)],32)
=> ? = 16 - 1
[1,1,0,0,1,0,1,0,1,0,1,0]
=> [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[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 = 2 - 1
[1,1,0,0,1,0,1,0,1,1,0,0]
=> [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[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 = 4 - 1
[1,1,0,0,1,0,1,1,0,0,1,0]
=> [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[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 = 4 - 1
Description
The rank of the boundary operator in degree 1 of the chain complex of the order complex of the poset.
Matching statistic: St000656
Mp00137: Dyck paths —to symmetric ASM⟶ Alternating sign matrices
Mp00001: Alternating sign matrices —to semistandard tableau via monotone triangles⟶ Semistandard tableaux
Mp00214: Semistandard tableaux —subcrystal⟶ Posets
St000656: Posets ⟶ ℤResult quality: 5% ●values known / values provided: 5%●distinct values known / distinct values provided: 6%
Mp00001: Alternating sign matrices —to semistandard tableau via monotone triangles⟶ Semistandard tableaux
Mp00214: Semistandard tableaux —subcrystal⟶ Posets
St000656: Posets ⟶ ℤResult quality: 5% ●values known / values provided: 5%●distinct values known / distinct values provided: 6%
Values
[1,0]
=> [[1]]
=> [[1]]
=> ([],1)
=> ? = 1
[1,0,1,0]
=> [[1,0],[0,1]]
=> [[1,1],[2]]
=> ([],1)
=> ? = 1
[1,1,0,0]
=> [[0,1],[1,0]]
=> [[1,2],[2]]
=> ([(0,1)],2)
=> 2
[1,0,1,0,1,0]
=> [[1,0,0],[0,1,0],[0,0,1]]
=> [[1,1,1],[2,2],[3]]
=> ([],1)
=> ? = 1
[1,0,1,1,0,0]
=> [[1,0,0],[0,0,1],[0,1,0]]
=> [[1,1,1],[2,3],[3]]
=> ([(0,1)],2)
=> 2
[1,1,0,0,1,0]
=> [[0,1,0],[1,0,0],[0,0,1]]
=> [[1,1,2],[2,2],[3]]
=> ([(0,1)],2)
=> 2
[1,1,0,1,0,0]
=> [[0,1,0],[1,-1,1],[0,1,0]]
=> [[1,1,2],[2,3],[3]]
=> ([(0,2),(2,1)],3)
=> 3
[1,1,1,0,0,0]
=> [[0,0,1],[0,1,0],[1,0,0]]
=> [[1,2,3],[2,3],[3]]
=> ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8)
=> ? = 5
[1,0,1,0,1,0,1,0]
=> [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,2],[3,3],[4]]
=> ([],1)
=> ? = 1
[1,0,1,0,1,1,0,0]
=> [[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)
=> 2
[1,0,1,1,0,0,1,0]
=> [[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)
=> 2
[1,0,1,1,0,1,0,0]
=> [[1,0,0,0],[0,0,1,0],[0,1,-1,1],[0,0,1,0]]
=> [[1,1,1,1],[2,2,3],[3,4],[4]]
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,1,1,0,0,0]
=> [[1,0,0,0],[0,0,0,1],[0,0,1,0],[0,1,0,0]]
=> [[1,1,1,1],[2,3,4],[3,4],[4]]
=> ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8)
=> ? = 5
[1,1,0,0,1,0,1,0]
=> [[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)
=> 2
[1,1,0,0,1,1,0,0]
=> [[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)
=> 4
[1,1,0,1,0,0,1,0]
=> [[0,1,0,0],[1,-1,1,0],[0,1,0,0],[0,0,0,1]]
=> [[1,1,1,2],[2,2,3],[3,3],[4]]
=> ([(0,2),(2,1)],3)
=> 3
[1,1,0,1,0,1,0,0]
=> [[0,1,0,0],[1,-1,1,0],[0,1,-1,1],[0,0,1,0]]
=> [[1,1,1,2],[2,2,3],[3,4],[4]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[1,1,0,1,1,0,0,0]
=> [[0,1,0,0],[1,-1,0,1],[0,0,1,0],[0,1,0,0]]
=> [[1,1,1,2],[2,3,4],[3,4],[4]]
=> ([(0,5),(0,6),(1,8),(2,9),(3,8),(3,9),(4,1),(5,4),(6,7),(7,2),(7,3),(8,10),(9,10)],11)
=> ? = 7
[1,1,1,0,0,0,1,0]
=> [[0,0,1,0],[0,1,0,0],[1,0,0,0],[0,0,0,1]]
=> [[1,1,2,3],[2,2,3],[3,3],[4]]
=> ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8)
=> ? = 5
[1,1,1,0,0,1,0,0]
=> [[0,0,1,0],[0,1,0,0],[1,0,-1,1],[0,0,1,0]]
=> [[1,1,2,3],[2,2,3],[3,4],[4]]
=> ([(0,3),(0,7),(1,8),(2,8),(3,9),(4,5),(5,1),(6,2),(7,4),(7,9),(9,6)],10)
=> ? = 7
[1,1,1,0,1,0,0,0]
=> [[0,0,1,0],[0,1,-1,1],[1,-1,1,0],[0,1,0,0]]
=> [[1,1,2,3],[2,3,4],[3,4],[4]]
=> ([(0,9),(0,11),(1,18),(2,17),(3,19),(4,13),(4,19),(5,12),(5,13),(6,16),(7,14),(8,5),(8,18),(9,10),(10,3),(10,4),(11,1),(11,8),(12,17),(13,15),(15,16),(16,14),(17,7),(18,2),(18,12),(19,6),(19,15)],20)
=> ? = 9
[1,1,1,1,0,0,0,0]
=> [[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)
=> ? = 14
[1,0,1,0,1,0,1,0,1,0]
=> [[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]]
=> [[1,1,1,1,1],[2,2,2,2],[3,3,3],[4,4],[5]]
=> ([],1)
=> ? = 1
[1,0,1,0,1,0,1,1,0,0]
=> [[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)
=> 2
[1,0,1,0,1,1,0,0,1,0]
=> [[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)
=> 2
[1,0,1,0,1,1,0,1,0,0]
=> [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
=> [[1,1,1,1,1],[2,2,2,2],[3,3,4],[4,5],[5]]
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,0,1,1,1,0,0,0]
=> [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0]]
=> [[1,1,1,1,1],[2,2,2,2],[3,4,5],[4,5],[5]]
=> ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8)
=> ? = 5
[1,0,1,1,0,0,1,0,1,0]
=> [[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)
=> 2
[1,0,1,1,0,0,1,1,0,0]
=> [[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)
=> 4
[1,0,1,1,0,1,0,0,1,0]
=> [[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [[1,1,1,1,1],[2,2,2,3],[3,3,4],[4,4],[5]]
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,1,0,1,0,1,0,0]
=> [[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
=> [[1,1,1,1,1],[2,2,2,3],[3,3,4],[4,5],[5]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[1,0,1,1,0,1,1,0,0,0]
=> [[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,0,1],[0,0,0,1,0],[0,0,1,0,0]]
=> [[1,1,1,1,1],[2,2,2,3],[3,4,5],[4,5],[5]]
=> ([(0,5),(0,6),(1,8),(2,9),(3,8),(3,9),(4,1),(5,4),(6,7),(7,2),(7,3),(8,10),(9,10)],11)
=> ? = 7
[1,0,1,1,1,0,0,0,1,0]
=> [[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [[1,1,1,1,1],[2,2,3,4],[3,3,4],[4,4],[5]]
=> ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8)
=> ? = 5
[1,0,1,1,1,0,0,1,0,0]
=> [[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,-1,1],[0,0,0,1,0]]
=> [[1,1,1,1,1],[2,2,3,4],[3,3,4],[4,5],[5]]
=> ([(0,3),(0,7),(1,8),(2,8),(3,9),(4,5),(5,1),(6,2),(7,4),(7,9),(9,6)],10)
=> ? = 7
[1,0,1,1,1,0,1,0,0,0]
=> [[1,0,0,0,0],[0,0,0,1,0],[0,0,1,-1,1],[0,1,-1,1,0],[0,0,1,0,0]]
=> [[1,1,1,1,1],[2,2,3,4],[3,4,5],[4,5],[5]]
=> ([(0,9),(0,11),(1,18),(2,17),(3,19),(4,13),(4,19),(5,12),(5,13),(6,16),(7,14),(8,5),(8,18),(9,10),(10,3),(10,4),(11,1),(11,8),(12,17),(13,15),(15,16),(16,14),(17,7),(18,2),(18,12),(19,6),(19,15)],20)
=> ? = 9
[1,0,1,1,1,1,0,0,0,0]
=> [[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)
=> ? = 14
[1,1,0,0,1,0,1,0,1,0]
=> [[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)
=> 2
[1,1,0,0,1,0,1,1,0,0]
=> [[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)
=> 4
[1,1,0,0,1,1,0,0,1,0]
=> [[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)
=> 4
[1,1,0,0,1,1,0,1,0,0]
=> [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
=> [[1,1,1,1,2],[2,2,2,2],[3,3,4],[4,5],[5]]
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 6
[1,1,0,0,1,1,1,0,0,0]
=> [[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)
=> ? = 10
[1,1,0,1,0,0,1,0,1,0]
=> [[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
=> [[1,1,1,1,2],[2,2,2,3],[3,3,3],[4,4],[5]]
=> ([(0,2),(2,1)],3)
=> 3
[1,1,0,1,0,0,1,1,0,0]
=> [[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
=> [[1,1,1,1,2],[2,2,2,3],[3,3,3],[4,5],[5]]
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 6
[1,1,0,1,0,1,0,0,1,0]
=> [[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [[1,1,1,1,2],[2,2,2,3],[3,3,4],[4,4],[5]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[1,1,0,1,0,1,0,1,0,0]
=> [[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
=> [[1,1,1,1,2],[2,2,2,3],[3,3,4],[4,5],[5]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[1,1,0,1,0,1,1,0,0,0]
=> [[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,0,1],[0,0,0,1,0],[0,0,1,0,0]]
=> [[1,1,1,1,2],[2,2,2,3],[3,4,5],[4,5],[5]]
=> ([(0,6),(0,7),(1,11),(2,9),(3,9),(3,10),(4,2),(5,1),(5,10),(6,4),(7,8),(8,3),(8,5),(9,12),(10,11),(10,12),(11,13),(12,13)],14)
=> ? = 9
[1,1,0,1,1,0,0,0,1,0]
=> [[0,1,0,0,0],[1,-1,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [[1,1,1,1,2],[2,2,3,4],[3,3,4],[4,4],[5]]
=> ([(0,5),(0,6),(1,8),(2,9),(3,8),(3,9),(4,1),(5,4),(6,7),(7,2),(7,3),(8,10),(9,10)],11)
=> ? = 7
[1,1,0,1,1,0,0,1,0,0]
=> [[0,1,0,0,0],[1,-1,0,1,0],[0,0,1,0,0],[0,1,0,-1,1],[0,0,0,1,0]]
=> [[1,1,1,1,2],[2,2,3,4],[3,3,4],[4,5],[5]]
=> ([(0,4),(0,7),(1,9),(2,10),(3,9),(3,10),(4,11),(5,8),(6,1),(7,5),(7,11),(8,2),(8,3),(9,12),(10,12),(11,6)],13)
=> ? = 9
[1,1,0,1,1,0,1,0,0,0]
=> [[0,1,0,0,0],[1,-1,0,1,0],[0,0,1,-1,1],[0,1,-1,1,0],[0,0,1,0,0]]
=> [[1,1,1,1,2],[2,2,3,4],[3,4,5],[4,5],[5]]
=> ([(0,10),(0,12),(1,23),(2,22),(3,14),(3,24),(4,15),(5,13),(5,14),(6,18),(7,16),(7,20),(8,5),(8,23),(9,4),(9,24),(10,11),(11,3),(11,9),(12,1),(12,8),(13,22),(14,19),(15,16),(15,21),(16,25),(18,17),(19,20),(19,21),(20,18),(20,25),(21,25),(22,6),(23,2),(23,13),(24,7),(24,15),(24,19),(25,17)],26)
=> ? = 12
[1,1,0,1,1,1,0,0,0,0]
=> [[0,1,0,0,0],[1,-1,0,0,1],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0]]
=> [[1,1,1,1,2],[2,3,4,5],[3,4,5],[4,5],[5]]
=> ([(0,5),(0,14),(0,15),(1,26),(2,9),(2,25),(3,13),(3,24),(4,16),(5,11),(5,12),(6,69),(7,64),(8,49),(9,6),(9,52),(10,20),(10,59),(11,19),(11,65),(12,17),(12,65),(13,18),(13,22),(13,71),(14,2),(14,29),(15,3),(15,29),(16,39),(16,55),(17,56),(17,68),(18,57),(18,66),(19,58),(19,67),(20,51),(20,53),(21,40),(21,41),(22,57),(22,72),(23,28),(23,54),(23,70),(24,58),(24,71),(25,52),(25,56),(26,27),(26,69),(26,72),(27,45),(27,60),(28,34),(28,48),(28,50),(29,1),(30,76),(31,75),(32,77),(33,74),(33,80),(34,73),(34,78),(35,73),(35,77),(36,82),(37,79),(38,80),(39,74),(40,7),(40,76),(41,8),(41,76),(42,55),(42,79),(43,59),(44,39),(45,53),(45,83),(46,33),(46,81),(47,32),(47,83),(48,42),(48,78),(49,44),(50,46),(50,73),(51,44),(52,10),(52,43),(53,62),(54,34),(54,75),(55,36),(55,74),(56,43),(57,63),(58,61),(59,49),(59,51),(60,35),(60,50),(60,83),(61,31),(61,70),(62,33),(62,38),(63,32),(63,35),(64,37),(64,42),(65,21),(65,67),(65,68),(66,31),(66,54),(67,30),(67,40),(68,30),(68,41),(69,45),(69,47),(70,48),(70,64),(70,75),(71,23),(71,61),(71,66),(72,47),(72,60),(72,63),(73,81),(74,82),(75,37),(75,78),(76,4),(77,38),(77,81),(78,79),(79,36),(80,82),(81,80),(83,46),(83,62),(83,77)],84)
=> ? = 19
[1,1,1,0,0,0,1,0,1,0]
=> [[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
=> [[1,1,1,2,3],[2,2,2,3],[3,3,3],[4,4],[5]]
=> ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8)
=> ? = 5
[1,1,1,0,0,0,1,1,0,0]
=> [[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)
=> ? = 10
[1,1,1,0,0,1,0,0,1,0]
=> [[0,0,1,0,0],[0,1,0,0,0],[1,0,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [[1,1,1,2,3],[2,2,2,3],[3,3,4],[4,4],[5]]
=> ([(0,3),(0,7),(1,8),(2,8),(3,9),(4,5),(5,1),(6,2),(7,4),(7,9),(9,6)],10)
=> ? = 7
[1,1,1,0,0,1,0,1,0,0]
=> [[0,0,1,0,0],[0,1,0,0,0],[1,0,-1,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
=> [[1,1,1,2,3],[2,2,2,3],[3,3,4],[4,5],[5]]
=> ([(0,3),(0,8),(1,10),(2,10),(3,9),(4,6),(5,4),(5,11),(6,2),(7,1),(8,5),(8,9),(9,11),(11,7)],12)
=> ? = 9
[1,1,1,0,0,1,1,0,0,0]
=> [[0,0,1,0,0],[0,1,0,0,0],[1,0,-1,0,1],[0,0,0,1,0],[0,0,1,0,0]]
=> [[1,1,1,2,3],[2,2,2,3],[3,4,5],[4,5],[5]]
=> ([(0,7),(0,8),(0,11),(1,25),(2,10),(2,24),(3,5),(3,12),(3,26),(4,28),(5,6),(5,29),(6,4),(6,27),(7,2),(7,19),(8,3),(8,18),(9,15),(9,16),(10,13),(10,23),(11,18),(11,19),(12,22),(12,23),(12,29),(13,31),(14,30),(15,30),(16,30),(17,20),(18,26),(19,24),(20,14),(21,16),(22,25),(22,31),(23,17),(23,31),(24,13),(25,9),(25,21),(26,1),(26,22),(27,20),(27,28),(28,14),(28,15),(29,17),(29,27),(31,21)],32)
=> ? = 16
[1,1,1,0,1,0,0,0,1,0]
=> [[0,0,1,0,0],[0,1,-1,1,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [[1,1,1,2,3],[2,2,3,4],[3,3,4],[4,4],[5]]
=> ([(0,9),(0,11),(1,18),(2,17),(3,19),(4,13),(4,19),(5,12),(5,13),(6,16),(7,14),(8,5),(8,18),(9,10),(10,3),(10,4),(11,1),(11,8),(12,17),(13,15),(15,16),(16,14),(17,7),(18,2),(18,12),(19,6),(19,15)],20)
=> ? = 9
[1,1,1,0,1,0,0,1,0,0]
=> [[0,0,1,0,0],[0,1,-1,1,0],[1,-1,1,0,0],[0,1,0,-1,1],[0,0,0,1,0]]
=> [[1,1,1,2,3],[2,2,3,4],[3,3,4],[4,5],[5]]
=> ([(0,10),(0,11),(1,13),(1,14),(2,21),(3,20),(4,14),(4,20),(5,17),(6,16),(7,18),(8,12),(9,1),(9,22),(10,5),(10,15),(11,8),(11,15),(12,3),(12,4),(13,21),(14,19),(15,9),(15,17),(17,22),(18,16),(19,18),(20,7),(20,19),(21,6),(22,2),(22,13)],23)
=> ? = 12
[1,1,1,0,1,0,1,0,0,0]
=> [[0,0,1,0,0],[0,1,-1,1,0],[1,-1,1,-1,1],[0,1,-1,1,0],[0,0,1,0,0]]
=> [[1,1,1,2,3],[2,2,3,4],[3,4,5],[4,5],[5]]
=> ([(0,2),(0,3),(1,9),(1,15),(2,1),(3,7),(3,8),(4,30),(5,31),(6,23),(7,16),(7,37),(8,10),(8,37),(9,11),(9,36),(10,34),(11,35),(12,25),(12,29),(13,19),(13,22),(14,21),(14,27),(15,26),(15,36),(16,26),(16,33),(17,39),(18,38),(19,12),(19,38),(20,6),(21,4),(21,39),(22,5),(22,38),(24,23),(25,28),(26,32),(27,25),(27,39),(28,24),(29,20),(30,24),(31,20),(32,17),(32,27),(33,18),(33,19),(34,18),(34,22),(35,17),(35,21),(36,14),(36,32),(36,35),(37,13),(37,33),(37,34),(38,29),(38,31),(39,28),(39,30)],40)
=> ? = 14
[1,1,1,0,1,1,0,0,0,0]
=> [[0,0,1,0,0],[0,1,-1,0,1],[1,-1,0,1,0],[0,0,1,0,0],[0,1,0,0,0]]
=> [[1,1,1,2,3],[2,3,4,5],[3,4,5],[4,5],[5]]
=> ([(0,4),(0,14),(0,15),(1,29),(2,6),(2,27),(3,13),(3,28),(4,10),(4,11),(5,102),(6,5),(6,87),(7,31),(7,99),(8,25),(8,98),(9,26),(9,72),(10,23),(10,109),(11,24),(11,33),(11,109),(12,22),(12,108),(13,17),(13,18),(13,107),(14,2),(14,38),(15,3),(15,38),(16,84),(16,85),(17,90),(17,111),(18,90),(18,101),(19,82),(19,83),(20,81),(20,100),(21,34),(21,89),(21,104),(22,86),(22,106),(23,91),(23,110),(24,80),(24,105),(25,78),(25,79),(26,52),(26,88),(27,87),(27,103),(28,91),(28,107),(29,30),(29,102),(29,111),(30,63),(30,96),(31,44),(31,71),(31,76),(32,37),(32,51),(32,77),(33,80),(33,94),(33,103),(34,62),(34,74),(34,75),(35,133),(36,9),(37,8),(37,127),(38,1),(39,118),(40,117),(40,122),(41,119),(42,119),(42,126),(43,116),(43,127),(44,112),(44,120),(45,112),(45,113),(46,114),(46,116),(47,121),(48,122),(49,125),(50,113),(51,20),(51,114),(51,127),(52,117),(53,72),(54,88),(54,121),(55,45),(55,132),(56,48),(57,84),(57,124),(58,76),(58,134),(59,66),(60,56),(61,54),(62,55),(62,126),(63,86),(63,129),(64,53),(64,134),(65,47),(66,70),(67,40),(68,40),(68,123),(69,41),(69,129),(70,39),(70,128),(71,54),(71,120),(72,52),(73,44),(73,118),(74,58),(74,115),(75,82),(75,115),(75,126),(76,68),(76,112),(77,16),(77,57),(77,114),(78,65),(79,61),(80,59),(80,130),(81,36),(82,60),(82,131),(83,53),(83,131),(84,78),(84,128),(85,73),(85,128),(86,92),(87,12),(87,95),(88,49),(88,117),(89,19),(89,75),(89,133),(90,97),(91,93),(92,45),(92,50),(93,35),(93,104),(94,46),(94,77),(94,130),(95,66),(95,108),(96,42),(96,62),(96,129),(97,41),(97,42),(98,36),(98,79),(99,61),(99,71),(100,58),(100,64),(101,35),(101,89),(102,63),(102,69),(103,59),(103,95),(104,74),(104,100),(104,133),(105,37),(105,43),(105,130),(106,39),(106,73),(107,21),(107,93),(107,101),(108,70),(108,85),(108,106),(109,32),(109,94),(109,105),(109,110),(110,43),(110,46),(110,51),(111,69),(111,96),(111,97),(112,123),(113,48),(113,123),(114,7),(114,124),(115,131),(115,134),(116,124),(117,125),(118,47),(118,120),(119,50),(119,132),(120,121),(121,49),(122,125),(123,122),(124,99),(126,60),(126,132),(127,81),(127,98),(128,65),(128,118),(129,55),(129,92),(129,119),(130,57),(130,116),(131,67),(132,56),(132,113),(133,64),(133,83),(133,115),(134,67),(134,68)],135)
=> ? = 23
[1,1,1,1,0,0,0,0,1,0]
=> [[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)
=> ? = 14
[1,1,1,1,0,0,0,1,0,0]
=> [[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[1,0,0,-1,1],[0,0,0,1,0]]
=> [[1,1,2,3,4],[2,2,3,4],[3,3,4],[4,5],[5]]
=> ([(0,16),(0,17),(0,28),(1,22),(2,19),(3,11),(3,21),(4,54),(5,55),(6,26),(6,57),(7,25),(7,67),(8,23),(8,64),(9,24),(9,65),(10,14),(10,56),(11,15),(11,58),(12,3),(12,37),(13,27),(13,66),(14,59),(15,60),(16,13),(16,53),(17,6),(17,61),(18,51),(18,52),(19,33),(19,34),(20,35),(20,36),(21,50),(21,58),(22,18),(22,59),(22,60),(23,41),(23,43),(24,42),(24,44),(25,50),(25,63),(26,29),(26,46),(27,29),(27,45),(28,12),(28,53),(28,61),(29,70),(30,71),(31,69),(32,68),(33,68),(34,68),(35,4),(35,69),(36,5),(36,69),(37,1),(38,33),(39,34),(40,64),(41,48),(42,49),(43,38),(44,39),(45,62),(45,70),(46,56),(46,70),(47,65),(48,32),(49,32),(50,40),(51,42),(51,71),(52,41),(52,71),(53,7),(53,66),(54,38),(55,39),(56,9),(56,47),(57,10),(57,46),(58,8),(58,40),(59,30),(59,51),(60,30),(60,52),(61,37),(61,57),(62,31),(62,36),(63,31),(63,35),(64,43),(64,54),(65,44),(65,55),(66,45),(66,67),(67,20),(67,62),(67,63),(69,2),(70,47),(71,48),(71,49)],72)
=> ? = 19
[1,1,1,1,0,0,1,0,0,0]
=> [[0,0,0,1,0],[0,0,1,0,0],[0,1,0,-1,1],[1,0,-1,1,0],[0,0,1,0,0]]
=> [[1,1,2,3,4],[2,2,3,4],[3,4,5],[4,5],[5]]
=> ([(0,15),(0,16),(0,30),(1,26),(2,14),(2,95),(3,78),(4,79),(5,92),(6,77),(7,29),(7,93),(8,27),(8,96),(9,28),(9,94),(10,12),(10,32),(10,80),(11,84),(12,13),(12,86),(13,11),(13,97),(14,19),(14,98),(15,10),(15,54),(16,2),(16,24),(16,76),(17,47),(17,71),(18,46),(18,72),(19,41),(19,91),(20,35),(20,73),(21,69),(21,87),(22,25),(22,75),(22,90),(23,45),(23,70),(24,31),(24,88),(24,95),(25,49),(25,50),(26,39),(26,40),(27,52),(27,53),(28,41),(28,89),(29,33),(29,57),(30,54),(30,76),(31,67),(31,68),(31,85),(32,56),(32,68),(32,86),(33,110),(34,106),(34,107),(35,21),(35,111),(36,100),(37,101),(37,106),(38,102),(39,102),(40,102),(41,99),(42,104),(43,113),(44,103),(45,6),(45,112),(46,7),(46,108),(47,5),(47,107),(48,3),(48,103),(49,55),(49,105),(50,33),(50,105),(51,61),(52,63),(53,61),(54,80),(55,52),(55,113),(56,79),(56,109),(57,60),(57,110),(58,90),(59,81),(60,62),(61,39),(62,40),(63,38),(64,38),(65,37),(65,111),(66,36),(66,108),(67,82),(67,109),(68,83),(68,109),(69,59),(70,48),(70,112),(71,42),(71,107),(72,69),(72,108),(73,23),(73,74),(73,111),(74,45),(74,101),(75,50),(75,100),(76,9),(76,88),(77,51),(78,62),(79,22),(79,58),(80,4),(80,56),(81,60),(81,78),(82,34),(82,47),(83,66),(83,72),(84,36),(84,75),(85,35),(85,65),(86,18),(86,83),(86,97),(87,44),(87,48),(88,67),(88,94),(89,34),(89,71),(89,99),(90,49),(90,92),(90,100),(91,37),(91,74),(91,99),(92,43),(92,55),(93,57),(93,81),(94,17),(94,82),(94,89),(95,20),(95,85),(95,98),(96,51),(96,53),(97,46),(97,66),(97,84),(98,65),(98,73),(98,91),(99,42),(99,106),(100,43),(100,105),(101,44),(101,112),(103,1),(104,96),(105,110),(105,113),(106,104),(107,8),(107,104),(108,59),(108,93),(109,58),(110,64),(111,70),(111,87),(111,101),(112,77),(112,103),(113,63),(113,64)],114)
=> ? = 23
[1,1,1,1,0,1,0,0,0,0]
=> [[0,0,0,1,0],[0,0,1,-1,1],[0,1,-1,1,0],[1,-1,1,0,0],[0,1,0,0,0]]
=> [[1,1,2,3,4],[2,3,4,5],[3,4,5],[4,5],[5]]
=> ([(0,2),(0,17),(0,18),(1,16),(1,41),(2,10),(2,15),(3,207),(4,50),(4,125),(5,181),(6,49),(6,180),(7,188),(8,138),(9,46),(9,208),(10,30),(10,206),(11,35),(11,54),(12,36),(12,97),(13,37),(13,163),(14,40),(14,44),(14,202),(15,28),(15,45),(15,206),(16,26),(16,27),(16,203),(17,1),(17,124),(18,14),(18,33),(18,124),(19,52),(19,201),(19,211),(20,196),(20,200),(21,89),(21,155),(22,149),(22,156),(23,150),(23,198),(24,154),(24,199),(25,90),(25,152),(26,162),(26,210),(27,162),(27,197),(28,159),(28,191),(29,153),(29,190),(30,161),(30,209),(31,144),(31,157),(32,141),(32,151),(33,145),(33,202),(34,143),(34,189),(35,147),(35,148),(36,142),(36,146),(37,88),(37,195),(38,87),(38,192),(39,51),(39,158),(39,194),(40,42),(40,160),(40,193),(41,161),(41,203),(42,102),(42,170),(43,122),(43,123),(43,178),(44,120),(44,160),(44,179),(45,159),(45,177),(45,179),(46,76),(46,119),(46,183),(47,64),(47,121),(47,140),(48,65),(48,86),(48,139),(49,60),(49,92),(49,93),(50,43),(50,169),(50,170),(50,210),(51,99),(51,100),(51,101),(52,104),(52,109),(52,165),(53,272),(54,13),(55,225),(55,275),(56,218),(56,219),(57,227),(57,270),(58,227),(58,269),(59,12),(60,219),(60,226),(61,255),(61,276),(62,253),(62,271),(63,277),(64,269),(64,270),(65,6),(65,265),(66,230),(67,231),(67,256),(68,236),(68,271),(69,236),(69,249),(70,229),(70,247),(71,214),(71,228),(72,235),(73,228),(73,265),(74,213),(74,229),(75,234),(76,225),(76,241),(77,231),(77,234),(78,272),(79,250),(80,274),(81,260),(82,230),(83,232),(84,239),(84,254),(85,237),(86,29),(86,214),(86,265),(87,223),(88,215),(89,244),(90,32),(90,264),(91,97),(92,107),(92,219),(93,128),(93,226),(94,83),(94,275),(95,66),(96,119),(96,266),(97,142),(98,82),(99,96),(99,216),(100,136),(100,220),(101,156),(101,216),(101,220),(102,116),(102,268),(103,91),(103,266),(104,175),(104,259),(105,121),(105,263),(106,140),(106,263),(107,84),(107,248),(108,135),(109,166),(109,259),(110,133),(110,223),(111,69),(112,76),(112,224),(113,88),(113,213),(114,117),(114,262),(115,70),(115,224),(116,54),(117,58),(117,273),(118,57),(118,220),(118,273),(119,127),(119,225),(120,157),(120,212),(121,163),(121,269),(122,106),(122,217),(123,104),(123,217),(123,262),(124,4),(124,145),(125,5),(125,169),(126,155),(127,134),(127,242),(128,132),(128,238),(129,67),(129,240),(130,74),(130,243),(130,258),(131,67),(131,235),(132,146),(132,239),(132,276),(133,70),(133,218),(133,243),(134,77),(134,222),(134,240),(135,62),(135,215),(135,232),(136,55),(136,233),(137,61),(137,238),(138,21),(138,126),(139,23),(139,186),(139,214),(140,24),(140,182),(140,270),(141,98),(142,75),(142,222),(143,171),(144,11),(144,116),(145,125),(146,79),(146,222),(147,113),(147,258),(148,80),(148,258),(149,91),(149,267),(150,112),(150,261),(151,95),(152,53),(152,264),(153,59),(154,72),(154,246),(155,66),(155,244),(156,34),(156,187),(156,267),(157,38),(157,185),(158,22),(158,101),(158,277),(159,20),(159,168),(159,221),(160,19),(160,167),(160,212),(161,174),(162,3),(162,204),(163,111),(163,195),(164,134),(164,171),(165,112),(165,115),(166,74),(166,113),(167,173),(167,211),(168,173),(168,196),(169,122),(169,181),(169,268),(170,114),(170,123),(170,268),(171,75),(171,77),(172,115),(172,133),(172,261),(173,110),(173,172),(174,63),(174,194),(175,55),(175,94),(176,56),(176,60),(176,260),(177,71),(177,139),(177,221),(178,100),(178,118),(178,262),(179,167),(179,168),(180,59),(180,93),(181,47),(181,105),(181,106),(182,135),(182,199),(182,245),(183,61),(183,132),(183,241),(184,129),(184,131),(185,192),(185,205),(186,176),(186,198),(186,252),(187,184),(187,189),(188,53),(188,78),(189,72),(189,131),(190,96),(190,103),(191,65),(191,73),(191,221),(192,130),(192,148),(192,223),(193,102),(193,144),(193,212),(194,99),(194,190),(194,277),(195,68),(195,69),(195,215),(196,87),(196,110),(197,63),(197,158),(198,56),(198,92),(198,261),(199,62),(199,68),(199,246),(200,81),(200,176),(201,109),(201,205),(202,31),(202,120),(202,193),(203,39),(203,174),(203,197),(204,117),(204,118),(204,207),(205,130),(205,147),(205,166),(206,48),(206,177),(206,191),(206,209),(207,57),(207,58),(207,64),(208,128),(208,137),(208,183),(209,71),(209,73),(209,86),(210,114),(210,178),(210,204),(211,150),(211,165),(211,172),(212,185),(212,201),(213,90),(213,251),(214,9),(214,252),(215,249),(215,271),(216,266),(216,267),(217,259),(217,263),(218,247),(218,248),(219,7),(219,248),(220,187),(220,233),(221,186),(221,200),(221,228),(222,234),(222,250),(223,80),(223,243),(224,84),(224,241),(224,247),(225,242),(226,238),(227,83),(227,245),(228,81),(228,252),(229,251),(231,257),(232,249),(232,253),(233,184),(233,275),(234,89),(234,257),(235,85),(235,256),(236,85),(236,279),(237,82),(238,8),(238,276),(239,79),(239,278),(240,231),(240,250),(241,239),(241,255),(242,240),(243,229),(243,274),(244,230),(245,232),(245,246),(246,235),(246,236),(246,253),(247,254),(247,255),(248,188),(248,254),(249,279),(250,257),(251,264),(252,208),(252,260),(253,256),(253,279),(254,78),(254,278),(255,278),(256,237),(257,244),(258,25),(258,213),(258,274),(259,108),(260,137),(260,226),(261,107),(261,218),(261,224),(262,136),(262,175),(262,273),(263,108),(263,182),(264,151),(264,272),(265,153),(265,180),(266,127),(266,164),(267,143),(267,164),(268,105),(268,217),(269,111),(270,154),(270,245),(271,141),(271,279),(272,95),(273,94),(273,227),(273,233),(274,152),(274,251),(275,129),(275,242),(276,138),(276,278),(277,103),(277,149),(277,216),(278,126),(279,98),(279,237)],280)
=> ? = 28
[1,1,1,1,1,0,0,0,0,0]
=> [[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0]]
=> [[1,2,3,4,5],[2,3,4,5],[3,4,5],[4,5],[5]]
=> 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=> ? = 42
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,4,4],[5,5],[6]]
=> ([],1)
=> ? = 1
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [[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)
=> 2
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[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)
=> 2
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [[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,-1,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,4,5],[5,6],[6]]
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,5,6],[5,6],[6]]
=> ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8)
=> ? = 5
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[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)
=> 2
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[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)
=> 4
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,4],[4,4,5],[5,5],[6]]
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,4],[4,4,5],[5,6],[6]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,4],[4,5,6],[5,6],[6]]
=> ([(0,5),(0,6),(1,8),(2,9),(3,8),(3,9),(4,1),(5,4),(6,7),(7,2),(7,3),(8,10),(9,10)],11)
=> ? = 7
[1,0,1,0,1,1,1,0,0,0,1,0]
=> [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,4,5],[4,4,5],[5,5],[6]]
=> ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8)
=> ? = 5
[1,0,1,0,1,1,1,0,0,1,0,0]
=> [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,4,5],[4,4,5],[5,6],[6]]
=> ([(0,3),(0,7),(1,8),(2,8),(3,9),(4,5),(5,1),(6,2),(7,4),(7,9),(9,6)],10)
=> ? = 7
[1,0,1,0,1,1,1,0,1,0,0,0]
=> [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,4,5],[4,5,6],[5,6],[6]]
=> ([(0,9),(0,11),(1,18),(2,17),(3,19),(4,13),(4,19),(5,12),(5,13),(6,16),(7,14),(8,5),(8,18),(9,10),(10,3),(10,4),(11,1),(11,8),(12,17),(13,15),(15,16),(16,14),(17,7),(18,2),(18,12),(19,6),(19,15)],20)
=> ? = 9
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,4,5,6],[4,5,6],[5,6],[6]]
=> ([(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)
=> ? = 14
[1,0,1,1,0,0,1,0,1,0,1,0]
=> [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[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)
=> 2
[1,0,1,1,0,0,1,0,1,1,0,0]
=> [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[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)
=> 4
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[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)
=> 4
[1,0,1,1,0,0,1,1,0,1,0,0]
=> [[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,-1,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,3],[4,4,5],[5,6],[6]]
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 6
[1,0,1,1,0,0,1,1,1,0,0,0]
=> [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,3],[4,5,6],[5,6],[6]]
=> ([(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)
=> ? = 10
[1,0,1,1,0,1,0,0,1,0,1,0]
=> [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,4],[4,4,4],[5,5],[6]]
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,1,0,1,0,0,1,1,0,0]
=> [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,4],[4,4,4],[5,6],[6]]
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 6
[1,0,1,1,0,1,0,1,0,0,1,0]
=> [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,4],[4,4,5],[5,5],[6]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[1,0,1,1,0,1,0,1,0,1,0,0]
=> [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,4],[4,4,5],[5,6],[6]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[1,0,1,1,0,1,0,1,1,0,0,0]
=> [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,4],[4,5,6],[5,6],[6]]
=> ([(0,6),(0,7),(1,11),(2,9),(3,9),(3,10),(4,2),(5,1),(5,10),(6,4),(7,8),(8,3),(8,5),(9,12),(10,11),(10,12),(11,13),(12,13)],14)
=> ? = 9
[1,0,1,1,0,1,1,0,0,0,1,0]
=> [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,4,5],[4,4,5],[5,5],[6]]
=> ([(0,5),(0,6),(1,8),(2,9),(3,8),(3,9),(4,1),(5,4),(6,7),(7,2),(7,3),(8,10),(9,10)],11)
=> ? = 7
[1,0,1,1,0,1,1,0,0,1,0,0]
=> [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,4,5],[4,4,5],[5,6],[6]]
=> ([(0,4),(0,7),(1,9),(2,10),(3,9),(3,10),(4,11),(5,8),(6,1),(7,5),(7,11),(8,2),(8,3),(9,12),(10,12),(11,6)],13)
=> ? = 9
[1,0,1,1,0,1,1,0,1,0,0,0]
=> [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,0,1,0],[0,0,0,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,4,5],[4,5,6],[5,6],[6]]
=> ([(0,10),(0,12),(1,23),(2,22),(3,14),(3,24),(4,15),(5,13),(5,14),(6,18),(7,16),(7,20),(8,5),(8,23),(9,4),(9,24),(10,11),(11,3),(11,9),(12,1),(12,8),(13,22),(14,19),(15,16),(15,21),(16,25),(18,17),(19,20),(19,21),(20,18),(20,25),(21,25),(22,6),(23,2),(23,13),(24,7),(24,15),(24,19),(25,17)],26)
=> ? = 12
[1,1,0,0,1,0,1,0,1,0,1,0]
=> [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[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)
=> 2
[1,1,0,0,1,0,1,0,1,1,0,0]
=> [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[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)
=> 4
[1,1,0,0,1,0,1,1,0,0,1,0]
=> [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[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)
=> 4
[1,1,0,0,1,0,1,1,0,1,0,0]
=> [[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,-1,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,3],[4,4,5],[5,6],[6]]
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 6
[1,1,0,0,1,1,0,0,1,0,1,0]
=> [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[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)
=> 4
[1,1,0,0,1,1,0,1,0,0,1,0]
=> [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,4],[4,4,5],[5,5],[6]]
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 6
[1,1,0,1,0,0,1,0,1,0,1,0]
=> [[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,3],[4,4,4],[5,5],[6]]
=> ([(0,2),(2,1)],3)
=> 3
[1,1,0,1,0,0,1,0,1,1,0,0]
=> [[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,3],[4,4,4],[5,6],[6]]
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 6
[1,1,0,1,0,0,1,1,0,0,1,0]
=> [[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,3],[4,4,5],[5,5],[6]]
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 6
Description
The number of cuts of a poset.
A cut is a subset $A$ of the poset such that the set of lower bounds of the set of upper bounds of $A$ is exactly $A$.
Matching statistic: St001880
Mp00137: Dyck paths —to symmetric ASM⟶ Alternating sign matrices
Mp00001: Alternating sign matrices —to semistandard tableau via monotone triangles⟶ Semistandard tableaux
Mp00214: Semistandard tableaux —subcrystal⟶ Posets
St001880: Posets ⟶ ℤResult quality: 4% ●values known / values provided: 4%●distinct values known / distinct values provided: 5%
Mp00001: Alternating sign matrices —to semistandard tableau via monotone triangles⟶ Semistandard tableaux
Mp00214: Semistandard tableaux —subcrystal⟶ Posets
St001880: Posets ⟶ ℤResult quality: 4% ●values known / values provided: 4%●distinct values known / distinct values provided: 5%
Values
[1,0]
=> [[1]]
=> [[1]]
=> ([],1)
=> ? = 1
[1,0,1,0]
=> [[1,0],[0,1]]
=> [[1,1],[2]]
=> ([],1)
=> ? = 1
[1,1,0,0]
=> [[0,1],[1,0]]
=> [[1,2],[2]]
=> ([(0,1)],2)
=> ? = 2
[1,0,1,0,1,0]
=> [[1,0,0],[0,1,0],[0,0,1]]
=> [[1,1,1],[2,2],[3]]
=> ([],1)
=> ? = 1
[1,0,1,1,0,0]
=> [[1,0,0],[0,0,1],[0,1,0]]
=> [[1,1,1],[2,3],[3]]
=> ([(0,1)],2)
=> ? = 2
[1,1,0,0,1,0]
=> [[0,1,0],[1,0,0],[0,0,1]]
=> [[1,1,2],[2,2],[3]]
=> ([(0,1)],2)
=> ? = 2
[1,1,0,1,0,0]
=> [[0,1,0],[1,-1,1],[0,1,0]]
=> [[1,1,2],[2,3],[3]]
=> ([(0,2),(2,1)],3)
=> 3
[1,1,1,0,0,0]
=> [[0,0,1],[0,1,0],[1,0,0]]
=> [[1,2,3],[2,3],[3]]
=> ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8)
=> ? = 5
[1,0,1,0,1,0,1,0]
=> [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,2],[3,3],[4]]
=> ([],1)
=> ? = 1
[1,0,1,0,1,1,0,0]
=> [[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)
=> ? = 2
[1,0,1,1,0,0,1,0]
=> [[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)
=> ? = 2
[1,0,1,1,0,1,0,0]
=> [[1,0,0,0],[0,0,1,0],[0,1,-1,1],[0,0,1,0]]
=> [[1,1,1,1],[2,2,3],[3,4],[4]]
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,1,1,0,0,0]
=> [[1,0,0,0],[0,0,0,1],[0,0,1,0],[0,1,0,0]]
=> [[1,1,1,1],[2,3,4],[3,4],[4]]
=> ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8)
=> ? = 5
[1,1,0,0,1,0,1,0]
=> [[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)
=> ? = 2
[1,1,0,0,1,1,0,0]
=> [[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)
=> 4
[1,1,0,1,0,0,1,0]
=> [[0,1,0,0],[1,-1,1,0],[0,1,0,0],[0,0,0,1]]
=> [[1,1,1,2],[2,2,3],[3,3],[4]]
=> ([(0,2),(2,1)],3)
=> 3
[1,1,0,1,0,1,0,0]
=> [[0,1,0,0],[1,-1,1,0],[0,1,-1,1],[0,0,1,0]]
=> [[1,1,1,2],[2,2,3],[3,4],[4]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[1,1,0,1,1,0,0,0]
=> [[0,1,0,0],[1,-1,0,1],[0,0,1,0],[0,1,0,0]]
=> [[1,1,1,2],[2,3,4],[3,4],[4]]
=> ([(0,5),(0,6),(1,8),(2,9),(3,8),(3,9),(4,1),(5,4),(6,7),(7,2),(7,3),(8,10),(9,10)],11)
=> ? = 7
[1,1,1,0,0,0,1,0]
=> [[0,0,1,0],[0,1,0,0],[1,0,0,0],[0,0,0,1]]
=> [[1,1,2,3],[2,2,3],[3,3],[4]]
=> ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8)
=> ? = 5
[1,1,1,0,0,1,0,0]
=> [[0,0,1,0],[0,1,0,0],[1,0,-1,1],[0,0,1,0]]
=> [[1,1,2,3],[2,2,3],[3,4],[4]]
=> ([(0,3),(0,7),(1,8),(2,8),(3,9),(4,5),(5,1),(6,2),(7,4),(7,9),(9,6)],10)
=> ? = 7
[1,1,1,0,1,0,0,0]
=> [[0,0,1,0],[0,1,-1,1],[1,-1,1,0],[0,1,0,0]]
=> [[1,1,2,3],[2,3,4],[3,4],[4]]
=> ([(0,9),(0,11),(1,18),(2,17),(3,19),(4,13),(4,19),(5,12),(5,13),(6,16),(7,14),(8,5),(8,18),(9,10),(10,3),(10,4),(11,1),(11,8),(12,17),(13,15),(15,16),(16,14),(17,7),(18,2),(18,12),(19,6),(19,15)],20)
=> ? = 9
[1,1,1,1,0,0,0,0]
=> [[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)
=> ? = 14
[1,0,1,0,1,0,1,0,1,0]
=> [[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]]
=> [[1,1,1,1,1],[2,2,2,2],[3,3,3],[4,4],[5]]
=> ([],1)
=> ? = 1
[1,0,1,0,1,0,1,1,0,0]
=> [[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)
=> ? = 2
[1,0,1,0,1,1,0,0,1,0]
=> [[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)
=> ? = 2
[1,0,1,0,1,1,0,1,0,0]
=> [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
=> [[1,1,1,1,1],[2,2,2,2],[3,3,4],[4,5],[5]]
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,0,1,1,1,0,0,0]
=> [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0]]
=> [[1,1,1,1,1],[2,2,2,2],[3,4,5],[4,5],[5]]
=> ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8)
=> ? = 5
[1,0,1,1,0,0,1,0,1,0]
=> [[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)
=> ? = 2
[1,0,1,1,0,0,1,1,0,0]
=> [[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)
=> 4
[1,0,1,1,0,1,0,0,1,0]
=> [[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [[1,1,1,1,1],[2,2,2,3],[3,3,4],[4,4],[5]]
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,1,0,1,0,1,0,0]
=> [[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
=> [[1,1,1,1,1],[2,2,2,3],[3,3,4],[4,5],[5]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[1,0,1,1,0,1,1,0,0,0]
=> [[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,0,1],[0,0,0,1,0],[0,0,1,0,0]]
=> [[1,1,1,1,1],[2,2,2,3],[3,4,5],[4,5],[5]]
=> ([(0,5),(0,6),(1,8),(2,9),(3,8),(3,9),(4,1),(5,4),(6,7),(7,2),(7,3),(8,10),(9,10)],11)
=> ? = 7
[1,0,1,1,1,0,0,0,1,0]
=> [[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [[1,1,1,1,1],[2,2,3,4],[3,3,4],[4,4],[5]]
=> ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8)
=> ? = 5
[1,0,1,1,1,0,0,1,0,0]
=> [[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,-1,1],[0,0,0,1,0]]
=> [[1,1,1,1,1],[2,2,3,4],[3,3,4],[4,5],[5]]
=> ([(0,3),(0,7),(1,8),(2,8),(3,9),(4,5),(5,1),(6,2),(7,4),(7,9),(9,6)],10)
=> ? = 7
[1,0,1,1,1,0,1,0,0,0]
=> [[1,0,0,0,0],[0,0,0,1,0],[0,0,1,-1,1],[0,1,-1,1,0],[0,0,1,0,0]]
=> [[1,1,1,1,1],[2,2,3,4],[3,4,5],[4,5],[5]]
=> ([(0,9),(0,11),(1,18),(2,17),(3,19),(4,13),(4,19),(5,12),(5,13),(6,16),(7,14),(8,5),(8,18),(9,10),(10,3),(10,4),(11,1),(11,8),(12,17),(13,15),(15,16),(16,14),(17,7),(18,2),(18,12),(19,6),(19,15)],20)
=> ? = 9
[1,0,1,1,1,1,0,0,0,0]
=> [[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)
=> ? = 14
[1,1,0,0,1,0,1,0,1,0]
=> [[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)
=> ? = 2
[1,1,0,0,1,0,1,1,0,0]
=> [[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)
=> 4
[1,1,0,0,1,1,0,0,1,0]
=> [[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)
=> 4
[1,1,0,0,1,1,0,1,0,0]
=> [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
=> [[1,1,1,1,2],[2,2,2,2],[3,3,4],[4,5],[5]]
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 6
[1,1,0,0,1,1,1,0,0,0]
=> [[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)
=> ? = 10
[1,1,0,1,0,0,1,0,1,0]
=> [[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
=> [[1,1,1,1,2],[2,2,2,3],[3,3,3],[4,4],[5]]
=> ([(0,2),(2,1)],3)
=> 3
[1,1,0,1,0,0,1,1,0,0]
=> [[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
=> [[1,1,1,1,2],[2,2,2,3],[3,3,3],[4,5],[5]]
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 6
[1,1,0,1,0,1,0,0,1,0]
=> [[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [[1,1,1,1,2],[2,2,2,3],[3,3,4],[4,4],[5]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[1,1,0,1,0,1,0,1,0,0]
=> [[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
=> [[1,1,1,1,2],[2,2,2,3],[3,3,4],[4,5],[5]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[1,1,0,1,0,1,1,0,0,0]
=> [[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,0,1],[0,0,0,1,0],[0,0,1,0,0]]
=> [[1,1,1,1,2],[2,2,2,3],[3,4,5],[4,5],[5]]
=> ([(0,6),(0,7),(1,11),(2,9),(3,9),(3,10),(4,2),(5,1),(5,10),(6,4),(7,8),(8,3),(8,5),(9,12),(10,11),(10,12),(11,13),(12,13)],14)
=> ? = 9
[1,1,0,1,1,0,0,0,1,0]
=> [[0,1,0,0,0],[1,-1,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [[1,1,1,1,2],[2,2,3,4],[3,3,4],[4,4],[5]]
=> ([(0,5),(0,6),(1,8),(2,9),(3,8),(3,9),(4,1),(5,4),(6,7),(7,2),(7,3),(8,10),(9,10)],11)
=> ? = 7
[1,1,0,1,1,0,0,1,0,0]
=> [[0,1,0,0,0],[1,-1,0,1,0],[0,0,1,0,0],[0,1,0,-1,1],[0,0,0,1,0]]
=> [[1,1,1,1,2],[2,2,3,4],[3,3,4],[4,5],[5]]
=> ([(0,4),(0,7),(1,9),(2,10),(3,9),(3,10),(4,11),(5,8),(6,1),(7,5),(7,11),(8,2),(8,3),(9,12),(10,12),(11,6)],13)
=> ? = 9
[1,1,0,1,1,0,1,0,0,0]
=> [[0,1,0,0,0],[1,-1,0,1,0],[0,0,1,-1,1],[0,1,-1,1,0],[0,0,1,0,0]]
=> [[1,1,1,1,2],[2,2,3,4],[3,4,5],[4,5],[5]]
=> ([(0,10),(0,12),(1,23),(2,22),(3,14),(3,24),(4,15),(5,13),(5,14),(6,18),(7,16),(7,20),(8,5),(8,23),(9,4),(9,24),(10,11),(11,3),(11,9),(12,1),(12,8),(13,22),(14,19),(15,16),(15,21),(16,25),(18,17),(19,20),(19,21),(20,18),(20,25),(21,25),(22,6),(23,2),(23,13),(24,7),(24,15),(24,19),(25,17)],26)
=> ? = 12
[1,1,0,1,1,1,0,0,0,0]
=> [[0,1,0,0,0],[1,-1,0,0,1],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0]]
=> [[1,1,1,1,2],[2,3,4,5],[3,4,5],[4,5],[5]]
=> ([(0,5),(0,14),(0,15),(1,26),(2,9),(2,25),(3,13),(3,24),(4,16),(5,11),(5,12),(6,69),(7,64),(8,49),(9,6),(9,52),(10,20),(10,59),(11,19),(11,65),(12,17),(12,65),(13,18),(13,22),(13,71),(14,2),(14,29),(15,3),(15,29),(16,39),(16,55),(17,56),(17,68),(18,57),(18,66),(19,58),(19,67),(20,51),(20,53),(21,40),(21,41),(22,57),(22,72),(23,28),(23,54),(23,70),(24,58),(24,71),(25,52),(25,56),(26,27),(26,69),(26,72),(27,45),(27,60),(28,34),(28,48),(28,50),(29,1),(30,76),(31,75),(32,77),(33,74),(33,80),(34,73),(34,78),(35,73),(35,77),(36,82),(37,79),(38,80),(39,74),(40,7),(40,76),(41,8),(41,76),(42,55),(42,79),(43,59),(44,39),(45,53),(45,83),(46,33),(46,81),(47,32),(47,83),(48,42),(48,78),(49,44),(50,46),(50,73),(51,44),(52,10),(52,43),(53,62),(54,34),(54,75),(55,36),(55,74),(56,43),(57,63),(58,61),(59,49),(59,51),(60,35),(60,50),(60,83),(61,31),(61,70),(62,33),(62,38),(63,32),(63,35),(64,37),(64,42),(65,21),(65,67),(65,68),(66,31),(66,54),(67,30),(67,40),(68,30),(68,41),(69,45),(69,47),(70,48),(70,64),(70,75),(71,23),(71,61),(71,66),(72,47),(72,60),(72,63),(73,81),(74,82),(75,37),(75,78),(76,4),(77,38),(77,81),(78,79),(79,36),(80,82),(81,80),(83,46),(83,62),(83,77)],84)
=> ? = 19
[1,1,1,0,0,0,1,0,1,0]
=> [[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
=> [[1,1,1,2,3],[2,2,2,3],[3,3,3],[4,4],[5]]
=> ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8)
=> ? = 5
[1,1,1,0,0,0,1,1,0,0]
=> [[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)
=> ? = 10
[1,1,1,0,0,1,0,0,1,0]
=> [[0,0,1,0,0],[0,1,0,0,0],[1,0,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [[1,1,1,2,3],[2,2,2,3],[3,3,4],[4,4],[5]]
=> ([(0,3),(0,7),(1,8),(2,8),(3,9),(4,5),(5,1),(6,2),(7,4),(7,9),(9,6)],10)
=> ? = 7
[1,1,1,0,0,1,0,1,0,0]
=> [[0,0,1,0,0],[0,1,0,0,0],[1,0,-1,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
=> [[1,1,1,2,3],[2,2,2,3],[3,3,4],[4,5],[5]]
=> ([(0,3),(0,8),(1,10),(2,10),(3,9),(4,6),(5,4),(5,11),(6,2),(7,1),(8,5),(8,9),(9,11),(11,7)],12)
=> ? = 9
[1,1,1,0,0,1,1,0,0,0]
=> [[0,0,1,0,0],[0,1,0,0,0],[1,0,-1,0,1],[0,0,0,1,0],[0,0,1,0,0]]
=> [[1,1,1,2,3],[2,2,2,3],[3,4,5],[4,5],[5]]
=> ([(0,7),(0,8),(0,11),(1,25),(2,10),(2,24),(3,5),(3,12),(3,26),(4,28),(5,6),(5,29),(6,4),(6,27),(7,2),(7,19),(8,3),(8,18),(9,15),(9,16),(10,13),(10,23),(11,18),(11,19),(12,22),(12,23),(12,29),(13,31),(14,30),(15,30),(16,30),(17,20),(18,26),(19,24),(20,14),(21,16),(22,25),(22,31),(23,17),(23,31),(24,13),(25,9),(25,21),(26,1),(26,22),(27,20),(27,28),(28,14),(28,15),(29,17),(29,27),(31,21)],32)
=> ? = 16
[1,1,1,0,1,0,0,0,1,0]
=> [[0,0,1,0,0],[0,1,-1,1,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [[1,1,1,2,3],[2,2,3,4],[3,3,4],[4,4],[5]]
=> ([(0,9),(0,11),(1,18),(2,17),(3,19),(4,13),(4,19),(5,12),(5,13),(6,16),(7,14),(8,5),(8,18),(9,10),(10,3),(10,4),(11,1),(11,8),(12,17),(13,15),(15,16),(16,14),(17,7),(18,2),(18,12),(19,6),(19,15)],20)
=> ? = 9
[1,1,1,0,1,0,0,1,0,0]
=> [[0,0,1,0,0],[0,1,-1,1,0],[1,-1,1,0,0],[0,1,0,-1,1],[0,0,0,1,0]]
=> [[1,1,1,2,3],[2,2,3,4],[3,3,4],[4,5],[5]]
=> ([(0,10),(0,11),(1,13),(1,14),(2,21),(3,20),(4,14),(4,20),(5,17),(6,16),(7,18),(8,12),(9,1),(9,22),(10,5),(10,15),(11,8),(11,15),(12,3),(12,4),(13,21),(14,19),(15,9),(15,17),(17,22),(18,16),(19,18),(20,7),(20,19),(21,6),(22,2),(22,13)],23)
=> ? = 12
[1,1,1,0,1,0,1,0,0,0]
=> [[0,0,1,0,0],[0,1,-1,1,0],[1,-1,1,-1,1],[0,1,-1,1,0],[0,0,1,0,0]]
=> [[1,1,1,2,3],[2,2,3,4],[3,4,5],[4,5],[5]]
=> ([(0,2),(0,3),(1,9),(1,15),(2,1),(3,7),(3,8),(4,30),(5,31),(6,23),(7,16),(7,37),(8,10),(8,37),(9,11),(9,36),(10,34),(11,35),(12,25),(12,29),(13,19),(13,22),(14,21),(14,27),(15,26),(15,36),(16,26),(16,33),(17,39),(18,38),(19,12),(19,38),(20,6),(21,4),(21,39),(22,5),(22,38),(24,23),(25,28),(26,32),(27,25),(27,39),(28,24),(29,20),(30,24),(31,20),(32,17),(32,27),(33,18),(33,19),(34,18),(34,22),(35,17),(35,21),(36,14),(36,32),(36,35),(37,13),(37,33),(37,34),(38,29),(38,31),(39,28),(39,30)],40)
=> ? = 14
[1,1,1,0,1,1,0,0,0,0]
=> [[0,0,1,0,0],[0,1,-1,0,1],[1,-1,0,1,0],[0,0,1,0,0],[0,1,0,0,0]]
=> [[1,1,1,2,3],[2,3,4,5],[3,4,5],[4,5],[5]]
=> ([(0,4),(0,14),(0,15),(1,29),(2,6),(2,27),(3,13),(3,28),(4,10),(4,11),(5,102),(6,5),(6,87),(7,31),(7,99),(8,25),(8,98),(9,26),(9,72),(10,23),(10,109),(11,24),(11,33),(11,109),(12,22),(12,108),(13,17),(13,18),(13,107),(14,2),(14,38),(15,3),(15,38),(16,84),(16,85),(17,90),(17,111),(18,90),(18,101),(19,82),(19,83),(20,81),(20,100),(21,34),(21,89),(21,104),(22,86),(22,106),(23,91),(23,110),(24,80),(24,105),(25,78),(25,79),(26,52),(26,88),(27,87),(27,103),(28,91),(28,107),(29,30),(29,102),(29,111),(30,63),(30,96),(31,44),(31,71),(31,76),(32,37),(32,51),(32,77),(33,80),(33,94),(33,103),(34,62),(34,74),(34,75),(35,133),(36,9),(37,8),(37,127),(38,1),(39,118),(40,117),(40,122),(41,119),(42,119),(42,126),(43,116),(43,127),(44,112),(44,120),(45,112),(45,113),(46,114),(46,116),(47,121),(48,122),(49,125),(50,113),(51,20),(51,114),(51,127),(52,117),(53,72),(54,88),(54,121),(55,45),(55,132),(56,48),(57,84),(57,124),(58,76),(58,134),(59,66),(60,56),(61,54),(62,55),(62,126),(63,86),(63,129),(64,53),(64,134),(65,47),(66,70),(67,40),(68,40),(68,123),(69,41),(69,129),(70,39),(70,128),(71,54),(71,120),(72,52),(73,44),(73,118),(74,58),(74,115),(75,82),(75,115),(75,126),(76,68),(76,112),(77,16),(77,57),(77,114),(78,65),(79,61),(80,59),(80,130),(81,36),(82,60),(82,131),(83,53),(83,131),(84,78),(84,128),(85,73),(85,128),(86,92),(87,12),(87,95),(88,49),(88,117),(89,19),(89,75),(89,133),(90,97),(91,93),(92,45),(92,50),(93,35),(93,104),(94,46),(94,77),(94,130),(95,66),(95,108),(96,42),(96,62),(96,129),(97,41),(97,42),(98,36),(98,79),(99,61),(99,71),(100,58),(100,64),(101,35),(101,89),(102,63),(102,69),(103,59),(103,95),(104,74),(104,100),(104,133),(105,37),(105,43),(105,130),(106,39),(106,73),(107,21),(107,93),(107,101),(108,70),(108,85),(108,106),(109,32),(109,94),(109,105),(109,110),(110,43),(110,46),(110,51),(111,69),(111,96),(111,97),(112,123),(113,48),(113,123),(114,7),(114,124),(115,131),(115,134),(116,124),(117,125),(118,47),(118,120),(119,50),(119,132),(120,121),(121,49),(122,125),(123,122),(124,99),(126,60),(126,132),(127,81),(127,98),(128,65),(128,118),(129,55),(129,92),(129,119),(130,57),(130,116),(131,67),(132,56),(132,113),(133,64),(133,83),(133,115),(134,67),(134,68)],135)
=> ? = 23
[1,1,1,1,0,0,0,0,1,0]
=> [[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)
=> ? = 14
[1,1,1,1,0,0,0,1,0,0]
=> [[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[1,0,0,-1,1],[0,0,0,1,0]]
=> [[1,1,2,3,4],[2,2,3,4],[3,3,4],[4,5],[5]]
=> ([(0,16),(0,17),(0,28),(1,22),(2,19),(3,11),(3,21),(4,54),(5,55),(6,26),(6,57),(7,25),(7,67),(8,23),(8,64),(9,24),(9,65),(10,14),(10,56),(11,15),(11,58),(12,3),(12,37),(13,27),(13,66),(14,59),(15,60),(16,13),(16,53),(17,6),(17,61),(18,51),(18,52),(19,33),(19,34),(20,35),(20,36),(21,50),(21,58),(22,18),(22,59),(22,60),(23,41),(23,43),(24,42),(24,44),(25,50),(25,63),(26,29),(26,46),(27,29),(27,45),(28,12),(28,53),(28,61),(29,70),(30,71),(31,69),(32,68),(33,68),(34,68),(35,4),(35,69),(36,5),(36,69),(37,1),(38,33),(39,34),(40,64),(41,48),(42,49),(43,38),(44,39),(45,62),(45,70),(46,56),(46,70),(47,65),(48,32),(49,32),(50,40),(51,42),(51,71),(52,41),(52,71),(53,7),(53,66),(54,38),(55,39),(56,9),(56,47),(57,10),(57,46),(58,8),(58,40),(59,30),(59,51),(60,30),(60,52),(61,37),(61,57),(62,31),(62,36),(63,31),(63,35),(64,43),(64,54),(65,44),(65,55),(66,45),(66,67),(67,20),(67,62),(67,63),(69,2),(70,47),(71,48),(71,49)],72)
=> ? = 19
[1,1,1,1,0,0,1,0,0,0]
=> [[0,0,0,1,0],[0,0,1,0,0],[0,1,0,-1,1],[1,0,-1,1,0],[0,0,1,0,0]]
=> [[1,1,2,3,4],[2,2,3,4],[3,4,5],[4,5],[5]]
=> ([(0,15),(0,16),(0,30),(1,26),(2,14),(2,95),(3,78),(4,79),(5,92),(6,77),(7,29),(7,93),(8,27),(8,96),(9,28),(9,94),(10,12),(10,32),(10,80),(11,84),(12,13),(12,86),(13,11),(13,97),(14,19),(14,98),(15,10),(15,54),(16,2),(16,24),(16,76),(17,47),(17,71),(18,46),(18,72),(19,41),(19,91),(20,35),(20,73),(21,69),(21,87),(22,25),(22,75),(22,90),(23,45),(23,70),(24,31),(24,88),(24,95),(25,49),(25,50),(26,39),(26,40),(27,52),(27,53),(28,41),(28,89),(29,33),(29,57),(30,54),(30,76),(31,67),(31,68),(31,85),(32,56),(32,68),(32,86),(33,110),(34,106),(34,107),(35,21),(35,111),(36,100),(37,101),(37,106),(38,102),(39,102),(40,102),(41,99),(42,104),(43,113),(44,103),(45,6),(45,112),(46,7),(46,108),(47,5),(47,107),(48,3),(48,103),(49,55),(49,105),(50,33),(50,105),(51,61),(52,63),(53,61),(54,80),(55,52),(55,113),(56,79),(56,109),(57,60),(57,110),(58,90),(59,81),(60,62),(61,39),(62,40),(63,38),(64,38),(65,37),(65,111),(66,36),(66,108),(67,82),(67,109),(68,83),(68,109),(69,59),(70,48),(70,112),(71,42),(71,107),(72,69),(72,108),(73,23),(73,74),(73,111),(74,45),(74,101),(75,50),(75,100),(76,9),(76,88),(77,51),(78,62),(79,22),(79,58),(80,4),(80,56),(81,60),(81,78),(82,34),(82,47),(83,66),(83,72),(84,36),(84,75),(85,35),(85,65),(86,18),(86,83),(86,97),(87,44),(87,48),(88,67),(88,94),(89,34),(89,71),(89,99),(90,49),(90,92),(90,100),(91,37),(91,74),(91,99),(92,43),(92,55),(93,57),(93,81),(94,17),(94,82),(94,89),(95,20),(95,85),(95,98),(96,51),(96,53),(97,46),(97,66),(97,84),(98,65),(98,73),(98,91),(99,42),(99,106),(100,43),(100,105),(101,44),(101,112),(103,1),(104,96),(105,110),(105,113),(106,104),(107,8),(107,104),(108,59),(108,93),(109,58),(110,64),(111,70),(111,87),(111,101),(112,77),(112,103),(113,63),(113,64)],114)
=> ? = 23
[1,1,1,1,0,1,0,0,0,0]
=> [[0,0,0,1,0],[0,0,1,-1,1],[0,1,-1,1,0],[1,-1,1,0,0],[0,1,0,0,0]]
=> [[1,1,2,3,4],[2,3,4,5],[3,4,5],[4,5],[5]]
=> ([(0,2),(0,17),(0,18),(1,16),(1,41),(2,10),(2,15),(3,207),(4,50),(4,125),(5,181),(6,49),(6,180),(7,188),(8,138),(9,46),(9,208),(10,30),(10,206),(11,35),(11,54),(12,36),(12,97),(13,37),(13,163),(14,40),(14,44),(14,202),(15,28),(15,45),(15,206),(16,26),(16,27),(16,203),(17,1),(17,124),(18,14),(18,33),(18,124),(19,52),(19,201),(19,211),(20,196),(20,200),(21,89),(21,155),(22,149),(22,156),(23,150),(23,198),(24,154),(24,199),(25,90),(25,152),(26,162),(26,210),(27,162),(27,197),(28,159),(28,191),(29,153),(29,190),(30,161),(30,209),(31,144),(31,157),(32,141),(32,151),(33,145),(33,202),(34,143),(34,189),(35,147),(35,148),(36,142),(36,146),(37,88),(37,195),(38,87),(38,192),(39,51),(39,158),(39,194),(40,42),(40,160),(40,193),(41,161),(41,203),(42,102),(42,170),(43,122),(43,123),(43,178),(44,120),(44,160),(44,179),(45,159),(45,177),(45,179),(46,76),(46,119),(46,183),(47,64),(47,121),(47,140),(48,65),(48,86),(48,139),(49,60),(49,92),(49,93),(50,43),(50,169),(50,170),(50,210),(51,99),(51,100),(51,101),(52,104),(52,109),(52,165),(53,272),(54,13),(55,225),(55,275),(56,218),(56,219),(57,227),(57,270),(58,227),(58,269),(59,12),(60,219),(60,226),(61,255),(61,276),(62,253),(62,271),(63,277),(64,269),(64,270),(65,6),(65,265),(66,230),(67,231),(67,256),(68,236),(68,271),(69,236),(69,249),(70,229),(70,247),(71,214),(71,228),(72,235),(73,228),(73,265),(74,213),(74,229),(75,234),(76,225),(76,241),(77,231),(77,234),(78,272),(79,250),(80,274),(81,260),(82,230),(83,232),(84,239),(84,254),(85,237),(86,29),(86,214),(86,265),(87,223),(88,215),(89,244),(90,32),(90,264),(91,97),(92,107),(92,219),(93,128),(93,226),(94,83),(94,275),(95,66),(96,119),(96,266),(97,142),(98,82),(99,96),(99,216),(100,136),(100,220),(101,156),(101,216),(101,220),(102,116),(102,268),(103,91),(103,266),(104,175),(104,259),(105,121),(105,263),(106,140),(106,263),(107,84),(107,248),(108,135),(109,166),(109,259),(110,133),(110,223),(111,69),(112,76),(112,224),(113,88),(113,213),(114,117),(114,262),(115,70),(115,224),(116,54),(117,58),(117,273),(118,57),(118,220),(118,273),(119,127),(119,225),(120,157),(120,212),(121,163),(121,269),(122,106),(122,217),(123,104),(123,217),(123,262),(124,4),(124,145),(125,5),(125,169),(126,155),(127,134),(127,242),(128,132),(128,238),(129,67),(129,240),(130,74),(130,243),(130,258),(131,67),(131,235),(132,146),(132,239),(132,276),(133,70),(133,218),(133,243),(134,77),(134,222),(134,240),(135,62),(135,215),(135,232),(136,55),(136,233),(137,61),(137,238),(138,21),(138,126),(139,23),(139,186),(139,214),(140,24),(140,182),(140,270),(141,98),(142,75),(142,222),(143,171),(144,11),(144,116),(145,125),(146,79),(146,222),(147,113),(147,258),(148,80),(148,258),(149,91),(149,267),(150,112),(150,261),(151,95),(152,53),(152,264),(153,59),(154,72),(154,246),(155,66),(155,244),(156,34),(156,187),(156,267),(157,38),(157,185),(158,22),(158,101),(158,277),(159,20),(159,168),(159,221),(160,19),(160,167),(160,212),(161,174),(162,3),(162,204),(163,111),(163,195),(164,134),(164,171),(165,112),(165,115),(166,74),(166,113),(167,173),(167,211),(168,173),(168,196),(169,122),(169,181),(169,268),(170,114),(170,123),(170,268),(171,75),(171,77),(172,115),(172,133),(172,261),(173,110),(173,172),(174,63),(174,194),(175,55),(175,94),(176,56),(176,60),(176,260),(177,71),(177,139),(177,221),(178,100),(178,118),(178,262),(179,167),(179,168),(180,59),(180,93),(181,47),(181,105),(181,106),(182,135),(182,199),(182,245),(183,61),(183,132),(183,241),(184,129),(184,131),(185,192),(185,205),(186,176),(186,198),(186,252),(187,184),(187,189),(188,53),(188,78),(189,72),(189,131),(190,96),(190,103),(191,65),(191,73),(191,221),(192,130),(192,148),(192,223),(193,102),(193,144),(193,212),(194,99),(194,190),(194,277),(195,68),(195,69),(195,215),(196,87),(196,110),(197,63),(197,158),(198,56),(198,92),(198,261),(199,62),(199,68),(199,246),(200,81),(200,176),(201,109),(201,205),(202,31),(202,120),(202,193),(203,39),(203,174),(203,197),(204,117),(204,118),(204,207),(205,130),(205,147),(205,166),(206,48),(206,177),(206,191),(206,209),(207,57),(207,58),(207,64),(208,128),(208,137),(208,183),(209,71),(209,73),(209,86),(210,114),(210,178),(210,204),(211,150),(211,165),(211,172),(212,185),(212,201),(213,90),(213,251),(214,9),(214,252),(215,249),(215,271),(216,266),(216,267),(217,259),(217,263),(218,247),(218,248),(219,7),(219,248),(220,187),(220,233),(221,186),(221,200),(221,228),(222,234),(222,250),(223,80),(223,243),(224,84),(224,241),(224,247),(225,242),(226,238),(227,83),(227,245),(228,81),(228,252),(229,251),(231,257),(232,249),(232,253),(233,184),(233,275),(234,89),(234,257),(235,85),(235,256),(236,85),(236,279),(237,82),(238,8),(238,276),(239,79),(239,278),(240,231),(240,250),(241,239),(241,255),(242,240),(243,229),(243,274),(244,230),(245,232),(245,246),(246,235),(246,236),(246,253),(247,254),(247,255),(248,188),(248,254),(249,279),(250,257),(251,264),(252,208),(252,260),(253,256),(253,279),(254,78),(254,278),(255,278),(256,237),(257,244),(258,25),(258,213),(258,274),(259,108),(260,137),(260,226),(261,107),(261,218),(261,224),(262,136),(262,175),(262,273),(263,108),(263,182),(264,151),(264,272),(265,153),(265,180),(266,127),(266,164),(267,143),(267,164),(268,105),(268,217),(269,111),(270,154),(270,245),(271,141),(271,279),(272,95),(273,94),(273,227),(273,233),(274,152),(274,251),(275,129),(275,242),(276,138),(276,278),(277,103),(277,149),(277,216),(278,126),(279,98),(279,237)],280)
=> ? = 28
[1,1,1,1,1,0,0,0,0,0]
=> [[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0]]
=> [[1,2,3,4,5],[2,3,4,5],[3,4,5],[4,5],[5]]
=> 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=> ? = 42
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,4,4],[5,5],[6]]
=> ([],1)
=> ? = 1
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [[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)
=> ? = 2
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [[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,-1,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,4,5],[5,6],[6]]
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[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)
=> 4
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,4],[4,4,5],[5,5],[6]]
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,4],[4,4,5],[5,6],[6]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[1,0,1,1,0,0,1,0,1,1,0,0]
=> [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[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)
=> 4
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[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)
=> 4
[1,0,1,1,0,0,1,1,0,1,0,0]
=> [[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,-1,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,3],[4,4,5],[5,6],[6]]
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 6
[1,0,1,1,0,1,0,0,1,0,1,0]
=> [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,4],[4,4,4],[5,5],[6]]
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,1,0,1,0,0,1,1,0,0]
=> [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,4],[4,4,4],[5,6],[6]]
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 6
[1,0,1,1,0,1,0,1,0,0,1,0]
=> [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,4],[4,4,5],[5,5],[6]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[1,0,1,1,0,1,0,1,0,1,0,0]
=> [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,4],[4,4,5],[5,6],[6]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[1,1,0,0,1,0,1,0,1,1,0,0]
=> [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[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)
=> 4
[1,1,0,0,1,0,1,1,0,0,1,0]
=> [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[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)
=> 4
[1,1,0,0,1,0,1,1,0,1,0,0]
=> [[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,-1,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,3],[4,4,5],[5,6],[6]]
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 6
[1,1,0,0,1,1,0,0,1,0,1,0]
=> [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[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)
=> 4
[1,1,0,0,1,1,0,1,0,0,1,0]
=> [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,4],[4,4,5],[5,5],[6]]
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 6
[1,1,0,1,0,0,1,0,1,0,1,0]
=> [[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,3],[4,4,4],[5,5],[6]]
=> ([(0,2),(2,1)],3)
=> 3
[1,1,0,1,0,0,1,0,1,1,0,0]
=> [[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,3],[4,4,4],[5,6],[6]]
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 6
[1,1,0,1,0,0,1,1,0,0,1,0]
=> [[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,3],[4,4,5],[5,5],[6]]
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 6
[1,1,0,1,0,1,0,0,1,0,1,0]
=> [[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,4],[4,4,4],[5,5],[6]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[1,1,0,1,0,1,0,1,0,0,1,0]
=> [[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]]
=> [[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,4],[4,4,5],[5,5],[6]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[1,1,0,1,0,1,0,1,0,1,0,0]
=> [[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]
=> [[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,4],[4,4,5],[5,6],[6]]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
Description
The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice.
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