Your data matches 7 different statistics following compositions of up to 3 maps.
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Matching statistic: St000771
(load all 2 compositions to match this statistic)
Mapping
Mp00324: Graphs —chromatic difference sequence⟶ Integer compositions
Mp00314: Integer compositions —Foata bijection⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000771: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => [1] => [1] => ([],1)
 => 1
([(0,1)],2)
 => [1,1] => [1,1] => ([(0,1)],2)
 => 1
([(1,2)],3)
 => [2,1] => [2,1] => ([(0,2),(1,2)],3)
 => 1
([(0,2),(1,2)],3)
 => [2,1] => [2,1] => ([(0,2),(1,2)],3)
 => 1
([(0,1),(0,2),(1,2)],3)
 => [1,1,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 2
([(2,3)],4)
 => [3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2
([(1,3),(2,3)],4)
 => [3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2
([(0,3),(1,3),(2,3)],4)
 => [3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2
([(1,2),(1,3),(2,3)],4)
 => [2,1,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => [2,1,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [2,1,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [1,1,1,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3
([(3,4)],5)
 => [4,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 3
([(2,4),(3,4)],5)
 => [4,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 3
([(1,4),(2,4),(3,4)],5)
 => [4,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 3
([(0,4),(1,4),(2,4),(3,4)],5)
 => [4,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 3
([(2,3),(2,4),(3,4)],5)
 => [3,1,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(1,4),(2,3),(2,4),(3,4)],5)
 => [3,1,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,1,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,1,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [3,1,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,1,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,1,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,1),(2,3),(2,4),(3,4)],5)
 => [2,2,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => [2,2,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => [2,2,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => [2,2,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [2,2,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => [2,2,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [2,2,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [2,1,1,1] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [2,1,1,1] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [2,1,1,1] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [2,2,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => [2,2,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [2,1,1,1] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [1,1,1,1,1] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4
([(4,5)],6)
 => [5,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 4
([(3,5),(4,5)],6)
 => [5,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 4
([(2,5),(3,5),(4,5)],6)
 => [5,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 4
([(1,5),(2,5),(3,5),(4,5)],6)
 => [5,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 4
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => [5,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 4
([(3,4),(3,5),(4,5)],6)
 => [4,1,1] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
([(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1,1] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1,1] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1,1] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1,1] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [4,1,1] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1,1] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [4,1,1] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
Description
The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. The distance Laplacian of a graph is the (symmetric) matrix with row and column sums $0$, which has the negative distances between two vertices as its off-diagonal entries. This statistic is the largest multiplicity of an eigenvalue. For example, the cycle on four vertices has distance Laplacian $$ \left(\begin{array}{rrrr} 4 & -1 & -2 & -1 \\ -1 & 4 & -1 & -2 \\ -2 & -1 & 4 & -1 \\ -1 & -2 & -1 & 4 \end{array}\right). $$ Its eigenvalues are $0,4,4,6$, so the statistic is $2$. The path on four vertices has eigenvalues $0, 4.7\dots, 6, 9.2\dots$ and therefore statistic $1$.
Matching statistic: St000774
Mapping
Mp00324: Graphs —chromatic difference sequence⟶ Integer compositions
Mp00314: Integer compositions —Foata bijection⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000774: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => [1] => [1] => ([],1)
 => 1
([(0,1)],2)
 => [1,1] => [1,1] => ([(0,1)],2)
 => 1
([(1,2)],3)
 => [2,1] => [2,1] => ([(0,2),(1,2)],3)
 => 1
([(0,2),(1,2)],3)
 => [2,1] => [2,1] => ([(0,2),(1,2)],3)
 => 1
([(0,1),(0,2),(1,2)],3)
 => [1,1,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 2
([(2,3)],4)
 => [3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2
([(1,3),(2,3)],4)
 => [3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2
([(0,3),(1,3),(2,3)],4)
 => [3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2
([(1,2),(1,3),(2,3)],4)
 => [2,1,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => [2,1,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [2,1,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [1,1,1,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3
([(3,4)],5)
 => [4,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 3
([(2,4),(3,4)],5)
 => [4,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 3
([(1,4),(2,4),(3,4)],5)
 => [4,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 3
([(0,4),(1,4),(2,4),(3,4)],5)
 => [4,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 3
([(2,3),(2,4),(3,4)],5)
 => [3,1,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(1,4),(2,3),(2,4),(3,4)],5)
 => [3,1,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,1,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,1,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [3,1,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,1,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,1,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,1),(2,3),(2,4),(3,4)],5)
 => [2,2,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => [2,2,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => [2,2,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => [2,2,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [2,2,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => [2,2,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [2,2,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [2,1,1,1] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [2,1,1,1] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [2,1,1,1] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [2,2,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => [2,2,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [2,1,1,1] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [1,1,1,1,1] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4
([(4,5)],6)
 => [5,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 4
([(3,5),(4,5)],6)
 => [5,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 4
([(2,5),(3,5),(4,5)],6)
 => [5,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 4
([(1,5),(2,5),(3,5),(4,5)],6)
 => [5,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 4
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => [5,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 4
([(3,4),(3,5),(4,5)],6)
 => [4,1,1] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
([(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1,1] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1,1] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1,1] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1,1] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [4,1,1] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1,1] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [4,1,1] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
Description
The maximal multiplicity of a Laplacian eigenvalue in a graph.
Matching statistic: St000455
Mapping
Mp00111: Graphs —complement⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
Mp00156: Graphs —line graph⟶ Graphs
St000455: Graphs ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 33%
Values
([],1)
 => ([],1)
 => ([],1)
 => ([],0)
 => ? = 1 - 3
([(0,1)],2)
 => ([],2)
 => ([],1)
 => ([],0)
 => ? = 1 - 3
([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],1)
 => ? = 1 - 3
([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => ([(0,1)],2)
 => ([],1)
 => ? = 1 - 3
([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([],1)
 => ([],0)
 => ? = 2 - 3
([(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => -1 = 2 - 3
([(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => -1 = 2 - 3
([(0,3),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => -1 = 2 - 3
([(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],1)
 => ? = 1 - 3
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],1)
 => ? = 1 - 3
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ([(0,1)],2)
 => ([],1)
 => ? = 1 - 3
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ([],1)
 => ([],0)
 => ? = 3 - 3
([(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 0 = 3 - 3
([(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 0 = 3 - 3
([(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 0 = 3 - 3
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 0 = 3 - 3
([(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => -1 = 2 - 3
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => -1 = 2 - 3
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => -1 = 2 - 3
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => -1 = 2 - 3
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => -1 = 2 - 3
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => -1 = 2 - 3
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => -1 = 2 - 3
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([],1)
 => ? = 1 - 3
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],1)
 => ? = 1 - 3
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([],1)
 => ? = 1 - 3
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ? = 1 - 3
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([],1)
 => ? = 1 - 3
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => ([],1)
 => ? = 1 - 3
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => ([],1)
 => ? = 1 - 3
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],1)
 => ? = 2 - 3
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],1)
 => ? = 2 - 3
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],1)
 => ? = 2 - 3
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],1)
 => ? = 1 - 3
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,3)],5)
 => ([(0,1)],2)
 => ([],1)
 => ? = 1 - 3
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(3,4)],5)
 => ([(0,1)],2)
 => ([],1)
 => ? = 2 - 3
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ([],1)
 => ([],0)
 => ? = 4 - 3
([(4,5)],6)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,6),(1,7),(1,8),(1,9),(2,3),(2,4),(2,5),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(4,9),(5,6),(5,8),(6,7),(6,8),(7,9),(8,9)],10)
 => ? = 4 - 3
([(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,6),(1,7),(1,8),(1,9),(2,3),(2,4),(2,5),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(4,9),(5,6),(5,8),(6,7),(6,8),(7,9),(8,9)],10)
 => ? = 4 - 3
([(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,6),(1,7),(1,8),(1,9),(2,3),(2,4),(2,5),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(4,9),(5,6),(5,8),(6,7),(6,8),(7,9),(8,9)],10)
 => ? = 4 - 3
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,6),(1,7),(1,8),(1,9),(2,3),(2,4),(2,5),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(4,9),(5,6),(5,8),(6,7),(6,8),(7,9),(8,9)],10)
 => ? = 4 - 3
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,6),(1,7),(1,8),(1,9),(2,3),(2,4),(2,5),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(4,9),(5,6),(5,8),(6,7),(6,8),(7,9),(8,9)],10)
 => ? = 4 - 3
([(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 0 = 3 - 3
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 0 = 3 - 3
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 0 = 3 - 3
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 0 = 3 - 3
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 0 = 3 - 3
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 0 = 3 - 3
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 0 = 3 - 3
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 0 = 3 - 3
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 0 = 3 - 3
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 0 = 3 - 3
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 0 = 3 - 3
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 0 = 3 - 3
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 0 = 3 - 3
([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => -1 = 2 - 3
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => -1 = 2 - 3
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => -1 = 2 - 3
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => -1 = 2 - 3
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => -1 = 2 - 3
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => -1 = 2 - 3
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,8),(0,9),(1,2),(1,4),(1,5),(1,7),(2,3),(2,5),(2,6),(3,6),(3,8),(4,7),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
 => ? = 2 - 3
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => -1 = 2 - 3
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => -1 = 2 - 3
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => -1 = 2 - 3
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => -1 = 2 - 3
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => -1 = 2 - 3
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => -1 = 2 - 3
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => -1 = 2 - 3
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => -1 = 2 - 3
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => ([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => -1 = 2 - 3
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => -1 = 2 - 3
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => -1 = 2 - 3
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => -1 = 2 - 3
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => -1 = 2 - 3
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => -1 = 2 - 3
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => -1 = 2 - 3
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => -1 = 2 - 3
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => -1 = 2 - 3
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([],1)
 => ? = 1 - 3
([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([],1)
 => ? = 1 - 3
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([],1)
 => ? = 1 - 3
([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],1)
 => ? = 1 - 3
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([],1)
 => ? = 1 - 3
([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],1)
 => ? = 1 - 3
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([],1)
 => ? = 1 - 3
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ? = 1 - 3
([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([],1)
 => ? = 1 - 3
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,5),(3,4),(4,5)],6)
 => ([(0,1)],2)
 => ([],1)
 => ? = 1 - 3
([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,1)],2)
 => ([],1)
 => ? = 1 - 3
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,1)],2)
 => ([],1)
 => ? = 1 - 3
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,1)],2)
 => ([],1)
 => ? = 1 - 3
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,1)],2)
 => ([],1)
 => ? = 1 - 3
([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],1)
 => ? = 3 - 3
([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],1)
 => ? = 3 - 3
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,5),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],1)
 => ? = 3 - 3
([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],1)
 => ? = 3 - 3
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],1)
 => ? = 1 - 3
([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,1)],2)
 => ([],1)
 => ? = 1 - 3
([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(1,2),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],1)
 => ? = 1 - 3
Description
The second largest eigenvalue of a graph if it is integral. This statistic is undefined if the second largest eigenvalue of the graph is not integral. Chapter 4 of [1] provides lots of context.
Matching statistic: St001630
Mapping
Mp00111: Graphs —complement⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
Mp00266: Graphs —connected vertex partitions⟶ Lattices
St001630: Lattices ⟶ ℤResult quality: 8% ●values known / values provided: 8%●distinct values known / distinct values provided: 17%
Values
([],1)
 => ([],1)
 => ([],1)
 => ([],1)
 => ? = 1
([(0,1)],2)
 => ([],2)
 => ([],1)
 => ([],1)
 => ? = 1
([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1
([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1
([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([],1)
 => ([],1)
 => ? = 2
([(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,3),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ([],1)
 => ([],1)
 => ? = 3
([(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3
([(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3
([(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3
([(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,26),(17,26),(18,26),(19,26),(20,26),(21,26),(22,26),(23,26),(24,26),(25,26)],27)
 => ? = 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 2
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 2
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 2
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 2
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ([],1)
 => ([],1)
 => ? = 4
([(4,5)],6)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(1,13),(1,14),(1,20),(1,28),(1,29),(1,31),(2,11),(2,12),(2,19),(2,26),(2,27),(2,31),(3,16),(3,18),(3,22),(3,27),(3,29),(3,30),(4,15),(4,17),(4,21),(4,26),(4,28),(4,30),(5,11),(5,15),(5,24),(5,29),(5,32),(5,34),(6,12),(6,16),(6,25),(6,28),(6,32),(6,35),(7,13),(7,17),(7,25),(7,27),(7,33),(7,34),(8,14),(8,18),(8,24),(8,26),(8,33),(8,35),(9,21),(9,22),(9,23),(9,31),(9,34),(9,35),(10,19),(10,20),(10,23),(10,30),(10,32),(10,33),(11,36),(11,40),(11,50),(12,36),(12,41),(12,49),(13,37),(13,42),(13,50),(14,37),(14,43),(14,49),(15,38),(15,40),(15,48),(16,39),(16,41),(16,48),(17,38),(17,42),(17,47),(18,39),(18,43),(18,47),(19,36),(19,44),(19,47),(20,37),(20,44),(20,48),(21,38),(21,45),(21,49),(22,39),(22,45),(22,50),(23,44),(23,45),(23,46),(24,40),(24,43),(24,46),(25,41),(25,42),(25,46),(26,40),(26,47),(26,49),(27,41),(27,47),(27,50),(28,42),(28,48),(28,49),(29,43),(29,48),(29,50),(30,45),(30,47),(30,48),(31,44),(31,49),(31,50),(32,36),(32,46),(32,48),(33,37),(33,46),(33,47),(34,38),(34,46),(34,50),(35,39),(35,46),(35,49),(36,51),(37,51),(38,51),(39,51),(40,51),(41,51),(42,51),(43,51),(44,51),(45,51),(46,51),(47,51),(48,51),(49,51),(50,51)],52)
 => ? = 4
([(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(1,13),(1,14),(1,20),(1,28),(1,29),(1,31),(2,11),(2,12),(2,19),(2,26),(2,27),(2,31),(3,16),(3,18),(3,22),(3,27),(3,29),(3,30),(4,15),(4,17),(4,21),(4,26),(4,28),(4,30),(5,11),(5,15),(5,24),(5,29),(5,32),(5,34),(6,12),(6,16),(6,25),(6,28),(6,32),(6,35),(7,13),(7,17),(7,25),(7,27),(7,33),(7,34),(8,14),(8,18),(8,24),(8,26),(8,33),(8,35),(9,21),(9,22),(9,23),(9,31),(9,34),(9,35),(10,19),(10,20),(10,23),(10,30),(10,32),(10,33),(11,36),(11,40),(11,50),(12,36),(12,41),(12,49),(13,37),(13,42),(13,50),(14,37),(14,43),(14,49),(15,38),(15,40),(15,48),(16,39),(16,41),(16,48),(17,38),(17,42),(17,47),(18,39),(18,43),(18,47),(19,36),(19,44),(19,47),(20,37),(20,44),(20,48),(21,38),(21,45),(21,49),(22,39),(22,45),(22,50),(23,44),(23,45),(23,46),(24,40),(24,43),(24,46),(25,41),(25,42),(25,46),(26,40),(26,47),(26,49),(27,41),(27,47),(27,50),(28,42),(28,48),(28,49),(29,43),(29,48),(29,50),(30,45),(30,47),(30,48),(31,44),(31,49),(31,50),(32,36),(32,46),(32,48),(33,37),(33,46),(33,47),(34,38),(34,46),(34,50),(35,39),(35,46),(35,49),(36,51),(37,51),(38,51),(39,51),(40,51),(41,51),(42,51),(43,51),(44,51),(45,51),(46,51),(47,51),(48,51),(49,51),(50,51)],52)
 => ? = 4
([(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(1,13),(1,14),(1,20),(1,28),(1,29),(1,31),(2,11),(2,12),(2,19),(2,26),(2,27),(2,31),(3,16),(3,18),(3,22),(3,27),(3,29),(3,30),(4,15),(4,17),(4,21),(4,26),(4,28),(4,30),(5,11),(5,15),(5,24),(5,29),(5,32),(5,34),(6,12),(6,16),(6,25),(6,28),(6,32),(6,35),(7,13),(7,17),(7,25),(7,27),(7,33),(7,34),(8,14),(8,18),(8,24),(8,26),(8,33),(8,35),(9,21),(9,22),(9,23),(9,31),(9,34),(9,35),(10,19),(10,20),(10,23),(10,30),(10,32),(10,33),(11,36),(11,40),(11,50),(12,36),(12,41),(12,49),(13,37),(13,42),(13,50),(14,37),(14,43),(14,49),(15,38),(15,40),(15,48),(16,39),(16,41),(16,48),(17,38),(17,42),(17,47),(18,39),(18,43),(18,47),(19,36),(19,44),(19,47),(20,37),(20,44),(20,48),(21,38),(21,45),(21,49),(22,39),(22,45),(22,50),(23,44),(23,45),(23,46),(24,40),(24,43),(24,46),(25,41),(25,42),(25,46),(26,40),(26,47),(26,49),(27,41),(27,47),(27,50),(28,42),(28,48),(28,49),(29,43),(29,48),(29,50),(30,45),(30,47),(30,48),(31,44),(31,49),(31,50),(32,36),(32,46),(32,48),(33,37),(33,46),(33,47),(34,38),(34,46),(34,50),(35,39),(35,46),(35,49),(36,51),(37,51),(38,51),(39,51),(40,51),(41,51),(42,51),(43,51),(44,51),(45,51),(46,51),(47,51),(48,51),(49,51),(50,51)],52)
 => ? = 4
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(1,13),(1,14),(1,20),(1,28),(1,29),(1,31),(2,11),(2,12),(2,19),(2,26),(2,27),(2,31),(3,16),(3,18),(3,22),(3,27),(3,29),(3,30),(4,15),(4,17),(4,21),(4,26),(4,28),(4,30),(5,11),(5,15),(5,24),(5,29),(5,32),(5,34),(6,12),(6,16),(6,25),(6,28),(6,32),(6,35),(7,13),(7,17),(7,25),(7,27),(7,33),(7,34),(8,14),(8,18),(8,24),(8,26),(8,33),(8,35),(9,21),(9,22),(9,23),(9,31),(9,34),(9,35),(10,19),(10,20),(10,23),(10,30),(10,32),(10,33),(11,36),(11,40),(11,50),(12,36),(12,41),(12,49),(13,37),(13,42),(13,50),(14,37),(14,43),(14,49),(15,38),(15,40),(15,48),(16,39),(16,41),(16,48),(17,38),(17,42),(17,47),(18,39),(18,43),(18,47),(19,36),(19,44),(19,47),(20,37),(20,44),(20,48),(21,38),(21,45),(21,49),(22,39),(22,45),(22,50),(23,44),(23,45),(23,46),(24,40),(24,43),(24,46),(25,41),(25,42),(25,46),(26,40),(26,47),(26,49),(27,41),(27,47),(27,50),(28,42),(28,48),(28,49),(29,43),(29,48),(29,50),(30,45),(30,47),(30,48),(31,44),(31,49),(31,50),(32,36),(32,46),(32,48),(33,37),(33,46),(33,47),(34,38),(34,46),(34,50),(35,39),(35,46),(35,49),(36,51),(37,51),(38,51),(39,51),(40,51),(41,51),(42,51),(43,51),(44,51),(45,51),(46,51),(47,51),(48,51),(49,51),(50,51)],52)
 => ? = 4
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(1,13),(1,14),(1,20),(1,28),(1,29),(1,31),(2,11),(2,12),(2,19),(2,26),(2,27),(2,31),(3,16),(3,18),(3,22),(3,27),(3,29),(3,30),(4,15),(4,17),(4,21),(4,26),(4,28),(4,30),(5,11),(5,15),(5,24),(5,29),(5,32),(5,34),(6,12),(6,16),(6,25),(6,28),(6,32),(6,35),(7,13),(7,17),(7,25),(7,27),(7,33),(7,34),(8,14),(8,18),(8,24),(8,26),(8,33),(8,35),(9,21),(9,22),(9,23),(9,31),(9,34),(9,35),(10,19),(10,20),(10,23),(10,30),(10,32),(10,33),(11,36),(11,40),(11,50),(12,36),(12,41),(12,49),(13,37),(13,42),(13,50),(14,37),(14,43),(14,49),(15,38),(15,40),(15,48),(16,39),(16,41),(16,48),(17,38),(17,42),(17,47),(18,39),(18,43),(18,47),(19,36),(19,44),(19,47),(20,37),(20,44),(20,48),(21,38),(21,45),(21,49),(22,39),(22,45),(22,50),(23,44),(23,45),(23,46),(24,40),(24,43),(24,46),(25,41),(25,42),(25,46),(26,40),(26,47),(26,49),(27,41),(27,47),(27,50),(28,42),(28,48),(28,49),(29,43),(29,48),(29,50),(30,45),(30,47),(30,48),(31,44),(31,49),(31,50),(32,36),(32,46),(32,48),(33,37),(33,46),(33,47),(34,38),(34,46),(34,50),(35,39),(35,46),(35,49),(36,51),(37,51),(38,51),(39,51),(40,51),(41,51),(42,51),(43,51),(44,51),(45,51),(46,51),(47,51),(48,51),(49,51),(50,51)],52)
 => ? = 4
([(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3
([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(1,20),(1,29),(1,30),(1,34),(1,35),(1,39),(1,40),(1,75),(2,19),(2,24),(2,28),(2,31),(2,33),(2,37),(2,40),(2,72),(3,18),(3,23),(3,27),(3,31),(3,32),(3,36),(3,39),(3,71),(4,17),(4,21),(4,26),(4,32),(4,34),(4,37),(4,38),(4,73),(5,16),(5,22),(5,25),(5,33),(5,35),(5,36),(5,38),(5,74),(6,12),(6,14),(6,16),(6,21),(6,23),(6,72),(6,75),(7,11),(7,15),(7,17),(7,22),(7,24),(7,71),(7,75),(8,11),(8,13),(8,18),(8,25),(8,29),(8,72),(8,73),(9,12),(9,13),(9,19),(9,26),(9,30),(9,71),(9,74),(10,14),(10,15),(10,20),(10,27),(10,28),(10,73),(10,74),(11,61),(11,81),(11,83),(11,105),(12,62),(12,82),(12,84),(12,104),(13,65),(13,81),(13,82),(13,101),(14,63),(14,84),(14,85),(14,103),(15,64),(15,83),(15,85),(15,102),(16,52),(16,55),(16,84),(16,87),(16,92),(17,51),(17,56),(17,83),(17,86),(17,93),(18,53),(18,57),(18,81),(18,88),(18,90),(19,54),(19,58),(19,82),(19,89),(19,91),(20,59),(20,60),(20,85),(20,94),(20,95),(21,52),(21,62),(21,66),(21,93),(21,103),(22,51),(22,61),(22,67),(22,92),(22,102),(23,55),(23,63),(23,66),(23,88),(23,104),(24,56),(24,64),(24,67),(24,89),(24,105),(25,53),(25,61),(25,69),(25,87),(25,101),(26,54),(26,62),(26,70),(26,86),(26,101),(27,59),(27,63),(27,68),(27,90),(27,102),(28,60),(28,64),(28,68),(28,91),(28,103),(29,57),(29,65),(29,69),(29,94),(29,105),(30,58),(30,65),(30,70),(30,95),(30,104),(31,41),(31,42),(31,48),(31,68),(31,88),(31,89),(32,41),(32,43),(32,46),(32,66),(32,86),(32,90),(33,42),(33,44),(33,47),(33,67),(33,87),(33,91),(34,43),(34,45),(34,50),(34,70),(34,93),(34,94),(35,44),(35,45),(35,49),(35,69),(35,92),(35,95),(36,42),(36,46),(36,49),(36,53),(36,55),(36,102),(37,41),(37,47),(37,50),(37,54),(37,56),(37,103),(38,45),(38,46),(38,47),(38,51),(38,52),(38,101),(39,43),(39,48),(39,49),(39,57),(39,59),(39,104),(40,44),(40,48),(40,50),(40,58),(40,60),(40,105),(41,97),(41,106),(41,111),(42,96),(42,107),(42,111),(43,99),(43,108),(43,111),(44,100),(44,109),(44,111),(45,98),(45,110),(45,111),(46,76),(46,111),(46,112),(47,77),(47,111),(47,113),(48,80),(48,111),(48,114),(49,78),(49,111),(49,115),(50,79),(50,111),(50,116),(51,77),(51,98),(51,112),(52,76),(52,98),(52,113),(53,78),(53,96),(53,112),(54,79),(54,97),(54,113),(55,76),(55,96),(55,115),(56,77),(56,97),(56,116),(57,78),(57,99),(57,114),(58,79),(58,100),(58,114),(59,80),(59,99),(59,115),(60,80),(60,100),(60,116),(61,109),(61,112),(62,108),(62,113),(63,106),(63,115),(64,107),(64,116),(65,110),(65,114),(66,76),(66,106),(66,108),(67,77),(67,107),(67,109),(68,80),(68,106),(68,107),(69,78),(69,109),(69,110),(70,79),(70,108),(70,110),(71,81),(71,86),(71,89),(71,102),(71,104),(72,82),(72,87),(72,88),(72,103),(72,105),(73,83),(73,90),(73,94),(73,101),(73,103),(74,84),(74,91),(74,95),(74,101),(74,102),(75,85),(75,92),(75,93),(75,104),(75,105),(76,117),(77,117),(78,117),(79,117),(80,117),(81,112),(81,114),(82,113),(82,114),(83,112),(83,116),(84,113),(84,115),(85,115),(85,116),(86,97),(86,108),(86,112),(87,96),(87,109),(87,113),(88,96),(88,106),(88,114),(89,97),(89,107),(89,114),(90,99),(90,106),(90,112),(91,100),(91,107),(91,113),(92,98),(92,109),(92,115),(93,98),(93,108),(93,116),(94,99),(94,110),(94,116),(95,100),(95,110),(95,115),(96,117),(97,117),(98,117),(99,117),(100,117),(101,110),(101,112),(101,113),(102,107),(102,112),(102,115),(103,106),(103,113),(103,116),(104,108),(104,114),(104,115),(105,109),(105,114),(105,116),(106,117),(107,117),(108,117),(109,117),(110,117),(111,117),(112,117),(113,117),(114,117),(115,117),(116,117)],118)
 => ? = 2
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => ([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
 => ([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1
([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1
([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1
Description
The global dimension of the incidence algebra of the lattice over the rational numbers.
Matching statistic: St001878
Mapping
Mp00111: Graphs —complement⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
Mp00266: Graphs —connected vertex partitions⟶ Lattices
St001878: Lattices ⟶ ℤResult quality: 8% ●values known / values provided: 8%●distinct values known / distinct values provided: 17%
Values
([],1)
 => ([],1)
 => ([],1)
 => ([],1)
 => ? = 1
([(0,1)],2)
 => ([],2)
 => ([],1)
 => ([],1)
 => ? = 1
([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1
([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1
([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([],1)
 => ([],1)
 => ? = 2
([(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,3),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ([],1)
 => ([],1)
 => ? = 3
([(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3
([(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3
([(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3
([(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,26),(17,26),(18,26),(19,26),(20,26),(21,26),(22,26),(23,26),(24,26),(25,26)],27)
 => ? = 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 2
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 2
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 2
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 2
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ([],1)
 => ([],1)
 => ? = 4
([(4,5)],6)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(1,13),(1,14),(1,20),(1,28),(1,29),(1,31),(2,11),(2,12),(2,19),(2,26),(2,27),(2,31),(3,16),(3,18),(3,22),(3,27),(3,29),(3,30),(4,15),(4,17),(4,21),(4,26),(4,28),(4,30),(5,11),(5,15),(5,24),(5,29),(5,32),(5,34),(6,12),(6,16),(6,25),(6,28),(6,32),(6,35),(7,13),(7,17),(7,25),(7,27),(7,33),(7,34),(8,14),(8,18),(8,24),(8,26),(8,33),(8,35),(9,21),(9,22),(9,23),(9,31),(9,34),(9,35),(10,19),(10,20),(10,23),(10,30),(10,32),(10,33),(11,36),(11,40),(11,50),(12,36),(12,41),(12,49),(13,37),(13,42),(13,50),(14,37),(14,43),(14,49),(15,38),(15,40),(15,48),(16,39),(16,41),(16,48),(17,38),(17,42),(17,47),(18,39),(18,43),(18,47),(19,36),(19,44),(19,47),(20,37),(20,44),(20,48),(21,38),(21,45),(21,49),(22,39),(22,45),(22,50),(23,44),(23,45),(23,46),(24,40),(24,43),(24,46),(25,41),(25,42),(25,46),(26,40),(26,47),(26,49),(27,41),(27,47),(27,50),(28,42),(28,48),(28,49),(29,43),(29,48),(29,50),(30,45),(30,47),(30,48),(31,44),(31,49),(31,50),(32,36),(32,46),(32,48),(33,37),(33,46),(33,47),(34,38),(34,46),(34,50),(35,39),(35,46),(35,49),(36,51),(37,51),(38,51),(39,51),(40,51),(41,51),(42,51),(43,51),(44,51),(45,51),(46,51),(47,51),(48,51),(49,51),(50,51)],52)
 => ? = 4
([(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(1,13),(1,14),(1,20),(1,28),(1,29),(1,31),(2,11),(2,12),(2,19),(2,26),(2,27),(2,31),(3,16),(3,18),(3,22),(3,27),(3,29),(3,30),(4,15),(4,17),(4,21),(4,26),(4,28),(4,30),(5,11),(5,15),(5,24),(5,29),(5,32),(5,34),(6,12),(6,16),(6,25),(6,28),(6,32),(6,35),(7,13),(7,17),(7,25),(7,27),(7,33),(7,34),(8,14),(8,18),(8,24),(8,26),(8,33),(8,35),(9,21),(9,22),(9,23),(9,31),(9,34),(9,35),(10,19),(10,20),(10,23),(10,30),(10,32),(10,33),(11,36),(11,40),(11,50),(12,36),(12,41),(12,49),(13,37),(13,42),(13,50),(14,37),(14,43),(14,49),(15,38),(15,40),(15,48),(16,39),(16,41),(16,48),(17,38),(17,42),(17,47),(18,39),(18,43),(18,47),(19,36),(19,44),(19,47),(20,37),(20,44),(20,48),(21,38),(21,45),(21,49),(22,39),(22,45),(22,50),(23,44),(23,45),(23,46),(24,40),(24,43),(24,46),(25,41),(25,42),(25,46),(26,40),(26,47),(26,49),(27,41),(27,47),(27,50),(28,42),(28,48),(28,49),(29,43),(29,48),(29,50),(30,45),(30,47),(30,48),(31,44),(31,49),(31,50),(32,36),(32,46),(32,48),(33,37),(33,46),(33,47),(34,38),(34,46),(34,50),(35,39),(35,46),(35,49),(36,51),(37,51),(38,51),(39,51),(40,51),(41,51),(42,51),(43,51),(44,51),(45,51),(46,51),(47,51),(48,51),(49,51),(50,51)],52)
 => ? = 4
([(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(1,13),(1,14),(1,20),(1,28),(1,29),(1,31),(2,11),(2,12),(2,19),(2,26),(2,27),(2,31),(3,16),(3,18),(3,22),(3,27),(3,29),(3,30),(4,15),(4,17),(4,21),(4,26),(4,28),(4,30),(5,11),(5,15),(5,24),(5,29),(5,32),(5,34),(6,12),(6,16),(6,25),(6,28),(6,32),(6,35),(7,13),(7,17),(7,25),(7,27),(7,33),(7,34),(8,14),(8,18),(8,24),(8,26),(8,33),(8,35),(9,21),(9,22),(9,23),(9,31),(9,34),(9,35),(10,19),(10,20),(10,23),(10,30),(10,32),(10,33),(11,36),(11,40),(11,50),(12,36),(12,41),(12,49),(13,37),(13,42),(13,50),(14,37),(14,43),(14,49),(15,38),(15,40),(15,48),(16,39),(16,41),(16,48),(17,38),(17,42),(17,47),(18,39),(18,43),(18,47),(19,36),(19,44),(19,47),(20,37),(20,44),(20,48),(21,38),(21,45),(21,49),(22,39),(22,45),(22,50),(23,44),(23,45),(23,46),(24,40),(24,43),(24,46),(25,41),(25,42),(25,46),(26,40),(26,47),(26,49),(27,41),(27,47),(27,50),(28,42),(28,48),(28,49),(29,43),(29,48),(29,50),(30,45),(30,47),(30,48),(31,44),(31,49),(31,50),(32,36),(32,46),(32,48),(33,37),(33,46),(33,47),(34,38),(34,46),(34,50),(35,39),(35,46),(35,49),(36,51),(37,51),(38,51),(39,51),(40,51),(41,51),(42,51),(43,51),(44,51),(45,51),(46,51),(47,51),(48,51),(49,51),(50,51)],52)
 => ? = 4
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(1,13),(1,14),(1,20),(1,28),(1,29),(1,31),(2,11),(2,12),(2,19),(2,26),(2,27),(2,31),(3,16),(3,18),(3,22),(3,27),(3,29),(3,30),(4,15),(4,17),(4,21),(4,26),(4,28),(4,30),(5,11),(5,15),(5,24),(5,29),(5,32),(5,34),(6,12),(6,16),(6,25),(6,28),(6,32),(6,35),(7,13),(7,17),(7,25),(7,27),(7,33),(7,34),(8,14),(8,18),(8,24),(8,26),(8,33),(8,35),(9,21),(9,22),(9,23),(9,31),(9,34),(9,35),(10,19),(10,20),(10,23),(10,30),(10,32),(10,33),(11,36),(11,40),(11,50),(12,36),(12,41),(12,49),(13,37),(13,42),(13,50),(14,37),(14,43),(14,49),(15,38),(15,40),(15,48),(16,39),(16,41),(16,48),(17,38),(17,42),(17,47),(18,39),(18,43),(18,47),(19,36),(19,44),(19,47),(20,37),(20,44),(20,48),(21,38),(21,45),(21,49),(22,39),(22,45),(22,50),(23,44),(23,45),(23,46),(24,40),(24,43),(24,46),(25,41),(25,42),(25,46),(26,40),(26,47),(26,49),(27,41),(27,47),(27,50),(28,42),(28,48),(28,49),(29,43),(29,48),(29,50),(30,45),(30,47),(30,48),(31,44),(31,49),(31,50),(32,36),(32,46),(32,48),(33,37),(33,46),(33,47),(34,38),(34,46),(34,50),(35,39),(35,46),(35,49),(36,51),(37,51),(38,51),(39,51),(40,51),(41,51),(42,51),(43,51),(44,51),(45,51),(46,51),(47,51),(48,51),(49,51),(50,51)],52)
 => ? = 4
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(1,13),(1,14),(1,20),(1,28),(1,29),(1,31),(2,11),(2,12),(2,19),(2,26),(2,27),(2,31),(3,16),(3,18),(3,22),(3,27),(3,29),(3,30),(4,15),(4,17),(4,21),(4,26),(4,28),(4,30),(5,11),(5,15),(5,24),(5,29),(5,32),(5,34),(6,12),(6,16),(6,25),(6,28),(6,32),(6,35),(7,13),(7,17),(7,25),(7,27),(7,33),(7,34),(8,14),(8,18),(8,24),(8,26),(8,33),(8,35),(9,21),(9,22),(9,23),(9,31),(9,34),(9,35),(10,19),(10,20),(10,23),(10,30),(10,32),(10,33),(11,36),(11,40),(11,50),(12,36),(12,41),(12,49),(13,37),(13,42),(13,50),(14,37),(14,43),(14,49),(15,38),(15,40),(15,48),(16,39),(16,41),(16,48),(17,38),(17,42),(17,47),(18,39),(18,43),(18,47),(19,36),(19,44),(19,47),(20,37),(20,44),(20,48),(21,38),(21,45),(21,49),(22,39),(22,45),(22,50),(23,44),(23,45),(23,46),(24,40),(24,43),(24,46),(25,41),(25,42),(25,46),(26,40),(26,47),(26,49),(27,41),(27,47),(27,50),(28,42),(28,48),(28,49),(29,43),(29,48),(29,50),(30,45),(30,47),(30,48),(31,44),(31,49),(31,50),(32,36),(32,46),(32,48),(33,37),(33,46),(33,47),(34,38),(34,46),(34,50),(35,39),(35,46),(35,49),(36,51),(37,51),(38,51),(39,51),(40,51),(41,51),(42,51),(43,51),(44,51),(45,51),(46,51),(47,51),(48,51),(49,51),(50,51)],52)
 => ? = 4
([(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3
([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(1,20),(1,29),(1,30),(1,34),(1,35),(1,39),(1,40),(1,75),(2,19),(2,24),(2,28),(2,31),(2,33),(2,37),(2,40),(2,72),(3,18),(3,23),(3,27),(3,31),(3,32),(3,36),(3,39),(3,71),(4,17),(4,21),(4,26),(4,32),(4,34),(4,37),(4,38),(4,73),(5,16),(5,22),(5,25),(5,33),(5,35),(5,36),(5,38),(5,74),(6,12),(6,14),(6,16),(6,21),(6,23),(6,72),(6,75),(7,11),(7,15),(7,17),(7,22),(7,24),(7,71),(7,75),(8,11),(8,13),(8,18),(8,25),(8,29),(8,72),(8,73),(9,12),(9,13),(9,19),(9,26),(9,30),(9,71),(9,74),(10,14),(10,15),(10,20),(10,27),(10,28),(10,73),(10,74),(11,61),(11,81),(11,83),(11,105),(12,62),(12,82),(12,84),(12,104),(13,65),(13,81),(13,82),(13,101),(14,63),(14,84),(14,85),(14,103),(15,64),(15,83),(15,85),(15,102),(16,52),(16,55),(16,84),(16,87),(16,92),(17,51),(17,56),(17,83),(17,86),(17,93),(18,53),(18,57),(18,81),(18,88),(18,90),(19,54),(19,58),(19,82),(19,89),(19,91),(20,59),(20,60),(20,85),(20,94),(20,95),(21,52),(21,62),(21,66),(21,93),(21,103),(22,51),(22,61),(22,67),(22,92),(22,102),(23,55),(23,63),(23,66),(23,88),(23,104),(24,56),(24,64),(24,67),(24,89),(24,105),(25,53),(25,61),(25,69),(25,87),(25,101),(26,54),(26,62),(26,70),(26,86),(26,101),(27,59),(27,63),(27,68),(27,90),(27,102),(28,60),(28,64),(28,68),(28,91),(28,103),(29,57),(29,65),(29,69),(29,94),(29,105),(30,58),(30,65),(30,70),(30,95),(30,104),(31,41),(31,42),(31,48),(31,68),(31,88),(31,89),(32,41),(32,43),(32,46),(32,66),(32,86),(32,90),(33,42),(33,44),(33,47),(33,67),(33,87),(33,91),(34,43),(34,45),(34,50),(34,70),(34,93),(34,94),(35,44),(35,45),(35,49),(35,69),(35,92),(35,95),(36,42),(36,46),(36,49),(36,53),(36,55),(36,102),(37,41),(37,47),(37,50),(37,54),(37,56),(37,103),(38,45),(38,46),(38,47),(38,51),(38,52),(38,101),(39,43),(39,48),(39,49),(39,57),(39,59),(39,104),(40,44),(40,48),(40,50),(40,58),(40,60),(40,105),(41,97),(41,106),(41,111),(42,96),(42,107),(42,111),(43,99),(43,108),(43,111),(44,100),(44,109),(44,111),(45,98),(45,110),(45,111),(46,76),(46,111),(46,112),(47,77),(47,111),(47,113),(48,80),(48,111),(48,114),(49,78),(49,111),(49,115),(50,79),(50,111),(50,116),(51,77),(51,98),(51,112),(52,76),(52,98),(52,113),(53,78),(53,96),(53,112),(54,79),(54,97),(54,113),(55,76),(55,96),(55,115),(56,77),(56,97),(56,116),(57,78),(57,99),(57,114),(58,79),(58,100),(58,114),(59,80),(59,99),(59,115),(60,80),(60,100),(60,116),(61,109),(61,112),(62,108),(62,113),(63,106),(63,115),(64,107),(64,116),(65,110),(65,114),(66,76),(66,106),(66,108),(67,77),(67,107),(67,109),(68,80),(68,106),(68,107),(69,78),(69,109),(69,110),(70,79),(70,108),(70,110),(71,81),(71,86),(71,89),(71,102),(71,104),(72,82),(72,87),(72,88),(72,103),(72,105),(73,83),(73,90),(73,94),(73,101),(73,103),(74,84),(74,91),(74,95),(74,101),(74,102),(75,85),(75,92),(75,93),(75,104),(75,105),(76,117),(77,117),(78,117),(79,117),(80,117),(81,112),(81,114),(82,113),(82,114),(83,112),(83,116),(84,113),(84,115),(85,115),(85,116),(86,97),(86,108),(86,112),(87,96),(87,109),(87,113),(88,96),(88,106),(88,114),(89,97),(89,107),(89,114),(90,99),(90,106),(90,112),(91,100),(91,107),(91,113),(92,98),(92,109),(92,115),(93,98),(93,108),(93,116),(94,99),(94,110),(94,116),(95,100),(95,110),(95,115),(96,117),(97,117),(98,117),(99,117),(100,117),(101,110),(101,112),(101,113),(102,107),(102,112),(102,115),(103,106),(103,113),(103,116),(104,108),(104,114),(104,115),(105,109),(105,114),(105,116),(106,117),(107,117),(108,117),(109,117),(110,117),(111,117),(112,117),(113,117),(114,117),(115,117),(116,117)],118)
 => ? = 2
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => ([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
 => ([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1
([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1
([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1
Description
The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L.
Matching statistic: St001875
Mapping
Mp00111: Graphs —complement⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
Mp00266: Graphs —connected vertex partitions⟶ Lattices
St001875: Lattices ⟶ ℤResult quality: 8% ●values known / values provided: 8%●distinct values known / distinct values provided: 17%
Values
([],1)
 => ([],1)
 => ([],1)
 => ([],1)
 => ? = 1 + 2
([(0,1)],2)
 => ([],2)
 => ([],1)
 => ([],1)
 => ? = 1 + 2
([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1 + 2
([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1 + 2
([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([],1)
 => ([],1)
 => ? = 2 + 2
([(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,3),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1 + 2
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1 + 2
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1 + 2
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ([],1)
 => ([],1)
 => ? = 3 + 2
([(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3 + 2
([(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3 + 2
([(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3 + 2
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3 + 2
([(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1 + 2
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1 + 2
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1 + 2
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,26),(17,26),(18,26),(19,26),(20,26),(21,26),(22,26),(23,26),(24,26),(25,26)],27)
 => ? = 1 + 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1 + 2
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1 + 2
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1 + 2
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 2 + 2
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 2 + 2
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 2 + 2
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1 + 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1 + 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 2 + 2
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ([],1)
 => ([],1)
 => ? = 4 + 2
([(4,5)],6)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(1,13),(1,14),(1,20),(1,28),(1,29),(1,31),(2,11),(2,12),(2,19),(2,26),(2,27),(2,31),(3,16),(3,18),(3,22),(3,27),(3,29),(3,30),(4,15),(4,17),(4,21),(4,26),(4,28),(4,30),(5,11),(5,15),(5,24),(5,29),(5,32),(5,34),(6,12),(6,16),(6,25),(6,28),(6,32),(6,35),(7,13),(7,17),(7,25),(7,27),(7,33),(7,34),(8,14),(8,18),(8,24),(8,26),(8,33),(8,35),(9,21),(9,22),(9,23),(9,31),(9,34),(9,35),(10,19),(10,20),(10,23),(10,30),(10,32),(10,33),(11,36),(11,40),(11,50),(12,36),(12,41),(12,49),(13,37),(13,42),(13,50),(14,37),(14,43),(14,49),(15,38),(15,40),(15,48),(16,39),(16,41),(16,48),(17,38),(17,42),(17,47),(18,39),(18,43),(18,47),(19,36),(19,44),(19,47),(20,37),(20,44),(20,48),(21,38),(21,45),(21,49),(22,39),(22,45),(22,50),(23,44),(23,45),(23,46),(24,40),(24,43),(24,46),(25,41),(25,42),(25,46),(26,40),(26,47),(26,49),(27,41),(27,47),(27,50),(28,42),(28,48),(28,49),(29,43),(29,48),(29,50),(30,45),(30,47),(30,48),(31,44),(31,49),(31,50),(32,36),(32,46),(32,48),(33,37),(33,46),(33,47),(34,38),(34,46),(34,50),(35,39),(35,46),(35,49),(36,51),(37,51),(38,51),(39,51),(40,51),(41,51),(42,51),(43,51),(44,51),(45,51),(46,51),(47,51),(48,51),(49,51),(50,51)],52)
 => ? = 4 + 2
([(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(1,13),(1,14),(1,20),(1,28),(1,29),(1,31),(2,11),(2,12),(2,19),(2,26),(2,27),(2,31),(3,16),(3,18),(3,22),(3,27),(3,29),(3,30),(4,15),(4,17),(4,21),(4,26),(4,28),(4,30),(5,11),(5,15),(5,24),(5,29),(5,32),(5,34),(6,12),(6,16),(6,25),(6,28),(6,32),(6,35),(7,13),(7,17),(7,25),(7,27),(7,33),(7,34),(8,14),(8,18),(8,24),(8,26),(8,33),(8,35),(9,21),(9,22),(9,23),(9,31),(9,34),(9,35),(10,19),(10,20),(10,23),(10,30),(10,32),(10,33),(11,36),(11,40),(11,50),(12,36),(12,41),(12,49),(13,37),(13,42),(13,50),(14,37),(14,43),(14,49),(15,38),(15,40),(15,48),(16,39),(16,41),(16,48),(17,38),(17,42),(17,47),(18,39),(18,43),(18,47),(19,36),(19,44),(19,47),(20,37),(20,44),(20,48),(21,38),(21,45),(21,49),(22,39),(22,45),(22,50),(23,44),(23,45),(23,46),(24,40),(24,43),(24,46),(25,41),(25,42),(25,46),(26,40),(26,47),(26,49),(27,41),(27,47),(27,50),(28,42),(28,48),(28,49),(29,43),(29,48),(29,50),(30,45),(30,47),(30,48),(31,44),(31,49),(31,50),(32,36),(32,46),(32,48),(33,37),(33,46),(33,47),(34,38),(34,46),(34,50),(35,39),(35,46),(35,49),(36,51),(37,51),(38,51),(39,51),(40,51),(41,51),(42,51),(43,51),(44,51),(45,51),(46,51),(47,51),(48,51),(49,51),(50,51)],52)
 => ? = 4 + 2
([(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(1,13),(1,14),(1,20),(1,28),(1,29),(1,31),(2,11),(2,12),(2,19),(2,26),(2,27),(2,31),(3,16),(3,18),(3,22),(3,27),(3,29),(3,30),(4,15),(4,17),(4,21),(4,26),(4,28),(4,30),(5,11),(5,15),(5,24),(5,29),(5,32),(5,34),(6,12),(6,16),(6,25),(6,28),(6,32),(6,35),(7,13),(7,17),(7,25),(7,27),(7,33),(7,34),(8,14),(8,18),(8,24),(8,26),(8,33),(8,35),(9,21),(9,22),(9,23),(9,31),(9,34),(9,35),(10,19),(10,20),(10,23),(10,30),(10,32),(10,33),(11,36),(11,40),(11,50),(12,36),(12,41),(12,49),(13,37),(13,42),(13,50),(14,37),(14,43),(14,49),(15,38),(15,40),(15,48),(16,39),(16,41),(16,48),(17,38),(17,42),(17,47),(18,39),(18,43),(18,47),(19,36),(19,44),(19,47),(20,37),(20,44),(20,48),(21,38),(21,45),(21,49),(22,39),(22,45),(22,50),(23,44),(23,45),(23,46),(24,40),(24,43),(24,46),(25,41),(25,42),(25,46),(26,40),(26,47),(26,49),(27,41),(27,47),(27,50),(28,42),(28,48),(28,49),(29,43),(29,48),(29,50),(30,45),(30,47),(30,48),(31,44),(31,49),(31,50),(32,36),(32,46),(32,48),(33,37),(33,46),(33,47),(34,38),(34,46),(34,50),(35,39),(35,46),(35,49),(36,51),(37,51),(38,51),(39,51),(40,51),(41,51),(42,51),(43,51),(44,51),(45,51),(46,51),(47,51),(48,51),(49,51),(50,51)],52)
 => ? = 4 + 2
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(1,13),(1,14),(1,20),(1,28),(1,29),(1,31),(2,11),(2,12),(2,19),(2,26),(2,27),(2,31),(3,16),(3,18),(3,22),(3,27),(3,29),(3,30),(4,15),(4,17),(4,21),(4,26),(4,28),(4,30),(5,11),(5,15),(5,24),(5,29),(5,32),(5,34),(6,12),(6,16),(6,25),(6,28),(6,32),(6,35),(7,13),(7,17),(7,25),(7,27),(7,33),(7,34),(8,14),(8,18),(8,24),(8,26),(8,33),(8,35),(9,21),(9,22),(9,23),(9,31),(9,34),(9,35),(10,19),(10,20),(10,23),(10,30),(10,32),(10,33),(11,36),(11,40),(11,50),(12,36),(12,41),(12,49),(13,37),(13,42),(13,50),(14,37),(14,43),(14,49),(15,38),(15,40),(15,48),(16,39),(16,41),(16,48),(17,38),(17,42),(17,47),(18,39),(18,43),(18,47),(19,36),(19,44),(19,47),(20,37),(20,44),(20,48),(21,38),(21,45),(21,49),(22,39),(22,45),(22,50),(23,44),(23,45),(23,46),(24,40),(24,43),(24,46),(25,41),(25,42),(25,46),(26,40),(26,47),(26,49),(27,41),(27,47),(27,50),(28,42),(28,48),(28,49),(29,43),(29,48),(29,50),(30,45),(30,47),(30,48),(31,44),(31,49),(31,50),(32,36),(32,46),(32,48),(33,37),(33,46),(33,47),(34,38),(34,46),(34,50),(35,39),(35,46),(35,49),(36,51),(37,51),(38,51),(39,51),(40,51),(41,51),(42,51),(43,51),(44,51),(45,51),(46,51),(47,51),(48,51),(49,51),(50,51)],52)
 => ? = 4 + 2
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(1,13),(1,14),(1,20),(1,28),(1,29),(1,31),(2,11),(2,12),(2,19),(2,26),(2,27),(2,31),(3,16),(3,18),(3,22),(3,27),(3,29),(3,30),(4,15),(4,17),(4,21),(4,26),(4,28),(4,30),(5,11),(5,15),(5,24),(5,29),(5,32),(5,34),(6,12),(6,16),(6,25),(6,28),(6,32),(6,35),(7,13),(7,17),(7,25),(7,27),(7,33),(7,34),(8,14),(8,18),(8,24),(8,26),(8,33),(8,35),(9,21),(9,22),(9,23),(9,31),(9,34),(9,35),(10,19),(10,20),(10,23),(10,30),(10,32),(10,33),(11,36),(11,40),(11,50),(12,36),(12,41),(12,49),(13,37),(13,42),(13,50),(14,37),(14,43),(14,49),(15,38),(15,40),(15,48),(16,39),(16,41),(16,48),(17,38),(17,42),(17,47),(18,39),(18,43),(18,47),(19,36),(19,44),(19,47),(20,37),(20,44),(20,48),(21,38),(21,45),(21,49),(22,39),(22,45),(22,50),(23,44),(23,45),(23,46),(24,40),(24,43),(24,46),(25,41),(25,42),(25,46),(26,40),(26,47),(26,49),(27,41),(27,47),(27,50),(28,42),(28,48),(28,49),(29,43),(29,48),(29,50),(30,45),(30,47),(30,48),(31,44),(31,49),(31,50),(32,36),(32,46),(32,48),(33,37),(33,46),(33,47),(34,38),(34,46),(34,50),(35,39),(35,46),(35,49),(36,51),(37,51),(38,51),(39,51),(40,51),(41,51),(42,51),(43,51),(44,51),(45,51),(46,51),(47,51),(48,51),(49,51),(50,51)],52)
 => ? = 4 + 2
([(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3 + 2
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3 + 2
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3 + 2
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3 + 2
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3 + 2
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3 + 2
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3 + 2
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3 + 2
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3 + 2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3 + 2
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3 + 2
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3 + 2
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3 + 2
([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(1,20),(1,29),(1,30),(1,34),(1,35),(1,39),(1,40),(1,75),(2,19),(2,24),(2,28),(2,31),(2,33),(2,37),(2,40),(2,72),(3,18),(3,23),(3,27),(3,31),(3,32),(3,36),(3,39),(3,71),(4,17),(4,21),(4,26),(4,32),(4,34),(4,37),(4,38),(4,73),(5,16),(5,22),(5,25),(5,33),(5,35),(5,36),(5,38),(5,74),(6,12),(6,14),(6,16),(6,21),(6,23),(6,72),(6,75),(7,11),(7,15),(7,17),(7,22),(7,24),(7,71),(7,75),(8,11),(8,13),(8,18),(8,25),(8,29),(8,72),(8,73),(9,12),(9,13),(9,19),(9,26),(9,30),(9,71),(9,74),(10,14),(10,15),(10,20),(10,27),(10,28),(10,73),(10,74),(11,61),(11,81),(11,83),(11,105),(12,62),(12,82),(12,84),(12,104),(13,65),(13,81),(13,82),(13,101),(14,63),(14,84),(14,85),(14,103),(15,64),(15,83),(15,85),(15,102),(16,52),(16,55),(16,84),(16,87),(16,92),(17,51),(17,56),(17,83),(17,86),(17,93),(18,53),(18,57),(18,81),(18,88),(18,90),(19,54),(19,58),(19,82),(19,89),(19,91),(20,59),(20,60),(20,85),(20,94),(20,95),(21,52),(21,62),(21,66),(21,93),(21,103),(22,51),(22,61),(22,67),(22,92),(22,102),(23,55),(23,63),(23,66),(23,88),(23,104),(24,56),(24,64),(24,67),(24,89),(24,105),(25,53),(25,61),(25,69),(25,87),(25,101),(26,54),(26,62),(26,70),(26,86),(26,101),(27,59),(27,63),(27,68),(27,90),(27,102),(28,60),(28,64),(28,68),(28,91),(28,103),(29,57),(29,65),(29,69),(29,94),(29,105),(30,58),(30,65),(30,70),(30,95),(30,104),(31,41),(31,42),(31,48),(31,68),(31,88),(31,89),(32,41),(32,43),(32,46),(32,66),(32,86),(32,90),(33,42),(33,44),(33,47),(33,67),(33,87),(33,91),(34,43),(34,45),(34,50),(34,70),(34,93),(34,94),(35,44),(35,45),(35,49),(35,69),(35,92),(35,95),(36,42),(36,46),(36,49),(36,53),(36,55),(36,102),(37,41),(37,47),(37,50),(37,54),(37,56),(37,103),(38,45),(38,46),(38,47),(38,51),(38,52),(38,101),(39,43),(39,48),(39,49),(39,57),(39,59),(39,104),(40,44),(40,48),(40,50),(40,58),(40,60),(40,105),(41,97),(41,106),(41,111),(42,96),(42,107),(42,111),(43,99),(43,108),(43,111),(44,100),(44,109),(44,111),(45,98),(45,110),(45,111),(46,76),(46,111),(46,112),(47,77),(47,111),(47,113),(48,80),(48,111),(48,114),(49,78),(49,111),(49,115),(50,79),(50,111),(50,116),(51,77),(51,98),(51,112),(52,76),(52,98),(52,113),(53,78),(53,96),(53,112),(54,79),(54,97),(54,113),(55,76),(55,96),(55,115),(56,77),(56,97),(56,116),(57,78),(57,99),(57,114),(58,79),(58,100),(58,114),(59,80),(59,99),(59,115),(60,80),(60,100),(60,116),(61,109),(61,112),(62,108),(62,113),(63,106),(63,115),(64,107),(64,116),(65,110),(65,114),(66,76),(66,106),(66,108),(67,77),(67,107),(67,109),(68,80),(68,106),(68,107),(69,78),(69,109),(69,110),(70,79),(70,108),(70,110),(71,81),(71,86),(71,89),(71,102),(71,104),(72,82),(72,87),(72,88),(72,103),(72,105),(73,83),(73,90),(73,94),(73,101),(73,103),(74,84),(74,91),(74,95),(74,101),(74,102),(75,85),(75,92),(75,93),(75,104),(75,105),(76,117),(77,117),(78,117),(79,117),(80,117),(81,112),(81,114),(82,113),(82,114),(83,112),(83,116),(84,113),(84,115),(85,115),(85,116),(86,97),(86,108),(86,112),(87,96),(87,109),(87,113),(88,96),(88,106),(88,114),(89,97),(89,107),(89,114),(90,99),(90,106),(90,112),(91,100),(91,107),(91,113),(92,98),(92,109),(92,115),(93,98),(93,108),(93,116),(94,99),(94,110),(94,116),(95,100),(95,110),(95,115),(96,117),(97,117),(98,117),(99,117),(100,117),(101,110),(101,112),(101,113),(102,107),(102,112),(102,115),(103,106),(103,113),(103,116),(104,108),(104,114),(104,115),(105,109),(105,114),(105,116),(106,117),(107,117),(108,117),(109,117),(110,117),(111,117),(112,117),(113,117),(114,117),(115,117),(116,117)],118)
 => ? = 2 + 2
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => ([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
 => ([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1 + 2
([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1 + 2
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1 + 2
([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1 + 2
Description
The number of simple modules with projective dimension at most 1.
Matching statistic: St001877
Mapping
Mp00111: Graphs —complement⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
Mp00266: Graphs —connected vertex partitions⟶ Lattices
St001877: Lattices ⟶ ℤResult quality: 8% ●values known / values provided: 8%●distinct values known / distinct values provided: 17%
Values
([],1)
 => ([],1)
 => ([],1)
 => ([],1)
 => ? = 1 + 2
([(0,1)],2)
 => ([],2)
 => ([],1)
 => ([],1)
 => ? = 1 + 2
([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1 + 2
([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1 + 2
([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([],1)
 => ([],1)
 => ? = 2 + 2
([(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,3),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1 + 2
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1 + 2
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1 + 2
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ([],1)
 => ([],1)
 => ? = 3 + 2
([(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3 + 2
([(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3 + 2
([(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3 + 2
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3 + 2
([(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1 + 2
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1 + 2
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1 + 2
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,26),(17,26),(18,26),(19,26),(20,26),(21,26),(22,26),(23,26),(24,26),(25,26)],27)
 => ? = 1 + 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1 + 2
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1 + 2
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1 + 2
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 2 + 2
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 2 + 2
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 2 + 2
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1 + 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1 + 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 2 + 2
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ([],1)
 => ([],1)
 => ? = 4 + 2
([(4,5)],6)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(1,13),(1,14),(1,20),(1,28),(1,29),(1,31),(2,11),(2,12),(2,19),(2,26),(2,27),(2,31),(3,16),(3,18),(3,22),(3,27),(3,29),(3,30),(4,15),(4,17),(4,21),(4,26),(4,28),(4,30),(5,11),(5,15),(5,24),(5,29),(5,32),(5,34),(6,12),(6,16),(6,25),(6,28),(6,32),(6,35),(7,13),(7,17),(7,25),(7,27),(7,33),(7,34),(8,14),(8,18),(8,24),(8,26),(8,33),(8,35),(9,21),(9,22),(9,23),(9,31),(9,34),(9,35),(10,19),(10,20),(10,23),(10,30),(10,32),(10,33),(11,36),(11,40),(11,50),(12,36),(12,41),(12,49),(13,37),(13,42),(13,50),(14,37),(14,43),(14,49),(15,38),(15,40),(15,48),(16,39),(16,41),(16,48),(17,38),(17,42),(17,47),(18,39),(18,43),(18,47),(19,36),(19,44),(19,47),(20,37),(20,44),(20,48),(21,38),(21,45),(21,49),(22,39),(22,45),(22,50),(23,44),(23,45),(23,46),(24,40),(24,43),(24,46),(25,41),(25,42),(25,46),(26,40),(26,47),(26,49),(27,41),(27,47),(27,50),(28,42),(28,48),(28,49),(29,43),(29,48),(29,50),(30,45),(30,47),(30,48),(31,44),(31,49),(31,50),(32,36),(32,46),(32,48),(33,37),(33,46),(33,47),(34,38),(34,46),(34,50),(35,39),(35,46),(35,49),(36,51),(37,51),(38,51),(39,51),(40,51),(41,51),(42,51),(43,51),(44,51),(45,51),(46,51),(47,51),(48,51),(49,51),(50,51)],52)
 => ? = 4 + 2
([(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(1,13),(1,14),(1,20),(1,28),(1,29),(1,31),(2,11),(2,12),(2,19),(2,26),(2,27),(2,31),(3,16),(3,18),(3,22),(3,27),(3,29),(3,30),(4,15),(4,17),(4,21),(4,26),(4,28),(4,30),(5,11),(5,15),(5,24),(5,29),(5,32),(5,34),(6,12),(6,16),(6,25),(6,28),(6,32),(6,35),(7,13),(7,17),(7,25),(7,27),(7,33),(7,34),(8,14),(8,18),(8,24),(8,26),(8,33),(8,35),(9,21),(9,22),(9,23),(9,31),(9,34),(9,35),(10,19),(10,20),(10,23),(10,30),(10,32),(10,33),(11,36),(11,40),(11,50),(12,36),(12,41),(12,49),(13,37),(13,42),(13,50),(14,37),(14,43),(14,49),(15,38),(15,40),(15,48),(16,39),(16,41),(16,48),(17,38),(17,42),(17,47),(18,39),(18,43),(18,47),(19,36),(19,44),(19,47),(20,37),(20,44),(20,48),(21,38),(21,45),(21,49),(22,39),(22,45),(22,50),(23,44),(23,45),(23,46),(24,40),(24,43),(24,46),(25,41),(25,42),(25,46),(26,40),(26,47),(26,49),(27,41),(27,47),(27,50),(28,42),(28,48),(28,49),(29,43),(29,48),(29,50),(30,45),(30,47),(30,48),(31,44),(31,49),(31,50),(32,36),(32,46),(32,48),(33,37),(33,46),(33,47),(34,38),(34,46),(34,50),(35,39),(35,46),(35,49),(36,51),(37,51),(38,51),(39,51),(40,51),(41,51),(42,51),(43,51),(44,51),(45,51),(46,51),(47,51),(48,51),(49,51),(50,51)],52)
 => ? = 4 + 2
([(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(1,13),(1,14),(1,20),(1,28),(1,29),(1,31),(2,11),(2,12),(2,19),(2,26),(2,27),(2,31),(3,16),(3,18),(3,22),(3,27),(3,29),(3,30),(4,15),(4,17),(4,21),(4,26),(4,28),(4,30),(5,11),(5,15),(5,24),(5,29),(5,32),(5,34),(6,12),(6,16),(6,25),(6,28),(6,32),(6,35),(7,13),(7,17),(7,25),(7,27),(7,33),(7,34),(8,14),(8,18),(8,24),(8,26),(8,33),(8,35),(9,21),(9,22),(9,23),(9,31),(9,34),(9,35),(10,19),(10,20),(10,23),(10,30),(10,32),(10,33),(11,36),(11,40),(11,50),(12,36),(12,41),(12,49),(13,37),(13,42),(13,50),(14,37),(14,43),(14,49),(15,38),(15,40),(15,48),(16,39),(16,41),(16,48),(17,38),(17,42),(17,47),(18,39),(18,43),(18,47),(19,36),(19,44),(19,47),(20,37),(20,44),(20,48),(21,38),(21,45),(21,49),(22,39),(22,45),(22,50),(23,44),(23,45),(23,46),(24,40),(24,43),(24,46),(25,41),(25,42),(25,46),(26,40),(26,47),(26,49),(27,41),(27,47),(27,50),(28,42),(28,48),(28,49),(29,43),(29,48),(29,50),(30,45),(30,47),(30,48),(31,44),(31,49),(31,50),(32,36),(32,46),(32,48),(33,37),(33,46),(33,47),(34,38),(34,46),(34,50),(35,39),(35,46),(35,49),(36,51),(37,51),(38,51),(39,51),(40,51),(41,51),(42,51),(43,51),(44,51),(45,51),(46,51),(47,51),(48,51),(49,51),(50,51)],52)
 => ? = 4 + 2
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(1,13),(1,14),(1,20),(1,28),(1,29),(1,31),(2,11),(2,12),(2,19),(2,26),(2,27),(2,31),(3,16),(3,18),(3,22),(3,27),(3,29),(3,30),(4,15),(4,17),(4,21),(4,26),(4,28),(4,30),(5,11),(5,15),(5,24),(5,29),(5,32),(5,34),(6,12),(6,16),(6,25),(6,28),(6,32),(6,35),(7,13),(7,17),(7,25),(7,27),(7,33),(7,34),(8,14),(8,18),(8,24),(8,26),(8,33),(8,35),(9,21),(9,22),(9,23),(9,31),(9,34),(9,35),(10,19),(10,20),(10,23),(10,30),(10,32),(10,33),(11,36),(11,40),(11,50),(12,36),(12,41),(12,49),(13,37),(13,42),(13,50),(14,37),(14,43),(14,49),(15,38),(15,40),(15,48),(16,39),(16,41),(16,48),(17,38),(17,42),(17,47),(18,39),(18,43),(18,47),(19,36),(19,44),(19,47),(20,37),(20,44),(20,48),(21,38),(21,45),(21,49),(22,39),(22,45),(22,50),(23,44),(23,45),(23,46),(24,40),(24,43),(24,46),(25,41),(25,42),(25,46),(26,40),(26,47),(26,49),(27,41),(27,47),(27,50),(28,42),(28,48),(28,49),(29,43),(29,48),(29,50),(30,45),(30,47),(30,48),(31,44),(31,49),(31,50),(32,36),(32,46),(32,48),(33,37),(33,46),(33,47),(34,38),(34,46),(34,50),(35,39),(35,46),(35,49),(36,51),(37,51),(38,51),(39,51),(40,51),(41,51),(42,51),(43,51),(44,51),(45,51),(46,51),(47,51),(48,51),(49,51),(50,51)],52)
 => ? = 4 + 2
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(1,13),(1,14),(1,20),(1,28),(1,29),(1,31),(2,11),(2,12),(2,19),(2,26),(2,27),(2,31),(3,16),(3,18),(3,22),(3,27),(3,29),(3,30),(4,15),(4,17),(4,21),(4,26),(4,28),(4,30),(5,11),(5,15),(5,24),(5,29),(5,32),(5,34),(6,12),(6,16),(6,25),(6,28),(6,32),(6,35),(7,13),(7,17),(7,25),(7,27),(7,33),(7,34),(8,14),(8,18),(8,24),(8,26),(8,33),(8,35),(9,21),(9,22),(9,23),(9,31),(9,34),(9,35),(10,19),(10,20),(10,23),(10,30),(10,32),(10,33),(11,36),(11,40),(11,50),(12,36),(12,41),(12,49),(13,37),(13,42),(13,50),(14,37),(14,43),(14,49),(15,38),(15,40),(15,48),(16,39),(16,41),(16,48),(17,38),(17,42),(17,47),(18,39),(18,43),(18,47),(19,36),(19,44),(19,47),(20,37),(20,44),(20,48),(21,38),(21,45),(21,49),(22,39),(22,45),(22,50),(23,44),(23,45),(23,46),(24,40),(24,43),(24,46),(25,41),(25,42),(25,46),(26,40),(26,47),(26,49),(27,41),(27,47),(27,50),(28,42),(28,48),(28,49),(29,43),(29,48),(29,50),(30,45),(30,47),(30,48),(31,44),(31,49),(31,50),(32,36),(32,46),(32,48),(33,37),(33,46),(33,47),(34,38),(34,46),(34,50),(35,39),(35,46),(35,49),(36,51),(37,51),(38,51),(39,51),(40,51),(41,51),(42,51),(43,51),(44,51),(45,51),(46,51),(47,51),(48,51),(49,51),(50,51)],52)
 => ? = 4 + 2
([(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3 + 2
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3 + 2
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3 + 2
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3 + 2
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3 + 2
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3 + 2
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3 + 2
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3 + 2
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3 + 2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3 + 2
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3 + 2
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3 + 2
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
 => ? = 3 + 2
([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(1,20),(1,29),(1,30),(1,34),(1,35),(1,39),(1,40),(1,75),(2,19),(2,24),(2,28),(2,31),(2,33),(2,37),(2,40),(2,72),(3,18),(3,23),(3,27),(3,31),(3,32),(3,36),(3,39),(3,71),(4,17),(4,21),(4,26),(4,32),(4,34),(4,37),(4,38),(4,73),(5,16),(5,22),(5,25),(5,33),(5,35),(5,36),(5,38),(5,74),(6,12),(6,14),(6,16),(6,21),(6,23),(6,72),(6,75),(7,11),(7,15),(7,17),(7,22),(7,24),(7,71),(7,75),(8,11),(8,13),(8,18),(8,25),(8,29),(8,72),(8,73),(9,12),(9,13),(9,19),(9,26),(9,30),(9,71),(9,74),(10,14),(10,15),(10,20),(10,27),(10,28),(10,73),(10,74),(11,61),(11,81),(11,83),(11,105),(12,62),(12,82),(12,84),(12,104),(13,65),(13,81),(13,82),(13,101),(14,63),(14,84),(14,85),(14,103),(15,64),(15,83),(15,85),(15,102),(16,52),(16,55),(16,84),(16,87),(16,92),(17,51),(17,56),(17,83),(17,86),(17,93),(18,53),(18,57),(18,81),(18,88),(18,90),(19,54),(19,58),(19,82),(19,89),(19,91),(20,59),(20,60),(20,85),(20,94),(20,95),(21,52),(21,62),(21,66),(21,93),(21,103),(22,51),(22,61),(22,67),(22,92),(22,102),(23,55),(23,63),(23,66),(23,88),(23,104),(24,56),(24,64),(24,67),(24,89),(24,105),(25,53),(25,61),(25,69),(25,87),(25,101),(26,54),(26,62),(26,70),(26,86),(26,101),(27,59),(27,63),(27,68),(27,90),(27,102),(28,60),(28,64),(28,68),(28,91),(28,103),(29,57),(29,65),(29,69),(29,94),(29,105),(30,58),(30,65),(30,70),(30,95),(30,104),(31,41),(31,42),(31,48),(31,68),(31,88),(31,89),(32,41),(32,43),(32,46),(32,66),(32,86),(32,90),(33,42),(33,44),(33,47),(33,67),(33,87),(33,91),(34,43),(34,45),(34,50),(34,70),(34,93),(34,94),(35,44),(35,45),(35,49),(35,69),(35,92),(35,95),(36,42),(36,46),(36,49),(36,53),(36,55),(36,102),(37,41),(37,47),(37,50),(37,54),(37,56),(37,103),(38,45),(38,46),(38,47),(38,51),(38,52),(38,101),(39,43),(39,48),(39,49),(39,57),(39,59),(39,104),(40,44),(40,48),(40,50),(40,58),(40,60),(40,105),(41,97),(41,106),(41,111),(42,96),(42,107),(42,111),(43,99),(43,108),(43,111),(44,100),(44,109),(44,111),(45,98),(45,110),(45,111),(46,76),(46,111),(46,112),(47,77),(47,111),(47,113),(48,80),(48,111),(48,114),(49,78),(49,111),(49,115),(50,79),(50,111),(50,116),(51,77),(51,98),(51,112),(52,76),(52,98),(52,113),(53,78),(53,96),(53,112),(54,79),(54,97),(54,113),(55,76),(55,96),(55,115),(56,77),(56,97),(56,116),(57,78),(57,99),(57,114),(58,79),(58,100),(58,114),(59,80),(59,99),(59,115),(60,80),(60,100),(60,116),(61,109),(61,112),(62,108),(62,113),(63,106),(63,115),(64,107),(64,116),(65,110),(65,114),(66,76),(66,106),(66,108),(67,77),(67,107),(67,109),(68,80),(68,106),(68,107),(69,78),(69,109),(69,110),(70,79),(70,108),(70,110),(71,81),(71,86),(71,89),(71,102),(71,104),(72,82),(72,87),(72,88),(72,103),(72,105),(73,83),(73,90),(73,94),(73,101),(73,103),(74,84),(74,91),(74,95),(74,101),(74,102),(75,85),(75,92),(75,93),(75,104),(75,105),(76,117),(77,117),(78,117),(79,117),(80,117),(81,112),(81,114),(82,113),(82,114),(83,112),(83,116),(84,113),(84,115),(85,115),(85,116),(86,97),(86,108),(86,112),(87,96),(87,109),(87,113),(88,96),(88,106),(88,114),(89,97),(89,107),(89,114),(90,99),(90,106),(90,112),(91,100),(91,107),(91,113),(92,98),(92,109),(92,115),(93,98),(93,108),(93,116),(94,99),(94,110),(94,116),(95,100),(95,110),(95,115),(96,117),(97,117),(98,117),(99,117),(100,117),(101,110),(101,112),(101,113),(102,107),(102,112),(102,115),(103,106),(103,113),(103,116),(104,108),(104,114),(104,115),(105,109),(105,114),(105,116),(106,117),(107,117),(108,117),(109,117),(110,117),(111,117),(112,117),(113,117),(114,117),(115,117),(116,117)],118)
 => ? = 2 + 2
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => ([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
 => ([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1 + 2
([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1 + 2
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1 + 2
([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 1 + 2
Description
Number of indecomposable injective modules with projective dimension 2.