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Matching statistic: St001050
St001050: Set partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1,2}}
=> 1 = 0 + 1
{{1},{2}}
=> 2 = 1 + 1
{{1,2,3}}
=> 1 = 0 + 1
{{1,2},{3}}
=> 2 = 1 + 1
{{1,3},{2}}
=> 2 = 1 + 1
{{1},{2,3}}
=> 1 = 0 + 1
{{1},{2},{3}}
=> 3 = 2 + 1
{{1,2,3,4}}
=> 1 = 0 + 1
{{1,2,3},{4}}
=> 2 = 1 + 1
{{1,2,4},{3}}
=> 2 = 1 + 1
{{1,2},{3,4}}
=> 1 = 0 + 1
{{1,2},{3},{4}}
=> 3 = 2 + 1
{{1,3,4},{2}}
=> 1 = 0 + 1
{{1,3},{2,4}}
=> 2 = 1 + 1
{{1,3},{2},{4}}
=> 3 = 2 + 1
{{1,4},{2,3}}
=> 2 = 1 + 1
{{1},{2,3,4}}
=> 1 = 0 + 1
{{1},{2,3},{4}}
=> 2 = 1 + 1
{{1,4},{2},{3}}
=> 3 = 2 + 1
{{1},{2,4},{3}}
=> 2 = 1 + 1
{{1},{2},{3,4}}
=> 1 = 0 + 1
{{1},{2},{3},{4}}
=> 4 = 3 + 1
{{1,2,3,4,5}}
=> 1 = 0 + 1
{{1,2,3,4},{5}}
=> 2 = 1 + 1
{{1,2,3,5},{4}}
=> 2 = 1 + 1
{{1,2,3},{4,5}}
=> 1 = 0 + 1
{{1,2,3},{4},{5}}
=> 3 = 2 + 1
{{1,2,4,5},{3}}
=> 1 = 0 + 1
{{1,2,4},{3,5}}
=> 2 = 1 + 1
{{1,2,4},{3},{5}}
=> 3 = 2 + 1
{{1,2,5},{3,4}}
=> 2 = 1 + 1
{{1,2},{3,4,5}}
=> 1 = 0 + 1
{{1,2},{3,4},{5}}
=> 2 = 1 + 1
{{1,2,5},{3},{4}}
=> 3 = 2 + 1
{{1,2},{3,5},{4}}
=> 2 = 1 + 1
{{1,2},{3},{4,5}}
=> 1 = 0 + 1
{{1,2},{3},{4},{5}}
=> 4 = 3 + 1
{{1,3,4,5},{2}}
=> 1 = 0 + 1
{{1,3,4},{2,5}}
=> 2 = 1 + 1
{{1,3,4},{2},{5}}
=> 2 = 1 + 1
{{1,3,5},{2,4}}
=> 2 = 1 + 1
{{1,3},{2,4,5}}
=> 1 = 0 + 1
{{1,3},{2,4},{5}}
=> 3 = 2 + 1
{{1,3,5},{2},{4}}
=> 2 = 1 + 1
{{1,3},{2,5},{4}}
=> 3 = 2 + 1
{{1,3},{2},{4,5}}
=> 1 = 0 + 1
{{1,3},{2},{4},{5}}
=> 4 = 3 + 1
{{1,4,5},{2,3}}
=> 1 = 0 + 1
{{1,4},{2,3,5}}
=> 2 = 1 + 1
{{1,4},{2,3},{5}}
=> 3 = 2 + 1
Description
The number of terminal closers of a set partition.
A closer of a set partition is a number that is maximal in its block. In particular, a singleton is a closer. This statistic counts the number of terminal closers. In other words, this is the number of closers such that all larger elements are also closers.
Matching statistic: St001051
St001051: Set partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1,2}}
=> 1 = 0 + 1
{{1},{2}}
=> 2 = 1 + 1
{{1,2,3}}
=> 1 = 0 + 1
{{1,2},{3}}
=> 2 = 1 + 1
{{1,3},{2}}
=> 1 = 0 + 1
{{1},{2,3}}
=> 2 = 1 + 1
{{1},{2},{3}}
=> 3 = 2 + 1
{{1,2,3,4}}
=> 1 = 0 + 1
{{1,2,3},{4}}
=> 2 = 1 + 1
{{1,2,4},{3}}
=> 1 = 0 + 1
{{1,2},{3,4}}
=> 2 = 1 + 1
{{1,2},{3},{4}}
=> 3 = 2 + 1
{{1,3,4},{2}}
=> 1 = 0 + 1
{{1,3},{2,4}}
=> 2 = 1 + 1
{{1,3},{2},{4}}
=> 2 = 1 + 1
{{1,4},{2,3}}
=> 1 = 0 + 1
{{1},{2,3,4}}
=> 2 = 1 + 1
{{1},{2,3},{4}}
=> 3 = 2 + 1
{{1,4},{2},{3}}
=> 1 = 0 + 1
{{1},{2,4},{3}}
=> 3 = 2 + 1
{{1},{2},{3,4}}
=> 2 = 1 + 1
{{1},{2},{3},{4}}
=> 4 = 3 + 1
{{1,2,3,4,5}}
=> 1 = 0 + 1
{{1,2,3,4},{5}}
=> 2 = 1 + 1
{{1,2,3,5},{4}}
=> 1 = 0 + 1
{{1,2,3},{4,5}}
=> 2 = 1 + 1
{{1,2,3},{4},{5}}
=> 3 = 2 + 1
{{1,2,4,5},{3}}
=> 1 = 0 + 1
{{1,2,4},{3,5}}
=> 2 = 1 + 1
{{1,2,4},{3},{5}}
=> 2 = 1 + 1
{{1,2,5},{3,4}}
=> 1 = 0 + 1
{{1,2},{3,4,5}}
=> 2 = 1 + 1
{{1,2},{3,4},{5}}
=> 3 = 2 + 1
{{1,2,5},{3},{4}}
=> 1 = 0 + 1
{{1,2},{3,5},{4}}
=> 3 = 2 + 1
{{1,2},{3},{4,5}}
=> 2 = 1 + 1
{{1,2},{3},{4},{5}}
=> 4 = 3 + 1
{{1,3,4,5},{2}}
=> 1 = 0 + 1
{{1,3,4},{2,5}}
=> 2 = 1 + 1
{{1,3,4},{2},{5}}
=> 2 = 1 + 1
{{1,3,5},{2,4}}
=> 1 = 0 + 1
{{1,3},{2,4,5}}
=> 2 = 1 + 1
{{1,3},{2,4},{5}}
=> 3 = 2 + 1
{{1,3,5},{2},{4}}
=> 1 = 0 + 1
{{1,3},{2,5},{4}}
=> 3 = 2 + 1
{{1,3},{2},{4,5}}
=> 2 = 1 + 1
{{1,3},{2},{4},{5}}
=> 3 = 2 + 1
{{1,4,5},{2,3}}
=> 1 = 0 + 1
{{1,4},{2,3,5}}
=> 2 = 1 + 1
{{1,4},{2,3},{5}}
=> 2 = 1 + 1
Description
The depth of the label 1 in the decreasing labelled unordered tree associated with the set partition.
The bijection between set partitions of {1,…,n} into k blocks and trees with n+1−k leaves is described in Theorem 1 of [1].
Matching statistic: St000745
Mp00258: Set partitions —Standard tableau associated to a set partition⟶ Standard tableaux
St000745: Standard tableaux ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
St000745: Standard tableaux ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1,2}}
=> [[1,2]]
=> 1 = 0 + 1
{{1},{2}}
=> [[1],[2]]
=> 2 = 1 + 1
{{1,2,3}}
=> [[1,2,3]]
=> 1 = 0 + 1
{{1,2},{3}}
=> [[1,2],[3]]
=> 1 = 0 + 1
{{1,3},{2}}
=> [[1,3],[2]]
=> 2 = 1 + 1
{{1},{2,3}}
=> [[1,3],[2]]
=> 2 = 1 + 1
{{1},{2},{3}}
=> [[1],[2],[3]]
=> 3 = 2 + 1
{{1,2,3,4}}
=> [[1,2,3,4]]
=> 1 = 0 + 1
{{1,2,3},{4}}
=> [[1,2,3],[4]]
=> 1 = 0 + 1
{{1,2,4},{3}}
=> [[1,2,4],[3]]
=> 1 = 0 + 1
{{1,2},{3,4}}
=> [[1,2],[3,4]]
=> 1 = 0 + 1
{{1,2},{3},{4}}
=> [[1,2],[3],[4]]
=> 1 = 0 + 1
{{1,3,4},{2}}
=> [[1,3,4],[2]]
=> 2 = 1 + 1
{{1,3},{2,4}}
=> [[1,3],[2,4]]
=> 2 = 1 + 1
{{1,3},{2},{4}}
=> [[1,3],[2],[4]]
=> 2 = 1 + 1
{{1,4},{2,3}}
=> [[1,3],[2,4]]
=> 2 = 1 + 1
{{1},{2,3,4}}
=> [[1,3,4],[2]]
=> 2 = 1 + 1
{{1},{2,3},{4}}
=> [[1,3],[2],[4]]
=> 2 = 1 + 1
{{1,4},{2},{3}}
=> [[1,4],[2],[3]]
=> 3 = 2 + 1
{{1},{2,4},{3}}
=> [[1,4],[2],[3]]
=> 3 = 2 + 1
{{1},{2},{3,4}}
=> [[1,4],[2],[3]]
=> 3 = 2 + 1
{{1},{2},{3},{4}}
=> [[1],[2],[3],[4]]
=> 4 = 3 + 1
{{1,2,3,4,5}}
=> [[1,2,3,4,5]]
=> 1 = 0 + 1
{{1,2,3,4},{5}}
=> [[1,2,3,4],[5]]
=> 1 = 0 + 1
{{1,2,3,5},{4}}
=> [[1,2,3,5],[4]]
=> 1 = 0 + 1
{{1,2,3},{4,5}}
=> [[1,2,3],[4,5]]
=> 1 = 0 + 1
{{1,2,3},{4},{5}}
=> [[1,2,3],[4],[5]]
=> 1 = 0 + 1
{{1,2,4,5},{3}}
=> [[1,2,4,5],[3]]
=> 1 = 0 + 1
{{1,2,4},{3,5}}
=> [[1,2,4],[3,5]]
=> 1 = 0 + 1
{{1,2,4},{3},{5}}
=> [[1,2,4],[3],[5]]
=> 1 = 0 + 1
{{1,2,5},{3,4}}
=> [[1,2,5],[3,4]]
=> 1 = 0 + 1
{{1,2},{3,4,5}}
=> [[1,2,5],[3,4]]
=> 1 = 0 + 1
{{1,2},{3,4},{5}}
=> [[1,2],[3,4],[5]]
=> 1 = 0 + 1
{{1,2,5},{3},{4}}
=> [[1,2,5],[3],[4]]
=> 1 = 0 + 1
{{1,2},{3,5},{4}}
=> [[1,2],[3,5],[4]]
=> 1 = 0 + 1
{{1,2},{3},{4,5}}
=> [[1,2],[3,5],[4]]
=> 1 = 0 + 1
{{1,2},{3},{4},{5}}
=> [[1,2],[3],[4],[5]]
=> 1 = 0 + 1
{{1,3,4,5},{2}}
=> [[1,3,4,5],[2]]
=> 2 = 1 + 1
{{1,3,4},{2,5}}
=> [[1,3,4],[2,5]]
=> 2 = 1 + 1
{{1,3,4},{2},{5}}
=> [[1,3,4],[2],[5]]
=> 2 = 1 + 1
{{1,3,5},{2,4}}
=> [[1,3,5],[2,4]]
=> 2 = 1 + 1
{{1,3},{2,4,5}}
=> [[1,3,5],[2,4]]
=> 2 = 1 + 1
{{1,3},{2,4},{5}}
=> [[1,3],[2,4],[5]]
=> 2 = 1 + 1
{{1,3,5},{2},{4}}
=> [[1,3,5],[2],[4]]
=> 2 = 1 + 1
{{1,3},{2,5},{4}}
=> [[1,3],[2,5],[4]]
=> 2 = 1 + 1
{{1,3},{2},{4,5}}
=> [[1,3],[2,5],[4]]
=> 2 = 1 + 1
{{1,3},{2},{4},{5}}
=> [[1,3],[2],[4],[5]]
=> 2 = 1 + 1
{{1,4,5},{2,3}}
=> [[1,3,5],[2,4]]
=> 2 = 1 + 1
{{1,4},{2,3,5}}
=> [[1,3,5],[2,4]]
=> 2 = 1 + 1
{{1,4},{2,3},{5}}
=> [[1,3],[2,4],[5]]
=> 2 = 1 + 1
Description
The index of the last row whose first entry is the row number in a standard Young tableau.
Matching statistic: St000297
Mp00258: Set partitions —Standard tableau associated to a set partition⟶ Standard tableaux
Mp00134: Standard tableaux —descent word⟶ Binary words
St000297: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00134: Standard tableaux —descent word⟶ Binary words
St000297: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1,2}}
=> [[1,2]]
=> 0 => 0
{{1},{2}}
=> [[1],[2]]
=> 1 => 1
{{1,2,3}}
=> [[1,2,3]]
=> 00 => 0
{{1,2},{3}}
=> [[1,2],[3]]
=> 01 => 0
{{1,3},{2}}
=> [[1,3],[2]]
=> 10 => 1
{{1},{2,3}}
=> [[1,3],[2]]
=> 10 => 1
{{1},{2},{3}}
=> [[1],[2],[3]]
=> 11 => 2
{{1,2,3,4}}
=> [[1,2,3,4]]
=> 000 => 0
{{1,2,3},{4}}
=> [[1,2,3],[4]]
=> 001 => 0
{{1,2,4},{3}}
=> [[1,2,4],[3]]
=> 010 => 0
{{1,2},{3,4}}
=> [[1,2],[3,4]]
=> 010 => 0
{{1,2},{3},{4}}
=> [[1,2],[3],[4]]
=> 011 => 0
{{1,3,4},{2}}
=> [[1,3,4],[2]]
=> 100 => 1
{{1,3},{2,4}}
=> [[1,3],[2,4]]
=> 101 => 1
{{1,3},{2},{4}}
=> [[1,3],[2],[4]]
=> 101 => 1
{{1,4},{2,3}}
=> [[1,3],[2,4]]
=> 101 => 1
{{1},{2,3,4}}
=> [[1,3,4],[2]]
=> 100 => 1
{{1},{2,3},{4}}
=> [[1,3],[2],[4]]
=> 101 => 1
{{1,4},{2},{3}}
=> [[1,4],[2],[3]]
=> 110 => 2
{{1},{2,4},{3}}
=> [[1,4],[2],[3]]
=> 110 => 2
{{1},{2},{3,4}}
=> [[1,4],[2],[3]]
=> 110 => 2
{{1},{2},{3},{4}}
=> [[1],[2],[3],[4]]
=> 111 => 3
{{1,2,3,4,5}}
=> [[1,2,3,4,5]]
=> 0000 => 0
{{1,2,3,4},{5}}
=> [[1,2,3,4],[5]]
=> 0001 => 0
{{1,2,3,5},{4}}
=> [[1,2,3,5],[4]]
=> 0010 => 0
{{1,2,3},{4,5}}
=> [[1,2,3],[4,5]]
=> 0010 => 0
{{1,2,3},{4},{5}}
=> [[1,2,3],[4],[5]]
=> 0011 => 0
{{1,2,4,5},{3}}
=> [[1,2,4,5],[3]]
=> 0100 => 0
{{1,2,4},{3,5}}
=> [[1,2,4],[3,5]]
=> 0101 => 0
{{1,2,4},{3},{5}}
=> [[1,2,4],[3],[5]]
=> 0101 => 0
{{1,2,5},{3,4}}
=> [[1,2,5],[3,4]]
=> 0100 => 0
{{1,2},{3,4,5}}
=> [[1,2,5],[3,4]]
=> 0100 => 0
{{1,2},{3,4},{5}}
=> [[1,2],[3,4],[5]]
=> 0101 => 0
{{1,2,5},{3},{4}}
=> [[1,2,5],[3],[4]]
=> 0110 => 0
{{1,2},{3,5},{4}}
=> [[1,2],[3,5],[4]]
=> 0110 => 0
{{1,2},{3},{4,5}}
=> [[1,2],[3,5],[4]]
=> 0110 => 0
{{1,2},{3},{4},{5}}
=> [[1,2],[3],[4],[5]]
=> 0111 => 0
{{1,3,4,5},{2}}
=> [[1,3,4,5],[2]]
=> 1000 => 1
{{1,3,4},{2,5}}
=> [[1,3,4],[2,5]]
=> 1001 => 1
{{1,3,4},{2},{5}}
=> [[1,3,4],[2],[5]]
=> 1001 => 1
{{1,3,5},{2,4}}
=> [[1,3,5],[2,4]]
=> 1010 => 1
{{1,3},{2,4,5}}
=> [[1,3,5],[2,4]]
=> 1010 => 1
{{1,3},{2,4},{5}}
=> [[1,3],[2,4],[5]]
=> 1011 => 1
{{1,3,5},{2},{4}}
=> [[1,3,5],[2],[4]]
=> 1010 => 1
{{1,3},{2,5},{4}}
=> [[1,3],[2,5],[4]]
=> 1010 => 1
{{1,3},{2},{4,5}}
=> [[1,3],[2,5],[4]]
=> 1010 => 1
{{1,3},{2},{4},{5}}
=> [[1,3],[2],[4],[5]]
=> 1011 => 1
{{1,4,5},{2,3}}
=> [[1,3,5],[2,4]]
=> 1010 => 1
{{1,4},{2,3,5}}
=> [[1,3,5],[2,4]]
=> 1010 => 1
{{1,4},{2,3},{5}}
=> [[1,3],[2,4],[5]]
=> 1011 => 1
Description
The number of leading ones in a binary word.
Matching statistic: St000326
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00236: Permutations —Clarke-Steingrimsson-Zeng inverse⟶ Permutations
Mp00130: Permutations —descent tops⟶ Binary words
St000326: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00236: Permutations —Clarke-Steingrimsson-Zeng inverse⟶ Permutations
Mp00130: Permutations —descent tops⟶ Binary words
St000326: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1,2}}
=> [2,1] => [2,1] => 1 => 1 = 0 + 1
{{1},{2}}
=> [1,2] => [1,2] => 0 => 2 = 1 + 1
{{1,2,3}}
=> [2,3,1] => [3,2,1] => 11 => 1 = 0 + 1
{{1,2},{3}}
=> [2,1,3] => [2,1,3] => 10 => 1 = 0 + 1
{{1,3},{2}}
=> [3,2,1] => [2,3,1] => 01 => 2 = 1 + 1
{{1},{2,3}}
=> [1,3,2] => [1,3,2] => 01 => 2 = 1 + 1
{{1},{2},{3}}
=> [1,2,3] => [1,2,3] => 00 => 3 = 2 + 1
{{1,2,3,4}}
=> [2,3,4,1] => [4,3,2,1] => 111 => 1 = 0 + 1
{{1,2,3},{4}}
=> [2,3,1,4] => [3,2,1,4] => 110 => 1 = 0 + 1
{{1,2,4},{3}}
=> [2,4,3,1] => [3,4,2,1] => 101 => 1 = 0 + 1
{{1,2},{3,4}}
=> [2,1,4,3] => [2,1,4,3] => 101 => 1 = 0 + 1
{{1,2},{3},{4}}
=> [2,1,3,4] => [2,1,3,4] => 100 => 1 = 0 + 1
{{1,3,4},{2}}
=> [3,2,4,1] => [2,4,3,1] => 011 => 2 = 1 + 1
{{1,3},{2,4}}
=> [3,4,1,2] => [4,1,3,2] => 011 => 2 = 1 + 1
{{1,3},{2},{4}}
=> [3,2,1,4] => [2,3,1,4] => 010 => 2 = 1 + 1
{{1,4},{2,3}}
=> [4,3,2,1] => [3,2,4,1] => 011 => 2 = 1 + 1
{{1},{2,3,4}}
=> [1,3,4,2] => [1,4,3,2] => 011 => 2 = 1 + 1
{{1},{2,3},{4}}
=> [1,3,2,4] => [1,3,2,4] => 010 => 2 = 1 + 1
{{1,4},{2},{3}}
=> [4,2,3,1] => [2,3,4,1] => 001 => 3 = 2 + 1
{{1},{2,4},{3}}
=> [1,4,3,2] => [1,3,4,2] => 001 => 3 = 2 + 1
{{1},{2},{3,4}}
=> [1,2,4,3] => [1,2,4,3] => 001 => 3 = 2 + 1
{{1},{2},{3},{4}}
=> [1,2,3,4] => [1,2,3,4] => 000 => 4 = 3 + 1
{{1,2,3,4,5}}
=> [2,3,4,5,1] => [5,4,3,2,1] => 1111 => 1 = 0 + 1
{{1,2,3,4},{5}}
=> [2,3,4,1,5] => [4,3,2,1,5] => 1110 => 1 = 0 + 1
{{1,2,3,5},{4}}
=> [2,3,5,4,1] => [4,5,3,2,1] => 1101 => 1 = 0 + 1
{{1,2,3},{4,5}}
=> [2,3,1,5,4] => [3,2,1,5,4] => 1101 => 1 = 0 + 1
{{1,2,3},{4},{5}}
=> [2,3,1,4,5] => [3,2,1,4,5] => 1100 => 1 = 0 + 1
{{1,2,4,5},{3}}
=> [2,4,3,5,1] => [3,5,4,2,1] => 1011 => 1 = 0 + 1
{{1,2,4},{3,5}}
=> [2,4,5,1,3] => [5,2,1,4,3] => 1011 => 1 = 0 + 1
{{1,2,4},{3},{5}}
=> [2,4,3,1,5] => [3,4,2,1,5] => 1010 => 1 = 0 + 1
{{1,2,5},{3,4}}
=> [2,5,4,3,1] => [4,3,5,2,1] => 1011 => 1 = 0 + 1
{{1,2},{3,4,5}}
=> [2,1,4,5,3] => [2,1,5,4,3] => 1011 => 1 = 0 + 1
{{1,2},{3,4},{5}}
=> [2,1,4,3,5] => [2,1,4,3,5] => 1010 => 1 = 0 + 1
{{1,2,5},{3},{4}}
=> [2,5,3,4,1] => [3,4,5,2,1] => 1001 => 1 = 0 + 1
{{1,2},{3,5},{4}}
=> [2,1,5,4,3] => [2,1,4,5,3] => 1001 => 1 = 0 + 1
{{1,2},{3},{4,5}}
=> [2,1,3,5,4] => [2,1,3,5,4] => 1001 => 1 = 0 + 1
{{1,2},{3},{4},{5}}
=> [2,1,3,4,5] => [2,1,3,4,5] => 1000 => 1 = 0 + 1
{{1,3,4,5},{2}}
=> [3,2,4,5,1] => [2,5,4,3,1] => 0111 => 2 = 1 + 1
{{1,3,4},{2,5}}
=> [3,5,4,1,2] => [4,1,5,3,2] => 0111 => 2 = 1 + 1
{{1,3,4},{2},{5}}
=> [3,2,4,1,5] => [2,4,3,1,5] => 0110 => 2 = 1 + 1
{{1,3,5},{2,4}}
=> [3,4,5,2,1] => [5,2,4,3,1] => 0111 => 2 = 1 + 1
{{1,3},{2,4,5}}
=> [3,4,1,5,2] => [5,4,1,3,2] => 0111 => 2 = 1 + 1
{{1,3},{2,4},{5}}
=> [3,4,1,2,5] => [4,1,3,2,5] => 0110 => 2 = 1 + 1
{{1,3,5},{2},{4}}
=> [3,2,5,4,1] => [2,4,5,3,1] => 0101 => 2 = 1 + 1
{{1,3},{2,5},{4}}
=> [3,5,1,4,2] => [4,5,1,3,2] => 0101 => 2 = 1 + 1
{{1,3},{2},{4,5}}
=> [3,2,1,5,4] => [2,3,1,5,4] => 0101 => 2 = 1 + 1
{{1,3},{2},{4},{5}}
=> [3,2,1,4,5] => [2,3,1,4,5] => 0100 => 2 = 1 + 1
{{1,4,5},{2,3}}
=> [4,3,2,5,1] => [3,2,5,4,1] => 0111 => 2 = 1 + 1
{{1,4},{2,3,5}}
=> [4,3,5,1,2] => [5,3,1,4,2] => 0111 => 2 = 1 + 1
{{1,4},{2,3},{5}}
=> [4,3,2,1,5] => [3,2,4,1,5] => 0110 => 2 = 1 + 1
Description
The position of the first one in a binary word after appending a 1 at the end.
Regarding the binary word as a subset of {1,…,n,n+1} that contains n+1, this is the minimal element of the set.
Matching statistic: St000382
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00258: Set partitions —Standard tableau associated to a set partition⟶ Standard tableaux
Mp00084: Standard tableaux —conjugate⟶ Standard tableaux
Mp00207: Standard tableaux —horizontal strip sizes⟶ Integer compositions
St000382: Integer compositions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00084: Standard tableaux —conjugate⟶ Standard tableaux
Mp00207: Standard tableaux —horizontal strip sizes⟶ Integer compositions
St000382: Integer compositions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1,2}}
=> [[1,2]]
=> [[1],[2]]
=> [1,1] => 1 = 0 + 1
{{1},{2}}
=> [[1],[2]]
=> [[1,2]]
=> [2] => 2 = 1 + 1
{{1,2,3}}
=> [[1,2,3]]
=> [[1],[2],[3]]
=> [1,1,1] => 1 = 0 + 1
{{1,2},{3}}
=> [[1,2],[3]]
=> [[1,3],[2]]
=> [1,2] => 1 = 0 + 1
{{1,3},{2}}
=> [[1,3],[2]]
=> [[1,2],[3]]
=> [2,1] => 2 = 1 + 1
{{1},{2,3}}
=> [[1,3],[2]]
=> [[1,2],[3]]
=> [2,1] => 2 = 1 + 1
{{1},{2},{3}}
=> [[1],[2],[3]]
=> [[1,2,3]]
=> [3] => 3 = 2 + 1
{{1,2,3,4}}
=> [[1,2,3,4]]
=> [[1],[2],[3],[4]]
=> [1,1,1,1] => 1 = 0 + 1
{{1,2,3},{4}}
=> [[1,2,3],[4]]
=> [[1,4],[2],[3]]
=> [1,1,2] => 1 = 0 + 1
{{1,2,4},{3}}
=> [[1,2,4],[3]]
=> [[1,3],[2],[4]]
=> [1,2,1] => 1 = 0 + 1
{{1,2},{3,4}}
=> [[1,2],[3,4]]
=> [[1,3],[2,4]]
=> [1,2,1] => 1 = 0 + 1
{{1,2},{3},{4}}
=> [[1,2],[3],[4]]
=> [[1,3,4],[2]]
=> [1,3] => 1 = 0 + 1
{{1,3,4},{2}}
=> [[1,3,4],[2]]
=> [[1,2],[3],[4]]
=> [2,1,1] => 2 = 1 + 1
{{1,3},{2,4}}
=> [[1,3],[2,4]]
=> [[1,2],[3,4]]
=> [2,2] => 2 = 1 + 1
{{1,3},{2},{4}}
=> [[1,3],[2],[4]]
=> [[1,2,4],[3]]
=> [2,2] => 2 = 1 + 1
{{1,4},{2,3}}
=> [[1,3],[2,4]]
=> [[1,2],[3,4]]
=> [2,2] => 2 = 1 + 1
{{1},{2,3,4}}
=> [[1,3,4],[2]]
=> [[1,2],[3],[4]]
=> [2,1,1] => 2 = 1 + 1
{{1},{2,3},{4}}
=> [[1,3],[2],[4]]
=> [[1,2,4],[3]]
=> [2,2] => 2 = 1 + 1
{{1,4},{2},{3}}
=> [[1,4],[2],[3]]
=> [[1,2,3],[4]]
=> [3,1] => 3 = 2 + 1
{{1},{2,4},{3}}
=> [[1,4],[2],[3]]
=> [[1,2,3],[4]]
=> [3,1] => 3 = 2 + 1
{{1},{2},{3,4}}
=> [[1,4],[2],[3]]
=> [[1,2,3],[4]]
=> [3,1] => 3 = 2 + 1
{{1},{2},{3},{4}}
=> [[1],[2],[3],[4]]
=> [[1,2,3,4]]
=> [4] => 4 = 3 + 1
{{1,2,3,4,5}}
=> [[1,2,3,4,5]]
=> [[1],[2],[3],[4],[5]]
=> [1,1,1,1,1] => 1 = 0 + 1
{{1,2,3,4},{5}}
=> [[1,2,3,4],[5]]
=> [[1,5],[2],[3],[4]]
=> [1,1,1,2] => 1 = 0 + 1
{{1,2,3,5},{4}}
=> [[1,2,3,5],[4]]
=> [[1,4],[2],[3],[5]]
=> [1,1,2,1] => 1 = 0 + 1
{{1,2,3},{4,5}}
=> [[1,2,3],[4,5]]
=> [[1,4],[2,5],[3]]
=> [1,1,2,1] => 1 = 0 + 1
{{1,2,3},{4},{5}}
=> [[1,2,3],[4],[5]]
=> [[1,4,5],[2],[3]]
=> [1,1,3] => 1 = 0 + 1
{{1,2,4,5},{3}}
=> [[1,2,4,5],[3]]
=> [[1,3],[2],[4],[5]]
=> [1,2,1,1] => 1 = 0 + 1
{{1,2,4},{3,5}}
=> [[1,2,4],[3,5]]
=> [[1,3],[2,5],[4]]
=> [1,2,2] => 1 = 0 + 1
{{1,2,4},{3},{5}}
=> [[1,2,4],[3],[5]]
=> [[1,3,5],[2],[4]]
=> [1,2,2] => 1 = 0 + 1
{{1,2,5},{3,4}}
=> [[1,2,5],[3,4]]
=> [[1,3],[2,4],[5]]
=> [1,2,1,1] => 1 = 0 + 1
{{1,2},{3,4,5}}
=> [[1,2,5],[3,4]]
=> [[1,3],[2,4],[5]]
=> [1,2,1,1] => 1 = 0 + 1
{{1,2},{3,4},{5}}
=> [[1,2],[3,4],[5]]
=> [[1,3,5],[2,4]]
=> [1,2,2] => 1 = 0 + 1
{{1,2,5},{3},{4}}
=> [[1,2,5],[3],[4]]
=> [[1,3,4],[2],[5]]
=> [1,3,1] => 1 = 0 + 1
{{1,2},{3,5},{4}}
=> [[1,2],[3,5],[4]]
=> [[1,3,4],[2,5]]
=> [1,3,1] => 1 = 0 + 1
{{1,2},{3},{4,5}}
=> [[1,2],[3,5],[4]]
=> [[1,3,4],[2,5]]
=> [1,3,1] => 1 = 0 + 1
{{1,2},{3},{4},{5}}
=> [[1,2],[3],[4],[5]]
=> [[1,3,4,5],[2]]
=> [1,4] => 1 = 0 + 1
{{1,3,4,5},{2}}
=> [[1,3,4,5],[2]]
=> [[1,2],[3],[4],[5]]
=> [2,1,1,1] => 2 = 1 + 1
{{1,3,4},{2,5}}
=> [[1,3,4],[2,5]]
=> [[1,2],[3,5],[4]]
=> [2,1,2] => 2 = 1 + 1
{{1,3,4},{2},{5}}
=> [[1,3,4],[2],[5]]
=> [[1,2,5],[3],[4]]
=> [2,1,2] => 2 = 1 + 1
{{1,3,5},{2,4}}
=> [[1,3,5],[2,4]]
=> [[1,2],[3,4],[5]]
=> [2,2,1] => 2 = 1 + 1
{{1,3},{2,4,5}}
=> [[1,3,5],[2,4]]
=> [[1,2],[3,4],[5]]
=> [2,2,1] => 2 = 1 + 1
{{1,3},{2,4},{5}}
=> [[1,3],[2,4],[5]]
=> [[1,2,5],[3,4]]
=> [2,3] => 2 = 1 + 1
{{1,3,5},{2},{4}}
=> [[1,3,5],[2],[4]]
=> [[1,2,4],[3],[5]]
=> [2,2,1] => 2 = 1 + 1
{{1,3},{2,5},{4}}
=> [[1,3],[2,5],[4]]
=> [[1,2,4],[3,5]]
=> [2,2,1] => 2 = 1 + 1
{{1,3},{2},{4,5}}
=> [[1,3],[2,5],[4]]
=> [[1,2,4],[3,5]]
=> [2,2,1] => 2 = 1 + 1
{{1,3},{2},{4},{5}}
=> [[1,3],[2],[4],[5]]
=> [[1,2,4,5],[3]]
=> [2,3] => 2 = 1 + 1
{{1,4,5},{2,3}}
=> [[1,3,5],[2,4]]
=> [[1,2],[3,4],[5]]
=> [2,2,1] => 2 = 1 + 1
{{1,4},{2,3,5}}
=> [[1,3,5],[2,4]]
=> [[1,2],[3,4],[5]]
=> [2,2,1] => 2 = 1 + 1
{{1,4},{2,3},{5}}
=> [[1,3],[2,4],[5]]
=> [[1,2,5],[3,4]]
=> [2,3] => 2 = 1 + 1
Description
The first part of an integer composition.
Matching statistic: St000383
Mp00258: Set partitions —Standard tableau associated to a set partition⟶ Standard tableaux
Mp00207: Standard tableaux —horizontal strip sizes⟶ Integer compositions
Mp00041: Integer compositions —conjugate⟶ Integer compositions
St000383: Integer compositions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00207: Standard tableaux —horizontal strip sizes⟶ Integer compositions
Mp00041: Integer compositions —conjugate⟶ Integer compositions
St000383: Integer compositions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1,2}}
=> [[1,2]]
=> [2] => [1,1] => 1 = 0 + 1
{{1},{2}}
=> [[1],[2]]
=> [1,1] => [2] => 2 = 1 + 1
{{1,2,3}}
=> [[1,2,3]]
=> [3] => [1,1,1] => 1 = 0 + 1
{{1,2},{3}}
=> [[1,2],[3]]
=> [2,1] => [2,1] => 1 = 0 + 1
{{1,3},{2}}
=> [[1,3],[2]]
=> [1,2] => [1,2] => 2 = 1 + 1
{{1},{2,3}}
=> [[1,3],[2]]
=> [1,2] => [1,2] => 2 = 1 + 1
{{1},{2},{3}}
=> [[1],[2],[3]]
=> [1,1,1] => [3] => 3 = 2 + 1
{{1,2,3,4}}
=> [[1,2,3,4]]
=> [4] => [1,1,1,1] => 1 = 0 + 1
{{1,2,3},{4}}
=> [[1,2,3],[4]]
=> [3,1] => [2,1,1] => 1 = 0 + 1
{{1,2,4},{3}}
=> [[1,2,4],[3]]
=> [2,2] => [1,2,1] => 1 = 0 + 1
{{1,2},{3,4}}
=> [[1,2],[3,4]]
=> [2,2] => [1,2,1] => 1 = 0 + 1
{{1,2},{3},{4}}
=> [[1,2],[3],[4]]
=> [2,1,1] => [3,1] => 1 = 0 + 1
{{1,3,4},{2}}
=> [[1,3,4],[2]]
=> [1,3] => [1,1,2] => 2 = 1 + 1
{{1,3},{2,4}}
=> [[1,3],[2,4]]
=> [1,2,1] => [2,2] => 2 = 1 + 1
{{1,3},{2},{4}}
=> [[1,3],[2],[4]]
=> [1,2,1] => [2,2] => 2 = 1 + 1
{{1,4},{2,3}}
=> [[1,3],[2,4]]
=> [1,2,1] => [2,2] => 2 = 1 + 1
{{1},{2,3,4}}
=> [[1,3,4],[2]]
=> [1,3] => [1,1,2] => 2 = 1 + 1
{{1},{2,3},{4}}
=> [[1,3],[2],[4]]
=> [1,2,1] => [2,2] => 2 = 1 + 1
{{1,4},{2},{3}}
=> [[1,4],[2],[3]]
=> [1,1,2] => [1,3] => 3 = 2 + 1
{{1},{2,4},{3}}
=> [[1,4],[2],[3]]
=> [1,1,2] => [1,3] => 3 = 2 + 1
{{1},{2},{3,4}}
=> [[1,4],[2],[3]]
=> [1,1,2] => [1,3] => 3 = 2 + 1
{{1},{2},{3},{4}}
=> [[1],[2],[3],[4]]
=> [1,1,1,1] => [4] => 4 = 3 + 1
{{1,2,3,4,5}}
=> [[1,2,3,4,5]]
=> [5] => [1,1,1,1,1] => 1 = 0 + 1
{{1,2,3,4},{5}}
=> [[1,2,3,4],[5]]
=> [4,1] => [2,1,1,1] => 1 = 0 + 1
{{1,2,3,5},{4}}
=> [[1,2,3,5],[4]]
=> [3,2] => [1,2,1,1] => 1 = 0 + 1
{{1,2,3},{4,5}}
=> [[1,2,3],[4,5]]
=> [3,2] => [1,2,1,1] => 1 = 0 + 1
{{1,2,3},{4},{5}}
=> [[1,2,3],[4],[5]]
=> [3,1,1] => [3,1,1] => 1 = 0 + 1
{{1,2,4,5},{3}}
=> [[1,2,4,5],[3]]
=> [2,3] => [1,1,2,1] => 1 = 0 + 1
{{1,2,4},{3,5}}
=> [[1,2,4],[3,5]]
=> [2,2,1] => [2,2,1] => 1 = 0 + 1
{{1,2,4},{3},{5}}
=> [[1,2,4],[3],[5]]
=> [2,2,1] => [2,2,1] => 1 = 0 + 1
{{1,2,5},{3,4}}
=> [[1,2,5],[3,4]]
=> [2,3] => [1,1,2,1] => 1 = 0 + 1
{{1,2},{3,4,5}}
=> [[1,2,5],[3,4]]
=> [2,3] => [1,1,2,1] => 1 = 0 + 1
{{1,2},{3,4},{5}}
=> [[1,2],[3,4],[5]]
=> [2,2,1] => [2,2,1] => 1 = 0 + 1
{{1,2,5},{3},{4}}
=> [[1,2,5],[3],[4]]
=> [2,1,2] => [1,3,1] => 1 = 0 + 1
{{1,2},{3,5},{4}}
=> [[1,2],[3,5],[4]]
=> [2,1,2] => [1,3,1] => 1 = 0 + 1
{{1,2},{3},{4,5}}
=> [[1,2],[3,5],[4]]
=> [2,1,2] => [1,3,1] => 1 = 0 + 1
{{1,2},{3},{4},{5}}
=> [[1,2],[3],[4],[5]]
=> [2,1,1,1] => [4,1] => 1 = 0 + 1
{{1,3,4,5},{2}}
=> [[1,3,4,5],[2]]
=> [1,4] => [1,1,1,2] => 2 = 1 + 1
{{1,3,4},{2,5}}
=> [[1,3,4],[2,5]]
=> [1,3,1] => [2,1,2] => 2 = 1 + 1
{{1,3,4},{2},{5}}
=> [[1,3,4],[2],[5]]
=> [1,3,1] => [2,1,2] => 2 = 1 + 1
{{1,3,5},{2,4}}
=> [[1,3,5],[2,4]]
=> [1,2,2] => [1,2,2] => 2 = 1 + 1
{{1,3},{2,4,5}}
=> [[1,3,5],[2,4]]
=> [1,2,2] => [1,2,2] => 2 = 1 + 1
{{1,3},{2,4},{5}}
=> [[1,3],[2,4],[5]]
=> [1,2,1,1] => [3,2] => 2 = 1 + 1
{{1,3,5},{2},{4}}
=> [[1,3,5],[2],[4]]
=> [1,2,2] => [1,2,2] => 2 = 1 + 1
{{1,3},{2,5},{4}}
=> [[1,3],[2,5],[4]]
=> [1,2,2] => [1,2,2] => 2 = 1 + 1
{{1,3},{2},{4,5}}
=> [[1,3],[2,5],[4]]
=> [1,2,2] => [1,2,2] => 2 = 1 + 1
{{1,3},{2},{4},{5}}
=> [[1,3],[2],[4],[5]]
=> [1,2,1,1] => [3,2] => 2 = 1 + 1
{{1,4,5},{2,3}}
=> [[1,3,5],[2,4]]
=> [1,2,2] => [1,2,2] => 2 = 1 + 1
{{1,4},{2,3,5}}
=> [[1,3,5],[2,4]]
=> [1,2,2] => [1,2,2] => 2 = 1 + 1
{{1,4},{2,3},{5}}
=> [[1,3],[2,4],[5]]
=> [1,2,1,1] => [3,2] => 2 = 1 + 1
Description
The last part of an integer composition.
Matching statistic: St000678
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St000678: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St000678: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1,2}}
=> [2,1] => [2,1] => [1,1,0,0]
=> 1 = 0 + 1
{{1},{2}}
=> [1,2] => [1,2] => [1,0,1,0]
=> 2 = 1 + 1
{{1,2,3}}
=> [2,3,1] => [3,1,2] => [1,1,1,0,0,0]
=> 1 = 0 + 1
{{1,2},{3}}
=> [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
=> 2 = 1 + 1
{{1,3},{2}}
=> [3,2,1] => [2,3,1] => [1,1,0,1,0,0]
=> 2 = 1 + 1
{{1},{2,3}}
=> [1,3,2] => [1,3,2] => [1,0,1,1,0,0]
=> 1 = 0 + 1
{{1},{2},{3}}
=> [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
=> 3 = 2 + 1
{{1,2,3,4}}
=> [2,3,4,1] => [4,1,2,3] => [1,1,1,1,0,0,0,0]
=> 1 = 0 + 1
{{1,2,3},{4}}
=> [2,3,1,4] => [3,1,2,4] => [1,1,1,0,0,0,1,0]
=> 2 = 1 + 1
{{1,2,4},{3}}
=> [2,4,3,1] => [3,4,1,2] => [1,1,1,0,1,0,0,0]
=> 2 = 1 + 1
{{1,2},{3,4}}
=> [2,1,4,3] => [2,1,4,3] => [1,1,0,0,1,1,0,0]
=> 1 = 0 + 1
{{1,2},{3},{4}}
=> [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
=> 3 = 2 + 1
{{1,3,4},{2}}
=> [3,2,4,1] => [2,4,1,3] => [1,1,0,1,1,0,0,0]
=> 1 = 0 + 1
{{1,3},{2,4}}
=> [3,4,1,2] => [3,1,4,2] => [1,1,1,0,0,1,0,0]
=> 2 = 1 + 1
{{1,3},{2},{4}}
=> [3,2,1,4] => [2,3,1,4] => [1,1,0,1,0,0,1,0]
=> 3 = 2 + 1
{{1,4},{2,3}}
=> [4,3,2,1] => [3,2,4,1] => [1,1,1,0,0,1,0,0]
=> 2 = 1 + 1
{{1},{2,3,4}}
=> [1,3,4,2] => [1,4,2,3] => [1,0,1,1,1,0,0,0]
=> 1 = 0 + 1
{{1},{2,3},{4}}
=> [1,3,2,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
=> 2 = 1 + 1
{{1,4},{2},{3}}
=> [4,2,3,1] => [2,3,4,1] => [1,1,0,1,0,1,0,0]
=> 3 = 2 + 1
{{1},{2,4},{3}}
=> [1,4,3,2] => [1,3,4,2] => [1,0,1,1,0,1,0,0]
=> 2 = 1 + 1
{{1},{2},{3,4}}
=> [1,2,4,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> 1 = 0 + 1
{{1},{2},{3},{4}}
=> [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> 4 = 3 + 1
{{1,2,3,4,5}}
=> [2,3,4,5,1] => [5,1,2,3,4] => [1,1,1,1,1,0,0,0,0,0]
=> 1 = 0 + 1
{{1,2,3,4},{5}}
=> [2,3,4,1,5] => [4,1,2,3,5] => [1,1,1,1,0,0,0,0,1,0]
=> 2 = 1 + 1
{{1,2,3,5},{4}}
=> [2,3,5,4,1] => [4,5,1,2,3] => [1,1,1,1,0,1,0,0,0,0]
=> 2 = 1 + 1
{{1,2,3},{4,5}}
=> [2,3,1,5,4] => [3,1,2,5,4] => [1,1,1,0,0,0,1,1,0,0]
=> 1 = 0 + 1
{{1,2,3},{4},{5}}
=> [2,3,1,4,5] => [3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0]
=> 3 = 2 + 1
{{1,2,4,5},{3}}
=> [2,4,3,5,1] => [3,5,1,2,4] => [1,1,1,0,1,1,0,0,0,0]
=> 1 = 0 + 1
{{1,2,4},{3,5}}
=> [2,4,5,1,3] => [4,1,2,5,3] => [1,1,1,1,0,0,0,1,0,0]
=> 2 = 1 + 1
{{1,2,4},{3},{5}}
=> [2,4,3,1,5] => [3,4,1,2,5] => [1,1,1,0,1,0,0,0,1,0]
=> 3 = 2 + 1
{{1,2,5},{3,4}}
=> [2,5,4,3,1] => [4,3,5,1,2] => [1,1,1,1,0,0,1,0,0,0]
=> 2 = 1 + 1
{{1,2},{3,4,5}}
=> [2,1,4,5,3] => [2,1,5,3,4] => [1,1,0,0,1,1,1,0,0,0]
=> 1 = 0 + 1
{{1,2},{3,4},{5}}
=> [2,1,4,3,5] => [2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0]
=> 2 = 1 + 1
{{1,2,5},{3},{4}}
=> [2,5,3,4,1] => [3,4,5,1,2] => [1,1,1,0,1,0,1,0,0,0]
=> 3 = 2 + 1
{{1,2},{3,5},{4}}
=> [2,1,5,4,3] => [2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0]
=> 2 = 1 + 1
{{1,2},{3},{4,5}}
=> [2,1,3,5,4] => [2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0]
=> 1 = 0 + 1
{{1,2},{3},{4},{5}}
=> [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
=> 4 = 3 + 1
{{1,3,4,5},{2}}
=> [3,2,4,5,1] => [2,5,1,3,4] => [1,1,0,1,1,1,0,0,0,0]
=> 1 = 0 + 1
{{1,3,4},{2,5}}
=> [3,5,4,1,2] => [4,1,3,5,2] => [1,1,1,1,0,0,0,1,0,0]
=> 2 = 1 + 1
{{1,3,4},{2},{5}}
=> [3,2,4,1,5] => [2,4,1,3,5] => [1,1,0,1,1,0,0,0,1,0]
=> 2 = 1 + 1
{{1,3,5},{2,4}}
=> [3,4,5,2,1] => [4,2,5,1,3] => [1,1,1,1,0,0,1,0,0,0]
=> 2 = 1 + 1
{{1,3},{2,4,5}}
=> [3,4,1,5,2] => [3,1,5,2,4] => [1,1,1,0,0,1,1,0,0,0]
=> 1 = 0 + 1
{{1,3},{2,4},{5}}
=> [3,4,1,2,5] => [3,1,4,2,5] => [1,1,1,0,0,1,0,0,1,0]
=> 3 = 2 + 1
{{1,3,5},{2},{4}}
=> [3,2,5,4,1] => [2,4,5,1,3] => [1,1,0,1,1,0,1,0,0,0]
=> 2 = 1 + 1
{{1,3},{2,5},{4}}
=> [3,5,1,4,2] => [3,1,4,5,2] => [1,1,1,0,0,1,0,1,0,0]
=> 3 = 2 + 1
{{1,3},{2},{4,5}}
=> [3,2,1,5,4] => [2,3,1,5,4] => [1,1,0,1,0,0,1,1,0,0]
=> 1 = 0 + 1
{{1,3},{2},{4},{5}}
=> [3,2,1,4,5] => [2,3,1,4,5] => [1,1,0,1,0,0,1,0,1,0]
=> 4 = 3 + 1
{{1,4,5},{2,3}}
=> [4,3,2,5,1] => [3,2,5,1,4] => [1,1,1,0,0,1,1,0,0,0]
=> 1 = 0 + 1
{{1,4},{2,3,5}}
=> [4,3,5,1,2] => [4,1,5,2,3] => [1,1,1,1,0,0,1,0,0,0]
=> 2 = 1 + 1
{{1,4},{2,3},{5}}
=> [4,3,2,1,5] => [3,2,4,1,5] => [1,1,1,0,0,1,0,0,1,0]
=> 3 = 2 + 1
Description
The number of up steps after the last double rise of a Dyck path.
Matching statistic: St000971
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00089: Permutations —Inverse Kreweras complement⟶ Permutations
Mp00240: Permutations —weak exceedance partition⟶ Set partitions
St000971: Set partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00089: Permutations —Inverse Kreweras complement⟶ Permutations
Mp00240: Permutations —weak exceedance partition⟶ Set partitions
St000971: Set partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1,2}}
=> [2,1] => [1,2] => {{1},{2}}
=> 1 = 0 + 1
{{1},{2}}
=> [1,2] => [2,1] => {{1,2}}
=> 2 = 1 + 1
{{1,2,3}}
=> [2,3,1] => [1,2,3] => {{1},{2},{3}}
=> 1 = 0 + 1
{{1,2},{3}}
=> [2,1,3] => [1,3,2] => {{1},{2,3}}
=> 1 = 0 + 1
{{1,3},{2}}
=> [3,2,1] => [2,1,3] => {{1,2},{3}}
=> 2 = 1 + 1
{{1},{2,3}}
=> [1,3,2] => [3,2,1] => {{1,3},{2}}
=> 2 = 1 + 1
{{1},{2},{3}}
=> [1,2,3] => [2,3,1] => {{1,2,3}}
=> 3 = 2 + 1
{{1,2,3,4}}
=> [2,3,4,1] => [1,2,3,4] => {{1},{2},{3},{4}}
=> 1 = 0 + 1
{{1,2,3},{4}}
=> [2,3,1,4] => [1,2,4,3] => {{1},{2},{3,4}}
=> 1 = 0 + 1
{{1,2,4},{3}}
=> [2,4,3,1] => [1,3,2,4] => {{1},{2,3},{4}}
=> 1 = 0 + 1
{{1,2},{3,4}}
=> [2,1,4,3] => [1,4,3,2] => {{1},{2,4},{3}}
=> 1 = 0 + 1
{{1,2},{3},{4}}
=> [2,1,3,4] => [1,3,4,2] => {{1},{2,3,4}}
=> 1 = 0 + 1
{{1,3,4},{2}}
=> [3,2,4,1] => [2,1,3,4] => {{1,2},{3},{4}}
=> 2 = 1 + 1
{{1,3},{2,4}}
=> [3,4,1,2] => [4,1,2,3] => {{1,4},{2},{3}}
=> 2 = 1 + 1
{{1,3},{2},{4}}
=> [3,2,1,4] => [2,1,4,3] => {{1,2},{3,4}}
=> 2 = 1 + 1
{{1,4},{2,3}}
=> [4,3,2,1] => [3,2,1,4] => {{1,3},{2},{4}}
=> 2 = 1 + 1
{{1},{2,3,4}}
=> [1,3,4,2] => [4,2,3,1] => {{1,4},{2},{3}}
=> 2 = 1 + 1
{{1},{2,3},{4}}
=> [1,3,2,4] => [3,2,4,1] => {{1,3,4},{2}}
=> 2 = 1 + 1
{{1,4},{2},{3}}
=> [4,2,3,1] => [2,3,1,4] => {{1,2,3},{4}}
=> 3 = 2 + 1
{{1},{2,4},{3}}
=> [1,4,3,2] => [4,3,2,1] => {{1,4},{2,3}}
=> 3 = 2 + 1
{{1},{2},{3,4}}
=> [1,2,4,3] => [2,4,3,1] => {{1,2,4},{3}}
=> 3 = 2 + 1
{{1},{2},{3},{4}}
=> [1,2,3,4] => [2,3,4,1] => {{1,2,3,4}}
=> 4 = 3 + 1
{{1,2,3,4,5}}
=> [2,3,4,5,1] => [1,2,3,4,5] => {{1},{2},{3},{4},{5}}
=> 1 = 0 + 1
{{1,2,3,4},{5}}
=> [2,3,4,1,5] => [1,2,3,5,4] => {{1},{2},{3},{4,5}}
=> 1 = 0 + 1
{{1,2,3,5},{4}}
=> [2,3,5,4,1] => [1,2,4,3,5] => {{1},{2},{3,4},{5}}
=> 1 = 0 + 1
{{1,2,3},{4,5}}
=> [2,3,1,5,4] => [1,2,5,4,3] => {{1},{2},{3,5},{4}}
=> 1 = 0 + 1
{{1,2,3},{4},{5}}
=> [2,3,1,4,5] => [1,2,4,5,3] => {{1},{2},{3,4,5}}
=> 1 = 0 + 1
{{1,2,4,5},{3}}
=> [2,4,3,5,1] => [1,3,2,4,5] => {{1},{2,3},{4},{5}}
=> 1 = 0 + 1
{{1,2,4},{3,5}}
=> [2,4,5,1,3] => [1,5,2,3,4] => {{1},{2,5},{3},{4}}
=> 1 = 0 + 1
{{1,2,4},{3},{5}}
=> [2,4,3,1,5] => [1,3,2,5,4] => {{1},{2,3},{4,5}}
=> 1 = 0 + 1
{{1,2,5},{3,4}}
=> [2,5,4,3,1] => [1,4,3,2,5] => {{1},{2,4},{3},{5}}
=> 1 = 0 + 1
{{1,2},{3,4,5}}
=> [2,1,4,5,3] => [1,5,3,4,2] => {{1},{2,5},{3},{4}}
=> 1 = 0 + 1
{{1,2},{3,4},{5}}
=> [2,1,4,3,5] => [1,4,3,5,2] => {{1},{2,4,5},{3}}
=> 1 = 0 + 1
{{1,2,5},{3},{4}}
=> [2,5,3,4,1] => [1,3,4,2,5] => {{1},{2,3,4},{5}}
=> 1 = 0 + 1
{{1,2},{3,5},{4}}
=> [2,1,5,4,3] => [1,5,4,3,2] => {{1},{2,5},{3,4}}
=> 1 = 0 + 1
{{1,2},{3},{4,5}}
=> [2,1,3,5,4] => [1,3,5,4,2] => {{1},{2,3,5},{4}}
=> 1 = 0 + 1
{{1,2},{3},{4},{5}}
=> [2,1,3,4,5] => [1,3,4,5,2] => {{1},{2,3,4,5}}
=> 1 = 0 + 1
{{1,3,4,5},{2}}
=> [3,2,4,5,1] => [2,1,3,4,5] => {{1,2},{3},{4},{5}}
=> 2 = 1 + 1
{{1,3,4},{2,5}}
=> [3,5,4,1,2] => [5,1,3,2,4] => {{1,5},{2},{3},{4}}
=> 2 = 1 + 1
{{1,3,4},{2},{5}}
=> [3,2,4,1,5] => [2,1,3,5,4] => {{1,2},{3},{4,5}}
=> 2 = 1 + 1
{{1,3,5},{2,4}}
=> [3,4,5,2,1] => [4,1,2,3,5] => {{1,4},{2},{3},{5}}
=> 2 = 1 + 1
{{1,3},{2,4,5}}
=> [3,4,1,5,2] => [5,1,2,4,3] => {{1,5},{2},{3},{4}}
=> 2 = 1 + 1
{{1,3},{2,4},{5}}
=> [3,4,1,2,5] => [4,1,2,5,3] => {{1,4,5},{2},{3}}
=> 2 = 1 + 1
{{1,3,5},{2},{4}}
=> [3,2,5,4,1] => [2,1,4,3,5] => {{1,2},{3,4},{5}}
=> 2 = 1 + 1
{{1,3},{2,5},{4}}
=> [3,5,1,4,2] => [5,1,4,2,3] => {{1,5},{2},{3,4}}
=> 2 = 1 + 1
{{1,3},{2},{4,5}}
=> [3,2,1,5,4] => [2,1,5,4,3] => {{1,2},{3,5},{4}}
=> 2 = 1 + 1
{{1,3},{2},{4},{5}}
=> [3,2,1,4,5] => [2,1,4,5,3] => {{1,2},{3,4,5}}
=> 2 = 1 + 1
{{1,4,5},{2,3}}
=> [4,3,2,5,1] => [3,2,1,4,5] => {{1,3},{2},{4},{5}}
=> 2 = 1 + 1
{{1,4},{2,3,5}}
=> [4,3,5,1,2] => [5,2,1,3,4] => {{1,5},{2},{3},{4}}
=> 2 = 1 + 1
{{1,4},{2,3},{5}}
=> [4,3,2,1,5] => [3,2,1,5,4] => {{1,3},{2},{4,5}}
=> 2 = 1 + 1
Description
The smallest closer of a set partition.
A closer (or right hand endpoint) of a set partition is a number that is maximal in its block. For this statistic, singletons are considered as closers.
In other words, this is the smallest among the maximal elements of the blocks.
Matching statistic: St000069
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00241: Permutations —invert Laguerre heap⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St000069: Posets ⟶ ℤResult quality: 70% ●values known / values provided: 70%●distinct values known / distinct values provided: 100%
Mp00241: Permutations —invert Laguerre heap⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St000069: Posets ⟶ ℤResult quality: 70% ●values known / values provided: 70%●distinct values known / distinct values provided: 100%
Values
{{1,2}}
=> [2,1] => [2,1] => ([],2)
=> 2 = 1 + 1
{{1},{2}}
=> [1,2] => [1,2] => ([(0,1)],2)
=> 1 = 0 + 1
{{1,2,3}}
=> [2,3,1] => [3,1,2] => ([(1,2)],3)
=> 2 = 1 + 1
{{1,2},{3}}
=> [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
=> 1 = 0 + 1
{{1,3},{2}}
=> [3,2,1] => [3,2,1] => ([],3)
=> 3 = 2 + 1
{{1},{2,3}}
=> [1,3,2] => [1,3,2] => ([(0,1),(0,2)],3)
=> 2 = 1 + 1
{{1},{2},{3}}
=> [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
=> 1 = 0 + 1
{{1,2,3,4}}
=> [2,3,4,1] => [4,1,2,3] => ([(1,2),(2,3)],4)
=> 2 = 1 + 1
{{1,2,3},{4}}
=> [2,3,1,4] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4)
=> 1 = 0 + 1
{{1,2,4},{3}}
=> [2,4,3,1] => [4,3,1,2] => ([(2,3)],4)
=> 3 = 2 + 1
{{1,2},{3,4}}
=> [2,1,4,3] => [2,1,4,3] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> 2 = 1 + 1
{{1,2},{3},{4}}
=> [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
=> 1 = 0 + 1
{{1,3,4},{2}}
=> [3,2,4,1] => [4,1,3,2] => ([(1,2),(1,3)],4)
=> 3 = 2 + 1
{{1,3},{2,4}}
=> [3,4,1,2] => [2,4,1,3] => ([(0,3),(1,2),(1,3)],4)
=> 2 = 1 + 1
{{1,3},{2},{4}}
=> [3,2,1,4] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
=> 1 = 0 + 1
{{1,4},{2,3}}
=> [4,3,2,1] => [4,3,2,1] => ([],4)
=> 4 = 3 + 1
{{1},{2,3,4}}
=> [1,3,4,2] => [1,4,2,3] => ([(0,2),(0,3),(3,1)],4)
=> 2 = 1 + 1
{{1},{2,3},{4}}
=> [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1 = 0 + 1
{{1,4},{2},{3}}
=> [4,2,3,1] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
=> 2 = 1 + 1
{{1},{2,4},{3}}
=> [1,4,3,2] => [1,4,3,2] => ([(0,1),(0,2),(0,3)],4)
=> 3 = 2 + 1
{{1},{2},{3,4}}
=> [1,2,4,3] => [1,2,4,3] => ([(0,3),(3,1),(3,2)],4)
=> 2 = 1 + 1
{{1},{2},{3},{4}}
=> [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 1 = 0 + 1
{{1,2,3,4,5}}
=> [2,3,4,5,1] => [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5)
=> 2 = 1 + 1
{{1,2,3,4},{5}}
=> [2,3,4,1,5] => [4,1,2,3,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
=> 1 = 0 + 1
{{1,2,3,5},{4}}
=> [2,3,5,4,1] => [5,4,1,2,3] => ([(2,3),(3,4)],5)
=> 3 = 2 + 1
{{1,2,3},{4,5}}
=> [2,3,1,5,4] => [3,1,2,5,4] => ([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
=> 2 = 1 + 1
{{1,2,3},{4},{5}}
=> [2,3,1,4,5] => [3,1,2,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
=> 1 = 0 + 1
{{1,2,4,5},{3}}
=> [2,4,3,5,1] => [5,1,2,4,3] => ([(1,4),(4,2),(4,3)],5)
=> 3 = 2 + 1
{{1,2,4},{3,5}}
=> [2,4,5,1,3] => [3,5,1,2,4] => ([(0,3),(1,2),(1,4),(3,4)],5)
=> 2 = 1 + 1
{{1,2,4},{3},{5}}
=> [2,4,3,1,5] => [4,3,1,2,5] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> 1 = 0 + 1
{{1,2,5},{3,4}}
=> [2,5,4,3,1] => [5,4,3,1,2] => ([(3,4)],5)
=> 4 = 3 + 1
{{1,2},{3,4,5}}
=> [2,1,4,5,3] => [2,1,5,3,4] => ([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> 2 = 1 + 1
{{1,2},{3,4},{5}}
=> [2,1,4,3,5] => [2,1,4,3,5] => ([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> 1 = 0 + 1
{{1,2,5},{3},{4}}
=> [2,5,3,4,1] => [4,1,2,5,3] => ([(0,4),(1,2),(2,3),(2,4)],5)
=> 2 = 1 + 1
{{1,2},{3,5},{4}}
=> [2,1,5,4,3] => [2,1,5,4,3] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> 3 = 2 + 1
{{1,2},{3},{4,5}}
=> [2,1,3,5,4] => [2,1,3,5,4] => ([(0,4),(1,4),(4,2),(4,3)],5)
=> 2 = 1 + 1
{{1,2},{3},{4},{5}}
=> [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
=> 1 = 0 + 1
{{1,3,4,5},{2}}
=> [3,2,4,5,1] => [5,1,3,2,4] => ([(1,2),(1,3),(2,4),(3,4)],5)
=> 2 = 1 + 1
{{1,3,4},{2,5}}
=> [3,5,4,1,2] => [2,5,4,1,3] => ([(0,4),(1,2),(1,3),(1,4)],5)
=> 3 = 2 + 1
{{1,3,4},{2},{5}}
=> [3,2,4,1,5] => [4,1,3,2,5] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 1 = 0 + 1
{{1,3,5},{2,4}}
=> [3,4,5,2,1] => [5,2,1,3,4] => ([(1,4),(2,4),(4,3)],5)
=> 2 = 1 + 1
{{1,3},{2,4,5}}
=> [3,4,1,5,2] => [5,2,4,1,3] => ([(1,4),(2,3),(2,4)],5)
=> 3 = 2 + 1
{{1,3},{2,4},{5}}
=> [3,4,1,2,5] => [2,4,1,3,5] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
=> 1 = 0 + 1
{{1,3,5},{2},{4}}
=> [3,2,5,4,1] => [5,4,1,3,2] => ([(2,3),(2,4)],5)
=> 4 = 3 + 1
{{1,3},{2,5},{4}}
=> [3,5,1,4,2] => [4,2,5,1,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
=> 2 = 1 + 1
{{1,3},{2},{4,5}}
=> [3,2,1,5,4] => [3,2,1,5,4] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 2 = 1 + 1
{{1,3},{2},{4},{5}}
=> [3,2,1,4,5] => [3,2,1,4,5] => ([(0,4),(1,4),(2,4),(4,3)],5)
=> 1 = 0 + 1
{{1,4,5},{2,3}}
=> [4,3,2,5,1] => [5,1,4,3,2] => ([(1,2),(1,3),(1,4)],5)
=> 4 = 3 + 1
{{1,4},{2,3,5}}
=> [4,3,5,1,2] => [2,5,1,4,3] => ([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> 3 = 2 + 1
{{1,4},{2,3},{5}}
=> [4,3,2,1,5] => [4,3,2,1,5] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 0 + 1
{{1,2,3,4,5},{6,7}}
=> [2,3,4,5,1,7,6] => [5,1,2,3,4,7,6] => ([(0,5),(0,6),(1,4),(2,5),(2,6),(3,2),(4,3)],7)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4} + 1
{{1,2,3,4,6,7},{5}}
=> [2,3,4,6,5,7,1] => [7,1,2,3,4,6,5] => ([(1,5),(4,6),(5,4),(6,2),(6,3)],7)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4} + 1
{{1,2,3,4},{5,6,7}}
=> [2,3,4,1,6,7,5] => [4,1,2,3,7,5,6] => ([(0,5),(0,6),(1,4),(3,5),(3,6),(4,3),(6,2)],7)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4} + 1
{{1,2,3,4},{5,6},{7}}
=> [2,3,4,1,6,5,7] => [4,1,2,3,6,5,7] => ([(0,2),(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4} + 1
{{1,2,3,4},{5,7},{6}}
=> [2,3,4,1,7,6,5] => [4,1,2,3,7,6,5] => ([(0,2),(1,4),(1,5),(1,6),(2,3),(3,4),(3,5),(3,6)],7)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4} + 1
{{1,2,3,4},{5},{6,7}}
=> [2,3,4,1,5,7,6] => [4,1,2,3,5,7,6] => ([(0,6),(1,5),(2,6),(5,2),(6,3),(6,4)],7)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4} + 1
{{1,2,3,5,6},{4,7}}
=> [2,3,5,7,6,1,4] => [4,7,6,1,2,3,5] => ([(0,5),(1,2),(1,3),(1,6),(4,6),(5,4)],7)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4} + 1
{{1,2,3,5},{4,6,7}}
=> [2,3,5,6,1,7,4] => [7,4,6,1,2,3,5] => ([(1,4),(2,3),(2,6),(4,5),(5,6)],7)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4} + 1
{{1,2,3,6},{4,5,7}}
=> [2,3,6,5,7,1,4] => [4,7,1,2,3,6,5] => ([(0,4),(1,3),(1,5),(1,6),(2,5),(2,6),(4,2)],7)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4} + 1
{{1,2,3},{4,5,6,7}}
=> [2,3,1,5,6,7,4] => [3,1,2,7,4,5,6] => ([(0,5),(0,6),(1,3),(3,5),(3,6),(4,2),(6,4)],7)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4} + 1
{{1,2,3},{4,5,6},{7}}
=> [2,3,1,5,6,4,7] => [3,1,2,6,4,5,7] => ([(0,3),(1,4),(1,6),(2,5),(3,4),(3,6),(4,2),(6,5)],7)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4} + 1
{{1,2,3},{4,5,7},{6}}
=> [2,3,1,5,7,6,4] => [3,1,2,7,6,4,5] => ([(0,3),(1,4),(1,5),(1,6),(3,4),(3,5),(3,6),(6,2)],7)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4} + 1
{{1,2,3},{4,5},{6,7}}
=> [2,3,1,5,4,7,6] => [3,1,2,5,4,7,6] => ([(0,2),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4} + 1
{{1,2,3},{4,5},{6},{7}}
=> [2,3,1,5,4,6,7] => [3,1,2,5,4,6,7] => ([(0,3),(1,5),(1,6),(3,5),(3,6),(4,2),(5,4),(6,4)],7)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4} + 1
{{1,2,3,6},{4},{5,7}}
=> [2,3,6,4,7,1,5] => [5,7,1,2,3,6,4] => ([(0,5),(1,3),(1,6),(4,2),(4,6),(5,4)],7)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4} + 1
{{1,2,3,6},{4},{5},{7}}
=> [2,3,6,4,5,1,7] => [5,1,2,3,6,4,7] => ([(0,6),(1,4),(2,5),(3,2),(3,6),(4,3),(6,5)],7)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4} + 1
{{1,2,3},{4,6,7},{5}}
=> [2,3,1,6,5,7,4] => [3,1,2,7,4,6,5] => ([(0,5),(0,6),(1,4),(4,5),(4,6),(6,2),(6,3)],7)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4} + 1
{{1,2,3},{4,6},{5,7}}
=> [2,3,1,6,7,4,5] => [3,1,2,5,7,4,6] => ([(0,3),(1,5),(1,6),(3,5),(3,6),(5,4),(6,2),(6,4)],7)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4} + 1
{{1,2,3},{4,6},{5},{7}}
=> [2,3,1,6,5,4,7] => [3,1,2,6,5,4,7] => ([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4} + 1
{{1,2,3},{4},{5,6,7}}
=> [2,3,1,4,6,7,5] => [3,1,2,4,7,5,6] => ([(0,6),(1,3),(3,6),(5,2),(6,4),(6,5)],7)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4} + 1
{{1,2,3},{4,7},{5},{6}}
=> [2,3,1,7,5,6,4] => [3,1,2,6,4,7,5] => ([(0,3),(1,5),(1,6),(3,5),(3,6),(5,4),(6,2),(6,4)],7)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4} + 1
{{1,2,3},{4},{5,7},{6}}
=> [2,3,1,4,7,6,5] => [3,1,2,4,7,6,5] => ([(0,6),(1,2),(2,6),(6,3),(6,4),(6,5)],7)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4} + 1
{{1,2,3},{4},{5},{6,7}}
=> [2,3,1,4,5,7,6] => [3,1,2,4,5,7,6] => ([(0,6),(1,4),(4,6),(5,2),(5,3),(6,5)],7)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4} + 1
{{1,2,4,5,6,7},{3}}
=> [2,4,3,5,6,7,1] => [7,1,2,4,3,5,6] => ([(1,5),(2,6),(3,6),(5,2),(5,3),(6,4)],7)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4} + 1
{{1,2,4,5,6},{3,7}}
=> [2,4,7,5,6,1,3] => [3,6,1,2,4,7,5] => ([(0,3),(1,4),(1,6),(3,6),(4,5),(6,2),(6,5)],7)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4} + 1
{{1,2,4,5,6},{3},{7}}
=> [2,4,3,5,6,1,7] => [6,1,2,4,3,5,7] => ([(0,6),(1,4),(2,5),(3,5),(4,2),(4,3),(5,6)],7)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4} + 1
{{1,2,4,5,7},{3,6}}
=> [2,4,6,5,7,3,1] => [7,3,1,2,4,6,5] => ([(1,6),(2,3),(3,6),(6,4),(6,5)],7)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4} + 1
{{1,2,4,5},{3,6},{7}}
=> [2,4,6,5,1,3,7] => [3,6,5,1,2,4,7] => ([(0,4),(1,2),(1,3),(1,5),(2,6),(3,6),(4,5),(5,6)],7)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4} + 1
{{1,2,4,5,7},{3},{6}}
=> [2,4,3,5,7,6,1] => [7,6,1,2,4,3,5] => ([(2,3),(3,4),(3,5),(4,6),(5,6)],7)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4} + 1
{{1,2,4,5},{3,7},{6}}
=> [2,4,7,5,1,6,3] => [6,3,7,5,1,2,4] => ([(0,5),(1,4),(2,3),(2,5),(2,6),(4,6)],7)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4} + 1
{{1,2,4,5},{3},{6},{7}}
=> [2,4,3,5,1,6,7] => [5,1,2,4,3,6,7] => ([(0,6),(1,5),(2,6),(3,6),(5,2),(5,3),(6,4)],7)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4} + 1
{{1,2,4,6},{3,5,7}}
=> [2,4,5,6,7,1,3] => [3,7,1,2,4,5,6] => ([(0,4),(1,3),(1,6),(4,6),(5,2),(6,5)],7)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4} + 1
{{1,2,4,7},{3,5,6}}
=> [2,4,5,7,6,3,1] => [7,6,3,1,2,4,5] => ([(2,6),(3,4),(4,6),(6,5)],7)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4} + 1
{{1,2,4},{3,5,6},{7}}
=> [2,4,5,1,6,3,7] => [6,3,5,1,2,4,7] => ([(0,6),(1,4),(2,3),(2,5),(3,6),(4,5),(5,6)],7)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4} + 1
{{1,2,4,7},{3,5},{6}}
=> [2,4,5,7,3,6,1] => [6,1,2,7,3,4,5] => ([(0,6),(1,5),(3,4),(4,2),(5,3),(5,6)],7)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4} + 1
{{1,2,4},{3,5,7},{6}}
=> [2,4,5,1,7,6,3] => [7,6,3,5,1,2,4] => ([(2,5),(3,4),(3,6),(5,6)],7)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4} + 1
{{1,2,4},{3,5},{6,7}}
=> [2,4,5,1,3,7,6] => [3,5,1,2,4,7,6] => ([(0,2),(1,3),(1,6),(2,6),(3,4),(3,5),(6,4),(6,5)],7)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4} + 1
{{1,2,4},{3,5},{6},{7}}
=> [2,4,5,1,3,6,7] => [3,5,1,2,4,6,7] => ([(0,4),(1,3),(1,5),(3,6),(4,5),(5,6),(6,2)],7)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4} + 1
{{1,2,4,6,7},{3},{5}}
=> [2,4,3,6,5,7,1] => [7,1,2,4,3,6,5] => ([(1,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3)],7)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4} + 1
{{1,2,4,6},{3},{5,7}}
=> [2,4,3,6,7,1,5] => [5,7,1,2,4,3,6] => ([(0,5),(1,4),(1,6),(2,6),(3,6),(5,2),(5,3)],7)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4} + 1
{{1,2,4,7},{3,6},{5}}
=> [2,4,6,7,5,3,1] => [7,5,3,1,2,4,6] => ([(1,6),(2,5),(3,4),(4,6),(6,5)],7)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4} + 1
{{1,2,4},{3,6,7},{5}}
=> [2,4,6,1,5,7,3] => [7,3,5,6,1,2,4] => ([(1,4),(2,3),(2,6),(3,5),(4,6)],7)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4} + 1
{{1,2,4,7},{3},{5},{6}}
=> [2,4,3,7,5,6,1] => [6,1,2,4,3,7,5] => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3)],7)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4} + 1
{{1,2,4},{3},{5,7},{6}}
=> [2,4,3,1,7,6,5] => [4,3,1,2,7,6,5] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(3,4),(3,5),(3,6)],7)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4} + 1
{{1,2,5,6,7},{3,4}}
=> [2,5,4,3,6,7,1] => [7,1,2,5,4,3,6] => ([(1,5),(2,6),(3,6),(4,6),(5,2),(5,3),(5,4)],7)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4} + 1
{{1,2,5,7},{3,4,6}}
=> [2,5,4,6,7,3,1] => [7,3,1,2,5,4,6] => ([(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4} + 1
{{1,2,5},{3,4,6,7}}
=> [2,5,4,6,1,7,3] => [7,3,6,1,2,5,4] => ([(1,4),(2,3),(2,5),(2,6),(4,5),(4,6)],7)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4} + 1
{{1,2,5},{3,4,6},{7}}
=> [2,5,4,6,1,3,7] => [3,6,1,2,5,4,7] => ([(0,3),(1,2),(1,4),(1,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4} + 1
{{1,2,5},{3,4,7},{6}}
=> [2,5,4,7,1,6,3] => [6,3,7,1,2,5,4] => ([(0,4),(1,4),(1,5),(1,6),(2,3),(3,5),(3,6)],7)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4} + 1
{{1,2,6,7},{3,4,5}}
=> [2,6,4,5,3,7,1] => [7,1,2,5,3,6,4] => ([(1,5),(3,6),(4,2),(4,6),(5,3),(5,4)],7)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4} + 1
Description
The number of maximal elements of a poset.
The following 31 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001124The multiplicity of the standard representation in the Kronecker square corresponding to a partition. St000772The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. St001199The dominant dimension of eAe for the corresponding Nakayama algebra A with minimal faithful projective-injective module eA. St000771The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. St000068The number of minimal elements in a poset. St000260The radius of a connected graph. St000541The number of indices greater than or equal to 2 of a permutation such that all smaller indices appear to its right. St000542The number of left-to-right-minima of a permutation. St000989The number of final rises of a permutation. St001876The number of 2-regular simple modules in the incidence algebra of the lattice. St001630The global dimension of the incidence algebra of the lattice over the rational numbers. St001877Number of indecomposable injective modules with projective dimension 2. St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L. St000990The first ascent of a permutation. St000007The number of saliances of the permutation. St000054The first entry of the permutation. St000031The number of cycles in the cycle decomposition of a permutation. St000314The number of left-to-right-maxima of a permutation. St000991The number of right-to-left minima of a permutation. St000454The largest eigenvalue of a graph if it is integral. St001632The number of indecomposable injective modules I with dimExt1(I,A)=1 for the incidence algebra A of a poset. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St001948The number of augmented double ascents of a permutation. St000338The number of pixed points of a permutation. St001640The number of ascent tops in the permutation such that all smaller elements appear before. St001744The number of occurrences of the arrow pattern 1-2 with an arrow from 1 to 2 in a permutation. St000193The row of the unique '1' in the first column of the alternating sign matrix. St000654The first descent of a permutation. St000455The second largest eigenvalue of a graph if it is integral. St000942The number of critical left to right maxima of the parking functions.
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