Identifier
Values
[1,1,1] => [3] => [[3],[]] => ([(0,2),(2,1)],3) => 3
[1,1,1,1] => [4] => [[4],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[1,2,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[1,1,1,1,1] => [5] => [[5],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,3,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[2,1,2] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[1,1,1,1,1,1] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[1,2,1,2] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[1,2,3] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[1,3,2] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[1,4,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[2,1,2,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[2,1,3] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[2,2,2] => [3] => [[3],[]] => ([(0,2),(2,1)],3) => 3
[2,3,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[3,1,2] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[3,2,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[1,1,1,1,1,1,1] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7
[1,2,1,2,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,2,1,3] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[1,2,3,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[1,2,4] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[1,3,1,2] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[1,3,2,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[1,4,2] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[1,5,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[2,1,3,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[2,1,4] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[2,3,2] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[2,4,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[3,1,2,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[3,1,3] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[4,1,2] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[4,2,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[1,2,1,3,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,2,1,4] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[1,2,3,2] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[1,2,4,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[1,2,5] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[1,3,1,2,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,3,1,3] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[1,3,4] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[1,4,1,2] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[1,4,2,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[1,4,3] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[1,5,2] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[1,6,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[2,1,2,1,2] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[2,1,2,3] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[2,1,3,2] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[2,1,4,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[2,1,5] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[2,2,2,2] => [4] => [[4],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[2,3,1,2] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[2,3,2,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[2,4,2] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[2,5,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[3,1,3,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[3,1,4] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[3,2,1,2] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[3,2,3] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[3,4,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[4,1,2,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[4,1,3] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[4,3,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[5,1,2] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[5,2,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[1,2,1,2,1,2] => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[1,2,1,2,3] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,2,1,3,2] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,2,1,4,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,2,1,5] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[1,2,3,1,2] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,2,3,2,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,2,4,2] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[1,2,5,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[1,2,6] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[1,3,1,3,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,3,1,4] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[1,3,2,1,2] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,3,2,3] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[1,3,4,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[1,3,5] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[1,4,1,2,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,4,1,3] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[1,4,3,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[1,5,1,2] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[1,5,2,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[1,5,3] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[1,6,2] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[1,7,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[2,1,2,1,2,1] => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[2,1,2,1,3] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[2,1,2,3,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[2,1,2,4] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[2,1,3,1,2] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[2,1,3,2,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[2,1,4,2] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[2,1,5,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[2,1,6] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[2,3,1,2,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
>>> Load all 431 entries. <<<
[2,3,1,3] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[2,3,4] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[2,4,1,2] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[2,4,2,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[2,4,3] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[2,5,2] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[2,6,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[3,1,2,1,2] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[3,1,2,3] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[3,1,3,2] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[3,1,4,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[3,1,5] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[3,2,1,2,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[3,2,1,3] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[3,2,3,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[3,2,4] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[3,3,3] => [3] => [[3],[]] => ([(0,2),(2,1)],3) => 3
[3,4,2] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[3,5,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[4,1,3,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[4,1,4] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[4,2,1,2] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[4,2,3] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[4,3,2] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[5,1,2,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[5,1,3] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[5,3,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[6,1,2] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[6,2,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[1,2,1,2,1,2,1] => [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7
[1,2,1,2,1,3] => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[1,2,1,2,3,1] => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[1,2,1,2,4] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,2,1,3,1,2] => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[1,2,1,3,2,1] => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[1,2,1,4,2] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,2,1,5,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,2,1,6] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[1,2,3,1,2,1] => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[1,2,3,1,3] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,2,3,4] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[1,2,4,1,2] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,2,4,2,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,2,4,3] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[1,2,5,2] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[1,2,6,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[1,2,7] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[1,3,1,2,1,2] => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[1,3,1,2,3] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,3,1,3,2] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,3,1,4,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,3,1,5] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[1,3,2,1,2,1] => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[1,3,2,1,3] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,3,2,3,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,3,2,4] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[1,3,4,2] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[1,3,5,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[1,3,6] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[1,4,1,3,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,4,1,4] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[1,4,2,1,2] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,4,2,3] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[1,4,3,2] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[1,4,5] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[1,5,1,2,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,5,1,3] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[1,5,3,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[1,5,4] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[1,6,1,2] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[1,6,2,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[1,6,3] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[1,7,2] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[1,8,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[2,1,2,1,3,1] => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[2,1,2,1,4] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[2,1,2,3,2] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[2,1,2,4,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[2,1,2,5] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[2,1,3,1,2,1] => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[2,1,3,1,3] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[2,1,3,4] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[2,1,4,1,2] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[2,1,4,2,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[2,1,4,3] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[2,1,5,2] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[2,1,6,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[2,1,7] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[2,2,2,2,2] => [5] => [[5],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[2,3,1,3,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[2,3,1,4] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[2,3,2,1,2] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[2,3,2,3] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[2,3,4,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[2,3,5] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[2,4,1,2,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[2,4,1,3] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[2,4,3,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[2,5,1,2] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[2,5,2,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[2,5,3] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[2,6,2] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[2,7,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[3,1,2,1,2,1] => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[3,1,2,1,3] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[3,1,2,3,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[3,1,2,4] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[3,1,3,1,2] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[3,1,3,2,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[3,1,4,2] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[3,1,5,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[3,1,6] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[3,2,1,3,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[3,2,1,4] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[3,2,3,2] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[3,2,4,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[3,2,5] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[3,4,1,2] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[3,4,2,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[3,4,3] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[3,5,2] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[3,6,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[4,1,2,1,2] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[4,1,2,3] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[4,1,3,2] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[4,1,4,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[4,1,5] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[4,2,1,2,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[4,2,1,3] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[4,2,3,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[4,2,4] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[4,3,1,2] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[4,3,2,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[4,5,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[5,1,3,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[5,1,4] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[5,2,1,2] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[5,2,3] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[5,3,2] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[5,4,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[6,1,2,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[6,1,3] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[6,3,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[7,1,2] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[7,2,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[1,7,2,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[1,6,3,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[1,5,4,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[1,4,5,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[1,3,6,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[1,2,7,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[2,2,2,2,2,2] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[2,1,2,1,2,4] => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[2,1,3,2,1,3] => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[2,1,4,5] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[3,3,3,3] => [4] => [[4],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[3,2,3,4] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[3,1,2,3,1,2] => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[3,1,3,5] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[4,3,2,3] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[4,2,1,2,1,2] => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[4,1,2,5] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[5,4,1,2] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[5,3,1,3] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[5,2,1,4] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[1,2,3,4,2] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,2,3,2,3,1] => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[1,2,4,3,2] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,2,4,2,3] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,2,5,4] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[1,3,4,3,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,3,5,3] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[1,3,2,3,2,1] => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[1,3,2,4,2] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,4,5,2] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[1,4,2,4,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,4,2,3,2] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,4,3,4] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[1,5,4,2] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[1,5,2,4] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[1,6,5] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[2,3,2,3,2] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[2,3,4,3] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[2,4,3,2,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[2,4,2,3,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[2,5,4,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[2,5,3,2] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[2,5,2,3] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[2,6,4] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[2,3,4,2,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[2,3,5,2] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[2,3,2,4,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[2,4,5,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[2,4,2,4] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[3,4,3,2] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[3,5,3,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[3,6,3] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[3,4,2,3] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[3,5,4] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[3,2,4,2,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[3,2,5,2] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[3,2,4,3] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[3,4,5] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[4,5,2,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[4,6,2] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[4,5,3] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[4,3,4,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[4,4,4] => [3] => [[3],[]] => ([(0,2),(2,1)],3) => 3
[4,2,5,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[4,2,4,2] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[4,3,5] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[5,6,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[5,4,3] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[5,3,4] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[5,2,5] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[1,8,2] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[1,7,1,2] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[1,9,2] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[1,7,3] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[1,8,1,2] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[1,5,2,1,2] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,2,1,3,1,3] => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[1,2,1,2,3,2] => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[1,2,1,2,1,4] => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[1,2,1,3,2,1,3] => [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7
[1,2,1,3,1,3,2] => [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7
[1,2,1,3,1,2,3] => [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7
[1,2,1,2,3,1,3] => [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7
[1,2,1,2,1,4,2] => [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7
[1,2,1,2,1,2,4] => [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7
[1,2,9] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[3,2,7] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[1,4,7] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[3,1,2,1,5] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,3,2,1,5] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[7,2,3] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[1,8,3] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[5,1,2,1,3] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,5,2,1,3] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[3,1,4,1,3] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,3,4,1,3] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[9,2,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[1,2,6,2,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[7,4,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[3,8,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[1,10,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[3,1,2,5,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,3,2,5,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[5,1,2,3,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,5,2,3,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[3,1,4,3,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,3,1,2,1,3,1] => [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7
[4,2,3,2,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[5,4,2,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[5,2,4,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[5,2,3,2] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[6,5,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[6,4,2] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[6,2,4] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[2,8,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[2,1,7,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[2,9,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[3,7,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[2,1,8,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[2,1,2,5,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[3,1,3,1,2,1] => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[2,3,2,1,2,1] => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[4,1,2,1,2,1] => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[3,1,2,3,1,2,1] => [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7
[2,3,1,3,1,2,1] => [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7
[3,2,1,3,1,2,1] => [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7
[3,1,3,2,1,2,1] => [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7
[2,4,1,2,1,2,1] => [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7
[4,2,1,2,1,2,1] => [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7
[1,3,5,2,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,5,3,2,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,9,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[1,2,3,2,1,2,1] => [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7
[1,3,1,3,1,2,1] => [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7
[1,4,1,2,1,2,1] => [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7
[2,1,2,3,1,2,1] => [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7
[2,1,3,2,1,2,1] => [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7
[2,3,1,2,1,2,1] => [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7
[3,2,1,2,1,2,1] => [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7
[1,3,1,3,1,3,1] => [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7
[1,3,1,2,3,2,1] => [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7
[1,3,1,2,1,4,1] => [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7
[1,2,3,2,1,3,1] => [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7
[1,2,3,1,3,2,1] => [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7
[1,2,1,4,1,3,1] => [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7
[1,2,1,3,1,4,1] => [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7
[1,2,1,2,1,5,1] => [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7
[1,2,3,2,4] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[2,3,2,5] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[1,3,1,5,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,3,1,2,1,2,1] => [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7
[1,5,1,3,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,6,1,2,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,4,1,4,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,4,3,2,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,2,1,2,1,3,1] => [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7
[1,2,1,6,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,2,1,3,1,2,1] => [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7
[1,2,3,4,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,2,5,2,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,3,1,7,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,3,1,4,1,2,1] => [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7
[1,5,1,5,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,5,1,2,1,2,1] => [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7
[1,7,1,3,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,11,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[1,8,1,2,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,6,1,4,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,6,3,2,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,4,1,2,1,3,1] => [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7
[1,4,1,6,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,4,1,3,1,2,1] => [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7
[1,4,3,4,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,4,5,2,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,2,1,8,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,2,1,5,1,2,1] => [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7
[1,2,3,6,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,2,5,4,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,2,7,2,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,6,4] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[1,4,6] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[1,3,7] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[1,2,8] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[1,2,5,3,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,2,3,5,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
search for individual values
searching the database for the individual values of this statistic
Description
The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice.
Map
to ribbon
Description
The ribbon shape corresponding to an integer composition.
For an integer composition $(a_1, \dots, a_n)$, this is the ribbon shape whose $i$th row from the bottom has $a_i$ cells.
Map
cell poset
Description
The Young diagram of a skew partition regarded as a poset.
This is the poset on the cells of the Young diagram, such that a cell $d$ is greater than a cell $c$ if the entry in $d$ must be larger than the entry of $c$ in any standard Young tableau on the skew partition.
Map
delta morphism
Description
Apply the delta morphism to an integer composition.
The delta morphism of a composition $C$ is the compositions composed of the lengths of consecutive runs of the same integer in $C$.