Identifier
-
Mp00202:
Integer partitions
—first row removal⟶
Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
St000420: Dyck paths ⟶ ℤ (values match St000419The number of Dyck paths that are weakly above the Dyck path, except for the path itself.)
Values
[1,1] => [1] => [1,0,1,0] => 2
[2,1] => [1] => [1,0,1,0] => 2
[1,1,1] => [1,1] => [1,0,1,1,0,0] => 3
[3,1] => [1] => [1,0,1,0] => 2
[2,2] => [2] => [1,1,0,0,1,0] => 3
[2,1,1] => [1,1] => [1,0,1,1,0,0] => 3
[1,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 4
[4,1] => [1] => [1,0,1,0] => 2
[3,2] => [2] => [1,1,0,0,1,0] => 3
[3,1,1] => [1,1] => [1,0,1,1,0,0] => 3
[2,2,1] => [2,1] => [1,0,1,0,1,0] => 5
[2,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 4
[1,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 5
[5,1] => [1] => [1,0,1,0] => 2
[4,2] => [2] => [1,1,0,0,1,0] => 3
[4,1,1] => [1,1] => [1,0,1,1,0,0] => 3
[3,3] => [3] => [1,1,1,0,0,0,1,0] => 4
[3,2,1] => [2,1] => [1,0,1,0,1,0] => 5
[3,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 4
[2,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 6
[2,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 7
[2,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 5
[1,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 6
[6,1] => [1] => [1,0,1,0] => 2
[5,2] => [2] => [1,1,0,0,1,0] => 3
[5,1,1] => [1,1] => [1,0,1,1,0,0] => 3
[4,3] => [3] => [1,1,1,0,0,0,1,0] => 4
[4,2,1] => [2,1] => [1,0,1,0,1,0] => 5
[4,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 4
[3,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => 7
[3,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 6
[3,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 7
[3,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 5
[2,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => 9
[2,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 9
[2,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 6
[1,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 7
[7,1] => [1] => [1,0,1,0] => 2
[6,2] => [2] => [1,1,0,0,1,0] => 3
[6,1,1] => [1,1] => [1,0,1,1,0,0] => 3
[5,3] => [3] => [1,1,1,0,0,0,1,0] => 4
[5,2,1] => [2,1] => [1,0,1,0,1,0] => 5
[5,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 4
[4,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => 5
[4,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => 7
[4,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 6
[4,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 7
[4,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 5
[3,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => 9
[3,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => 10
[3,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => 9
[3,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 9
[3,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 6
[2,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 10
[2,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 12
[2,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 11
[2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 7
[1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[8,1] => [1] => [1,0,1,0] => 2
[7,2] => [2] => [1,1,0,0,1,0] => 3
[7,1,1] => [1,1] => [1,0,1,1,0,0] => 3
[6,3] => [3] => [1,1,1,0,0,0,1,0] => 4
[6,2,1] => [2,1] => [1,0,1,0,1,0] => 5
[6,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 4
[5,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => 5
[5,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => 7
[5,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 6
[5,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 7
[5,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 5
[4,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 9
[4,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => 9
[4,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => 10
[4,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => 9
[4,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 9
[4,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 6
[3,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 10
[3,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => 14
[3,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 13
[3,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 10
[3,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 12
[3,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 11
[3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 7
[2,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 14
[2,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 15
[2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 13
[2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[9,1] => [1] => [1,0,1,0] => 2
[8,2] => [2] => [1,1,0,0,1,0] => 3
[8,1,1] => [1,1] => [1,0,1,1,0,0] => 3
[7,3] => [3] => [1,1,1,0,0,0,1,0] => 4
[7,2,1] => [2,1] => [1,0,1,0,1,0] => 5
[7,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 4
[6,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => 5
[6,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => 7
[6,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 6
[6,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 7
[6,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 5
[5,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[5,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 9
[5,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => 9
[5,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => 10
>>> Load all 1220 entries. <<<[5,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => 9
[5,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 9
[5,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 6
[4,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 12
[4,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 13
[4,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 10
[4,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => 14
[4,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 13
[4,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 10
[4,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 12
[4,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 11
[4,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 7
[3,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 16
[3,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 16
[3,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 19
[3,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 16
[3,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 14
[3,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 15
[3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 13
[3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[2,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 15
[2,2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 18
[2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 18
[2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 15
[10,1] => [1] => [1,0,1,0] => 2
[9,2] => [2] => [1,1,0,0,1,0] => 3
[9,1,1] => [1,1] => [1,0,1,1,0,0] => 3
[8,3] => [3] => [1,1,1,0,0,0,1,0] => 4
[8,2,1] => [2,1] => [1,0,1,0,1,0] => 5
[8,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 4
[7,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => 5
[7,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => 7
[7,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 6
[7,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 7
[7,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 5
[6,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[6,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 9
[6,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => 9
[6,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => 10
[6,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => 9
[6,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 9
[6,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 6
[5,5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 11
[5,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 12
[5,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 13
[5,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 10
[5,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => 14
[5,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 13
[5,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 10
[5,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 12
[5,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 11
[5,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 7
[4,4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 14
[4,4,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 19
[4,4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 17
[4,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 16
[4,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 16
[4,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 19
[4,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 16
[4,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 14
[4,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 15
[4,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 13
[4,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[3,3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 19
[3,3,3,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 22
[3,3,2,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 23
[3,3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 24
[3,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 19
[3,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 15
[3,2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 18
[3,2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 18
[3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 15
[2,2,2,2,2,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 20
[2,2,2,2,1,1,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 22
[2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 21
[11,1] => [1] => [1,0,1,0] => 2
[10,2] => [2] => [1,1,0,0,1,0] => 3
[10,1,1] => [1,1] => [1,0,1,1,0,0] => 3
[9,3] => [3] => [1,1,1,0,0,0,1,0] => 4
[9,2,1] => [2,1] => [1,0,1,0,1,0] => 5
[9,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 4
[8,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => 5
[8,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => 7
[8,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 6
[8,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 7
[8,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 5
[7,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[7,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 9
[7,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => 9
[7,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => 10
[7,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => 9
[7,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 9
[7,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 6
[6,6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 11
[6,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 12
[6,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 13
[6,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 10
[6,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => 14
[6,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 13
[6,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 10
[6,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 12
[6,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 11
[6,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 7
[5,5,2] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 15
[5,5,1,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 16
[5,4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 14
[5,4,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 19
[5,4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 17
[5,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 16
[5,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 16
[5,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 19
[5,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 16
[5,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 14
[5,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 15
[5,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 13
[5,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[4,4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 15
[4,4,3,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 23
[4,4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 22
[4,4,2,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 26
[4,4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 21
[4,3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 19
[4,3,3,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 22
[4,3,2,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 23
[4,3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 24
[4,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 19
[4,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 15
[4,2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 18
[4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 18
[4,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 15
[3,3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 20
[3,3,3,2,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 28
[3,3,3,1,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 28
[3,3,2,2,2] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 25
[3,3,2,2,1,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 30
[3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 29
[3,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 22
[3,2,2,2,2,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 20
[3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 22
[3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 21
[2,2,2,2,2,2] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 21
[2,2,2,2,2,1,1] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 25
[2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 26
[12,1] => [1] => [1,0,1,0] => 2
[11,2] => [2] => [1,1,0,0,1,0] => 3
[11,1,1] => [1,1] => [1,0,1,1,0,0] => 3
[10,3] => [3] => [1,1,1,0,0,0,1,0] => 4
[10,2,1] => [2,1] => [1,0,1,0,1,0] => 5
[10,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 4
[9,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => 5
[9,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => 7
[9,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 6
[9,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 7
[9,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 5
[8,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[8,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 9
[8,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => 9
[8,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => 10
[8,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => 9
[8,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 9
[8,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 6
[7,6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[7,5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 11
[7,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 12
[7,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 13
[7,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 10
[7,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => 14
[7,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 13
[7,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 10
[7,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 12
[7,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 11
[7,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,6,1] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 13
[6,5,2] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 15
[6,5,1,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 16
[6,4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 14
[6,4,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 19
[6,4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 17
[6,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 16
[6,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 16
[6,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 19
[6,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 16
[6,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 14
[6,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 15
[6,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 13
[6,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[5,5,3] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 18
[5,5,2,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 24
[5,5,1,1,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 21
[5,4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 15
[5,4,3,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 23
[5,4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 22
[5,4,2,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 26
[5,4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 21
[5,3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 19
[5,3,3,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 22
[5,3,2,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 23
[5,3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 24
[5,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 19
[5,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 15
[5,2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 18
[5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 18
[5,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 15
[4,4,4,1] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => 25
[4,4,3,2] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 28
[4,4,3,1,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 32
[4,4,2,2,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 32
[4,4,2,1,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 33
[4,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 25
[4,3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 20
[4,3,3,2,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 28
[4,3,3,1,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 28
[4,3,2,2,2] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 25
[4,3,2,2,1,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 30
[4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 29
[4,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 22
[4,2,2,2,2,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 20
[4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 22
[4,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 21
[3,3,3,3,1] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => 30
[3,3,3,2,2] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 31
[3,3,3,2,1,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 37
[3,3,3,1,1,1,1] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 34
[3,3,2,2,2,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 34
[3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 37
[3,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 34
[3,2,2,2,2,2] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 21
[3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 25
[3,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 26
[2,2,2,2,2,2,1] => [2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 27
[2,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 30
[13,1] => [1] => [1,0,1,0] => 2
[12,2] => [2] => [1,1,0,0,1,0] => 3
[12,1,1] => [1,1] => [1,0,1,1,0,0] => 3
[11,3] => [3] => [1,1,1,0,0,0,1,0] => 4
[11,2,1] => [2,1] => [1,0,1,0,1,0] => 5
[11,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 4
[10,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => 5
[10,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => 7
[10,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 6
[10,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 7
[10,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 5
[9,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[9,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 9
[9,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => 9
[9,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => 10
[9,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => 9
[9,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 9
[9,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 6
[8,6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[8,5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 11
[8,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 12
[8,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 13
[8,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 10
[8,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => 14
[8,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 13
[8,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 10
[8,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 12
[8,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 11
[8,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 7
[7,6,1] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 13
[7,5,2] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 15
[7,5,1,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 16
[7,4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 14
[7,4,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 19
[7,4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 17
[7,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 16
[7,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 16
[7,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 19
[7,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 16
[7,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 14
[7,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 15
[7,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 13
[7,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[6,6,2] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 18
[6,6,1,1] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 19
[6,5,3] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 18
[6,5,2,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 24
[6,5,1,1,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 21
[6,4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 15
[6,4,3,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 23
[6,4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 22
[6,4,2,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 26
[6,4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 21
[6,3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 19
[6,3,3,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 22
[6,3,2,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 23
[6,3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 24
[6,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 19
[6,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 15
[6,2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 18
[6,2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 18
[6,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 15
[5,5,4] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 20
[5,5,3,1] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => 30
[5,5,2,2] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 28
[5,5,2,1,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 33
[5,5,1,1,1,1] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 26
[5,4,4,1] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => 25
[5,4,3,2] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 28
[5,4,3,1,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 32
[5,4,2,2,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 32
[5,4,2,1,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 33
[5,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 25
[5,3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 20
[5,3,3,2,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 28
[5,3,3,1,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 28
[5,3,2,2,2] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 25
[5,3,2,2,1,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 30
[5,3,2,1,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 29
[5,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 22
[5,2,2,2,2,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 20
[5,2,2,2,1,1,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 22
[5,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 21
[4,4,4,2] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => 31
[4,4,4,1,1] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => 35
[4,4,3,3] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => 30
[4,4,3,2,1] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 42
[4,4,3,1,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 41
[4,4,2,2,2] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 35
[4,4,2,2,1,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 42
[4,4,2,1,1,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 40
[4,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 29
[4,3,3,3,1] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => 30
[4,3,3,2,2] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 31
[4,3,3,2,1,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 37
[4,3,3,1,1,1,1] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 34
[4,3,2,2,2,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 34
[4,3,2,2,1,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 37
[4,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 34
[4,2,2,2,2,2] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 21
[4,2,2,2,2,1,1] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 25
[4,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 26
[3,3,3,3,2] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => 34
[3,3,3,3,1,1] => [3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => 40
[3,3,3,2,2,1] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => 43
[3,3,3,2,1,1,1] => [3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 46
[3,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 40
[3,3,2,2,2,2] => [3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 36
[3,3,2,2,2,1,1] => [3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 43
[3,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 44
[3,2,2,2,2,2,1] => [2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 27
[3,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 30
[2,2,2,2,2,2,2] => [2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 28
[2,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 33
[14,1] => [1] => [1,0,1,0] => 2
[13,2] => [2] => [1,1,0,0,1,0] => 3
[13,1,1] => [1,1] => [1,0,1,1,0,0] => 3
[12,3] => [3] => [1,1,1,0,0,0,1,0] => 4
[12,2,1] => [2,1] => [1,0,1,0,1,0] => 5
[12,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 4
[11,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => 5
[11,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => 7
[11,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 6
[11,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 7
[11,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 5
[10,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[10,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 9
[10,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => 9
[10,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => 10
[10,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => 9
[10,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 9
[10,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 6
[9,6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[9,5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 11
[9,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 12
[9,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 13
[9,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 10
[9,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => 14
[9,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 13
[9,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 10
[9,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 12
[9,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 11
[9,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 7
[8,6,1] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 13
[8,5,2] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 15
[8,5,1,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 16
[8,4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 14
[8,4,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 19
[8,4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 17
[8,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 16
[8,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 16
[8,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 19
[8,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 16
[8,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 14
[8,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 15
[8,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 13
[8,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,2] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 18
[7,6,1,1] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 19
[7,5,3] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 18
[7,5,2,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 24
[7,5,1,1,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 21
[7,4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 15
[7,4,3,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 23
[7,4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 22
[7,4,2,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 26
[7,4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 21
[7,3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 19
[7,3,3,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 22
[7,3,2,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 23
[7,3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 24
[7,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 19
[7,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 15
[7,2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 18
[7,2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 18
[7,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 15
[6,6,3] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 22
[6,6,2,1] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 29
[6,6,1,1,1] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 25
[6,5,4] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 20
[6,5,3,1] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => 30
[6,5,2,2] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 28
[6,5,2,1,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 33
[6,5,1,1,1,1] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 26
[6,4,4,1] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => 25
[6,4,3,2] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 28
[6,4,3,1,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 32
[6,4,2,2,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 32
[6,4,2,1,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 33
[6,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 25
[6,3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 20
[6,3,3,2,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 28
[6,3,3,1,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 28
[6,3,2,2,2] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 25
[6,3,2,2,1,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 30
[6,3,2,1,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 29
[6,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 22
[6,2,2,2,2,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 20
[6,2,2,2,1,1,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 22
[6,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 21
[5,5,5] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 21
[5,5,4,1] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => 34
[5,5,3,2] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => 37
[5,5,3,1,1] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => 42
[5,5,2,2,1] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => 41
[5,5,2,1,1,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => 42
[5,5,1,1,1,1,1] => [5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 31
[5,4,4,2] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => 31
[5,4,4,1,1] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => 35
[5,4,3,3] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => 30
[5,4,3,2,1] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 42
[5,4,3,1,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 41
[5,4,2,2,2] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 35
[5,4,2,2,1,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 42
[5,4,2,1,1,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 40
[5,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 29
[5,3,3,3,1] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => 30
[5,3,3,2,2] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 31
[5,3,3,2,1,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 37
[5,3,3,1,1,1,1] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 34
[5,3,2,2,2,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 34
[5,3,2,2,1,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 37
[5,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 34
[5,2,2,2,2,2] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 21
[5,2,2,2,2,1,1] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 25
[5,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 26
[4,4,4,3] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => 34
[4,4,4,2,1] => [4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => 47
[4,4,4,1,1,1] => [4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => 45
[4,4,3,3,1] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => 46
[4,4,3,2,2] => [4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => 47
[4,4,3,2,1,1] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 56
[4,4,3,1,1,1,1] => [4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 50
[4,4,2,2,2,1] => [4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 48
[4,4,2,2,1,1,1] => [4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 52
[4,4,2,1,1,1,1,1] => [4,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 47
[4,3,3,3,2] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => 34
[4,3,3,3,1,1] => [3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => 40
[4,3,3,2,2,1] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => 43
[4,3,3,2,1,1,1] => [3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 46
[4,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 40
[4,3,2,2,2,2] => [3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 36
[4,3,2,2,2,1,1] => [3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 43
[4,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 44
[4,2,2,2,2,2,1] => [2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 27
[4,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 30
[3,3,3,3,3] => [3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 35
[3,3,3,3,2,1] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => 48
[3,3,3,3,1,1,1] => [3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 50
[3,3,3,2,2,2] => [3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 46
[3,3,3,2,2,1,1] => [3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 55
[3,3,3,2,1,1,1,1] => [3,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 55
[3,3,2,2,2,2,1] => [3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 47
[3,3,2,2,2,1,1,1] => [3,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 52
[3,2,2,2,2,2,2] => [2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 28
[3,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 33
[2,2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 35
[15,1] => [1] => [1,0,1,0] => 2
[14,2] => [2] => [1,1,0,0,1,0] => 3
[14,1,1] => [1,1] => [1,0,1,1,0,0] => 3
[13,3] => [3] => [1,1,1,0,0,0,1,0] => 4
[13,2,1] => [2,1] => [1,0,1,0,1,0] => 5
[13,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 4
[12,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => 5
[12,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => 7
[12,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 6
[12,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 7
[12,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 5
[11,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[11,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 9
[11,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => 9
[11,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => 10
[11,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => 9
[11,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 9
[11,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 6
[10,6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[10,5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 11
[10,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 12
[10,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 13
[10,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 10
[10,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => 14
[10,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 13
[10,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 10
[10,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 12
[10,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 11
[10,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 7
[9,6,1] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 13
[9,5,2] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 15
[9,5,1,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 16
[9,4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 14
[9,4,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 19
[9,4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 17
[9,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 16
[9,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 16
[9,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 19
[9,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 16
[9,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 14
[9,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 15
[9,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 13
[9,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[8,6,2] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 18
[8,6,1,1] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 19
[8,5,3] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 18
[8,5,2,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 24
[8,5,1,1,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 21
[8,4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 15
[8,4,3,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 23
[8,4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 22
[8,4,2,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 26
[8,4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 21
[8,3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 19
[8,3,3,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 22
[8,3,2,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 23
[8,3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 24
[8,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 19
[8,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 15
[8,2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 18
[8,2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 18
[8,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 15
[7,6,3] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 22
[7,6,2,1] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 29
[7,6,1,1,1] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 25
[7,5,4] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 20
[7,5,3,1] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => 30
[7,5,2,2] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 28
[7,5,2,1,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 33
[7,5,1,1,1,1] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 26
[7,4,4,1] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => 25
[7,4,3,2] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 28
[7,4,3,1,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 32
[7,4,2,2,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 32
[7,4,2,1,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 33
[7,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 25
[7,3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 20
[7,3,3,2,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 28
[7,3,3,1,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 28
[7,3,2,2,2] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 25
[7,3,2,2,1,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 30
[7,3,2,1,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 29
[7,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 22
[7,2,2,2,2,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 20
[7,2,2,2,1,1,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 22
[7,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 21
[6,6,4] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 25
[6,6,3,1] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 37
[6,6,2,2] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 34
[6,6,2,1,1] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 40
[6,6,1,1,1,1] => [6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 31
[6,5,5] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 21
[6,5,4,1] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => 34
[6,5,3,2] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => 37
[6,5,3,1,1] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => 42
[6,5,2,2,1] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => 41
[6,5,2,1,1,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => 42
[6,5,1,1,1,1,1] => [5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 31
[6,4,4,2] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => 31
[6,4,4,1,1] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => 35
[6,4,3,3] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => 30
[6,4,3,2,1] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 42
[6,4,3,1,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 41
[6,4,2,2,2] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 35
[6,4,2,2,1,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 42
[6,4,2,1,1,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 40
[6,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 29
[6,3,3,3,1] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => 30
[6,3,3,2,2] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 31
[6,3,3,2,1,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 37
[6,3,3,1,1,1,1] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 34
[6,3,2,2,2,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 34
[6,3,2,2,1,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 37
[6,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 34
[6,2,2,2,2,2] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 21
[6,2,2,2,2,1,1] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 25
[6,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 26
[5,5,5,1] => [5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 36
[5,5,4,2] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => 43
[5,5,4,1,1] => [5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => 48
[5,5,3,3] => [5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => 40
[5,5,3,2,1] => [5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => 56
[5,5,3,1,1,1] => [5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => 54
[5,5,2,2,2] => [5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => 45
[5,5,2,2,1,1] => [5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => 54
[5,5,2,1,1,1,1] => [5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 51
[5,5,1,1,1,1,1,1] => [5,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 36
[5,4,4,3] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => 34
[5,4,4,2,1] => [4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => 47
[5,4,4,1,1,1] => [4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => 45
[5,4,3,3,1] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => 46
[5,4,3,2,2] => [4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => 47
[5,4,3,2,1,1] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 56
[5,4,3,1,1,1,1] => [4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 50
[5,4,2,2,2,1] => [4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 48
[5,4,2,2,1,1,1] => [4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 52
[5,4,2,1,1,1,1,1] => [4,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 47
[5,3,3,3,2] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => 34
[5,3,3,3,1,1] => [3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => 40
[5,3,3,2,2,1] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => 43
[5,3,3,2,1,1,1] => [3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 46
[5,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 40
[5,3,2,2,2,2] => [3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 36
[5,3,2,2,2,1,1] => [3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 43
[5,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 44
[5,2,2,2,2,2,1] => [2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 27
[5,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 30
[4,4,4,4] => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 35
[4,4,4,3,1] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => 53
[4,4,4,2,2] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 53
[4,4,4,2,1,1] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => 63
[4,4,4,1,1,1,1] => [4,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 55
[4,4,3,3,2] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => 53
[4,4,3,3,1,1] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => 62
[4,4,3,2,2,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 66
[4,4,3,2,1,1,1] => [4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 70
[4,4,3,1,1,1,1,1] => [4,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 59
[4,4,2,2,2,2] => [4,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 51
[4,4,2,2,2,1,1] => [4,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 61
[4,4,2,2,1,1,1,1] => [4,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 62
[4,3,3,3,3] => [3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 35
[4,3,3,3,2,1] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => 48
[4,3,3,3,1,1,1] => [3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 50
[4,3,3,2,2,2] => [3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 46
[4,3,3,2,2,1,1] => [3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 55
[4,3,3,2,1,1,1,1] => [3,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 55
[4,3,2,2,2,2,1] => [3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 47
[4,3,2,2,2,1,1,1] => [3,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 52
[4,2,2,2,2,2,2] => [2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 28
[4,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 33
[3,3,3,3,3,1] => [3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 50
[3,3,3,3,2,2] => [3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 52
[3,3,3,3,2,1,1] => [3,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 62
[3,3,3,3,1,1,1,1] => [3,3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 60
[3,3,3,2,2,2,1] => [3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 61
[3,3,3,2,2,1,1,1] => [3,3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 67
[3,3,2,2,2,2,2] => [3,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 49
[3,3,2,2,2,2,1,1] => [3,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 58
[3,2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 35
[16,1] => [1] => [1,0,1,0] => 2
[15,2] => [2] => [1,1,0,0,1,0] => 3
[15,1,1] => [1,1] => [1,0,1,1,0,0] => 3
[14,3] => [3] => [1,1,1,0,0,0,1,0] => 4
[14,2,1] => [2,1] => [1,0,1,0,1,0] => 5
[14,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 4
[13,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => 5
[13,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => 7
[13,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 6
[13,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 7
[13,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 5
[12,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[12,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 9
[12,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => 9
[12,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => 10
[12,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => 9
[12,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 9
[12,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 6
[11,6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[11,5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 11
[11,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 12
[11,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 13
[11,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 10
[11,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => 14
[11,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 13
[11,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 10
[11,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 12
[11,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 11
[11,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 7
[10,6,1] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 13
[10,5,2] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 15
[10,5,1,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 16
[10,4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 14
[10,4,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 19
[10,4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 17
[10,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 16
[10,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 16
[10,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 19
[10,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 16
[10,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 14
[10,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 15
[10,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 13
[10,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[9,6,2] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 18
[9,6,1,1] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 19
[9,5,3] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 18
[9,5,2,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 24
[9,5,1,1,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 21
[9,4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 15
[9,4,3,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 23
[9,4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 22
[9,4,2,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 26
[9,4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 21
[9,3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 19
[9,3,3,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 22
[9,3,2,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 23
[9,3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 24
[9,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 19
[9,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 15
[9,2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 18
[9,2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 18
[9,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 15
[8,6,3] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 22
[8,6,2,1] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 29
[8,6,1,1,1] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 25
[8,5,4] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 20
[8,5,3,1] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => 30
[8,5,2,2] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 28
[8,5,2,1,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 33
[8,5,1,1,1,1] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 26
[8,4,4,1] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => 25
[8,4,3,2] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 28
[8,4,3,1,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 32
[8,4,2,2,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 32
[8,4,2,1,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 33
[8,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 25
[8,3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 20
[8,3,3,2,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 28
[8,3,3,1,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 28
[8,3,2,2,2] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 25
[8,3,2,2,1,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 30
[8,3,2,1,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 29
[8,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 22
[8,2,2,2,2,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 20
[8,2,2,2,1,1,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 22
[8,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 21
[7,6,4] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 25
[7,6,3,1] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 37
[7,6,2,2] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 34
[7,6,2,1,1] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 40
[7,6,1,1,1,1] => [6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 31
[7,5,5] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 21
[7,5,4,1] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => 34
[7,5,3,2] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => 37
[7,5,3,1,1] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => 42
[7,5,2,2,1] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => 41
[7,5,2,1,1,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => 42
[7,5,1,1,1,1,1] => [5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 31
[7,4,4,2] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => 31
[7,4,4,1,1] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => 35
[7,4,3,3] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => 30
[7,4,3,2,1] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 42
[7,4,3,1,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 41
[7,4,2,2,2] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 35
[7,4,2,2,1,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 42
[7,4,2,1,1,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 40
[7,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 29
[7,3,3,3,1] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => 30
[7,3,3,2,2] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 31
[7,3,3,2,1,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 37
[7,3,3,1,1,1,1] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 34
[7,3,2,2,2,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 34
[7,3,2,2,1,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 37
[7,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 34
[7,2,2,2,2,2] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 21
[7,2,2,2,2,1,1] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 25
[7,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 26
[6,6,5] => [6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 27
[6,6,4,1] => [6,4,1] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 43
[6,6,3,2] => [6,3,2] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 46
[6,6,3,1,1] => [6,3,1,1] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 52
[6,6,2,2,1] => [6,2,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 50
[6,6,2,1,1,1] => [6,2,1,1,1] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 51
[6,6,1,1,1,1,1] => [6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 37
[6,5,5,1] => [5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 36
[6,5,4,2] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => 43
[6,5,4,1,1] => [5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => 48
[6,5,3,3] => [5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => 40
[6,5,3,2,1] => [5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => 56
[6,5,3,1,1,1] => [5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => 54
[6,5,2,2,2] => [5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => 45
[6,5,2,2,1,1] => [5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => 54
[6,5,2,1,1,1,1] => [5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 51
[6,5,1,1,1,1,1,1] => [5,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 36
[6,4,4,3] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => 34
[6,4,4,2,1] => [4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => 47
[6,4,4,1,1,1] => [4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => 45
[6,4,3,3,1] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => 46
[6,4,3,2,2] => [4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => 47
[6,4,3,2,1,1] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 56
[6,4,3,1,1,1,1] => [4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 50
[6,4,2,2,2,1] => [4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 48
[6,4,2,2,1,1,1] => [4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 52
[6,4,2,1,1,1,1,1] => [4,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 47
[6,3,3,3,2] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => 34
[6,3,3,3,1,1] => [3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => 40
[6,3,3,2,2,1] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => 43
[6,3,3,2,1,1,1] => [3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 46
[6,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 40
[6,3,2,2,2,2] => [3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 36
[6,3,2,2,2,1,1] => [3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 43
[6,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 44
[6,2,2,2,2,2,1] => [2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 27
[6,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 30
[5,5,5,2] => [5,5,2] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 46
[5,5,5,1,1] => [5,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 51
[5,5,4,3] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => 48
[5,5,4,2,1] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 66
[5,5,4,1,1,1] => [5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 62
[5,5,3,3,1] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => 62
[5,5,3,2,2] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => 63
[5,5,3,2,1,1] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => 75
[5,5,3,1,1,1,1] => [5,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 66
[5,5,2,2,2,1] => [5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 62
[5,5,2,2,1,1,1] => [5,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 67
[5,5,2,1,1,1,1,1] => [5,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 60
[5,4,4,4] => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 35
[5,4,4,3,1] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => 53
[5,4,4,2,2] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 53
[5,4,4,2,1,1] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => 63
[5,4,4,1,1,1,1] => [4,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 55
[5,4,3,3,2] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => 53
[5,4,3,3,1,1] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => 62
[5,4,3,2,2,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 66
[5,4,3,2,1,1,1] => [4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 70
[5,4,3,1,1,1,1,1] => [4,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 59
[5,4,2,2,2,2] => [4,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 51
[5,4,2,2,2,1,1] => [4,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 61
[5,4,2,2,1,1,1,1] => [4,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 62
[5,3,3,3,3] => [3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 35
[5,3,3,3,2,1] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => 48
[5,3,3,3,1,1,1] => [3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 50
[5,3,3,2,2,2] => [3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 46
[5,3,3,2,2,1,1] => [3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 55
[5,3,3,2,1,1,1,1] => [3,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 55
[5,3,2,2,2,2,1] => [3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 47
[5,3,2,2,2,1,1,1] => [3,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 52
[5,2,2,2,2,2,2] => [2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 28
[5,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 33
[4,4,4,4,1] => [4,4,4,1] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 55
[4,4,4,3,2] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 62
[4,4,4,3,1,1] => [4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => 72
[4,4,4,2,2,1] => [4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => 75
[4,4,4,2,1,1,1] => [4,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 79
[4,4,4,1,1,1,1,1] => [4,4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 65
[4,4,3,3,3] => [4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 55
[4,4,3,3,2,1] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 76
[4,4,3,3,1,1,1] => [4,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 78
[4,4,3,2,2,2] => [4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 71
[4,4,3,2,2,1,1] => [4,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 85
[4,4,3,2,1,1,1,1] => [4,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 84
[4,4,2,2,2,2,1] => [4,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 67
[4,4,2,2,2,1,1,1] => [4,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 74
[4,3,3,3,3,1] => [3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 50
[4,3,3,3,2,2] => [3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 52
[4,3,3,3,2,1,1] => [3,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 62
[4,3,3,3,1,1,1,1] => [3,3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 60
[4,3,3,2,2,2,1] => [3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 61
[4,3,3,2,2,1,1,1] => [3,3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 67
[4,3,2,2,2,2,2] => [3,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 49
[4,3,2,2,2,2,1,1] => [3,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 58
[4,2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 35
[3,3,3,3,3,2] => [3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 55
[3,3,3,3,3,1,1] => [3,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 65
[3,3,3,3,2,2,1] => [3,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 70
[3,3,3,3,2,1,1,1] => [3,3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 76
[3,3,3,2,2,2,2] => [3,3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 64
[3,3,3,2,2,2,1,1] => [3,3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 76
[3,3,2,2,2,2,2,1] => [3,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 62
[6,5,4,3,2,1] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 132
[5,5,4,3,2,1] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 132
[6,4,4,3,2,1] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 90
[5,4,4,3,2,1] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 90
[4,4,4,3,2,1] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 90
[6,5,3,3,2,1] => [5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 104
[5,5,3,3,2,1] => [5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 104
[6,4,3,3,2,1] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 76
[5,4,3,3,2,1] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 76
[6,3,3,3,2,1] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => 48
[6,5,4,2,2,1] => [5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 107
[5,5,4,2,2,1] => [5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 107
[6,4,4,2,2,1] => [4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => 75
[5,4,4,2,2,1] => [4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => 75
[6,5,3,2,2,1] => [5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => 89
[5,5,3,2,2,1] => [5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => 89
[6,4,3,2,2,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 66
[6,5,2,2,2,1] => [5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 62
[6,5,4,3,1,1] => [5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 104
[5,5,4,3,1,1] => [5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 104
[6,4,4,3,1,1] => [4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => 72
[5,4,4,3,1,1] => [4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => 72
[6,5,3,3,1,1] => [5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 84
[5,5,3,3,1,1] => [5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 84
[6,4,3,3,1,1] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => 62
[6,5,4,2,1,1] => [5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => 89
[5,5,4,2,1,1] => [5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => 89
[6,4,4,2,1,1] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => 63
[6,5,3,2,1,1] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => 75
[6,5,4,1,1,1] => [5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 62
[6,5,4,3,2] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => 90
[5,5,4,3,2] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => 90
[6,4,4,3,2] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 62
[5,4,4,3,2] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 62
[6,5,3,3,2] => [5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => 72
[5,5,3,3,2] => [5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => 72
[6,4,3,3,2] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => 53
[6,5,4,2,2] => [5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => 75
[5,5,4,2,2] => [5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => 75
[6,4,4,2,2] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 53
[6,5,3,2,2] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => 63
[6,5,4,3,1] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => 76
[5,5,4,3,1] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => 76
[6,4,4,3,1] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => 53
[6,5,3,3,1] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => 62
[6,5,4,2,1] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 66
[6,5,4,3] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => 48
[7,6,5,4,3,2,1] => [6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 429
[6,6,5,4,3,2,1] => [6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 429
[7,5,5,4,3,2,1] => [5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 297
[6,5,5,4,3,2,1] => [5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 297
[5,5,5,4,3,2,1] => [5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 297
[7,6,4,4,3,2,1] => [6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 345
[6,6,4,4,3,2,1] => [6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 345
[7,5,4,4,3,2,1] => [5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 255
[6,5,4,4,3,2,1] => [5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 255
[5,5,4,4,3,2,1] => [5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 255
[7,4,4,4,3,2,1] => [4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 165
[6,4,4,4,3,2,1] => [4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 165
[5,4,4,4,3,2,1] => [4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 165
[4,4,4,4,3,2,1] => [4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 165
[6,6,5,3,3,2,1] => [6,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 359
[6,5,4,3,3,2,1] => [5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 227
[6,5,3,3,3,2,1] => [5,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 171
[6,4,3,3,3,2,1] => [4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 123
[5,4,3,3,3,2,1] => [4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 123
[6,3,3,3,3,2,1] => [3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 75
[3,3,3,3,3,2,1] => [3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 75
[6,6,5,4,2,2,1] => [6,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 359
[6,5,5,4,2,2,1] => [5,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 252
[6,5,4,4,2,2,1] => [5,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 220
[6,5,4,3,2,2,1] => [5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 202
[5,5,4,3,2,2,1] => [5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 202
[7,6,5,2,2,2,1] => [6,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 233
[6,5,4,2,2,2,1] => [5,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 157
[6,5,3,2,2,2,1] => [5,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 129
[6,4,3,2,2,2,1] => [4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 95
[5,4,3,2,2,2,1] => [4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 95
[6,5,2,2,2,2,1] => [5,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 87
[7,2,2,2,2,2,1] => [2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 27
[7,6,5,4,3,1,1] => [6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 345
[6,6,5,4,3,1,1] => [6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 345
[6,5,5,4,3,1,1] => [5,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 241
[6,6,5,4,2,1,1] => [6,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 303
[6,5,5,4,2,1,1] => [5,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 214
[4,4,4,4,2,1,1] => [4,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 125
[6,5,4,3,2,1,1] => [5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 174
[5,5,4,3,2,1,1] => [5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 174
[5,4,4,3,2,1,1] => [4,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 118
[7,6,5,4,1,1,1] => [6,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 219
[6,5,5,4,1,1,1] => [5,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 157
[6,5,4,3,1,1,1] => [5,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 132
[7,6,5,2,1,1,1] => [6,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 163
[5,5,5,2,1,1,1] => [5,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 121
[7,5,4,2,1,1,1] => [5,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 112
[6,5,4,2,1,1,1] => [5,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 112
[7,6,3,2,1,1,1] => [6,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 118
[7,4,3,2,1,1,1] => [4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 70
[6,4,3,2,1,1,1] => [4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 70
[6,5,4,1,1,1,1] => [5,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 76
[6,6,2,1,1,1,1] => [6,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 62
[7,6,1,1,1,1,1] => [6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 37
[7,6,5,4,3,2] => [6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 297
[6,6,5,4,3,2] => [6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 297
[7,5,5,4,3,2] => [5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 207
[6,5,5,4,3,2] => [5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 207
[5,5,5,4,3,2] => [5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 207
[7,6,4,4,3,2] => [6,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 241
[6,5,4,4,3,2] => [5,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 179
[6,5,4,3,3,2] => [5,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 161
[5,4,3,3,3,2] => [4,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 89
[4,3,3,3,3,2] => [3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 55
[6,5,4,3,2,2] => [5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 146
[4,4,4,3,2,2] => [4,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 99
[7,6,5,2,2,2] => [6,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 171
[6,5,4,2,2,2] => [5,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 116
[5,4,3,2,2,2] => [4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 71
[6,6,2,2,2,2] => [6,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 81
[7,6,5,4,3,1] => [6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 255
[6,6,5,4,3,1] => [6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 255
[6,5,5,4,3,1] => [5,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 179
[4,4,4,4,3,1] => [4,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 103
[7,6,5,4,2,1] => [6,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 227
[5,5,5,4,2,1] => [5,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 161
[4,4,4,4,2,1] => [4,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 95
[7,6,5,3,2,1] => [6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 202
[6,6,5,3,2,1] => [6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 202
[5,5,5,3,2,1] => [5,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 146
[7,6,4,3,2,1] => [6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 174
[6,6,4,3,2,1] => [6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 174
[7,5,4,3,2,1] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 132
[7,4,4,3,2,1] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 90
[7,6,3,3,2,1] => [6,3,3,2,1] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 132
[7,4,3,3,2,1] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 76
[7,3,3,3,2,1] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => 48
[7,6,5,2,2,1] => [6,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 157
[7,6,3,2,2,1] => [6,3,2,2,1] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 112
[7,6,2,2,2,1] => [6,2,2,2,1] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 76
[7,6,5,4,1,1] => [6,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 171
[7,6,5,2,1,1] => [6,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 129
[7,6,3,2,1,1] => [6,3,2,1,1] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 94
[7,4,3,2,1,1] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 56
[7,6,5,1,1,1] => [6,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 87
[7,6,5,4,3] => [6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 165
[6,6,5,4,3] => [6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 165
[6,5,5,4,3] => [5,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 117
[5,4,4,4,3] => [4,4,4,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 69
[5,4,3,3,3] => [4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 55
[7,3,3,3,3] => [3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 35
[7,6,5,4,2] => [6,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 151
[4,4,4,4,2] => [4,4,4,2] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 65
[7,6,5,3,2] => [6,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 136
[7,6,4,3,2] => [6,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 118
[7,5,4,3,2] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => 90
[7,6,5,4,1] => [6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 123
[7,5,4,3,1] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => 76
[7,6,5,2,1] => [6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 95
[6,6,5,2,1] => [6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 95
[7,6,4,2,1] => [6,4,2,1] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 85
[6,6,4,2,1] => [6,4,2,1] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 85
[7,5,4,2,1] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 66
[7,6,3,2,1] => [6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 70
[6,6,3,2,1] => [6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 70
[7,6,5,4] => [6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 75
[6,5,5,4] => [5,5,4] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 55
[7,6,5,3] => [6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 70
[7,6,4,3] => [6,4,3] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 62
[7,5,4,3] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => 48
[7,6,5,2] => [6,5,2] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 61
[7,6,5] => [6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 27
[3,3,3,3,3,2,2] => [3,3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 80
[6,2,2,2,2,2,2] => [2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 28
[10,4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 15
[8,2,2,2,2,2,2] => [2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 28
[9,6,3] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 22
[8,6,4,2] => [6,4,2] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 55
[8,6,4] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 25
[10,6,4] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 25
[15,5,5] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 21
[8,7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1430
[7,7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1430
[7,6,6,5,4,3,2,1] => [6,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1001
[7,6,5,5,4,3,2,1] => [6,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 869
[7,6,5,4,4,3,2,1] => [6,5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 785
[7,6,5,4,3,3,2,1] => [6,5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 715
[7,6,5,4,3,2,2,1] => [6,5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 645
[7,6,5,4,3,2,1,1] => [6,5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 561
[6,6,6,5,4,3,2,1] => [6,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1001
[7,5,5,5,4,3,2,1] => [5,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 572
[7,6,4,4,4,3,2,1] => [6,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 605
[7,6,5,3,3,3,2,1] => [6,5,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 575
[7,6,5,4,2,2,2,1] => [6,5,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 519
[7,6,5,4,3,1,1,1] => [6,5,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 435
[8,7,6,5,4,3,2] => [7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1001
[8,7,6,5,4,3,1] => [7,6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 869
[8,6,5,4,3,2,1] => [6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 429
[8,5,5,4,3,2,1] => [5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 297
[9,7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1430
[9,6,4] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 25
[8,5,4,2] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => 43
[9,6,5,3] => [6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 70
[9,6,4,3] => [6,4,3] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 62
[8,6,5,3,1] => [6,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 113
[8,5,5,1] => [5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 36
[9,5,5,1] => [5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 36
[8,5,4,3,2,1] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 132
[7,7,1,1,1,1,1,1] => [7,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 50
[5,4,3,2,1,1,1,1] => [4,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 84
[6,5,4,3,2,1,1,1] => [5,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 216
[6,5,4,3,1,1,1,1] => [5,4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 160
[8,6,5,4,3,2] => [6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 297
[7,5,4,3,2,1,1,1] => [5,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 216
[7,6,4,3,2,2,2,1] => [6,4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 381
[7,6,5,5,4,2,2,1] => [6,5,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 754
[7,6,6,5,4,3,1,1] => [6,6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 821
[7,7,6,5,4,3,2] => [7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1001
[6,5,5,5,4,3,2,1] => [5,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 572
[6,5,4,4,4,3,2,1] => [5,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 440
[6,5,4,3,3,3,2,1] => [5,4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 356
[5,4,3,2,2,2,2] => [4,3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 100
[6,5,4,3,2,2,2,1] => [5,4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 286
[7,6,6,5,4,3,2] => [6,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 704
[7,6,6,5,4,3,1] => [6,6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 614
[7,7,6,5,4,3,1] => [7,6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 869
[7,7,6,5,4,3,1,1] => [7,6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1166
[8,7,6,5,4,1,1,1] => [7,6,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 770
[8,6,6,5,4,3,2] => [6,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 704
[7,7,5,5,4,3,2,1] => [7,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1166
[6,5,4,3,2,2,2] => [5,4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 216
[8,5,4,3,2,1,1] => [5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 174
[6,6,5,4,3,2,1,1] => [6,5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 561
[7,6,5,4,3,2,2] => [6,5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 471
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Description
The number of Dyck paths that are weakly above a Dyck path.
Map
first row removal
Description
Removes the first entry of an integer partition
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.
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