- FindStat

Identifier

Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00027: Dyck paths —to partition⟶ Integer partitions
St000620: Integer partitions ⟶ ℤ

Values

[1,0,1,0,1,0] => [2,1] => [1,0,1,1,0,0] => [1,1] => 1

[1,0,1,0,1,0,1,0] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => 7

[1,0,1,0,1,1,0,0] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2] => 0

[1,0,1,1,0,0,1,0] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [3,2,2,1] => 45

[1,0,1,1,0,1,0,0] => [2,1,1] => [1,0,1,1,0,1,0,0] => [2,1,1] => 2

[1,1,0,0,1,0,1,0] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1] => 1

[1,1,0,1,0,0,1,0] => [3,1] => [1,0,1,0,1,1,0,0] => [2,2,1] => 3

[1,1,0,1,0,1,0,0] => [2,1] => [1,0,1,1,0,0] => [1,1] => 1

[1,1,1,0,0,0,1,0] => [3] => [1,0,1,0,1,0] => [2,1] => 1

[1,0,1,0,1,0,1,0,1,0] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1,1] => 2422

[1,0,1,0,1,0,1,1,0,0] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,1] => 6

[1,0,1,0,1,1,0,1,0,0] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,1,1,1] => 24

[1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [3] => 1

[1,0,1,1,0,0,1,1,0,0] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,3,1] => 42

[1,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [4,3,1,1,1] => 340

[1,0,1,1,0,1,1,0,0,0] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2] => 3

[1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [4,3,2,2,1] => 3710

[1,0,1,1,1,0,1,0,0,0] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => 23

[1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [2,1] => 1

[1,1,0,0,1,0,1,0,1,0] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => 10

[1,1,0,0,1,0,1,1,0,0] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [1,1] => 1

[1,1,0,0,1,1,0,0,1,0] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [2,2,2,2,1] => 28

[1,1,0,0,1,1,0,1,0,0] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => 1

[1,1,0,1,0,0,1,0,1,0] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [4,2,1,1,1] => 125

[1,1,0,1,0,0,1,1,0,0] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [3,1] => 2

[1,1,0,1,0,1,0,0,1,0] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [4,2,2,2,1] => 749

[1,1,0,1,0,1,0,1,0,0] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => 7

[1,1,0,1,0,1,1,0,0,0] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2] => 0

[1,1,0,1,1,0,0,1,0,0] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [3,2,2,1] => 45

[1,1,0,1,1,0,1,0,0,0] => [2,1,1] => [1,0,1,1,0,1,0,0] => [2,1,1] => 2

[1,1,1,0,0,0,1,0,1,0] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [2,1,1,1] => 3

[1,1,1,0,0,1,0,0,1,0] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => 9

[1,1,1,0,0,1,0,1,0,0] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1] => 1

[1,1,1,0,1,0,0,0,1,0] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [3,3,2,1] => 107

[1,1,1,0,1,0,0,1,0,0] => [3,1] => [1,0,1,0,1,1,0,0] => [2,2,1] => 3

[1,1,1,0,1,0,1,0,0,0] => [2,1] => [1,0,1,1,0,0] => [1,1] => 1

[1,1,1,1,0,0,0,0,1,0] => [4] => [1,0,1,0,1,0,1,0] => [3,2,1] => 10

[1,1,1,1,0,0,0,1,0,0] => [3] => [1,0,1,0,1,0] => [2,1] => 1

[1,0,1,0,1,0,1,0,1,1,0,0] => [4,4,3,2,1] => [1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1] => 2300

[1,0,1,0,1,0,1,1,1,0,0,0] => [3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,2] => 8

[1,0,1,0,1,1,0,1,1,0,0,0] => [3,3,2,2,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1] => 117

[1,0,1,0,1,1,1,0,1,0,0,0] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1,1] => 614

[1,0,1,0,1,1,1,1,0,0,0,0] => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => [4,1] => 2

[1,0,1,1,0,0,1,1,1,0,0,0] => [3,3,3,1,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4] => 24

[1,0,1,1,0,1,0,1,1,0,0,0] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1] => 703

[1,0,1,1,0,1,1,1,0,0,0,0] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3] => 8

[1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [4,3,2] => 102

[1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,1] => 1484

[1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [3,2,1] => 10

[1,1,0,0,1,0,1,0,1,1,0,0] => [4,4,3,2] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1] => 7

[1,1,0,0,1,0,1,1,0,1,0,0] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1,1] => 16

[1,1,0,0,1,0,1,1,1,0,0,0] => [3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => [2] => 0

[1,1,0,0,1,1,0,0,1,1,0,0] => [4,4,2,2] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => 45

[1,1,0,0,1,1,0,1,0,1,0,0] => [4,3,2,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1,1] => 217

[1,1,0,0,1,1,0,1,1,0,0,0] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,1] => 2

[1,1,0,0,1,1,1,0,0,1,0,0] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2,1] => 777

[1,1,0,0,1,1,1,0,1,0,0,0] => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => 4

[1,1,0,1,0,0,1,0,1,1,0,0] => [4,4,3,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1] => 22

[1,1,0,1,0,0,1,1,0,1,0,0] => [4,3,3,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1,1] => 86

[1,1,0,1,0,0,1,1,1,0,0,0] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [4] => 0

[1,1,0,1,0,1,0,0,1,1,0,0] => [4,4,2,1] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1] => 325

[1,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1,1] => 2422

[1,1,0,1,0,1,0,1,1,0,0,0] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,1] => 6

[1,1,0,1,0,1,1,0,1,0,0,0] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,1,1,1] => 24

[1,1,0,1,0,1,1,1,0,0,0,0] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [3] => 1

[1,1,0,1,1,0,0,0,1,1,0,0] => [4,4,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1] => 3535

[1,1,0,1,1,0,0,1,1,0,0,0] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,3,1] => 42

[1,1,0,1,1,0,1,0,1,0,0,0] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [4,3,1,1,1] => 340

[1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2] => 3

[1,1,0,1,1,1,0,0,1,0,0,0] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [4,3,2,2,1] => 3710

[1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => 23

[1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [2,1] => 1

[1,1,1,0,0,0,1,0,1,0,1,0] => [5,4,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1,1] => 34

[1,1,1,0,0,0,1,0,1,1,0,0] => [4,4,3] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1] => 1

[1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2,1] => 90

[1,1,1,0,0,0,1,1,0,1,0,0] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1

[1,1,1,0,0,1,0,0,1,0,1,0] => [5,4,2] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1,1] => 667

[1,1,1,0,0,1,0,0,1,1,0,0] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => [2,2,1] => 3

[1,1,1,0,0,1,0,1,0,1,0,0] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => 10

[1,1,1,0,0,1,0,1,1,0,0,0] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [1,1] => 1

[1,1,1,0,0,1,1,0,0,1,0,0] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [2,2,2,2,1] => 28

[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => 1

[1,1,1,0,1,0,0,0,1,1,0,0] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => [4,2,1] => 21

[1,1,1,0,1,0,0,1,0,1,0,0] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [4,2,1,1,1] => 125

[1,1,1,0,1,0,0,1,1,0,0,0] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [3,1] => 2

[1,1,1,0,1,0,1,0,0,1,0,0] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [4,2,2,2,1] => 749

[1,1,1,0,1,0,1,0,1,0,0,0] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => 7

[1,1,1,0,1,0,1,1,0,0,0,0] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2] => 0

[1,1,1,0,1,1,0,0,1,0,0,0] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [3,2,2,1] => 45

[1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,1] => [1,0,1,1,0,1,0,0] => [2,1,1] => 2

[1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => 44

[1,1,1,1,0,0,0,0,1,1,0,0] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [2,1] => 1

[1,1,1,1,0,0,0,1,0,0,1,0] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [3,2,2,2,1] => 190

[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [2,1,1,1] => 3

[1,1,1,1,0,0,1,0,0,0,1,0] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [3,3,3,2,1] => 1368

[1,1,1,1,0,0,1,0,0,1,0,0] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => 9

[1,1,1,1,0,0,1,0,1,0,0,0] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1] => 1

[1,1,1,1,0,1,0,0,0,1,0,0] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [3,3,2,1] => 107

[1,1,1,1,0,1,0,0,1,0,0,0] => [3,1] => [1,0,1,0,1,1,0,0] => [2,2,1] => 3

[1,1,1,1,0,1,0,1,0,0,0,0] => [2,1] => [1,0,1,1,0,0] => [1,1] => 1

[1,1,1,1,1,0,0,0,0,0,1,0] => [5] => [1,0,1,0,1,0,1,0,1,0] => [4,3,2,1] => 480

>>> Load all 492 entries. <<<

[1,1,1,1,1,0,0,0,0,1,0,0] => [4] => [1,0,1,0,1,0,1,0] => [3,2,1] => 10

[1,1,1,1,1,0,0,0,1,0,0,0] => [3] => [1,0,1,0,1,0] => [2,1] => 1

[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,3] => 27

[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => [1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [6,3,2] => 587

[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,2,1] => 38

[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5] => 75

[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,4,1] => 170

[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [5,4,3] => 1270

[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,1] => 480

[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [5,5,4,3,2] => [1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,2,2,1,1,1] => 2422

[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2] => [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [4,1,1] => 6

[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2] => [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1] => 24

[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1,1] => 62

[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3] => 1

[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => [1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [4,3,1] => 42

[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2] => [1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1] => 340

[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1,1,1] => 1428

[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,2] => 3

[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2] => [1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1] => 3710

[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1] => 23

[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1,1] => 75

[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => [2,1] => 1

[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [6,1,1] => 12

[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1] => 80

[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1,1,1] => 314

[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => 1

[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1] => [1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [6,3,1] => 184

[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1] => [1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1] => 2300

[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,2] => 8

[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1] => 117

[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1,1] => 614

[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => [4,1] => 2

[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [6,5,1] => 674

[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4] => 24

[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1] => 703

[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3] => 8

[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [4,3,2] => 102

[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,1] => 1484

[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [3,2,1] => 10

[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1] => 10

[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1,1] => 21

[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1] => 1

[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1] => 28

[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1,1] => 117

[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1] => 1

[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1

[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [5,5,4,2] => [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1] => 125

[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1,1] => 420

[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [3,1] => 2

[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2] => [1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1] => 749

[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1] => 7

[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1,1] => 16

[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => [2] => 0

[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => 45

[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1,1] => 217

[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,1] => 2

[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2,1] => 777

[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => 4

[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1] => [1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1] => 580

[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,1] => 3

[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1] => 22

[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1,1] => 86

[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [4] => 0

[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1] => 325

[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1,1] => 2422

[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,1] => 6

[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,1,1,1] => 24

[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [3] => 1

[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1] => 3535

[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,3,1] => 42

[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [4,3,1,1,1] => 340

[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2] => 3

[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [4,3,2,2,1] => 3710

[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => 23

[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [2,1] => 1

[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [6,5,4] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1,1] => 976

[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,5,4] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1] => 3

[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [5,4,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 5

[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [5,5,3] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1] => 9

[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [5,4,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1,1] => 34

[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,4,3] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1] => 1

[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [5,3,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2,1] => 90

[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1

[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,5,2] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1] => 107

[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,4,2] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1,1] => 667

[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => [2,2,1] => 3

[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => 10

[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [1,1] => 1

[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [2,2,2,2,1] => 28

[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => 1

[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,5,1] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1] => 1423

[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => [4,2,1] => 21

[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [4,2,1,1,1] => 125

[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [3,1] => 2

[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [4,2,2,2,1] => 749

[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => 7

[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2] => 0

[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [3,2,2,1] => 45

[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,1,1] => [1,0,1,1,0,1,0,0] => [2,1,1] => 2

[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,5] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1,1] => 3712

[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => [3,2,1] => 10

[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => 44

[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [2,1] => 1

[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [3,2,2,2,1] => 190

[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [2,1,1,1] => 3

[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [3,3,3,2,1] => 1368

[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => 9

[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1] => 1

[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [3,3,2,1] => 107

[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [3,1] => [1,0,1,0,1,1,0,0] => [2,2,1] => 3

[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1] => [1,0,1,1,0,0] => [1,1] => 1

[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => [1,0,1,0,1,0,1,0,1,0] => [4,3,2,1] => 480

[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [4] => [1,0,1,0,1,0,1,0] => [3,2,1] => 10

[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3] => [1,0,1,0,1,0] => [2,1] => 1

[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1] => 3424

[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [4,1] => 2

[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [4,3] => 8

[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [4,3,2] => 102

[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1] => 1484

[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1] => 10

[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3,1] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [7,2] => 15

[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,1] => 3

[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,3] => 27

[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1] => [1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [6,3,2] => 587

[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,2,1] => 38

[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5] => 75

[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,4,1] => 170

[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [5,4,3] => 1270

[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,1] => 480

[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [5,4,4,4,3] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1,1,1,1,1] => 29

[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1] => 4

[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => 6

[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,2] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4] => 0

[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,2] => [1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,2,2,1,1,1] => 2422

[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,2] => [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [4,1,1] => 6

[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2] => [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1] => 24

[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1,1] => 62

[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3] => 1

[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2] => [1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [4,3,1] => 42

[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2] => [1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1] => 340

[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1,1,1] => 1428

[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,2] => 3

[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2] => [1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1] => 3710

[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1] => 23

[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1,1] => 75

[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => [2,1] => 1

[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 0

[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [6,1,1] => 12

[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1] => 80

[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1,1,1] => 314

[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => 1

[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1] => [1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [6,3,1] => 184

[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1] => [1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1] => 2300

[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,2] => 8

[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1] => 117

[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1,1] => 614

[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => [4,1] => 2

[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [6,5,1] => 674

[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4] => 24

[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1] => 703

[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3] => 8

[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [4,3,2] => 102

[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,1] => 1484

[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [3,2,1] => 10

[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [6,5,5,4] => [1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1,1,1,1] => 83

[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [5,4,4,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1

[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1] => 10

[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1,1] => 21

[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1] => 1

[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3] => [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1] => 28

[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1,1] => 117

[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1] => 1

[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1

[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [5,5,5,2] => [1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [4,2,1] => 21

[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2] => [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1] => 125

[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1,1] => 420

[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [3,1] => 2

[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2] => [1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1] => 749

[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1] => 7

[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1,1] => 16

[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => [2] => 0

[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => 45

[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1,1] => 217

[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,1] => 2

[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2,1] => 777

[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => 4

[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [6,2,1] => 61

[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1] => [1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1] => 580

[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,1] => 3

[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1] => 22

[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1,1] => 86

[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [4] => 0

[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1] => 325

[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1,1] => 2422

[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,1] => 6

[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,1,1,1] => 24

[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [3] => 1

[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1] => 3535

[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,3,1] => 42

[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [4,3,1,1,1] => 340

[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2] => 3

[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [4,3,2,2,1] => 3710

[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => 23

[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [2,1] => 1

[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [6,6,5] => [1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1] => 44

[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [6,5,5] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1,1] => 118

[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1] => 1

[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [6,6,4] => [1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1] => 190

[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [6,5,4] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1,1] => 976

[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,5,4] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1] => 3

[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 5

[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [6,6,3] => [1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1] => 1368

[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [5,5,3] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1] => 9

[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,4,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1,1] => 34

[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [4,4,3] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1] => 1

[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [5,3,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2,1] => 90

[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1

[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,5,2] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1] => 107

[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [5,4,2] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1,1] => 667

[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => [2,2,1] => 3

[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => 10

[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [1,1] => 1

[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [2,2,2,2,1] => 28

[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => 1

[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [5,5,1] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1] => 1423

[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => [4,2,1] => 21

[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [4,2,1,1,1] => 125

[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [3,1] => 2

[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [4,2,2,2,1] => 749

[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => 7

[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2] => 0

[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [3,2,2,1] => 45

[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [2,1,1] => [1,0,1,1,0,1,0,0] => [2,1,1] => 2

[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1] => 480

[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1,1] => 3712

[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => [3,2,1] => 10

[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => 44

[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [2,1] => 1

[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [3,2,2,2,1] => 190

[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [2,1,1,1] => 3

[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [3,3,3,2,1] => 1368

[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => 9

[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1] => 1

[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [3,3,2,1] => 107

[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [3,1] => [1,0,1,0,1,1,0,0] => [2,2,1] => 3

[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => [1,0,1,1,0,0] => [1,1] => 1

[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5] => [1,0,1,0,1,0,1,0,1,0] => [4,3,2,1] => 480

[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4] => [1,0,1,0,1,0,1,0] => [3,2,1] => 10

[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => [1,0,1,0,1,0] => [2,1] => 1

[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1] => 480

[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1] => 3424

[1,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3,2] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [4,1] => 2

[1,1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,3,2,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1] => 1484

[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1] => 10

[1,1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [4,4,4,4,3,1] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [7,2] => 15

[1,1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,1] => 3

[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,2,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,3] => 27

[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,2,1] => 38

[1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,4,1] => 170

[1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [5,4,3] => 1270

[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,1] => 480

[1,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0,0] => [4,3,3,3,3] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => 6

[1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0] => [5,5,4,3,2] => [1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,2,2,1,1,1] => 2422

[1,1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0,0] => [4,4,4,3,2] => [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [4,1,1] => 6

[1,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0,0] => [4,4,3,3,2] => [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1] => 24

[1,1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1,1] => 75

[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => [2,1] => 1

[1,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,4,4,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 0

[1,1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => 1

[1,1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0,0] => [4,4,4,2,1] => [1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [6,3,1] => 184

[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,4,3,2,1] => [1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1] => 2300

[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => [3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,2] => 8

[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1,1] => 614

[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => [4,1] => 2

[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3] => 8

[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [4,3,2] => 102

[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,1] => 1484

[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [3,2,1] => 10

[1,1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0,0] => [6,5,5,4] => [1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1,1,1,1] => 83

[1,1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0,0] => [5,5,4,3] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1] => 10

[1,1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0,0] => [4,4,4,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1] => 1

[1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0] => [5,5,3,3] => [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1] => 28

[1,1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0,0] => [4,3,3,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1

[1,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,0] => [4,4,3,2] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1] => 7

[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0] => [4,4,2,2] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => 45

[1,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,1] => 2

[1,1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,0] => [5,5,5,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [6,2,1] => 61

[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => [4,3,3,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1,1] => 86

[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [4] => 0

[1,1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,0] => [4,4,2,1] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1] => 325

[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1,1] => 2422

[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,1] => 6

[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,1,1,1] => 24

[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [3] => 1

[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,3,1] => 42

[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [4,3,1,1,1] => 340

[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2] => 3

[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [4,3,2,2,1] => 3710

[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => 23

[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [2,1] => 1

[1,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,0] => [6,6,5] => [1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1] => 44

[1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0] => [6,5,5] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1,1] => 118

[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0] => [5,5,5] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1] => 1

[1,1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0,0] => [5,4,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 5

[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1,1] => 34

[1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0] => [4,4,3] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1] => 1

[1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1

[1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1,1] => 667

[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => [2,2,1] => 3

[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => 10

[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [1,1] => 1

[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [2,2,2,2,1] => 28

[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => 1

[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => [4,2,1] => 21

[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [4,2,1,1,1] => 125

[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [3,1] => 2

[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [4,2,2,2,1] => 749

[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => 7

[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2] => 0

[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [3,2,2,1] => 45

[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1] => [1,0,1,1,0,1,0,0] => [2,1,1] => 2

[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1] => 480

[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => [3,2,1] => 10

[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [2,1] => 1

[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [2,1,1,1] => 3

[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => 9

[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1] => 1

[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [3,3,2,1] => 107

[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [3,1] => [1,0,1,0,1,1,0,0] => [2,2,1] => 3

[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,1] => [1,0,1,1,0,0] => [1,1] => 1

[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [5] => [1,0,1,0,1,0,1,0,1,0] => [4,3,2,1] => 480

[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [4] => [1,0,1,0,1,0,1,0] => [3,2,1] => 10

[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [3] => [1,0,1,0,1,0] => [2,1] => 1

[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => 1

[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,6,6] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,2,1] => 10

[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,3,3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1] => 10

[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,6,6,6] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,1] => 1

[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [7,7,7] => [1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1] => 480

[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [4,4,3,2,1] => [1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1] => 2300

[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2] => 0

[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1] => 1

[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [2,1] => 1

[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [3,2,1] => 10

[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,1] => 480

[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3,3,1] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1] => 92

[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,4,4,4,4,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [7] => 1

[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,5,5,5,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [7,1] => 4

[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3,2,2] => [1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1] => 170

[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [4,4,4,3,3,3] => [1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1] => 23

[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => [5,4,4,4,4] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1] => 1

[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => [6,5,5,5] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1] => 7

[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [5] => [1,0,1,0,1,0,1,0,1,0] => [4,3,2,1] => 480

[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [4,3,3,3,3,3] => [1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1,1,1,1] => 175

[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [4] => [1,0,1,0,1,0,1,0] => [3,2,1] => 10

[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [3] => [1,0,1,0,1,0] => [2,1] => 1

[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1] => [1,0,1,1,0,1,0,0] => [2,1,1] => 2

[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => 10

[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0] => [3,1] => [1,0,1,0,1,1,0,0] => [2,2,1] => 3

[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0] => [6,6,6] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,2,1] => 10

[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1] => 480

[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [2,1] => [1,0,1,1,0,0] => [1,1] => 1

[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1] => [1,0,1,1,0,0] => [1,1] => 1

[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1,1] => 2422

[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => 7

[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0] => [3] => [1,0,1,0,1,0] => [2,1] => 1

[1,1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [3,3,3,3,2,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,3] => 27

[1,1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1] => 3424

[1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => 1

[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1] => 480

[1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0] => [3,1] => [1,0,1,0,1,1,0,0] => [2,2,1] => 3

[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => 9

[1,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,2,1] => 38

[1,1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [5,5,4,3,2] => [1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,2,2,1,1,1] => 2422

[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [4,2,1,1,1] => 125

[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1] => 10

[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [3,3,2,1] => 107

[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => 23

[1,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,1] => 1484

[1,1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1,1] => [1,0,1,1,0,1,0,0] => [2,1,1] => 2

[1,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,1,1,1] => 24

[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [3,2,2,1] => 45

[1,1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [4,4,4,4,4,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [7] => 1

[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2] => 3

[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [4,3,1,1,1] => 340

[1,1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [4,3,3,3,3,3] => [1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1,1,1,1] => 175

[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0] => [3] => [1,0,1,0,1,0] => [2,1] => 1

[1,1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0,0] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [3,3,2,1] => 107

[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => [3,2,1] => 10

[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [2,1] => 1

[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [3] => 1

[1,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [1,1] => 1

search for individual values

searching the database for the individual values of this statistic

Description

The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is odd.
To be precise, this is given for a partition

$\lambda \vdash n$ by the number of standard tableaux

$T$ of shape

$\lambda$ such that

$\min\big( \operatorname{Des}(T) \cup \{n\} \big)$ is odd.
The case of an even minimum is St000621The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is even..

Map

parallelogram polyomino

Description

Return the Dyck path corresponding to the partition interpreted as a parallogram polyomino.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.

Map

to partition

Description

The cut-out partition of a Dyck path.
The partition

$\lambda$ associated to a Dyck path is defined to be the complementary partition inside the staircase partition

$(n-1,\ldots,2,1)$ when cutting out

$D$ considered as a path from

$(0,0)$ to

$(n,n)$ .
In other words,

$\lambda_{i}$ is the number of down-steps before the

$(n+1-i)$ -th up-step of

$D$ .
This map is a bijection between Dyck paths of size

$n$ and partitions inside the staircase partition

$(n-1,\ldots,2,1)$ .