- FindStat

Identifier

Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00132: Dyck paths —switch returns and last double rise⟶ Dyck paths
Mp00099: Dyck paths —bounce path⟶ Dyck paths
St000476: Dyck paths ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 726 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[7,5,3,1] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 7

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[7,6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 7

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

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

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

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

[7,5,3,2] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 7

[7,5,3,1,1] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 7

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7

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

[7,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 7

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

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

[7,6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 7

[7,5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 7

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[7,6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 7

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

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

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

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

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

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

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

[7,6,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 7

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

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

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

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

[7,5,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 7

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

[7,6,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 7

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

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

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

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

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

[7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7

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

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

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

[7,6,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 7

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

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

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

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

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

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

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

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

[7,6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 7

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

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

[7,6,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 7

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

[7,6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 7

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

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

[7,6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 7

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

[7,5,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 7

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

[7,6,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 7

[7,6,3,2,1,1] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 7

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

[7,6,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 7

[7,6,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 7

[7,6,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 7

[7,5,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 7

[7,6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 7

[7,5,4,3,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 7

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

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

[7,6,4,2,1] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 7

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

[7,5,4,2,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 7

[7,6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 7

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

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

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$F_{1} = q$

$F_{2} = q + q^{2}$

$F_{3} = q + q^{2} + q^{3}$

$F_{4} = q + 2\ q^{2} + q^{3} + q^{4}$

$F_{5} = q + 2\ q^{2} + 2\ q^{3} + q^{4} + q^{5}$

$F_{6} = q + 3\ q^{2} + 3\ q^{3} + 2\ q^{4} + q^{5} + q^{6}$

Description

The sum of the semi-lengths of tunnels before a valley of a Dyck path.
For each valley

$v$ in a Dyck path

$D$ there is a corresponding tunnel, which
is the factor

$T_v = s_i\dots s_j$ of

$D$ where

$s_i$ is the step after the first intersection of

$D$ with the line

$y = ht(v)$ to the left of

$s_j$ . This statistic is

$\sum_v (j_v-i_v)/2.$

Map

switch returns and last double rise

Description

An alternative to the Adin-Bagno-Roichman transformation of a Dyck path.
This is a bijection preserving the number of up steps before each peak and exchanging the number of components with the position of the last double rise.

Map

to Dyck path

Description

Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.

Map

bounce path

Description

Sends a Dyck path

$D$ of length

$2n$ to its bounce path.
This path is formed by starting at the endpoint

$(n,n)$ of

$D$ and travelling west until encountering the first vertical step of

$D$ , then south until hitting the diagonal, then west again to hit

$D$ , etc. until the point

$(0,0)$ is reached.
This map is the first part of the zeta map Mp00030zeta map.