Processing math: 100%

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Identifier
  • St000012: Dyck paths ⟶ ℤ (values match St001295Gives the vector space dimension of the homomorphism space between J^2 and J^2.)
Values
[1,0] => 0
[1,0,1,0] => 0
[1,1,0,0] => 1
[1,0,1,0,1,0] => 0
[1,0,1,1,0,0] => 1
[1,1,0,0,1,0] => 1
[1,1,0,1,0,0] => 2
[1,1,1,0,0,0] => 3
[1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,0,0,0] => 3
[1,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,0] => 4
[1,1,1,0,0,0,1,0] => 3
[1,1,1,0,0,1,0,0] => 4
[1,1,1,0,1,0,0,0] => 5
[1,1,1,1,0,0,0,0] => 6
[1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,0,0] => 3
[1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,0,0] => 4
[1,0,1,1,1,0,0,0,1,0] => 3
[1,0,1,1,1,0,0,1,0,0] => 4
[1,0,1,1,1,0,1,0,0,0] => 5
[1,0,1,1,1,1,0,0,0,0] => 6
[1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,1,0,0] => 3
[1,1,0,0,1,1,1,0,0,0] => 4
[1,1,0,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,1,0,0] => 3
[1,1,0,1,0,1,0,0,1,0] => 3
[1,1,0,1,0,1,0,1,0,0] => 4
[1,1,0,1,0,1,1,0,0,0] => 5
[1,1,0,1,1,0,0,0,1,0] => 4
[1,1,0,1,1,0,0,1,0,0] => 5
[1,1,0,1,1,0,1,0,0,0] => 6
[1,1,0,1,1,1,0,0,0,0] => 7
[1,1,1,0,0,0,1,0,1,0] => 3
[1,1,1,0,0,0,1,1,0,0] => 4
[1,1,1,0,0,1,0,0,1,0] => 4
[1,1,1,0,0,1,0,1,0,0] => 5
[1,1,1,0,0,1,1,0,0,0] => 6
[1,1,1,0,1,0,0,0,1,0] => 5
[1,1,1,0,1,0,0,1,0,0] => 6
[1,1,1,0,1,0,1,0,0,0] => 7
[1,1,1,0,1,1,0,0,0,0] => 8
[1,1,1,1,0,0,0,0,1,0] => 6
[1,1,1,1,0,0,0,1,0,0] => 7
[1,1,1,1,0,0,1,0,0,0] => 8
[1,1,1,1,0,1,0,0,0,0] => 9
[1,1,1,1,1,0,0,0,0,0] => 10
[1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,1,0,0,0] => 3
[1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,0,1,1,0,0,0] => 4
[1,0,1,0,1,1,1,0,0,0,1,0] => 3
[1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,0,1,0,1,1,1,0,1,0,0,0] => 5
[1,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,0] => 3
[1,0,1,1,0,0,1,1,1,0,0,0] => 4
[1,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,0,1,1,0,1,0,1,0,0,1,0] => 3
[1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,0,1,1,0,1,0,1,1,0,0,0] => 5
[1,0,1,1,0,1,1,0,0,0,1,0] => 4
[1,0,1,1,0,1,1,0,0,1,0,0] => 5
[1,0,1,1,0,1,1,0,1,0,0,0] => 6
[1,0,1,1,0,1,1,1,0,0,0,0] => 7
[1,0,1,1,1,0,0,0,1,0,1,0] => 3
[1,0,1,1,1,0,0,0,1,1,0,0] => 4
[1,0,1,1,1,0,0,1,0,0,1,0] => 4
[1,0,1,1,1,0,0,1,0,1,0,0] => 5
[1,0,1,1,1,0,0,1,1,0,0,0] => 6
[1,0,1,1,1,0,1,0,0,0,1,0] => 5
[1,0,1,1,1,0,1,0,0,1,0,0] => 6
[1,0,1,1,1,0,1,0,1,0,0,0] => 7
[1,0,1,1,1,0,1,1,0,0,0,0] => 8
>>> Load all 1200 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => 6
[1,0,1,1,1,1,0,0,0,1,0,0] => 7
[1,0,1,1,1,1,0,0,1,0,0,0] => 8
[1,0,1,1,1,1,0,1,0,0,0,0] => 9
[1,0,1,1,1,1,1,0,0,0,0,0] => 10
[1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,1,0,0] => 3
[1,1,0,0,1,0,1,1,1,0,0,0] => 4
[1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,0,1,1,0,1,0,0,1,0] => 3
[1,1,0,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,0,1,1,0,1,1,0,0,0] => 5
[1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,1,0,0,1,1,1,0,0,1,0,0] => 5
[1,1,0,0,1,1,1,0,1,0,0,0] => 6
[1,1,0,0,1,1,1,1,0,0,0,0] => 7
[1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,1,0,0,1,1,0,1,0,0] => 4
[1,1,0,1,0,0,1,1,1,0,0,0] => 5
[1,1,0,1,0,1,0,0,1,0,1,0] => 3
[1,1,0,1,0,1,0,0,1,1,0,0] => 4
[1,1,0,1,0,1,0,1,0,0,1,0] => 4
[1,1,0,1,0,1,0,1,0,1,0,0] => 5
[1,1,0,1,0,1,0,1,1,0,0,0] => 6
[1,1,0,1,0,1,1,0,0,0,1,0] => 5
[1,1,0,1,0,1,1,0,0,1,0,0] => 6
[1,1,0,1,0,1,1,0,1,0,0,0] => 7
[1,1,0,1,0,1,1,1,0,0,0,0] => 8
[1,1,0,1,1,0,0,0,1,0,1,0] => 4
[1,1,0,1,1,0,0,0,1,1,0,0] => 5
[1,1,0,1,1,0,0,1,0,0,1,0] => 5
[1,1,0,1,1,0,0,1,0,1,0,0] => 6
[1,1,0,1,1,0,0,1,1,0,0,0] => 7
[1,1,0,1,1,0,1,0,0,0,1,0] => 6
[1,1,0,1,1,0,1,0,0,1,0,0] => 7
[1,1,0,1,1,0,1,0,1,0,0,0] => 8
[1,1,0,1,1,0,1,1,0,0,0,0] => 9
[1,1,0,1,1,1,0,0,0,0,1,0] => 7
[1,1,0,1,1,1,0,0,0,1,0,0] => 8
[1,1,0,1,1,1,0,0,1,0,0,0] => 9
[1,1,0,1,1,1,0,1,0,0,0,0] => 10
[1,1,0,1,1,1,1,0,0,0,0,0] => 11
[1,1,1,0,0,0,1,0,1,0,1,0] => 3
[1,1,1,0,0,0,1,0,1,1,0,0] => 4
[1,1,1,0,0,0,1,1,0,0,1,0] => 4
[1,1,1,0,0,0,1,1,0,1,0,0] => 5
[1,1,1,0,0,0,1,1,1,0,0,0] => 6
[1,1,1,0,0,1,0,0,1,0,1,0] => 4
[1,1,1,0,0,1,0,0,1,1,0,0] => 5
[1,1,1,0,0,1,0,1,0,0,1,0] => 5
[1,1,1,0,0,1,0,1,0,1,0,0] => 6
[1,1,1,0,0,1,0,1,1,0,0,0] => 7
[1,1,1,0,0,1,1,0,0,0,1,0] => 6
[1,1,1,0,0,1,1,0,0,1,0,0] => 7
[1,1,1,0,0,1,1,0,1,0,0,0] => 8
[1,1,1,0,0,1,1,1,0,0,0,0] => 9
[1,1,1,0,1,0,0,0,1,0,1,0] => 5
[1,1,1,0,1,0,0,0,1,1,0,0] => 6
[1,1,1,0,1,0,0,1,0,0,1,0] => 6
[1,1,1,0,1,0,0,1,0,1,0,0] => 7
[1,1,1,0,1,0,0,1,1,0,0,0] => 8
[1,1,1,0,1,0,1,0,0,0,1,0] => 7
[1,1,1,0,1,0,1,0,0,1,0,0] => 8
[1,1,1,0,1,0,1,0,1,0,0,0] => 9
[1,1,1,0,1,0,1,1,0,0,0,0] => 10
[1,1,1,0,1,1,0,0,0,0,1,0] => 8
[1,1,1,0,1,1,0,0,0,1,0,0] => 9
[1,1,1,0,1,1,0,0,1,0,0,0] => 10
[1,1,1,0,1,1,0,1,0,0,0,0] => 11
[1,1,1,0,1,1,1,0,0,0,0,0] => 12
[1,1,1,1,0,0,0,0,1,0,1,0] => 6
[1,1,1,1,0,0,0,0,1,1,0,0] => 7
[1,1,1,1,0,0,0,1,0,0,1,0] => 7
[1,1,1,1,0,0,0,1,0,1,0,0] => 8
[1,1,1,1,0,0,0,1,1,0,0,0] => 9
[1,1,1,1,0,0,1,0,0,0,1,0] => 8
[1,1,1,1,0,0,1,0,0,1,0,0] => 9
[1,1,1,1,0,0,1,0,1,0,0,0] => 10
[1,1,1,1,0,0,1,1,0,0,0,0] => 11
[1,1,1,1,0,1,0,0,0,0,1,0] => 9
[1,1,1,1,0,1,0,0,0,1,0,0] => 10
[1,1,1,1,0,1,0,0,1,0,0,0] => 11
[1,1,1,1,0,1,0,1,0,0,0,0] => 12
[1,1,1,1,0,1,1,0,0,0,0,0] => 13
[1,1,1,1,1,0,0,0,0,0,1,0] => 10
[1,1,1,1,1,0,0,0,0,1,0,0] => 11
[1,1,1,1,1,0,0,0,1,0,0,0] => 12
[1,1,1,1,1,0,0,1,0,0,0,0] => 13
[1,1,1,1,1,0,1,0,0,0,0,0] => 14
[1,1,1,1,1,1,0,0,0,0,0,0] => 15
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 3
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 5
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 4
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 3
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 5
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 4
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 5
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 6
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 7
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 4
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 4
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 5
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 6
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 5
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 6
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 7
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 8
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 6
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 7
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 8
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 9
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 10
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 3
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 4
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 5
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 5
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 6
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 7
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 4
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 5
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 3
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 4
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 4
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 5
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 6
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 5
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 6
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 7
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 8
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 4
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 5
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 5
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 6
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 7
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 6
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 7
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 8
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 9
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 7
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 8
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 9
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 10
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 11
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 3
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 4
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 4
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 5
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 6
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 5
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 5
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 6
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 7
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 6
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 7
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 8
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 9
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 5
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 6
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 6
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 7
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 8
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 7
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 8
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 9
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 10
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 8
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 9
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 10
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 11
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 12
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 6
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 7
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 7
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 8
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 9
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 8
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 9
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 10
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 11
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 9
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 10
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 11
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 12
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 13
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 10
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 11
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 12
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 13
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 14
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 15
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 3
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 4
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 5
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 4
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 6
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 7
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 4
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 5
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 3
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 4
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 5
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 6
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 5
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 6
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 7
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 8
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 4
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 5
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 5
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 6
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 7
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 6
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 7
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 8
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 9
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 7
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 8
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 9
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 10
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 11
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 3
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 3
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 5
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 4
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 5
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 6
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 5
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 6
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 7
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 8
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 3
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 4
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 4
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 5
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 6
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 4
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 5
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 6
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 7
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 6
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 7
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 8
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 9
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 5
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 6
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 6
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 7
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 8
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 7
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 8
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 9
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 10
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 8
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 9
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 10
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 11
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 12
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 5
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 5
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 6
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 7
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 5
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 6
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 6
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 7
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 8
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 7
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 8
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 9
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 10
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 6
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 7
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 7
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 8
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 9
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 8
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 9
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 10
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 11
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 9
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 10
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 11
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 12
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 13
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 7
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 8
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 8
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 9
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 10
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 9
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 10
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 11
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 12
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 10
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 11
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 12
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 13
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 14
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 11
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 12
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 13
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 14
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 15
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 16
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 3
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 4
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 4
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 5
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 6
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 5
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 5
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 6
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 7
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 6
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 7
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 8
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 9
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 5
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 5
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 6
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 7
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 6
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 6
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 7
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 8
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 7
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 8
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 9
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 10
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 6
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 7
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 7
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 8
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 9
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 8
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 9
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 10
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 11
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 9
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 10
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 11
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 12
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 13
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 5
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 6
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 6
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 7
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 8
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 6
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 7
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 7
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 8
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 9
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 8
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 9
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 10
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 11
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 7
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 8
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 8
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 9
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 10
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 9
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 10
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 11
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 12
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 10
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 11
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 12
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 13
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 14
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 8
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 9
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 9
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 10
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 11
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 10
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 11
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 12
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 13
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 11
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 12
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 13
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 14
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 15
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 12
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 13
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 14
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 15
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 16
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 17
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 6
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 7
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 7
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 8
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 9
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 7
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 8
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 8
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 9
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 10
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 9
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 10
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 11
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 12
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 8
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 9
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 9
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 10
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 11
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 10
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 11
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 12
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 13
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 11
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 12
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 13
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 14
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 15
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 9
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 10
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 10
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 11
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 12
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 11
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 12
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 13
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 14
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 12
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 13
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 14
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 15
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 16
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 13
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 14
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 15
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 16
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 17
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 18
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 10
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 11
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 11
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 12
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 13
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 12
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 13
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 14
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 15
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 13
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 14
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 15
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 16
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 17
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 14
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 15
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 16
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 17
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 18
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 19
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 15
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 16
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 17
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 18
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 19
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 20
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 21
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 3
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 5
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 4
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 3
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 5
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 4
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 5
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 6
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 7
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 4
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 4
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 5
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 6
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 5
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 6
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 7
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 8
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 6
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 7
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 8
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 9
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 10
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 3
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 4
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 5
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 5
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 6
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 7
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 4
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 5
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 3
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 4
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 4
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 5
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 6
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 5
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 6
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 7
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 8
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 4
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 5
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 5
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 6
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 7
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 6
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 7
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 8
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 9
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 7
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 8
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 9
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 10
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 11
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 3
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 4
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 4
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 5
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 6
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 5
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 5
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 6
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 7
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 6
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 7
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 8
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 9
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 5
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 6
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 6
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 7
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 8
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 7
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 8
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 9
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 10
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 8
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 9
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 10
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 11
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 12
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 6
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 7
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 7
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 8
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 9
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 8
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 9
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 10
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 11
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 9
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 10
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 11
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 12
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 13
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 10
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 11
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 12
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 13
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 14
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 15
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 3
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 4
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 5
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 4
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 6
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 7
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 4
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 5
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 3
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 4
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 5
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 6
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 5
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 6
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 7
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 8
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 4
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 5
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 5
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 6
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 7
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 6
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 7
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 8
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 9
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 7
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 8
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 9
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 10
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 11
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 3
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 3
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 5
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 4
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 5
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 6
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 5
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 6
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 7
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 8
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 3
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 4
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 4
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 5
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 6
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 4
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 5
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 5
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 6
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 7
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 6
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 7
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 8
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 9
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 5
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 6
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 6
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 7
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 8
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 7
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 8
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 9
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 10
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 8
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 9
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 10
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 11
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 12
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 5
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 5
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 6
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 7
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 5
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 6
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 6
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 7
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 8
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 7
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 8
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 9
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 10
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 6
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 7
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 7
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 8
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 9
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 8
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 9
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 10
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 11
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 9
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 10
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 11
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 12
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 13
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 7
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 8
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 8
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 9
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 10
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 9
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 10
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 11
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 12
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 10
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 11
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 12
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 13
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 14
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 11
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 12
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 13
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 14
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 15
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 16
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 3
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 4
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 4
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 5
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 6
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 4
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 5
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 5
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 6
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 7
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 6
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 7
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 8
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 9
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 4
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 5
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 5
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 6
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 7
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 6
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 6
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 7
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 8
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 7
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 8
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 9
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 10
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 6
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 7
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 7
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 8
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 9
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 8
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 9
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 10
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 11
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 9
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 10
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 11
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 12
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 13
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 5
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 6
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 6
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 7
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 8
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 6
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 7
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 7
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 8
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 9
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 8
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 9
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 10
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 11
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 7
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 8
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 8
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 9
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 10
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 9
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 10
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 11
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 12
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 10
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 11
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 12
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 13
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 14
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 8
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 9
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 9
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 10
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 11
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 10
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 11
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 12
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 13
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 11
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 12
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 13
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 14
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 15
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 12
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 13
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 14
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 15
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 16
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 17
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 6
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 7
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 7
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 8
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 9
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 7
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 8
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 8
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 9
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 10
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 9
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 10
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 11
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 12
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 8
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 9
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 9
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 10
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 11
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 10
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 11
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 12
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 13
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 11
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 12
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 13
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 14
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 15
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 9
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 10
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 10
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 11
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 12
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 11
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 12
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 13
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 14
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 12
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 13
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 14
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 15
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 16
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 13
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 14
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 15
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 16
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 17
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 18
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 10
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 11
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 11
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 12
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 13
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 12
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 13
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 14
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 15
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 13
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 14
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 15
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 16
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 17
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 14
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 15
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 16
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 17
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 18
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 19
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 15
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 16
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 17
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 18
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 19
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 20
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 21
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 3
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 4
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 3
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 5
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 4
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => 6
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 7
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 4
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 5
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 3
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 4
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 5
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => 6
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 5
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => 6
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => 7
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => 8
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 4
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 5
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 5
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 6
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => 7
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 6
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 7
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => 8
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => 9
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 7
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 8
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 9
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => 10
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 11
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 5
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 4
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 5
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 6
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 5
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 6
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 7
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 8
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 3
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 4
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 4
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 5
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 6
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 4
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 5
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 5
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 6
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 7
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => 6
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 7
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 8
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 9
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 5
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 6
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 6
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 7
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 8
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => 7
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 8
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 9
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 10
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => 8
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 9
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 10
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 11
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 12
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 5
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 5
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 6
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 7
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 5
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 6
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 6
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 7
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 8
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 7
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 8
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 9
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 10
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 6
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 7
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 7
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 8
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 9
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => 8
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 9
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 10
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 11
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => 9
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 10
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 11
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 12
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 13
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 7
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 8
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 8
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 9
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 10
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 9
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 10
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 11
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 12
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 10
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 11
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 12
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 13
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 14
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 11
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 12
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 13
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 14
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 15
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 16
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 3
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 3
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => 5
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 4
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 4
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 6
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => 5
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 6
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => 7
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 8
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Description
The area of a Dyck path.
This is the number of complete squares in the integer lattice which are below the path and above the x-axis. The 'half-squares' directly above the axis do not contribute to this statistic.
1. Dyck paths are bijection with area sequences (a1,,an) such that a1=0,ak+1ak+1.
2. The generating function Dn(q)=DDnqarea(D) satisfy the recurrence Dn+1(q)=qkDk(q)Dnk(q).
3. The area is equidistributed with St000005The bounce statistic of a Dyck path. and St000006The dinv of a Dyck path.. Pairs of these statistics play an important role in the theory of q,t-Catalan numbers.
References
[1] Haglund, J. The q,t-Catalan numbers and the space of diagonal harmonics MathSciNet:2371044
Code
def statistic(x):
    return x.area()
Created
Sep 27, 2011 at 19:29 by Chris Berg
Updated
Jun 17, 2019 at 17:03 by Christian Stump