Identifier
- St001161: Dyck paths ⟶ ℤ
Values
=>
Cc0005;cc-rep
[1,0]=>0
[1,0,1,0]=>1
[1,1,0,0]=>0
[1,0,1,0,1,0]=>3
[1,0,1,1,0,0]=>1
[1,1,0,0,1,0]=>2
[1,1,0,1,0,0]=>2
[1,1,1,0,0,0]=>0
[1,0,1,0,1,0,1,0]=>6
[1,0,1,0,1,1,0,0]=>3
[1,0,1,1,0,0,1,0]=>4
[1,0,1,1,0,1,0,0]=>4
[1,0,1,1,1,0,0,0]=>1
[1,1,0,0,1,0,1,0]=>5
[1,1,0,0,1,1,0,0]=>2
[1,1,0,1,0,0,1,0]=>5
[1,1,0,1,0,1,0,0]=>5
[1,1,0,1,1,0,0,0]=>2
[1,1,1,0,0,0,1,0]=>3
[1,1,1,0,0,1,0,0]=>3
[1,1,1,0,1,0,0,0]=>3
[1,1,1,1,0,0,0,0]=>0
[1,0,1,0,1,0,1,0,1,0]=>10
[1,0,1,0,1,0,1,1,0,0]=>6
[1,0,1,0,1,1,0,0,1,0]=>7
[1,0,1,0,1,1,0,1,0,0]=>7
[1,0,1,0,1,1,1,0,0,0]=>3
[1,0,1,1,0,0,1,0,1,0]=>8
[1,0,1,1,0,0,1,1,0,0]=>4
[1,0,1,1,0,1,0,0,1,0]=>8
[1,0,1,1,0,1,0,1,0,0]=>8
[1,0,1,1,0,1,1,0,0,0]=>4
[1,0,1,1,1,0,0,0,1,0]=>5
[1,0,1,1,1,0,0,1,0,0]=>5
[1,0,1,1,1,0,1,0,0,0]=>5
[1,0,1,1,1,1,0,0,0,0]=>1
[1,1,0,0,1,0,1,0,1,0]=>9
[1,1,0,0,1,0,1,1,0,0]=>5
[1,1,0,0,1,1,0,0,1,0]=>6
[1,1,0,0,1,1,0,1,0,0]=>6
[1,1,0,0,1,1,1,0,0,0]=>2
[1,1,0,1,0,0,1,0,1,0]=>9
[1,1,0,1,0,0,1,1,0,0]=>5
[1,1,0,1,0,1,0,0,1,0]=>9
[1,1,0,1,0,1,0,1,0,0]=>9
[1,1,0,1,0,1,1,0,0,0]=>5
[1,1,0,1,1,0,0,0,1,0]=>6
[1,1,0,1,1,0,0,1,0,0]=>6
[1,1,0,1,1,0,1,0,0,0]=>6
[1,1,0,1,1,1,0,0,0,0]=>2
[1,1,1,0,0,0,1,0,1,0]=>7
[1,1,1,0,0,0,1,1,0,0]=>3
[1,1,1,0,0,1,0,0,1,0]=>7
[1,1,1,0,0,1,0,1,0,0]=>7
[1,1,1,0,0,1,1,0,0,0]=>3
[1,1,1,0,1,0,0,0,1,0]=>7
[1,1,1,0,1,0,0,1,0,0]=>7
[1,1,1,0,1,0,1,0,0,0]=>7
[1,1,1,0,1,1,0,0,0,0]=>3
[1,1,1,1,0,0,0,0,1,0]=>4
[1,1,1,1,0,0,0,1,0,0]=>4
[1,1,1,1,0,0,1,0,0,0]=>4
[1,1,1,1,0,1,0,0,0,0]=>4
[1,1,1,1,1,0,0,0,0,0]=>0
[1,0,1,0,1,0,1,0,1,0,1,0]=>15
[1,0,1,0,1,0,1,0,1,1,0,0]=>10
[1,0,1,0,1,0,1,1,0,0,1,0]=>11
[1,0,1,0,1,0,1,1,0,1,0,0]=>11
[1,0,1,0,1,0,1,1,1,0,0,0]=>6
[1,0,1,0,1,1,0,0,1,0,1,0]=>12
[1,0,1,0,1,1,0,0,1,1,0,0]=>7
[1,0,1,0,1,1,0,1,0,0,1,0]=>12
[1,0,1,0,1,1,0,1,0,1,0,0]=>12
[1,0,1,0,1,1,0,1,1,0,0,0]=>7
[1,0,1,0,1,1,1,0,0,0,1,0]=>8
[1,0,1,0,1,1,1,0,0,1,0,0]=>8
[1,0,1,0,1,1,1,0,1,0,0,0]=>8
[1,0,1,0,1,1,1,1,0,0,0,0]=>3
[1,0,1,1,0,0,1,0,1,0,1,0]=>13
[1,0,1,1,0,0,1,0,1,1,0,0]=>8
[1,0,1,1,0,0,1,1,0,0,1,0]=>9
[1,0,1,1,0,0,1,1,0,1,0,0]=>9
[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]=>13
[1,0,1,1,0,1,0,0,1,1,0,0]=>8
[1,0,1,1,0,1,0,1,0,0,1,0]=>13
[1,0,1,1,0,1,0,1,0,1,0,0]=>13
[1,0,1,1,0,1,0,1,1,0,0,0]=>8
[1,0,1,1,0,1,1,0,0,0,1,0]=>9
[1,0,1,1,0,1,1,0,0,1,0,0]=>9
[1,0,1,1,0,1,1,0,1,0,0,0]=>9
[1,0,1,1,0,1,1,1,0,0,0,0]=>4
[1,0,1,1,1,0,0,0,1,0,1,0]=>10
[1,0,1,1,1,0,0,0,1,1,0,0]=>5
[1,0,1,1,1,0,0,1,0,0,1,0]=>10
[1,0,1,1,1,0,0,1,0,1,0,0]=>10
[1,0,1,1,1,0,0,1,1,0,0,0]=>5
[1,0,1,1,1,0,1,0,0,0,1,0]=>10
[1,0,1,1,1,0,1,0,0,1,0,0]=>10
[1,0,1,1,1,0,1,0,1,0,0,0]=>10
[1,0,1,1,1,0,1,1,0,0,0,0]=>5
[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]=>6
[1,0,1,1,1,1,0,0,1,0,0,0]=>6
[1,0,1,1,1,1,0,1,0,0,0,0]=>6
[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[1,1,0,0,1,0,1,0,1,0,1,0]=>14
[1,1,0,0,1,0,1,0,1,1,0,0]=>9
[1,1,0,0,1,0,1,1,0,0,1,0]=>10
[1,1,0,0,1,0,1,1,0,1,0,0]=>10
[1,1,0,0,1,0,1,1,1,0,0,0]=>5
[1,1,0,0,1,1,0,0,1,0,1,0]=>11
[1,1,0,0,1,1,0,0,1,1,0,0]=>6
[1,1,0,0,1,1,0,1,0,0,1,0]=>11
[1,1,0,0,1,1,0,1,0,1,0,0]=>11
[1,1,0,0,1,1,0,1,1,0,0,0]=>6
[1,1,0,0,1,1,1,0,0,0,1,0]=>7
[1,1,0,0,1,1,1,0,0,1,0,0]=>7
[1,1,0,0,1,1,1,0,1,0,0,0]=>7
[1,1,0,0,1,1,1,1,0,0,0,0]=>2
[1,1,0,1,0,0,1,0,1,0,1,0]=>14
[1,1,0,1,0,0,1,0,1,1,0,0]=>9
[1,1,0,1,0,0,1,1,0,0,1,0]=>10
[1,1,0,1,0,0,1,1,0,1,0,0]=>10
[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]=>14
[1,1,0,1,0,1,0,0,1,1,0,0]=>9
[1,1,0,1,0,1,0,1,0,0,1,0]=>14
[1,1,0,1,0,1,0,1,0,1,0,0]=>14
[1,1,0,1,0,1,0,1,1,0,0,0]=>9
[1,1,0,1,0,1,1,0,0,0,1,0]=>10
[1,1,0,1,0,1,1,0,0,1,0,0]=>10
[1,1,0,1,0,1,1,0,1,0,0,0]=>10
[1,1,0,1,0,1,1,1,0,0,0,0]=>5
[1,1,0,1,1,0,0,0,1,0,1,0]=>11
[1,1,0,1,1,0,0,0,1,1,0,0]=>6
[1,1,0,1,1,0,0,1,0,0,1,0]=>11
[1,1,0,1,1,0,0,1,0,1,0,0]=>11
[1,1,0,1,1,0,0,1,1,0,0,0]=>6
[1,1,0,1,1,0,1,0,0,0,1,0]=>11
[1,1,0,1,1,0,1,0,0,1,0,0]=>11
[1,1,0,1,1,0,1,0,1,0,0,0]=>11
[1,1,0,1,1,0,1,1,0,0,0,0]=>6
[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]=>7
[1,1,0,1,1,1,0,0,1,0,0,0]=>7
[1,1,0,1,1,1,0,1,0,0,0,0]=>7
[1,1,0,1,1,1,1,0,0,0,0,0]=>2
[1,1,1,0,0,0,1,0,1,0,1,0]=>12
[1,1,1,0,0,0,1,0,1,1,0,0]=>7
[1,1,1,0,0,0,1,1,0,0,1,0]=>8
[1,1,1,0,0,0,1,1,0,1,0,0]=>8
[1,1,1,0,0,0,1,1,1,0,0,0]=>3
[1,1,1,0,0,1,0,0,1,0,1,0]=>12
[1,1,1,0,0,1,0,0,1,1,0,0]=>7
[1,1,1,0,0,1,0,1,0,0,1,0]=>12
[1,1,1,0,0,1,0,1,0,1,0,0]=>12
[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]=>8
[1,1,1,0,0,1,1,0,0,1,0,0]=>8
[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]=>3
[1,1,1,0,1,0,0,0,1,0,1,0]=>12
[1,1,1,0,1,0,0,0,1,1,0,0]=>7
[1,1,1,0,1,0,0,1,0,0,1,0]=>12
[1,1,1,0,1,0,0,1,0,1,0,0]=>12
[1,1,1,0,1,0,0,1,1,0,0,0]=>7
[1,1,1,0,1,0,1,0,0,0,1,0]=>12
[1,1,1,0,1,0,1,0,0,1,0,0]=>12
[1,1,1,0,1,0,1,0,1,0,0,0]=>12
[1,1,1,0,1,0,1,1,0,0,0,0]=>7
[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]=>8
[1,1,1,0,1,1,0,0,1,0,0,0]=>8
[1,1,1,0,1,1,0,1,0,0,0,0]=>8
[1,1,1,0,1,1,1,0,0,0,0,0]=>3
[1,1,1,1,0,0,0,0,1,0,1,0]=>9
[1,1,1,1,0,0,0,0,1,1,0,0]=>4
[1,1,1,1,0,0,0,1,0,0,1,0]=>9
[1,1,1,1,0,0,0,1,0,1,0,0]=>9
[1,1,1,1,0,0,0,1,1,0,0,0]=>4
[1,1,1,1,0,0,1,0,0,0,1,0]=>9
[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]=>9
[1,1,1,1,0,0,1,1,0,0,0,0]=>4
[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]=>9
[1,1,1,1,0,1,0,0,1,0,0,0]=>9
[1,1,1,1,0,1,0,1,0,0,0,0]=>9
[1,1,1,1,0,1,1,0,0,0,0,0]=>4
[1,1,1,1,1,0,0,0,0,0,1,0]=>5
[1,1,1,1,1,0,0,0,0,1,0,0]=>5
[1,1,1,1,1,0,0,0,1,0,0,0]=>5
[1,1,1,1,1,0,0,1,0,0,0,0]=>5
[1,1,1,1,1,0,1,0,0,0,0,0]=>5
[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>21
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>15
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>16
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>16
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>10
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>17
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>11
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>17
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>17
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>11
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>12
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>12
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>12
[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]=>18
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>12
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>13
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>13
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>7
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>18
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>12
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>18
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>18
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>12
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>13
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>13
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>13
[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]=>14
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>8
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>14
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>14
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>8
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>14
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>14
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>14
[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]=>9
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>9
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>9
[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]=>3
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>19
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>13
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>14
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>14
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>8
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>15
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>9
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>15
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>15
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>9
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>10
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>10
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>10
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>4
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>19
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>13
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>14
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>14
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>8
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>19
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>13
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>19
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>19
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>13
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>14
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>14
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>14
[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]=>15
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>9
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>15
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>15
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>9
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>15
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>15
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>15
[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]=>10
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>10
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>10
[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]=>4
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>16
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>10
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>11
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>11
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>5
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>16
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>10
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>16
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>16
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>10
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>11
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>11
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>11
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>5
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>16
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>10
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>16
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>16
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>10
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>16
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>16
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>16
[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]=>11
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>11
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>11
[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]=>5
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>12
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>6
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>12
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>12
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>6
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>12
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>12
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>12
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>6
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>12
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>12
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>12
[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]=>6
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>7
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>7
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>7
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>7
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>7
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>20
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>14
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>15
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>15
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>9
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>16
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>10
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>16
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>16
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>10
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>11
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>11
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>11
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>5
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>17
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>11
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>12
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>12
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>6
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>17
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>11
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>17
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>17
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>11
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>12
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>12
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>12
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>6
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>13
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>7
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>13
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>13
[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]=>13
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>13
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>13
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>7
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>8
[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]=>8
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>8
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>20
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>14
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>15
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>15
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>9
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>16
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>10
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>16
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>16
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>10
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>11
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>11
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>11
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>5
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>20
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>14
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>15
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>15
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>9
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>20
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>14
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>20
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>20
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>14
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>15
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>15
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>15
[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]=>16
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>10
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>16
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>16
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>10
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>16
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>16
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>16
[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]=>11
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>11
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>11
[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]=>5
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>17
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>11
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>12
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>12
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>6
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>17
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>11
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>17
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>17
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>11
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>12
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>12
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>12
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>6
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>17
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>11
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>17
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>17
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>11
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>17
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>17
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>17
[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]=>12
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>12
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>12
[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]=>6
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>13
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>7
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>13
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>13
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>7
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>13
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>13
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>13
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>7
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>13
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>13
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>13
[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]=>7
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>8
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>8
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>8
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>8
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>8
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>18
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>12
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>13
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>13
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>7
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>14
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>8
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>14
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>14
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>8
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>9
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>9
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>9
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>3
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>18
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>12
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>13
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>13
[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]=>18
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>12
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>18
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>18
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>12
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>13
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>13
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>13
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>7
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>14
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>8
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>14
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>14
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>8
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>14
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>14
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>14
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>8
[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]=>9
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>9
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>9
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>3
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>18
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>12
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>13
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>13
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>7
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>18
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>12
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>18
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>18
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>12
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>13
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>13
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>13
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>7
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>18
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>12
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>18
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>18
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>12
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>18
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>18
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>18
[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]=>13
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>13
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>13
[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]=>7
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>14
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>8
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>14
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>14
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>8
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>14
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>14
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>14
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>8
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>14
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>14
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>14
[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]=>8
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>9
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>9
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>9
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>9
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>9
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>3
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>15
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>9
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>10
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>10
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>4
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>15
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>9
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>15
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>15
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>9
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>10
[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]=>10
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>4
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>15
[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]=>15
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>15
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>9
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>15
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>15
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>15
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>9
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>10
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>10
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>10
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>10
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>4
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>15
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>9
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>15
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>15
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>9
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>15
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>15
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>15
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>9
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>15
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>15
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>15
[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]=>9
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>10
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>10
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>10
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>10
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>10
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>4
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>11
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>5
[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]=>11
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>5
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>11
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>11
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>11
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>5
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>11
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>11
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>11
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>11
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>5
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>11
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>11
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>11
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>11
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>11
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>5
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>6
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>6
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>6
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>6
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>6
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>6
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>28
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>21
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>22
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>22
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>15
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>23
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>16
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>23
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>23
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>16
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>17
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>17
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>17
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>10
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>24
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>17
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>18
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>18
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>11
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>24
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>17
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>24
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>24
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>17
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>18
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>18
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>18
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>11
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>19
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>12
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>19
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>19
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>12
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>19
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>19
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>19
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>12
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>13
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>13
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>13
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>13
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>6
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>25
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>18
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>19
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>19
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>12
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>20
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>13
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>20
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>20
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>13
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>14
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>14
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>14
[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]=>25
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>18
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>19
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>19
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>12
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>25
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>18
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>25
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>25
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>18
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>19
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>19
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>19
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>12
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>20
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>13
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>20
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>20
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>13
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>20
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>20
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>20
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>13
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>14
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>14
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>14
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>14
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>7
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>21
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>14
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>15
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>15
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>8
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>21
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>14
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>21
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>21
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>14
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>15
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>15
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>15
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>8
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>21
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>14
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>21
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>21
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>14
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>21
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>21
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>21
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>14
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>15
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>15
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>15
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>15
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>8
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>16
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>9
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>16
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>16
[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]=>16
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>16
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>16
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>9
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>16
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>16
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>16
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>16
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>9
[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]=>10
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>10
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>10
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>10
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>3
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>26
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>19
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>20
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>20
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>13
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>21
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>14
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>21
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>21
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>14
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>15
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>15
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>15
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>8
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>22
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>15
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>16
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>16
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>9
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>22
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>15
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>22
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>22
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>15
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>16
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>16
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>16
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>9
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>17
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>10
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>17
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>17
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>10
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>17
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>17
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>17
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>10
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>11
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>11
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>11
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>11
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>4
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>26
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>19
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>20
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>20
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>13
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>21
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>14
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>21
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>21
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>14
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>15
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>15
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>15
[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]=>26
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>19
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>20
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>20
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>13
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>26
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>19
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>26
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>26
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>19
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>20
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>20
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>20
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>13
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>21
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>14
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>21
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>21
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>14
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>21
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>21
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>21
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>14
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>15
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>15
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>15
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>15
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>8
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>22
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>15
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>16
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>16
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>9
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>22
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>15
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>22
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>22
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>15
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>16
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>16
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>16
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>9
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>22
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>15
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>22
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>22
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>15
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>22
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>22
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>22
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>15
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>16
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>16
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>16
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>16
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>9
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>17
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>10
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>17
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>17
[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]=>17
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>17
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>17
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>10
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>17
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>17
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>17
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>17
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>10
[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]=>11
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>11
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>11
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>11
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>4
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>23
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>16
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>17
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>17
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>10
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>18
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>11
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>18
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>18
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>11
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>12
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>12
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>12
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>5
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>23
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>16
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>17
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>17
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>10
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>23
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>16
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>23
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>23
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>16
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>17
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>17
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>17
[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]=>18
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>11
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>18
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>18
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>11
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>18
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>18
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>18
[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]=>12
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>12
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>12
[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]=>5
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>23
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>16
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>17
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>17
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>10
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>23
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>16
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>23
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>23
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>16
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>17
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>17
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>17
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>10
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>23
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>16
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>23
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>23
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>16
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>23
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>23
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>23
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>16
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>17
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>17
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>17
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>17
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>10
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>18
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>11
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>18
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>18
[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]=>18
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>18
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>18
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>11
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>18
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>18
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>18
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>18
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>11
[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]=>12
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>12
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>12
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>12
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>5
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>19
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>12
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>13
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>13
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>6
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>19
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>12
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>19
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>19
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>12
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>13
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>13
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>13
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>6
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>19
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>12
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>19
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>19
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>12
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>19
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>19
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>19
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>12
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>13
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>13
[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]=>13
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>6
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>19
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>12
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>19
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>19
[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]=>19
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>19
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>19
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>12
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>19
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>19
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>19
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>19
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>12
[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]=>13
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>13
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>13
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>13
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>6
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>14
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>7
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>14
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>14
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>7
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>14
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>14
[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]=>7
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>14
[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]=>14
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>14
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>7
[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]=>14
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>14
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>14
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>14
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>7
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>8
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>8
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>8
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>8
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>8
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>8
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>27
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>20
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>21
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>21
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>14
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>22
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>15
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>22
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>22
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>15
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>16
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>16
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>16
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>9
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>23
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>16
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>17
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>17
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>10
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>23
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>16
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>23
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>23
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>16
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>17
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>17
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>17
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>10
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>18
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>11
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>18
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>18
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>11
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>18
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>18
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>18
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>11
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>12
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>12
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>12
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>12
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>5
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>24
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>17
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>18
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>18
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>11
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>19
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>12
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>19
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>19
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>12
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>13
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>13
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>13
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>6
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>24
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>17
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>18
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>18
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>11
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>24
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>17
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>24
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>24
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>17
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>18
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>18
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>18
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>11
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>19
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>12
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>19
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>19
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>12
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>19
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>19
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>19
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>12
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>13
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>13
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>13
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>13
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>6
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>20
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>13
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>14
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>14
[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]=>20
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>13
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>20
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>20
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>13
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>14
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>14
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>14
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>7
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>20
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>13
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>20
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>20
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>13
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>20
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>20
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>20
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>13
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>14
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>14
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>14
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>14
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>7
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>15
[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]=>15
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>15
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>8
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>15
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>15
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>15
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>8
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>15
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>15
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>15
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>15
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>8
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>9
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>9
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>9
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>9
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>9
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>27
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>20
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>21
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>21
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>14
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>22
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>15
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>22
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>22
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>15
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>16
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>16
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>16
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>9
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Description
The major index north count of a Dyck path.
The descent set $\operatorname{des}(D)$ of a Dyck path $D = D_1 \cdots D_{2n}$ with $D_i \in \{N,E\}$ is given by all indices $i$ such that $D_i = E$ and $D_{i+1} = N$. This is, the positions of the valleys of $D$.
The major index of a Dyck path is then the sum of the positions of the valleys, $\sum_{i \in \operatorname{des}(D)} i$, see St000027The major index of a Dyck path..
The major index north count is given by $\sum_{i \in \operatorname{des}(D)} \#\{ j \leq i \mid D_j = N\}$.
The descent set $\operatorname{des}(D)$ of a Dyck path $D = D_1 \cdots D_{2n}$ with $D_i \in \{N,E\}$ is given by all indices $i$ such that $D_i = E$ and $D_{i+1} = N$. This is, the positions of the valleys of $D$.
The major index of a Dyck path is then the sum of the positions of the valleys, $\sum_{i \in \operatorname{des}(D)} i$, see St000027The major index of a Dyck path..
The major index north count is given by $\sum_{i \in \operatorname{des}(D)} \#\{ j \leq i \mid D_j = N\}$.
References
[1] Stump, C. On bijections between $231$-avoiding permutations and Dyck paths MathSciNet:2734176
Code
def statistic(D): vals = D.valleys() return sum(1 for d in vals for i in range(d+1) if D[i] == 1)
Created
Apr 25, 2018 at 11:56 by Christian Stump
Updated
Apr 25, 2018 at 11:56 by Christian Stump
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