Identifier
- St000032: Dyck paths ⟶ ℤ
Values
=>
Cc0005;cc-rep
[1,0]=>1
[1,0,1,0]=>1
[1,1,0,0]=>2
[1,0,1,0,1,0]=>1
[1,0,1,1,0,0]=>2
[1,1,0,0,1,0]=>2
[1,1,0,1,0,0]=>3
[1,1,1,0,0,0]=>5
[1,0,1,0,1,0,1,0]=>1
[1,0,1,0,1,1,0,0]=>2
[1,0,1,1,0,0,1,0]=>2
[1,0,1,1,0,1,0,0]=>3
[1,0,1,1,1,0,0,0]=>5
[1,1,0,0,1,0,1,0]=>2
[1,1,0,0,1,1,0,0]=>4
[1,1,0,1,0,0,1,0]=>3
[1,1,0,1,0,1,0,0]=>4
[1,1,0,1,1,0,0,0]=>7
[1,1,1,0,0,0,1,0]=>5
[1,1,1,0,0,1,0,0]=>7
[1,1,1,0,1,0,0,0]=>9
[1,1,1,1,0,0,0,0]=>14
[1,0,1,0,1,0,1,0,1,0]=>1
[1,0,1,0,1,0,1,1,0,0]=>2
[1,0,1,0,1,1,0,0,1,0]=>2
[1,0,1,0,1,1,0,1,0,0]=>3
[1,0,1,0,1,1,1,0,0,0]=>5
[1,0,1,1,0,0,1,0,1,0]=>2
[1,0,1,1,0,0,1,1,0,0]=>4
[1,0,1,1,0,1,0,0,1,0]=>3
[1,0,1,1,0,1,0,1,0,0]=>4
[1,0,1,1,0,1,1,0,0,0]=>7
[1,0,1,1,1,0,0,0,1,0]=>5
[1,0,1,1,1,0,0,1,0,0]=>7
[1,0,1,1,1,0,1,0,0,0]=>9
[1,0,1,1,1,1,0,0,0,0]=>14
[1,1,0,0,1,0,1,0,1,0]=>2
[1,1,0,0,1,0,1,1,0,0]=>4
[1,1,0,0,1,1,0,0,1,0]=>4
[1,1,0,0,1,1,0,1,0,0]=>6
[1,1,0,0,1,1,1,0,0,0]=>10
[1,1,0,1,0,0,1,0,1,0]=>3
[1,1,0,1,0,0,1,1,0,0]=>6
[1,1,0,1,0,1,0,0,1,0]=>4
[1,1,0,1,0,1,0,1,0,0]=>5
[1,1,0,1,0,1,1,0,0,0]=>9
[1,1,0,1,1,0,0,0,1,0]=>7
[1,1,0,1,1,0,0,1,0,0]=>9
[1,1,0,1,1,0,1,0,0,0]=>12
[1,1,0,1,1,1,0,0,0,0]=>19
[1,1,1,0,0,0,1,0,1,0]=>5
[1,1,1,0,0,0,1,1,0,0]=>10
[1,1,1,0,0,1,0,0,1,0]=>7
[1,1,1,0,0,1,0,1,0,0]=>9
[1,1,1,0,0,1,1,0,0,0]=>16
[1,1,1,0,1,0,0,0,1,0]=>9
[1,1,1,0,1,0,0,1,0,0]=>12
[1,1,1,0,1,0,1,0,0,0]=>14
[1,1,1,0,1,1,0,0,0,0]=>23
[1,1,1,1,0,0,0,0,1,0]=>14
[1,1,1,1,0,0,0,1,0,0]=>19
[1,1,1,1,0,0,1,0,0,0]=>23
[1,1,1,1,0,1,0,0,0,0]=>28
[1,1,1,1,1,0,0,0,0,0]=>42
[1,0,1,0,1,0,1,0,1,0,1,0]=>1
[1,0,1,0,1,0,1,0,1,1,0,0]=>2
[1,0,1,0,1,0,1,1,0,0,1,0]=>2
[1,0,1,0,1,0,1,1,0,1,0,0]=>3
[1,0,1,0,1,0,1,1,1,0,0,0]=>5
[1,0,1,0,1,1,0,0,1,0,1,0]=>2
[1,0,1,0,1,1,0,0,1,1,0,0]=>4
[1,0,1,0,1,1,0,1,0,0,1,0]=>3
[1,0,1,0,1,1,0,1,0,1,0,0]=>4
[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]=>5
[1,0,1,0,1,1,1,0,0,1,0,0]=>7
[1,0,1,0,1,1,1,0,1,0,0,0]=>9
[1,0,1,0,1,1,1,1,0,0,0,0]=>14
[1,0,1,1,0,0,1,0,1,0,1,0]=>2
[1,0,1,1,0,0,1,0,1,1,0,0]=>4
[1,0,1,1,0,0,1,1,0,0,1,0]=>4
[1,0,1,1,0,0,1,1,0,1,0,0]=>6
[1,0,1,1,0,0,1,1,1,0,0,0]=>10
[1,0,1,1,0,1,0,0,1,0,1,0]=>3
[1,0,1,1,0,1,0,0,1,1,0,0]=>6
[1,0,1,1,0,1,0,1,0,0,1,0]=>4
[1,0,1,1,0,1,0,1,0,1,0,0]=>5
[1,0,1,1,0,1,0,1,1,0,0,0]=>9
[1,0,1,1,0,1,1,0,0,0,1,0]=>7
[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]=>12
[1,0,1,1,0,1,1,1,0,0,0,0]=>19
[1,0,1,1,1,0,0,0,1,0,1,0]=>5
[1,0,1,1,1,0,0,0,1,1,0,0]=>10
[1,0,1,1,1,0,0,1,0,0,1,0]=>7
[1,0,1,1,1,0,0,1,0,1,0,0]=>9
[1,0,1,1,1,0,0,1,1,0,0,0]=>16
[1,0,1,1,1,0,1,0,0,0,1,0]=>9
[1,0,1,1,1,0,1,0,0,1,0,0]=>12
[1,0,1,1,1,0,1,0,1,0,0,0]=>14
[1,0,1,1,1,0,1,1,0,0,0,0]=>23
[1,0,1,1,1,1,0,0,0,0,1,0]=>14
[1,0,1,1,1,1,0,0,0,1,0,0]=>19
[1,0,1,1,1,1,0,0,1,0,0,0]=>23
[1,0,1,1,1,1,0,1,0,0,0,0]=>28
[1,0,1,1,1,1,1,0,0,0,0,0]=>42
[1,1,0,0,1,0,1,0,1,0,1,0]=>2
[1,1,0,0,1,0,1,0,1,1,0,0]=>4
[1,1,0,0,1,0,1,1,0,0,1,0]=>4
[1,1,0,0,1,0,1,1,0,1,0,0]=>6
[1,1,0,0,1,0,1,1,1,0,0,0]=>10
[1,1,0,0,1,1,0,0,1,0,1,0]=>4
[1,1,0,0,1,1,0,0,1,1,0,0]=>8
[1,1,0,0,1,1,0,1,0,0,1,0]=>6
[1,1,0,0,1,1,0,1,0,1,0,0]=>8
[1,1,0,0,1,1,0,1,1,0,0,0]=>14
[1,1,0,0,1,1,1,0,0,0,1,0]=>10
[1,1,0,0,1,1,1,0,0,1,0,0]=>14
[1,1,0,0,1,1,1,0,1,0,0,0]=>18
[1,1,0,0,1,1,1,1,0,0,0,0]=>28
[1,1,0,1,0,0,1,0,1,0,1,0]=>3
[1,1,0,1,0,0,1,0,1,1,0,0]=>6
[1,1,0,1,0,0,1,1,0,0,1,0]=>6
[1,1,0,1,0,0,1,1,0,1,0,0]=>9
[1,1,0,1,0,0,1,1,1,0,0,0]=>15
[1,1,0,1,0,1,0,0,1,0,1,0]=>4
[1,1,0,1,0,1,0,0,1,1,0,0]=>8
[1,1,0,1,0,1,0,1,0,0,1,0]=>5
[1,1,0,1,0,1,0,1,0,1,0,0]=>6
[1,1,0,1,0,1,0,1,1,0,0,0]=>11
[1,1,0,1,0,1,1,0,0,0,1,0]=>9
[1,1,0,1,0,1,1,0,0,1,0,0]=>11
[1,1,0,1,0,1,1,0,1,0,0,0]=>15
[1,1,0,1,0,1,1,1,0,0,0,0]=>24
[1,1,0,1,1,0,0,0,1,0,1,0]=>7
[1,1,0,1,1,0,0,0,1,1,0,0]=>14
[1,1,0,1,1,0,0,1,0,0,1,0]=>9
[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]=>20
[1,1,0,1,1,0,1,0,0,0,1,0]=>12
[1,1,0,1,1,0,1,0,0,1,0,0]=>15
[1,1,0,1,1,0,1,0,1,0,0,0]=>18
[1,1,0,1,1,0,1,1,0,0,0,0]=>30
[1,1,0,1,1,1,0,0,0,0,1,0]=>19
[1,1,0,1,1,1,0,0,0,1,0,0]=>24
[1,1,0,1,1,1,0,0,1,0,0,0]=>30
[1,1,0,1,1,1,0,1,0,0,0,0]=>37
[1,1,0,1,1,1,1,0,0,0,0,0]=>56
[1,1,1,0,0,0,1,0,1,0,1,0]=>5
[1,1,1,0,0,0,1,0,1,1,0,0]=>10
[1,1,1,0,0,0,1,1,0,0,1,0]=>10
[1,1,1,0,0,0,1,1,0,1,0,0]=>15
[1,1,1,0,0,0,1,1,1,0,0,0]=>25
[1,1,1,0,0,1,0,0,1,0,1,0]=>7
[1,1,1,0,0,1,0,0,1,1,0,0]=>14
[1,1,1,0,0,1,0,1,0,0,1,0]=>9
[1,1,1,0,0,1,0,1,0,1,0,0]=>11
[1,1,1,0,0,1,0,1,1,0,0,0]=>20
[1,1,1,0,0,1,1,0,0,0,1,0]=>16
[1,1,1,0,0,1,1,0,0,1,0,0]=>20
[1,1,1,0,0,1,1,0,1,0,0,0]=>27
[1,1,1,0,0,1,1,1,0,0,0,0]=>43
[1,1,1,0,1,0,0,0,1,0,1,0]=>9
[1,1,1,0,1,0,0,0,1,1,0,0]=>18
[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]=>15
[1,1,1,0,1,0,0,1,1,0,0,0]=>27
[1,1,1,0,1,0,1,0,0,0,1,0]=>14
[1,1,1,0,1,0,1,0,0,1,0,0]=>18
[1,1,1,0,1,0,1,0,1,0,0,0]=>20
[1,1,1,0,1,0,1,1,0,0,0,0]=>34
[1,1,1,0,1,1,0,0,0,0,1,0]=>23
[1,1,1,0,1,1,0,0,0,1,0,0]=>30
[1,1,1,0,1,1,0,0,1,0,0,0]=>34
[1,1,1,0,1,1,0,1,0,0,0,0]=>43
[1,1,1,0,1,1,1,0,0,0,0,0]=>66
[1,1,1,1,0,0,0,0,1,0,1,0]=>14
[1,1,1,1,0,0,0,0,1,1,0,0]=>28
[1,1,1,1,0,0,0,1,0,0,1,0]=>19
[1,1,1,1,0,0,0,1,0,1,0,0]=>24
[1,1,1,1,0,0,0,1,1,0,0,0]=>43
[1,1,1,1,0,0,1,0,0,0,1,0]=>23
[1,1,1,1,0,0,1,0,0,1,0,0]=>30
[1,1,1,1,0,0,1,0,1,0,0,0]=>34
[1,1,1,1,0,0,1,1,0,0,0,0]=>57
[1,1,1,1,0,1,0,0,0,0,1,0]=>28
[1,1,1,1,0,1,0,0,0,1,0,0]=>37
[1,1,1,1,0,1,0,0,1,0,0,0]=>43
[1,1,1,1,0,1,0,1,0,0,0,0]=>48
[1,1,1,1,0,1,1,0,0,0,0,0]=>76
[1,1,1,1,1,0,0,0,0,0,1,0]=>42
[1,1,1,1,1,0,0,0,0,1,0,0]=>56
[1,1,1,1,1,0,0,0,1,0,0,0]=>66
[1,1,1,1,1,0,0,1,0,0,0,0]=>76
[1,1,1,1,1,0,1,0,0,0,0,0]=>90
[1,1,1,1,1,1,0,0,0,0,0,0]=>132
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>2
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>3
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>5
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>4
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>3
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>4
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>7
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>5
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>7
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>9
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>14
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>4
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>4
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>6
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>10
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>3
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>6
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>4
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>5
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>9
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>7
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>9
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>12
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>19
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>5
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>10
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>7
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>9
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>16
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>9
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>12
[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]=>23
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>14
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>19
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>23
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>28
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>42
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>4
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>4
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>6
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>10
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>4
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>8
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>6
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>8
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>14
[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]=>14
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>18
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>28
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>3
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>6
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>6
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>9
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>15
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>4
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>8
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>5
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>6
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>11
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>9
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>11
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>15
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>24
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>7
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>14
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>9
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>11
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>20
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>12
[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]=>18
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>30
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>19
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>24
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>30
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>37
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>56
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>5
[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]=>10
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>15
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>25
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>7
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>14
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>9
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>11
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>20
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>16
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>20
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>27
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>43
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>9
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>18
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>12
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>15
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>27
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>14
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>18
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>20
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>34
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>23
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>30
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>34
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>43
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>66
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>14
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>28
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>19
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>24
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>43
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>23
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>30
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>34
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>57
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>28
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>37
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>43
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>48
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>76
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>42
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>56
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>66
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>76
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>90
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>132
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>2
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>4
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>4
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>6
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>10
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>4
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>8
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>6
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>8
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>14
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>10
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>14
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>18
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>28
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>4
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>8
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>8
[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]=>20
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>6
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>12
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>8
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>10
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>18
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>14
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>18
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>24
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>38
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>10
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>20
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>14
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>18
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>32
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>18
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>24
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>28
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>46
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>28
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>38
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>46
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>56
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>84
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>3
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>6
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>6
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>9
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>15
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>6
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>12
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>9
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>12
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>21
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>15
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>21
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>27
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>42
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>4
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>8
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>8
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>12
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>20
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>5
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>10
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>6
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>7
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>13
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>11
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>13
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>18
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>29
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>9
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>18
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>11
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>13
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>24
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>15
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>18
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>22
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>37
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>24
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>29
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>37
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>46
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>70
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>7
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>14
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>14
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>21
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>35
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>9
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>18
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>11
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>13
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>24
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>20
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>24
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>33
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>53
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>12
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>24
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>15
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>18
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>33
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>18
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>22
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>25
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>43
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>30
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>37
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>43
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>55
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>85
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>19
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>38
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>24
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>29
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>53
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>30
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>37
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>43
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>73
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>37
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>46
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>55
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>62
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>99
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>56
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>70
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>85
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>99
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>118
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>174
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>5
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>10
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>10
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>15
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>25
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>10
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>20
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>15
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>20
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>35
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>25
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>35
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>45
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>70
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>7
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>14
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>14
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>21
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>35
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>9
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>18
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>11
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>13
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>24
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>20
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>24
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>33
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>53
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>16
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>32
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>20
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>24
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>44
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>27
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>33
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>40
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>67
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>43
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>53
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>67
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>83
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>126
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>9
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>18
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>18
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>27
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>45
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>12
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>24
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>15
[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]=>33
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>27
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>33
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>45
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>72
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>14
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>28
[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]=>22
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>40
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>20
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>25
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>27
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>47
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>34
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>43
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>47
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>61
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>95
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>23
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>46
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>30
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>37
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>67
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>34
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>43
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>47
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>81
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>43
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>55
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>61
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>70
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>113
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>66
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>85
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>95
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>113
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>136
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>202
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>14
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>28
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>28
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>42
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>70
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>19
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>38
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>24
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>29
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>53
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>43
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>53
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>72
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>115
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>23
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>46
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>30
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>37
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>67
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>34
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>43
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>47
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>81
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>57
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>73
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>81
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>104
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>161
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>28
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>56
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>37
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>46
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>83
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>43
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>55
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>61
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>104
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>48
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>62
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>70
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>75
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>123
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>76
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>99
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>113
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>123
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>151
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>227
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>42
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>84
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>56
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>70
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>126
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>66
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>85
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>95
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>161
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>76
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>99
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>113
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>123
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>199
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>90
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>118
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>136
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>151
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>165
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>255
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>132
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>174
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>202
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>227
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>255
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>297
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>429
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>2
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>3
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>5
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>2
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>4
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>3
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>4
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>7
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>5
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>7
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>9
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>14
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>2
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>4
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>4
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>6
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>10
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>3
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>6
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>4
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>5
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>9
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>7
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>9
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>12
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>19
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>5
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>10
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>7
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>9
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>16
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>9
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>12
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>14
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>23
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>14
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>19
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>23
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>28
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>42
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>2
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>4
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>4
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>6
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>10
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>4
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>8
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>6
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>8
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>14
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>10
[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]=>18
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>28
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>3
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>6
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>6
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>9
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>15
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>4
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>8
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>5
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>6
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>11
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>9
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>11
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>15
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>24
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>7
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>14
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>9
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>11
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>20
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>12
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>15
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>18
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>30
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>19
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>24
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>30
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>37
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>56
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>5
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>10
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>10
[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]=>25
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>7
[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]=>9
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>11
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>20
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>16
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>20
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>27
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>43
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>9
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>18
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>12
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>15
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>27
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>14
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>18
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>20
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>34
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>23
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>30
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>34
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>43
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>66
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>14
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>28
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>19
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>24
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>43
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>23
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>30
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>34
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>57
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>28
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>37
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>43
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>48
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>76
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>42
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>56
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>66
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>76
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>90
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>132
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>2
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>4
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>4
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>6
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>10
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>4
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>8
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>6
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>8
[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]=>10
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>14
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>18
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>28
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>4
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>8
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>8
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>12
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>20
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>6
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>12
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>8
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>10
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>18
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>14
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>18
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>24
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>38
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>10
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>20
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>14
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>18
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>32
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>18
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>24
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>28
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>46
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>28
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>38
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>46
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>56
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>84
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>3
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>6
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>6
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>9
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>15
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>6
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>12
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>9
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>12
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>21
[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]=>21
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>27
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>42
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>4
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>8
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>8
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>12
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>20
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>5
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>10
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>6
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>7
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>13
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>11
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>13
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>18
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>29
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>9
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>18
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>11
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>13
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>24
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>15
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>18
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>22
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>37
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>24
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>29
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>37
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>46
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>70
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>7
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>14
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>14
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>21
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>35
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>9
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>18
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>11
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>13
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>24
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>20
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>24
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>33
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>53
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>12
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>24
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>15
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>18
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>33
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>18
[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]=>25
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>43
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>30
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>37
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>43
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>55
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>85
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>19
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>38
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>24
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>29
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>53
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>30
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>37
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>43
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>73
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>37
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>46
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>55
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>62
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>99
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>56
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>70
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>85
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>99
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>118
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>174
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>5
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>10
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>10
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>15
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>25
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>10
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>20
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>15
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>20
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>35
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>25
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>35
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>45
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>70
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>7
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>14
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>14
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>21
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>35
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>9
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>18
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>11
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>13
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>24
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>20
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>24
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>33
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>53
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>16
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>32
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>20
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>24
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>44
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>27
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>33
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>40
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>67
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>43
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>53
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>67
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>83
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>126
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>9
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>18
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>18
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>27
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>45
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>12
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>24
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>15
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>18
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>33
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>27
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>33
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>45
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>72
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>14
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>28
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>18
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>22
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>40
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>20
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>25
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>27
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>47
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>34
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>43
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>47
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>61
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>95
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>23
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>46
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>30
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>37
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>67
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>34
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>43
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>47
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>81
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>43
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>55
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>61
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>70
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>113
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>66
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>85
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>95
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>113
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>136
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>202
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>14
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>28
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>28
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>42
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>70
[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]=>38
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>24
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>29
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>53
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>43
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>53
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>72
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>115
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>23
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>46
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>30
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>37
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>67
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>34
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>43
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>47
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Description
The number of elements smaller than the given Dyck path in the Tamari Order.
References
[1] wikipedia:Tamari_lattice
[2] Pons, V., Chatel, G. Counting smaller trees in the Tamari order arXiv:1212.0751
[2] Pons, V., Chatel, G. Counting smaller trees in the Tamari order arXiv:1212.0751
Code
def statistic(x): return len(x.to_binary_tree_tamari().tamari_smaller())
Created
Feb 13, 2013 at 01:13 by Viviane Pons
Updated
May 29, 2015 at 16:14 by Martin Rubey
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