Identifier
- St000027: Dyck paths ⟶ ℤ
Values
=>
Cc0005;cc-rep
[]=>0
[1,0]=>0
[1,0,1,0]=>2
[1,1,0,0]=>0
[1,0,1,0,1,0]=>6
[1,0,1,1,0,0]=>2
[1,1,0,0,1,0]=>4
[1,1,0,1,0,0]=>3
[1,1,1,0,0,0]=>0
[1,0,1,0,1,0,1,0]=>12
[1,0,1,0,1,1,0,0]=>6
[1,0,1,1,0,0,1,0]=>8
[1,0,1,1,0,1,0,0]=>7
[1,0,1,1,1,0,0,0]=>2
[1,1,0,0,1,0,1,0]=>10
[1,1,0,0,1,1,0,0]=>4
[1,1,0,1,0,0,1,0]=>9
[1,1,0,1,0,1,0,0]=>8
[1,1,0,1,1,0,0,0]=>3
[1,1,1,0,0,0,1,0]=>6
[1,1,1,0,0,1,0,0]=>5
[1,1,1,0,1,0,0,0]=>4
[1,1,1,1,0,0,0,0]=>0
[1,0,1,0,1,0,1,0,1,0]=>20
[1,0,1,0,1,0,1,1,0,0]=>12
[1,0,1,0,1,1,0,0,1,0]=>14
[1,0,1,0,1,1,0,1,0,0]=>13
[1,0,1,0,1,1,1,0,0,0]=>6
[1,0,1,1,0,0,1,0,1,0]=>16
[1,0,1,1,0,0,1,1,0,0]=>8
[1,0,1,1,0,1,0,0,1,0]=>15
[1,0,1,1,0,1,0,1,0,0]=>14
[1,0,1,1,0,1,1,0,0,0]=>7
[1,0,1,1,1,0,0,0,1,0]=>10
[1,0,1,1,1,0,0,1,0,0]=>9
[1,0,1,1,1,0,1,0,0,0]=>8
[1,0,1,1,1,1,0,0,0,0]=>2
[1,1,0,0,1,0,1,0,1,0]=>18
[1,1,0,0,1,0,1,1,0,0]=>10
[1,1,0,0,1,1,0,0,1,0]=>12
[1,1,0,0,1,1,0,1,0,0]=>11
[1,1,0,0,1,1,1,0,0,0]=>4
[1,1,0,1,0,0,1,0,1,0]=>17
[1,1,0,1,0,0,1,1,0,0]=>9
[1,1,0,1,0,1,0,0,1,0]=>16
[1,1,0,1,0,1,0,1,0,0]=>15
[1,1,0,1,0,1,1,0,0,0]=>8
[1,1,0,1,1,0,0,0,1,0]=>11
[1,1,0,1,1,0,0,1,0,0]=>10
[1,1,0,1,1,0,1,0,0,0]=>9
[1,1,0,1,1,1,0,0,0,0]=>3
[1,1,1,0,0,0,1,0,1,0]=>14
[1,1,1,0,0,0,1,1,0,0]=>6
[1,1,1,0,0,1,0,0,1,0]=>13
[1,1,1,0,0,1,0,1,0,0]=>12
[1,1,1,0,0,1,1,0,0,0]=>5
[1,1,1,0,1,0,0,0,1,0]=>12
[1,1,1,0,1,0,0,1,0,0]=>11
[1,1,1,0,1,0,1,0,0,0]=>10
[1,1,1,0,1,1,0,0,0,0]=>4
[1,1,1,1,0,0,0,0,1,0]=>8
[1,1,1,1,0,0,0,1,0,0]=>7
[1,1,1,1,0,0,1,0,0,0]=>6
[1,1,1,1,0,1,0,0,0,0]=>5
[1,1,1,1,1,0,0,0,0,0]=>0
[1,0,1,0,1,0,1,0,1,0,1,0]=>30
[1,0,1,0,1,0,1,0,1,1,0,0]=>20
[1,0,1,0,1,0,1,1,0,0,1,0]=>22
[1,0,1,0,1,0,1,1,0,1,0,0]=>21
[1,0,1,0,1,0,1,1,1,0,0,0]=>12
[1,0,1,0,1,1,0,0,1,0,1,0]=>24
[1,0,1,0,1,1,0,0,1,1,0,0]=>14
[1,0,1,0,1,1,0,1,0,0,1,0]=>23
[1,0,1,0,1,1,0,1,0,1,0,0]=>22
[1,0,1,0,1,1,0,1,1,0,0,0]=>13
[1,0,1,0,1,1,1,0,0,0,1,0]=>16
[1,0,1,0,1,1,1,0,0,1,0,0]=>15
[1,0,1,0,1,1,1,0,1,0,0,0]=>14
[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]=>26
[1,0,1,1,0,0,1,0,1,1,0,0]=>16
[1,0,1,1,0,0,1,1,0,0,1,0]=>18
[1,0,1,1,0,0,1,1,0,1,0,0]=>17
[1,0,1,1,0,0,1,1,1,0,0,0]=>8
[1,0,1,1,0,1,0,0,1,0,1,0]=>25
[1,0,1,1,0,1,0,0,1,1,0,0]=>15
[1,0,1,1,0,1,0,1,0,0,1,0]=>24
[1,0,1,1,0,1,0,1,0,1,0,0]=>23
[1,0,1,1,0,1,0,1,1,0,0,0]=>14
[1,0,1,1,0,1,1,0,0,0,1,0]=>17
[1,0,1,1,0,1,1,0,0,1,0,0]=>16
[1,0,1,1,0,1,1,0,1,0,0,0]=>15
[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]=>20
[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]=>19
[1,0,1,1,1,0,0,1,0,1,0,0]=>18
[1,0,1,1,1,0,0,1,1,0,0,0]=>9
[1,0,1,1,1,0,1,0,0,0,1,0]=>18
[1,0,1,1,1,0,1,0,0,1,0,0]=>17
[1,0,1,1,1,0,1,0,1,0,0,0]=>16
[1,0,1,1,1,0,1,1,0,0,0,0]=>8
[1,0,1,1,1,1,0,0,0,0,1,0]=>12
[1,0,1,1,1,1,0,0,0,1,0,0]=>11
[1,0,1,1,1,1,0,0,1,0,0,0]=>10
[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]=>2
[1,1,0,0,1,0,1,0,1,0,1,0]=>28
[1,1,0,0,1,0,1,0,1,1,0,0]=>18
[1,1,0,0,1,0,1,1,0,0,1,0]=>20
[1,1,0,0,1,0,1,1,0,1,0,0]=>19
[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]=>22
[1,1,0,0,1,1,0,0,1,1,0,0]=>12
[1,1,0,0,1,1,0,1,0,0,1,0]=>21
[1,1,0,0,1,1,0,1,0,1,0,0]=>20
[1,1,0,0,1,1,0,1,1,0,0,0]=>11
[1,1,0,0,1,1,1,0,0,0,1,0]=>14
[1,1,0,0,1,1,1,0,0,1,0,0]=>13
[1,1,0,0,1,1,1,0,1,0,0,0]=>12
[1,1,0,0,1,1,1,1,0,0,0,0]=>4
[1,1,0,1,0,0,1,0,1,0,1,0]=>27
[1,1,0,1,0,0,1,0,1,1,0,0]=>17
[1,1,0,1,0,0,1,1,0,0,1,0]=>19
[1,1,0,1,0,0,1,1,0,1,0,0]=>18
[1,1,0,1,0,0,1,1,1,0,0,0]=>9
[1,1,0,1,0,1,0,0,1,0,1,0]=>26
[1,1,0,1,0,1,0,0,1,1,0,0]=>16
[1,1,0,1,0,1,0,1,0,0,1,0]=>25
[1,1,0,1,0,1,0,1,0,1,0,0]=>24
[1,1,0,1,0,1,0,1,1,0,0,0]=>15
[1,1,0,1,0,1,1,0,0,0,1,0]=>18
[1,1,0,1,0,1,1,0,0,1,0,0]=>17
[1,1,0,1,0,1,1,0,1,0,0,0]=>16
[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]=>21
[1,1,0,1,1,0,0,0,1,1,0,0]=>11
[1,1,0,1,1,0,0,1,0,0,1,0]=>20
[1,1,0,1,1,0,0,1,0,1,0,0]=>19
[1,1,0,1,1,0,0,1,1,0,0,0]=>10
[1,1,0,1,1,0,1,0,0,0,1,0]=>19
[1,1,0,1,1,0,1,0,0,1,0,0]=>18
[1,1,0,1,1,0,1,0,1,0,0,0]=>17
[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]=>13
[1,1,0,1,1,1,0,0,0,1,0,0]=>12
[1,1,0,1,1,1,0,0,1,0,0,0]=>11
[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]=>3
[1,1,1,0,0,0,1,0,1,0,1,0]=>24
[1,1,1,0,0,0,1,0,1,1,0,0]=>14
[1,1,1,0,0,0,1,1,0,0,1,0]=>16
[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]=>6
[1,1,1,0,0,1,0,0,1,0,1,0]=>23
[1,1,1,0,0,1,0,0,1,1,0,0]=>13
[1,1,1,0,0,1,0,1,0,0,1,0]=>22
[1,1,1,0,0,1,0,1,0,1,0,0]=>21
[1,1,1,0,0,1,0,1,1,0,0,0]=>12
[1,1,1,0,0,1,1,0,0,0,1,0]=>15
[1,1,1,0,0,1,1,0,0,1,0,0]=>14
[1,1,1,0,0,1,1,0,1,0,0,0]=>13
[1,1,1,0,0,1,1,1,0,0,0,0]=>5
[1,1,1,0,1,0,0,0,1,0,1,0]=>22
[1,1,1,0,1,0,0,0,1,1,0,0]=>12
[1,1,1,0,1,0,0,1,0,0,1,0]=>21
[1,1,1,0,1,0,0,1,0,1,0,0]=>20
[1,1,1,0,1,0,0,1,1,0,0,0]=>11
[1,1,1,0,1,0,1,0,0,0,1,0]=>20
[1,1,1,0,1,0,1,0,0,1,0,0]=>19
[1,1,1,0,1,0,1,0,1,0,0,0]=>18
[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]=>14
[1,1,1,0,1,1,0,0,0,1,0,0]=>13
[1,1,1,0,1,1,0,0,1,0,0,0]=>12
[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]=>4
[1,1,1,1,0,0,0,0,1,0,1,0]=>18
[1,1,1,1,0,0,0,0,1,1,0,0]=>8
[1,1,1,1,0,0,0,1,0,0,1,0]=>17
[1,1,1,1,0,0,0,1,0,1,0,0]=>16
[1,1,1,1,0,0,0,1,1,0,0,0]=>7
[1,1,1,1,0,0,1,0,0,0,1,0]=>16
[1,1,1,1,0,0,1,0,0,1,0,0]=>15
[1,1,1,1,0,0,1,0,1,0,0,0]=>14
[1,1,1,1,0,0,1,1,0,0,0,0]=>6
[1,1,1,1,0,1,0,0,0,0,1,0]=>15
[1,1,1,1,0,1,0,0,0,1,0,0]=>14
[1,1,1,1,0,1,0,0,1,0,0,0]=>13
[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]=>5
[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]=>9
[1,1,1,1,1,0,0,0,1,0,0,0]=>8
[1,1,1,1,1,0,0,1,0,0,0,0]=>7
[1,1,1,1,1,0,1,0,0,0,0,0]=>6
[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]=>42
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>30
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>32
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>31
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>20
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>34
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>22
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>33
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>32
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>21
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>24
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>23
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>22
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>12
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>36
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>24
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>26
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>25
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>14
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>35
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>23
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>34
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>33
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>22
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>25
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>24
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>23
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>13
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>28
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>16
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>27
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>26
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>15
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>26
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>25
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>24
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>14
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>18
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>17
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>16
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>15
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>6
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>38
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>26
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>28
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>27
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>16
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>30
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>18
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>29
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>28
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>17
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>20
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>19
[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]=>8
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>37
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>25
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>27
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>26
[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]=>36
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>24
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>35
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>34
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>23
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>26
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>25
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>24
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>14
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>29
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>17
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>28
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>27
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>16
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>27
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>26
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>25
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>15
[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]=>18
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>17
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>16
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>7
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>32
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>20
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>22
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>21
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>10
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>31
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>19
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>30
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>29
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>18
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>21
[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]=>19
[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]=>30
[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]=>29
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>28
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>17
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>28
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>27
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>26
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>16
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>20
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>19
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>18
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>17
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>8
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>24
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>12
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>23
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>22
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>11
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>22
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>21
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>20
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>10
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>21
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>20
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>19
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>18
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>9
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>14
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>13
[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]=>11
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>10
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>40
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>28
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>30
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>29
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>18
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>32
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>20
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>31
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>30
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>19
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>22
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>21
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>20
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>10
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>34
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>22
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>24
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>23
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>12
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>33
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>21
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>32
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>31
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>20
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>23
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>22
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>21
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>11
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>26
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>14
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>25
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>24
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>13
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>24
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>23
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>22
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>12
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>16
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>15
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>14
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>13
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>4
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>39
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>27
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>29
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>28
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>17
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>31
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>19
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>30
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>29
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>18
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>21
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>20
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>19
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>9
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>38
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>26
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>28
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>27
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>16
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>37
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>25
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>36
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>35
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>24
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>27
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>26
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>25
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>15
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>30
[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]=>29
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>28
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>17
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>28
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>27
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>26
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>16
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>20
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>19
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>18
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>17
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>8
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>33
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>21
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>23
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>22
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>11
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>32
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>20
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>31
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>30
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>19
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>22
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>21
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>20
[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]=>31
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>19
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>30
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>29
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>18
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>29
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>28
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>27
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>17
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>21
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>20
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>19
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>18
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>9
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>25
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>13
[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]=>23
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>12
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>23
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>22
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>21
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>11
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>22
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>21
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>20
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>19
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>10
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>15
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>14
[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]=>12
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>11
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>3
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>36
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>24
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>26
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>25
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>14
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>28
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>16
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>27
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>26
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>15
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>18
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>17
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>16
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>6
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>35
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>23
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>25
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>24
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>13
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>34
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>22
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>33
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>32
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>21
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>24
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>23
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>22
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>12
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>27
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>15
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>26
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>25
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>14
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>25
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>24
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>23
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>13
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>17
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>16
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>15
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>14
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>5
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>34
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>22
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>24
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>23
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>12
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>33
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>21
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>32
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>31
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>20
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>23
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>22
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>21
[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]=>32
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>20
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>31
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>30
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>19
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>30
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>29
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>28
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>18
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>22
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>21
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>20
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>19
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>10
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>26
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>14
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>25
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>24
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>13
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>24
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>23
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>22
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>12
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>23
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>22
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>21
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>20
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>11
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>16
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>15
[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]=>13
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>12
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>4
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>30
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>18
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>20
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>19
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>8
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>29
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>17
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>28
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>27
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>16
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>19
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>18
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>17
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>7
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>28
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>16
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>27
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>26
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>15
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>26
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>25
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>24
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>14
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>18
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>17
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>16
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>15
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>6
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>27
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>15
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>26
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>25
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>14
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>25
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>24
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>23
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>13
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>24
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>23
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>22
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>21
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>12
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>17
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>16
[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]=>14
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>13
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>5
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>22
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>10
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>21
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>20
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>9
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>20
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>19
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>18
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>8
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>19
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>18
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>17
[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]=>7
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>18
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>17
[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]=>15
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>14
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>6
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>12
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>11
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>10
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>9
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>8
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>7
[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]=>56
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>42
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>44
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>43
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>30
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>46
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>32
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>45
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>44
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>31
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>34
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>33
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>32
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>20
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>48
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>34
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>36
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>35
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>22
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>47
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>33
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>46
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>45
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>32
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>35
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>34
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>33
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>21
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>38
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>24
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>37
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>36
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>23
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>36
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>35
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>34
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>22
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>26
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>25
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>24
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>23
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>12
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>50
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>36
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>38
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>37
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>24
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>40
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>26
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>39
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>38
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>25
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>28
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>27
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>26
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>14
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>49
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>35
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>37
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>36
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>23
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>48
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>34
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>47
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>46
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>33
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>36
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>35
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>34
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>22
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>39
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>25
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>38
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>37
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>24
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>37
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>36
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>35
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>23
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>27
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>26
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>25
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>24
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>13
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>42
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>28
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>30
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>29
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>16
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>41
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>27
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>40
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>39
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>26
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>29
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>28
[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]=>15
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>40
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>26
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>39
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>38
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>25
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>38
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>37
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>36
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>24
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>28
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>27
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>26
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>25
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>14
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>32
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>18
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>31
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>30
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>17
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>30
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>29
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>28
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>16
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>29
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>28
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>27
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>26
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>15
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>20
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>19
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>18
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>17
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>16
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>6
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>52
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>38
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>40
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>39
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>26
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>42
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>28
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>41
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>40
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>27
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>30
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>29
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>28
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>16
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>44
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>30
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>32
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>31
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>18
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>43
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>29
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>42
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>41
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>28
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>31
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>30
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>29
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>17
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>34
[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]=>33
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>32
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>19
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>32
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>31
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>30
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>18
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>22
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>21
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>20
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>19
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>8
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>51
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>37
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>39
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>38
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>25
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>41
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>27
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>40
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>39
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>26
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>29
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>28
[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]=>15
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>50
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>36
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>38
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>37
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>24
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>49
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>35
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>48
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>47
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>34
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>37
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>36
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>35
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>23
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>40
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>26
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>39
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>38
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>25
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>38
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>37
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>36
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>24
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>28
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>27
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>26
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>25
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>14
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>43
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>29
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>31
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>30
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>17
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>42
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>28
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>41
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>40
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>27
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>30
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>29
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>28
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>16
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>41
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>27
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>40
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>39
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>26
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>39
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>38
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>37
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>25
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>29
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>28
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>27
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>26
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>15
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>33
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>19
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>32
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>31
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>18
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>31
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>30
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>29
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>17
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>30
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>29
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>28
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>27
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>16
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>21
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>20
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>19
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>18
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>17
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>7
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>46
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>32
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>34
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>33
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>20
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>36
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>22
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>35
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>34
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>21
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>24
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>23
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>22
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>10
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>45
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>31
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>33
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>32
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>19
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>44
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>30
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>43
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>42
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>29
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>32
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>31
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>30
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>18
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>35
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>21
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>34
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>33
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>20
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>33
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>32
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>31
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>19
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>23
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>22
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>21
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>20
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>9
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>44
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>30
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>32
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>31
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>18
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>43
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>29
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>42
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>41
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>28
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>31
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>30
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>29
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>17
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>42
[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]=>41
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>40
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>27
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>40
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>39
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>38
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>26
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>30
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>29
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>28
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>27
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>16
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>34
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>20
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>33
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>32
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>19
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>32
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>31
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>30
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>18
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>31
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>30
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>29
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>28
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>17
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>22
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>21
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>20
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>19
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>18
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>8
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>38
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>24
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>26
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>25
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>12
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>37
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>23
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>36
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>35
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>22
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>25
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>24
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>23
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>11
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>36
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>22
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>35
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>34
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>21
[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]=>33
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>32
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>20
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>24
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>23
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>22
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>21
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>10
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>35
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>21
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>34
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>33
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>20
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>33
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>32
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>31
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>19
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>32
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>31
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>30
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>29
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>18
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>23
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>22
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>21
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>20
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>19
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>9
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>28
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>14
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>27
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>26
[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]=>26
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>25
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>24
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>12
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>25
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>24
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>23
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>22
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>11
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>24
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>23
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>22
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>21
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>20
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>10
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>16
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>15
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>14
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>13
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>12
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>11
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>54
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>40
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>42
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>41
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>28
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>44
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>30
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>43
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>42
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>29
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>32
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>31
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>30
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>18
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>46
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>32
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>34
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>33
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>20
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>45
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>31
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>44
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>43
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>30
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>33
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>32
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>31
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>19
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>36
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>22
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>35
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>34
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>21
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>34
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>33
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>32
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>20
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>24
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>23
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>22
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>21
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>10
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>48
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>34
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>36
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>35
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>22
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>38
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>24
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>37
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>36
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>23
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>26
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>25
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>24
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>12
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>47
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>33
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>35
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>34
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>21
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>46
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>32
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>45
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>44
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>31
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>34
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>33
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>32
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>20
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>37
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>23
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>36
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>35
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>22
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>35
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>34
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>33
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>21
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>25
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>24
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>23
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>22
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>11
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>40
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>26
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>28
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>27
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>14
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>39
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>25
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>38
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>37
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>24
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>27
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>26
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>25
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>13
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>38
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>24
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>37
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>36
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>23
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>36
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>35
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>34
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>22
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>26
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>25
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>24
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>23
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>12
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>30
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>16
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>29
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>28
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>15
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>28
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>27
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>26
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>14
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>27
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>26
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>25
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>24
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>13
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>18
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>17
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>16
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>15
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>14
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>4
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>53
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>39
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>41
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>40
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>27
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>43
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>29
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>42
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>41
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>28
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>31
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>30
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>29
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>17
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>30
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>32
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>51
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>37
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>50
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>36
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>49
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>48
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>35
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>37
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>36
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>24
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>39
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>37
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>44
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>41
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>47
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>43
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>32
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>32
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>34
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>15
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>13
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>12
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>3
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>50
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>36
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>37
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>20
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>47
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>46
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>45
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>38
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>24
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>24
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>12
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>34
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>44
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>35
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>46
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>43
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>44
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>30
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>42
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>41
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>40
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>28
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>24
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>24
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>12
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>36
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>16
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>24
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>13
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>18
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>16
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>15
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>14
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>13
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>4
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>20
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>20
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>8
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>36
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>38
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>24
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>26
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>24
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>22
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>12
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>17
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>24
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>13
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>19
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>18
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>17
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>16
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>14
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>5
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>20
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>22
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>20
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>8
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>19
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>21
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>19
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>7
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>18
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>28
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>27
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>24
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>14
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>20
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>19
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>18
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>17
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>16
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>15
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>6
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>12
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>23
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>22
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>20
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>9
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>22
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>21
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>19
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>18
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>8
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>21
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>20
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>18
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>17
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>16
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>7
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>14
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>13
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>12
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>11
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>10
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>9
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>8
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>16
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>24
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>12
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>25
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>23
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>13
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>11
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0]=>22
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]=>24
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>14
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>4
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>18
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>21
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>15
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>6
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0]=>22
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0]=>20
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>16
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>14
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>63
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>48
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>50
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>49
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>58
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>14
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>13
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>3
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>60
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>59
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>55
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>54
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>4
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>16
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>22
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>18
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>17
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>24
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>23
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>8
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>15
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>14
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>10
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>9
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>56
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>57
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>45
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>44
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>22
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>52
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>8
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>62
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>32
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>16
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>70
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>54
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>56
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>20
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>66
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>65
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>64
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>63
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>55
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>54
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>53
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>53
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>56
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>58
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>61
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>47
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>49
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>59
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>32
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>40
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>41
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>39
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>33
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>31
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>18
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>2
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>27
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>13
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]=>26
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>14
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>16
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>4
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>20
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0]=>24
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>16
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>6
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>72
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>73
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>80
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>77
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>24
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>36
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>88
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>70
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>84
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>81
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>63
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>11
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>71
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>3
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>17
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>26
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>10
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>70
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>40
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>42
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>43
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>44
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>46
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>44
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>46
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>46
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>48
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>46
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>48
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>49
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>50
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>52
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>45
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>47
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>48
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>49
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>51
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>48
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>50
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>50
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>52
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>49
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>51
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>52
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>53
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>55
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>48
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>50
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>51
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>52
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0]=>54
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>52
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>54
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>54
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>56
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>54
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0]=>56
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>57
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]=>58
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>60
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>72
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0]=>19
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0]=>45
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>35
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>20
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>90
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>91
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>99
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>108
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>12
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>19
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>11
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>88
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>0
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>4
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]=>18
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>40
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>26
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>57
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0]=>59
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0]=>60
[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0]=>61
[1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0]=>63
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0]=>61
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0]=>63
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0]=>63
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0]=>65
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0]=>63
[1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0]=>65
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0]=>66
[1,0,1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0]=>67
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0]=>69
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>62
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>64
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>65
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>66
[1,0,1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>68
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>65
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0]=>67
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>67
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>69
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0]=>66
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0]=>68
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>69
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0]=>70
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>72
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0]=>65
[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0]=>67
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0]=>68
[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0]=>69
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0]=>71
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>69
[1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>71
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0]=>71
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>73
[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0]=>71
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0]=>73
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>74
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0]=>75
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>77
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>63
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>65
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>66
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>67
[1,1,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>69
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>67
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>69
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>69
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>71
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>69
[1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>71
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>72
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>73
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>75
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>67
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>69
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>70
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>71
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>73
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>69
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>71
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>72
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>73
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>75
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0]=>69
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0]=>71
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>71
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>73
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>72
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>74
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>73
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>75
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>75
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>77
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0]=>69
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0]=>71
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>72
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0]=>73
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>75
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>73
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>75
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>75
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>77
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0]=>75
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>77
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>78
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>79
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>81
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0]=>67
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0]=>69
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0,1,0]=>70
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0,1,0]=>71
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,1,0]=>73
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>71
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>73
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0,1,0]=>73
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>75
[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0,1,0]=>73
[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0]=>75
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>76
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0]=>77
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0]=>79
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>72
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>74
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>75
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>76
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0]=>78
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>75
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>77
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>77
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>79
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0]=>76
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>78
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>79
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>80
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>82
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,1,0]=>75
[1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0,1,0]=>77
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>78
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0]=>79
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0]=>81
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>79
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0]=>81
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>81
[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>83
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0]=>81
[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0]=>83
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]=>84
[1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0]=>85
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>87
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Description
The major index of a Dyck path.
This is the sum over all $i+j$ for which $(i,j)$ is a valley of $D$.
The generating function of the major index yields MacMahon 's $q$-Catalan numbers
$$\sum_{D \in \mathfrak{D}_n} q^{\operatorname{maj}(D)} = \frac{1}{[n+1]_q}\begin{bmatrix} 2n \\ n \end{bmatrix}_q,$$
where $[k]_q := 1+q+\ldots+q^{k-1}$ is the usual $q$-extension of the integer $k$, $[k]_q!:= [1]_q[2]_q \cdots [k]_q$ is the $q$-factorial of $k$ and $\left[\begin{smallmatrix} k \\ l \end{smallmatrix}\right]_q:=[k]_q!/[l]_q![k-l]_q!$ is the $q$-binomial coefficient.
The major index was first studied by P.A.MacMahon in [1], where he proved this generating function identity.
There is a bijection $\psi$ between Dyck paths and noncrossing permutations which simultaneously sends the area of a Dyck path St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation., and the major index of the Dyck path to $n(n-1)$ minus the sum of the major index and the major index of the inverse [2].
For the major index on other collections, see St000004The major index of a permutation. for permutations and St000290The major index of a binary word. for binary words.
This is the sum over all $i+j$ for which $(i,j)$ is a valley of $D$.
The generating function of the major index yields MacMahon 's $q$-Catalan numbers
$$\sum_{D \in \mathfrak{D}_n} q^{\operatorname{maj}(D)} = \frac{1}{[n+1]_q}\begin{bmatrix} 2n \\ n \end{bmatrix}_q,$$
where $[k]_q := 1+q+\ldots+q^{k-1}$ is the usual $q$-extension of the integer $k$, $[k]_q!:= [1]_q[2]_q \cdots [k]_q$ is the $q$-factorial of $k$ and $\left[\begin{smallmatrix} k \\ l \end{smallmatrix}\right]_q:=[k]_q!/[l]_q![k-l]_q!$ is the $q$-binomial coefficient.
The major index was first studied by P.A.MacMahon in [1], where he proved this generating function identity.
There is a bijection $\psi$ between Dyck paths and noncrossing permutations which simultaneously sends the area of a Dyck path St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation., and the major index of the Dyck path to $n(n-1)$ minus the sum of the major index and the major index of the inverse [2].
For the major index on other collections, see St000004The major index of a permutation. for permutations and St000290The major index of a binary word. for binary words.
References
[1] MacMahon, P. A. Combinatory analysis MathSciNet:0141605
[2] Stump, C. More bijective Catalan combinatorics on permutations and on signed permutations arXiv:0808.2822
[2] Stump, C. More bijective Catalan combinatorics on permutations and on signed permutations arXiv:0808.2822
Code
def statistic(x): return x.major_index()
Created
Jun 10, 2012 at 08:35 by Christian Stump
Updated
Feb 12, 2018 at 22:26 by Martin Rubey
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