Identifier
-
Mp00102:
Dyck paths
—rise composition⟶
Integer compositions
St000008: Integer compositions ⟶ ℤ
Values
=>
Cc0005;cc-rep-0
[1,0]=>[1]=>0
[1,0,1,0]=>[1,1]=>1
[1,1,0,0]=>[2]=>0
[1,0,1,0,1,0]=>[1,1,1]=>3
[1,0,1,1,0,0]=>[1,2]=>1
[1,1,0,0,1,0]=>[2,1]=>2
[1,1,0,1,0,0]=>[2,1]=>2
[1,1,1,0,0,0]=>[3]=>0
[1,0,1,0,1,0,1,0]=>[1,1,1,1]=>6
[1,0,1,0,1,1,0,0]=>[1,1,2]=>3
[1,0,1,1,0,0,1,0]=>[1,2,1]=>4
[1,0,1,1,0,1,0,0]=>[1,2,1]=>4
[1,0,1,1,1,0,0,0]=>[1,3]=>1
[1,1,0,0,1,0,1,0]=>[2,1,1]=>5
[1,1,0,0,1,1,0,0]=>[2,2]=>2
[1,1,0,1,0,0,1,0]=>[2,1,1]=>5
[1,1,0,1,0,1,0,0]=>[2,1,1]=>5
[1,1,0,1,1,0,0,0]=>[2,2]=>2
[1,1,1,0,0,0,1,0]=>[3,1]=>3
[1,1,1,0,0,1,0,0]=>[3,1]=>3
[1,1,1,0,1,0,0,0]=>[3,1]=>3
[1,1,1,1,0,0,0,0]=>[4]=>0
[1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1]=>10
[1,0,1,0,1,0,1,1,0,0]=>[1,1,1,2]=>6
[1,0,1,0,1,1,0,0,1,0]=>[1,1,2,1]=>7
[1,0,1,0,1,1,0,1,0,0]=>[1,1,2,1]=>7
[1,0,1,0,1,1,1,0,0,0]=>[1,1,3]=>3
[1,0,1,1,0,0,1,0,1,0]=>[1,2,1,1]=>8
[1,0,1,1,0,0,1,1,0,0]=>[1,2,2]=>4
[1,0,1,1,0,1,0,0,1,0]=>[1,2,1,1]=>8
[1,0,1,1,0,1,0,1,0,0]=>[1,2,1,1]=>8
[1,0,1,1,0,1,1,0,0,0]=>[1,2,2]=>4
[1,0,1,1,1,0,0,0,1,0]=>[1,3,1]=>5
[1,0,1,1,1,0,0,1,0,0]=>[1,3,1]=>5
[1,0,1,1,1,0,1,0,0,0]=>[1,3,1]=>5
[1,0,1,1,1,1,0,0,0,0]=>[1,4]=>1
[1,1,0,0,1,0,1,0,1,0]=>[2,1,1,1]=>9
[1,1,0,0,1,0,1,1,0,0]=>[2,1,2]=>5
[1,1,0,0,1,1,0,0,1,0]=>[2,2,1]=>6
[1,1,0,0,1,1,0,1,0,0]=>[2,2,1]=>6
[1,1,0,0,1,1,1,0,0,0]=>[2,3]=>2
[1,1,0,1,0,0,1,0,1,0]=>[2,1,1,1]=>9
[1,1,0,1,0,0,1,1,0,0]=>[2,1,2]=>5
[1,1,0,1,0,1,0,0,1,0]=>[2,1,1,1]=>9
[1,1,0,1,0,1,0,1,0,0]=>[2,1,1,1]=>9
[1,1,0,1,0,1,1,0,0,0]=>[2,1,2]=>5
[1,1,0,1,1,0,0,0,1,0]=>[2,2,1]=>6
[1,1,0,1,1,0,0,1,0,0]=>[2,2,1]=>6
[1,1,0,1,1,0,1,0,0,0]=>[2,2,1]=>6
[1,1,0,1,1,1,0,0,0,0]=>[2,3]=>2
[1,1,1,0,0,0,1,0,1,0]=>[3,1,1]=>7
[1,1,1,0,0,0,1,1,0,0]=>[3,2]=>3
[1,1,1,0,0,1,0,0,1,0]=>[3,1,1]=>7
[1,1,1,0,0,1,0,1,0,0]=>[3,1,1]=>7
[1,1,1,0,0,1,1,0,0,0]=>[3,2]=>3
[1,1,1,0,1,0,0,0,1,0]=>[3,1,1]=>7
[1,1,1,0,1,0,0,1,0,0]=>[3,1,1]=>7
[1,1,1,0,1,0,1,0,0,0]=>[3,1,1]=>7
[1,1,1,0,1,1,0,0,0,0]=>[3,2]=>3
[1,1,1,1,0,0,0,0,1,0]=>[4,1]=>4
[1,1,1,1,0,0,0,1,0,0]=>[4,1]=>4
[1,1,1,1,0,0,1,0,0,0]=>[4,1]=>4
[1,1,1,1,0,1,0,0,0,0]=>[4,1]=>4
[1,1,1,1,1,0,0,0,0,0]=>[5]=>0
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1]=>15
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,2]=>10
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,2,1]=>11
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,2,1]=>11
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,3]=>6
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,2,1,1]=>12
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,2,2]=>7
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,2,1,1]=>12
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,2,1,1]=>12
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,2,2]=>7
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,3,1]=>8
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,3,1]=>8
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,3,1]=>8
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,4]=>3
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,1,1,1]=>13
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,1,2]=>8
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,2,1]=>9
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,1]=>9
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,3]=>4
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,1,1,1]=>13
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,1,2]=>8
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,1,1,1]=>13
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,1,1,1]=>13
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,1,2]=>8
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,2,1]=>9
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,2,1]=>9
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,1]=>9
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,3]=>4
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,3,1,1]=>10
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,2]=>5
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,3,1,1]=>10
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,3,1,1]=>10
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,3,2]=>5
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,3,1,1]=>10
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,3,1,1]=>10
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,3,1,1]=>10
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,3,2]=>5
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,4,1]=>6
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,4,1]=>6
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,4,1]=>6
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,4,1]=>6
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,5]=>1
[1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1]=>14
[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,1,2]=>9
[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,2,1]=>10
[1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,2,1]=>10
[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3]=>5
[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,2,1,1]=>11
[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2]=>6
[1,1,0,0,1,1,0,1,0,0,1,0]=>[2,2,1,1]=>11
[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,2,1,1]=>11
[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2]=>6
[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1]=>7
[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1]=>7
[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1]=>7
[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4]=>2
[1,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,1,1,1]=>14
[1,1,0,1,0,0,1,0,1,1,0,0]=>[2,1,1,2]=>9
[1,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,2,1]=>10
[1,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,2,1]=>10
[1,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,3]=>5
[1,1,0,1,0,1,0,0,1,0,1,0]=>[2,1,1,1,1]=>14
[1,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,1,2]=>9
[1,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,1,1,1]=>14
[1,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,1,1,1]=>14
[1,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,1,2]=>9
[1,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,2,1]=>10
[1,1,0,1,0,1,1,0,0,1,0,0]=>[2,1,2,1]=>10
[1,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,2,1]=>10
[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,3]=>5
[1,1,0,1,1,0,0,0,1,0,1,0]=>[2,2,1,1]=>11
[1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,2]=>6
[1,1,0,1,1,0,0,1,0,0,1,0]=>[2,2,1,1]=>11
[1,1,0,1,1,0,0,1,0,1,0,0]=>[2,2,1,1]=>11
[1,1,0,1,1,0,0,1,1,0,0,0]=>[2,2,2]=>6
[1,1,0,1,1,0,1,0,0,0,1,0]=>[2,2,1,1]=>11
[1,1,0,1,1,0,1,0,0,1,0,0]=>[2,2,1,1]=>11
[1,1,0,1,1,0,1,0,1,0,0,0]=>[2,2,1,1]=>11
[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2]=>6
[1,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,1]=>7
[1,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,1]=>7
[1,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,1]=>7
[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,1]=>7
[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,4]=>2
[1,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,1,1]=>12
[1,1,1,0,0,0,1,0,1,1,0,0]=>[3,1,2]=>7
[1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1]=>8
[1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1]=>8
[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,3]=>3
[1,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,1,1]=>12
[1,1,1,0,0,1,0,0,1,1,0,0]=>[3,1,2]=>7
[1,1,1,0,0,1,0,1,0,0,1,0]=>[3,1,1,1]=>12
[1,1,1,0,0,1,0,1,0,1,0,0]=>[3,1,1,1]=>12
[1,1,1,0,0,1,0,1,1,0,0,0]=>[3,1,2]=>7
[1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,1]=>8
[1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,1]=>8
[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,1]=>8
[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,3]=>3
[1,1,1,0,1,0,0,0,1,0,1,0]=>[3,1,1,1]=>12
[1,1,1,0,1,0,0,0,1,1,0,0]=>[3,1,2]=>7
[1,1,1,0,1,0,0,1,0,0,1,0]=>[3,1,1,1]=>12
[1,1,1,0,1,0,0,1,0,1,0,0]=>[3,1,1,1]=>12
[1,1,1,0,1,0,0,1,1,0,0,0]=>[3,1,2]=>7
[1,1,1,0,1,0,1,0,0,0,1,0]=>[3,1,1,1]=>12
[1,1,1,0,1,0,1,0,0,1,0,0]=>[3,1,1,1]=>12
[1,1,1,0,1,0,1,0,1,0,0,0]=>[3,1,1,1]=>12
[1,1,1,0,1,0,1,1,0,0,0,0]=>[3,1,2]=>7
[1,1,1,0,1,1,0,0,0,0,1,0]=>[3,2,1]=>8
[1,1,1,0,1,1,0,0,0,1,0,0]=>[3,2,1]=>8
[1,1,1,0,1,1,0,0,1,0,0,0]=>[3,2,1]=>8
[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,1]=>8
[1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3]=>3
[1,1,1,1,0,0,0,0,1,0,1,0]=>[4,1,1]=>9
[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,2]=>4
[1,1,1,1,0,0,0,1,0,0,1,0]=>[4,1,1]=>9
[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,1,1]=>9
[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,2]=>4
[1,1,1,1,0,0,1,0,0,0,1,0]=>[4,1,1]=>9
[1,1,1,1,0,0,1,0,0,1,0,0]=>[4,1,1]=>9
[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,1,1]=>9
[1,1,1,1,0,0,1,1,0,0,0,0]=>[4,2]=>4
[1,1,1,1,0,1,0,0,0,0,1,0]=>[4,1,1]=>9
[1,1,1,1,0,1,0,0,0,1,0,0]=>[4,1,1]=>9
[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,1,1]=>9
[1,1,1,1,0,1,0,1,0,0,0,0]=>[4,1,1]=>9
[1,1,1,1,0,1,1,0,0,0,0,0]=>[4,2]=>4
[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,1]=>5
[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1]=>5
[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,1]=>5
[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,1]=>5
[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,1]=>5
[1,1,1,1,1,1,0,0,0,0,0,0]=>[6]=>0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1]=>21
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,2]=>15
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,2,1]=>16
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,2,1]=>16
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,3]=>10
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,2,1,1]=>17
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,2,2]=>11
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,2,1,1]=>17
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,2,1,1]=>17
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,2,2]=>11
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,3,1]=>12
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,3,1]=>12
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,3,1]=>12
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,4]=>6
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,2,1,1,1]=>18
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,2,1,2]=>12
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,2,2,1]=>13
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,2,1]=>13
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,3]=>7
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,2,1,1,1]=>18
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,2]=>12
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,2,1,1,1]=>18
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,2,1,1,1]=>18
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,2]=>12
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,2,2,1]=>13
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,2,2,1]=>13
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,2,2,1]=>13
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,2,3]=>7
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,3,1,1]=>14
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,3,2]=>8
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,3,1,1]=>14
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,3,1,1]=>14
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,3,2]=>8
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,3,1,1]=>14
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,3,1,1]=>14
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,3,1,1]=>14
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,3,2]=>8
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,4,1]=>9
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,4,1]=>9
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,4,1]=>9
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,4,1]=>9
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,5]=>3
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1]=>19
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,2]=>13
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,2,1,2,1]=>14
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,2,1]=>14
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,3]=>8
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,2,1,1]=>15
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]=>9
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,2,1,1]=>15
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,2,1,1]=>15
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]=>9
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,2,3,1]=>10
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,1]=>10
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,1]=>10
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4]=>4
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,2,1,1,1,1]=>19
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,2,1,1,2]=>13
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,2,1,2,1]=>14
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,2,1]=>14
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,3]=>8
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,2,1,1,1,1]=>19
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,2,1,1,2]=>13
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,2,1,1,1,1]=>19
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,1,1,1,1]=>19
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,1,1,2]=>13
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,2,1,2,1]=>14
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,2,1,2,1]=>14
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,2,1]=>14
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,3]=>8
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,2,2,1,1]=>15
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2]=>9
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,2,2,1,1]=>15
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,2,2,1,1]=>15
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2]=>9
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,2,2,1,1]=>15
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,2,2,1,1]=>15
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,2,1,1]=>15
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2]=>9
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,2,3,1]=>10
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,3,1]=>10
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,3,1]=>10
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,3,1]=>10
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,4]=>4
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,3,1,1,1]=>16
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,1,2]=>10
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,1]=>11
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,1]=>11
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3]=>5
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,3,1,1,1]=>16
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,3,1,2]=>10
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,3,1,1,1]=>16
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,3,1,1,1]=>16
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,1,2]=>10
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,3,2,1]=>11
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,1]=>11
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,2,1]=>11
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,3]=>5
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,3,1,1,1]=>16
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,3,1,2]=>10
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,3,1,1,1]=>16
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,3,1,1,1]=>16
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,1,2]=>10
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,3,1,1,1]=>16
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,3,1,1,1]=>16
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,1,1,1]=>16
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,3,1,2]=>10
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,3,2,1]=>11
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,2,1]=>11
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,2,1]=>11
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,2,1]=>11
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,3]=>5
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,4,1,1]=>12
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,4,2]=>6
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,4,1,1]=>12
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,4,1,1]=>12
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,4,2]=>6
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,4,1,1]=>12
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,4,1,1]=>12
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,4,1,1]=>12
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,4,2]=>6
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,4,1,1]=>12
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,4,1,1]=>12
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,4,1,1]=>12
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,4,1,1]=>12
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,4,2]=>6
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,5,1]=>7
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,5,1]=>7
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,5,1]=>7
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,5,1]=>7
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,5,1]=>7
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,6]=>1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1]=>20
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,2]=>14
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,1,2,1]=>15
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,2,1]=>15
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,3]=>9
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,2,1,1]=>16
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]=>10
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,2,1,1]=>16
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]=>16
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]=>10
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,1]=>11
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]=>11
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]=>11
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,4]=>5
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,2,1,1,1]=>17
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,2,1,2]=>11
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,2,2,1]=>12
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,1]=>12
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,3]=>6
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,2,1,1,1]=>17
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,2,1,2]=>11
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,2,1,1,1]=>17
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1]=>17
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,2,1,2]=>11
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,2,2,1]=>12
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,2,2,1]=>12
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,2,1]=>12
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,3]=>6
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,3,1,1]=>13
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,2]=>7
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,3,1,1]=>13
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,1,1]=>13
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,2]=>7
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,3,1,1]=>13
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,1,1]=>13
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,1,1]=>13
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,2]=>7
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,4,1]=>8
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,4,1]=>8
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,4,1]=>8
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,4,1]=>8
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,5]=>2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1]=>20
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,2]=>14
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,1,2,1]=>15
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,1,2,1]=>15
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,1,3]=>9
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,2,1,1]=>16
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]=>10
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,2,1,1]=>16
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]=>16
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]=>10
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,3,1]=>11
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]=>11
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]=>11
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4]=>5
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,1,1,1,1]=>20
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,1,1,1,2]=>14
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,1,2,1]=>15
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,1,2,1]=>15
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,1,3]=>9
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,1,1,1,1,1]=>20
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,1,1,2]=>14
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,1,1,1,1]=>20
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,1,1,1,1]=>20
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,1,1,2]=>14
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,1,2,1]=>15
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,1,1,2,1]=>15
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,1,2,1]=>15
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,1,3]=>9
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,2,1,1]=>16
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,2,2]=>10
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,1,2,1,1]=>16
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,1,2,1,1]=>16
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,1,2,2]=>10
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,1,2,1,1]=>16
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,1,2,1,1]=>16
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,1,2,1,1]=>16
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,2,2]=>10
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,3,1]=>11
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,1,3,1]=>11
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,1,3,1]=>11
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,3,1]=>11
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,4]=>5
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,2,1,1,1]=>17
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,2,1,2]=>11
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,2,2,1]=>12
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,2,2,1]=>12
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,2,3]=>6
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,2,1,1,1]=>17
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,2,1,2]=>11
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,2,1,1,1]=>17
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,2,1,1,1]=>17
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,2,1,2]=>11
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,2,2,1]=>12
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,2,2,1]=>12
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,2,2,1]=>12
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,2,3]=>6
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,2,1,1,1]=>17
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,2,1,2]=>11
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,2,1,1,1]=>17
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,2,1,1,1]=>17
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,2,1,2]=>11
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,2,1,1,1]=>17
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,2,1,1,1]=>17
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,2,1,1,1]=>17
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,2,1,2]=>11
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,2,2,1]=>12
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,2,2,1]=>12
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,2,2,1]=>12
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,2,2,1]=>12
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,3]=>6
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,1,1]=>13
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,2]=>7
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,3,1,1]=>13
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,1,1]=>13
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,2]=>7
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,3,1,1]=>13
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,3,1,1]=>13
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,3,1,1]=>13
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,2]=>7
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,3,1,1]=>13
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,3,1,1]=>13
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,3,1,1]=>13
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,1,1]=>13
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,2]=>7
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1]=>8
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,4,1]=>8
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,4,1]=>8
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,4,1]=>8
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,4,1]=>8
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,5]=>2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1]=>18
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,1,1,2]=>12
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,1,2,1]=>13
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,1,2,1]=>13
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,1,3]=>7
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,1]=>14
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,2]=>8
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,1]=>14
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,1]=>14
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,2]=>8
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,3,1]=>9
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,3,1]=>9
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,3,1]=>9
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,4]=>3
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,1,1,1,1]=>18
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,1,1,2]=>12
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,1,2,1]=>13
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,1,2,1]=>13
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,1,3]=>7
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,1,1,1,1]=>18
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,1,1,2]=>12
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,1,1,1,1]=>18
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,1,1,1,1]=>18
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,1,1,2]=>12
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,1,2,1]=>13
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,1,2,1]=>13
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,1,2,1]=>13
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,1,3]=>7
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,1,1]=>14
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,2]=>8
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,1,1]=>14
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,1,1]=>14
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,2]=>8
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,1,1]=>14
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,1,1]=>14
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,1,1]=>14
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,2]=>8
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,3,1]=>9
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,3,1]=>9
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,3,1]=>9
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,3,1]=>9
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4]=>3
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,1,1,1,1]=>18
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,1,1,2]=>12
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,1,2,1]=>13
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,1,2,1]=>13
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,1,3]=>7
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,1,1,1,1]=>18
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,1,1,2]=>12
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,1,1,1,1]=>18
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,1,1,1,1]=>18
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,1,1,2]=>12
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,1,2,1]=>13
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,1,2,1]=>13
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,1,2,1]=>13
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,1,3]=>7
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,1,1,1,1]=>18
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,1,1,2]=>12
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,1,1,1,1]=>18
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,1,1,1,1]=>18
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,1,1,2]=>12
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,1,1,1,1]=>18
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,1,1,1,1]=>18
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,1,1,1,1]=>18
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,1,1,2]=>12
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,1,2,1]=>13
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,1,2,1]=>13
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,1,2,1]=>13
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,1,2,1]=>13
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,1,3]=>7
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,2,1,1]=>14
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,2,2]=>8
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,2,1,1]=>14
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,2,1,1]=>14
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,2,2]=>8
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,2,1,1]=>14
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,2,1,1]=>14
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,2,1,1]=>14
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,2,2]=>8
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,2,1,1]=>14
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,2,1,1]=>14
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,2,1,1]=>14
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1]=>14
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,2,2]=>8
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,3,1]=>9
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,3,1]=>9
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,3,1]=>9
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,3,1]=>9
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,3,1]=>9
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4]=>3
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,1,1,1]=>15
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,1,2]=>9
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,2,1]=>10
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,2,1]=>10
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3]=>4
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,1,1,1]=>15
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,1,2]=>9
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,1,1,1]=>15
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,1,1,1]=>15
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,1,2]=>9
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,2,1]=>10
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,2,1]=>10
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,2,1]=>10
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3]=>4
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[4,1,1,1]=>15
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,1,2]=>9
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,1,1,1]=>15
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[4,1,1,1]=>15
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,1,2]=>9
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[4,1,1,1]=>15
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[4,1,1,1]=>15
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,1,1,1]=>15
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,1,2]=>9
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,2,1]=>10
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,2,1]=>10
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,2,1]=>10
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,2,1]=>10
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,3]=>4
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[4,1,1,1]=>15
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,1,2]=>9
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[4,1,1,1]=>15
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[4,1,1,1]=>15
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,1,2]=>9
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,1,1,1]=>15
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[4,1,1,1]=>15
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,1,1,1]=>15
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,1,2]=>9
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,1,1,1]=>15
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[4,1,1,1]=>15
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,1,1,1]=>15
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,1,1,1]=>15
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,1,2]=>9
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,2,1]=>10
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,2,1]=>10
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,2,1]=>10
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,1]=>10
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,2,1]=>10
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[4,3]=>4
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,1,1]=>11
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,2]=>5
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[5,1,1]=>11
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,1,1]=>11
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,2]=>5
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[5,1,1]=>11
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,1,1]=>11
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,1,1]=>11
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,2]=>5
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[5,1,1]=>11
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,1,1]=>11
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,1,1]=>11
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,1,1]=>11
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[5,2]=>5
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[5,1,1]=>11
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,1,1]=>11
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,1,1]=>11
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,1,1]=>11
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[5,1,1]=>11
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[5,2]=>5
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>6
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>6
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>6
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>6
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>6
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>6
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7]=>0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1]=>28
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,2]=>21
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,2,1]=>22
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,2,1]=>22
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,3]=>15
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,2,1,1]=>23
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,2,2]=>16
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,2,1,1]=>23
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,2,1,1]=>23
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,2,2]=>16
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,3,1]=>17
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,3,1]=>17
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,3,1]=>17
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,4]=>10
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,2,1,1,1]=>24
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,2,1,2]=>17
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,2,2,1]=>18
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,2,2,1]=>18
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,2,3]=>11
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,2,1,1,1]=>24
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,2,1,2]=>17
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,2,1,1,1]=>24
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,2,1,1,1]=>24
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,2,1,2]=>17
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,2,2,1]=>18
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,2,2,1]=>18
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,2,2,1]=>18
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,2,3]=>11
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,3,1,1]=>19
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,3,2]=>12
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,3,1,1]=>19
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,3,1,1]=>19
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,3,2]=>12
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,3,1,1]=>19
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,3,1,1]=>19
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,3,1,1]=>19
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,3,2]=>12
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,4,1]=>13
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,4,1]=>13
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,4,1]=>13
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,4,1]=>13
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,5]=>6
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,2,1,1,1,1]=>25
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,2,1,1,2]=>18
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,2,1,2,1]=>19
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,2,1,2,1]=>19
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,2,1,3]=>12
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,2,2,1,1]=>20
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,2,2,2]=>13
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,2,2,1,1]=>20
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,2,2,1,1]=>20
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,2,2,2]=>13
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,2,3,1]=>14
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,2,3,1]=>14
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,2,3,1]=>14
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,2,4]=>7
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,2,1,1,1,1]=>25
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,2,1,1,2]=>18
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,2,1,2,1]=>19
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,2,1,2,1]=>19
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,2,1,3]=>12
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,2,1,1,1,1]=>25
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,1,2]=>18
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,2,1,1,1,1]=>25
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,2,1,1,1,1]=>25
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,1,2]=>18
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,2,1,2,1]=>19
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,2,1,2,1]=>19
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,2,1,2,1]=>19
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,2,1,3]=>12
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,2,2,1,1]=>20
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,2,2,2]=>13
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,2,2,1,1]=>20
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,2,2,1,1]=>20
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,2,2,2]=>13
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,2,2,1,1]=>20
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,2,2,1,1]=>20
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,2,2,1,1]=>20
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,2,2,2]=>13
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,2,3,1]=>14
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,2,3,1]=>14
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,2,3,1]=>14
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,2,3,1]=>14
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,2,4]=>7
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,3,1,1,1]=>21
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,3,1,2]=>14
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,3,2,1]=>15
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,3,2,1]=>15
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,3,3]=>8
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,3,1,1,1]=>21
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,3,1,2]=>14
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,3,1,1,1]=>21
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,3,1,1,1]=>21
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,3,1,2]=>14
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,3,2,1]=>15
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,3,2,1]=>15
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,3,2,1]=>15
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,3,3]=>8
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,3,1,1,1]=>21
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,3,1,2]=>14
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,3,1,1,1]=>21
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,3,1,1,1]=>21
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,3,1,2]=>14
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,3,1,1,1]=>21
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,3,1,1,1]=>21
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,3,1,1,1]=>21
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,3,1,2]=>14
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,3,2,1]=>15
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,3,2,1]=>15
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,3,2,1]=>15
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,3,2,1]=>15
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,3,3]=>8
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,4,1,1]=>16
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,4,2]=>9
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,4,1,1]=>16
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,4,1,1]=>16
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,4,2]=>9
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,4,1,1]=>16
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,4,1,1]=>16
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,4,1,1]=>16
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,4,2]=>9
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,4,1,1]=>16
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,4,1,1]=>16
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,4,1,1]=>16
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,4,1,1]=>16
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,4,2]=>9
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,5,1]=>10
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,5,1]=>10
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,5,1]=>10
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,5,1]=>10
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,5,1]=>10
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,6]=>3
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1]=>26
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,1,2]=>19
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,1,1,2,1]=>20
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,1,1,2,1]=>20
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,1,1,3]=>13
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,1,2,1,1]=>21
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,1,2,2]=>14
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,1,2,1,1]=>21
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,1,2,1,1]=>21
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,1,2,2]=>14
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,1,3,1]=>15
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,1,3,1]=>15
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,1,3,1]=>15
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,1,4]=>8
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,2,1,1,1]=>22
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,2,1,2]=>15
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,2,2,1]=>16
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,2,1]=>16
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,2,3]=>9
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,2,1,1,1]=>22
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,2,1,2]=>15
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,2,1,1,1]=>22
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,2,1,1,1]=>22
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,2,1,2]=>15
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,2,2,1]=>16
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,2,2,1]=>16
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]=>16
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,2,3]=>9
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,3,1,1]=>17
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,3,2]=>10
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,3,1,1]=>17
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,3,1,1]=>17
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,3,2]=>10
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,3,1,1]=>17
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,3,1,1]=>17
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,3,1,1]=>17
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,3,2]=>10
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,4,1]=>11
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,4,1]=>11
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,4,1]=>11
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,4,1]=>11
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,5]=>4
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1]=>26
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,1,2]=>19
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,2,1,1,2,1]=>20
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,1,2,1]=>20
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,1,3]=>13
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,1,2,1,1]=>21
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,1,2,2]=>14
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,1,2,1,1]=>21
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,1,2,1,1]=>21
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,1,2,2]=>14
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,2,1,3,1]=>15
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,1,3,1]=>15
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,1,3,1]=>15
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,1,4]=>8
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1]=>26
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,2,1,1,1,2]=>19
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,2,1,1,2,1]=>20
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,1,2,1]=>20
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,1,3]=>13
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,2,1,1,1,1,1]=>26
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,2,1,1,1,2]=>19
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,2,1,1,1,1,1]=>26
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,1,1,1,1,1]=>26
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,1,1,1,2]=>19
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,2,1,1,2,1]=>20
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,2,1,1,2,1]=>20
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,1,2,1]=>20
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,1,3]=>13
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,2,1,2,1,1]=>21
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,1,2,2]=>14
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,2,1,2,1,1]=>21
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,2,1,2,1,1]=>21
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,1,2,2]=>14
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,2,1,2,1,1]=>21
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,2,1,2,1,1]=>21
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,1,2,1,1]=>21
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,1,2,2]=>14
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,2,1,3,1]=>15
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,1,3,1]=>15
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,1,3,1]=>15
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,1,3,1]=>15
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,1,4]=>8
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,2,2,1,1,1]=>22
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,2,2,1,2]=>15
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,2,2,2,1]=>16
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,2,2,2,1]=>16
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,2,3]=>9
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,2,2,1,1,1]=>22
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,2,2,1,2]=>15
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,2,2,1,1,1]=>22
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,2,2,1,1,1]=>22
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,2,2,1,2]=>15
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,2,2,2,1]=>16
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,2,2,2,1]=>16
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]=>16
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,2,2,3]=>9
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,2,2,1,1,1]=>22
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,2,2,1,2]=>15
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,2,2,1,1,1]=>22
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,2,2,1,1,1]=>22
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,2,2,1,2]=>15
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,2,2,1,1,1]=>22
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,2,2,1,1,1]=>22
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,2,2,1,1,1]=>22
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,2,2,1,2]=>15
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,2,2,2,1]=>16
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,2,2,2,1]=>16
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,2,2,2,1]=>16
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,2,2,2,1]=>16
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,2,3]=>9
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,2,3,1,1]=>17
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,2,3,2]=>10
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,2,3,1,1]=>17
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,2,3,1,1]=>17
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,2,3,2]=>10
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,2,3,1,1]=>17
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,2,3,1,1]=>17
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,2,3,1,1]=>17
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,2,3,2]=>10
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,2,3,1,1]=>17
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,2,3,1,1]=>17
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,2,3,1,1]=>17
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,2,3,1,1]=>17
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,2,3,2]=>10
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,2,4,1]=>11
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,2,4,1]=>11
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,4,1]=>11
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,2,4,1]=>11
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,4,1]=>11
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,5]=>4
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,3,1,1,1,1]=>23
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,3,1,1,2]=>16
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,3,1,2,1]=>17
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,3,1,2,1]=>17
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,3,1,3]=>10
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,1,1]=>18
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,2]=>11
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,1,1]=>18
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,1,1]=>18
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,2]=>11
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,3,3,1]=>12
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,3,3,1]=>12
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,3,3,1]=>12
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,3,4]=>5
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,3,1,1,1,1]=>23
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,3,1,1,2]=>16
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,3,1,2,1]=>17
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,3,1,2,1]=>17
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,3,1,3]=>10
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,3,1,1,1,1]=>23
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,3,1,1,2]=>16
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,3,1,1,1,1]=>23
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,3,1,1,1,1]=>23
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,3,1,1,2]=>16
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,3,1,2,1]=>17
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,3,1,2,1]=>17
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,3,1,2,1]=>17
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,3,1,3]=>10
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,3,2,1,1]=>18
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,3,2,2]=>11
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,3,2,1,1]=>18
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,3,2,1,1]=>18
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,3,2,2]=>11
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,3,2,1,1]=>18
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,3,2,1,1]=>18
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,3,2,1,1]=>18
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,3,2,2]=>11
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,3,3,1]=>12
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,3,3,1]=>12
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,3,3,1]=>12
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,3,3,1]=>12
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,3,4]=>5
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,3,1,1,1,1]=>23
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,3,1,1,2]=>16
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,3,1,2,1]=>17
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,3,1,2,1]=>17
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,3,1,3]=>10
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,3,1,1,1,1]=>23
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,3,1,1,2]=>16
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,3,1,1,1,1]=>23
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,3,1,1,1,1]=>23
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,3,1,1,2]=>16
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,3,1,2,1]=>17
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,3,1,2,1]=>17
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,3,1,2,1]=>17
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,3,1,3]=>10
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,3,1,1,1,1]=>23
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,3,1,1,2]=>16
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,3,1,1,1,1]=>23
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,3,1,1,1,1]=>23
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,3,1,1,2]=>16
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,3,1,1,1,1]=>23
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,3,1,1,1,1]=>23
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,3,1,1,1,1]=>23
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,3,1,1,2]=>16
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,3,1,2,1]=>17
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,3,1,2,1]=>17
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,3,1,2,1]=>17
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,3,1,2,1]=>17
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,3,1,3]=>10
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,3,2,1,1]=>18
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,2]=>11
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,3,2,1,1]=>18
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,3,2,1,1]=>18
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,3,2,2]=>11
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,3,2,1,1]=>18
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,3,2,1,1]=>18
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,3,2,1,1]=>18
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,3,2,2]=>11
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,3,2,1,1]=>18
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,3,2,1,1]=>18
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,3,2,1,1]=>18
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,3,2,1,1]=>18
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,3,2,2]=>11
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,3,3,1]=>12
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,3,3,1]=>12
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,3,3,1]=>12
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,3,3,1]=>12
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,3,3,1]=>12
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,3,4]=>5
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,4,1,1,1]=>19
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,4,1,2]=>12
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,4,2,1]=>13
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,4,2,1]=>13
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,4,3]=>6
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,4,1,1,1]=>19
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,4,1,2]=>12
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,4,1,1,1]=>19
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,4,1,1,1]=>19
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,4,1,2]=>12
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,4,2,1]=>13
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,4,2,1]=>13
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,4,2,1]=>13
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,4,3]=>6
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,4,1,1,1]=>19
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,4,1,2]=>12
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,4,1,1,1]=>19
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,4,1,1,1]=>19
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,4,1,2]=>12
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,4,1,1,1]=>19
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,4,1,1,1]=>19
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,4,1,1,1]=>19
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,4,1,2]=>12
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,4,2,1]=>13
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,4,2,1]=>13
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,4,2,1]=>13
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,4,2,1]=>13
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,4,3]=>6
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,4,1,1,1]=>19
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,4,1,2]=>12
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,4,1,1,1]=>19
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,4,1,1,1]=>19
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,4,1,2]=>12
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,4,1,1,1]=>19
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,4,1,1,1]=>19
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,4,1,1,1]=>19
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,4,1,2]=>12
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,4,1,1,1]=>19
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,4,1,1,1]=>19
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,4,1,1,1]=>19
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,4,1,1,1]=>19
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,4,1,2]=>12
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,4,2,1]=>13
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,4,2,1]=>13
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,4,2,1]=>13
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,4,2,1]=>13
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,4,2,1]=>13
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,4,3]=>6
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,5,1,1]=>14
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,5,2]=>7
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,5,1,1]=>14
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,5,1,1]=>14
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,5,2]=>7
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,5,1,1]=>14
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,5,1,1]=>14
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,5,1,1]=>14
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,5,2]=>7
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,5,1,1]=>14
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,5,1,1]=>14
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,5,1,1]=>14
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,5,1,1]=>14
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,5,2]=>7
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,5,1,1]=>14
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,5,1,1]=>14
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,5,1,1]=>14
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,5,1,1]=>14
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,5,1,1]=>14
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,5,2]=>7
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,6,1]=>8
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,6,1]=>8
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,6,1]=>8
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,6,1]=>8
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,6,1]=>8
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,6,1]=>8
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,7]=>1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1]=>27
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,2]=>20
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,1,1,2,1]=>21
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,1,2,1]=>21
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,1,3]=>14
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,1,2,1,1]=>22
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,1,2,2]=>15
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,1,2,1,1]=>22
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,1,2,1,1]=>22
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,1,2,2]=>15
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,1,3,1]=>16
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,1,3,1]=>16
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,1,3,1]=>16
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,1,4]=>9
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,2,1,1,1]=>23
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,2,1,2]=>16
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,2,2,1]=>17
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,2,2,1]=>17
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,2,3]=>10
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,2,1,1,1]=>23
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,2,1,2]=>16
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,2,1,1,1]=>23
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,2,1,1,1]=>23
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,2,1,2]=>16
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,2,2,1]=>17
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,2,2,1]=>17
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,2,2,1]=>17
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,2,3]=>10
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,3,1,1]=>18
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,2]=>11
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,3,1,1]=>18
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,3,1,1]=>18
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,3,2]=>11
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,3,1,1]=>18
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,3,1,1]=>18
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,3,1,1]=>18
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,3,2]=>11
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,1]=>12
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,4,1]=>12
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,4,1]=>12
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,4,1]=>12
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,5]=>5
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,2,1,1,1,1]=>24
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,2,1,1,2]=>17
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[2,2,1,2,1]=>18
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,2,1,2,1]=>18
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,2,1,3]=>11
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,2,2,1,1]=>19
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]=>12
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[2,2,2,1,1]=>19
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,2,2,1,1]=>19
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2]=>12
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,2,3,1]=>13
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,2,3,1]=>13
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,2,3,1]=>13
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,2,4]=>6
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,2,1,1,1,1]=>24
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,2,1,1,2]=>17
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[2,2,1,2,1]=>18
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[2,2,1,2,1]=>18
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,2,1,3]=>11
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[2,2,1,1,1,1]=>24
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,2,1,1,2]=>17
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,2,1,1,1,1]=>24
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1,1]=>24
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,2,1,1,2]=>17
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[2,2,1,2,1]=>18
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[2,2,1,2,1]=>18
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,2,1,2,1]=>18
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,2,1,3]=>11
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,2,2,1,1]=>19
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2]=>12
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[2,2,2,1,1]=>19
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,2,2,1,1]=>19
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,2,2,2]=>12
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[2,2,2,1,1]=>19
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,2,2,1,1]=>19
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,2,2,1,1]=>19
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2]=>12
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[2,2,3,1]=>13
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,2,3,1]=>13
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,2,3,1]=>13
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,2,3,1]=>13
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,4]=>6
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,1,1,1]=>20
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,3,1,2]=>13
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,2,1]=>14
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,3,2,1]=>14
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,3]=>7
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[2,3,1,1,1]=>20
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,3,1,2]=>13
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[2,3,1,1,1]=>20
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,1,1,1]=>20
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,3,1,2]=>13
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[2,3,2,1]=>14
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,2,1]=>14
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,2,1]=>14
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,3]=>7
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,3,1,1,1]=>20
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,3,1,2]=>13
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[2,3,1,1,1]=>20
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,3,1,1,1]=>20
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[2,3,1,2]=>13
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[2,3,1,1,1]=>20
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,3,1,1,1]=>20
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,1,1,1]=>20
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[2,3,1,2]=>13
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[2,3,2,1]=>14
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,3,2,1]=>14
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,3,2,1]=>14
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,2,1]=>14
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,3]=>7
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,4,1,1]=>15
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,4,2]=>8
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[2,4,1,1]=>15
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,4,1,1]=>15
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,4,2]=>8
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[2,4,1,1]=>15
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,4,1,1]=>15
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,4,1,1]=>15
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,4,2]=>8
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[2,4,1,1]=>15
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,4,1,1]=>15
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,4,1,1]=>15
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,4,1,1]=>15
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,4,2]=>8
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,5,1]=>9
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,5,1]=>9
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,5,1]=>9
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,5,1]=>9
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,5,1]=>9
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,6]=>2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1]=>27
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,2]=>20
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,1,1,2,1]=>21
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,1,2,1]=>21
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,1,3]=>14
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,1,2,1,1]=>22
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,1,2,2]=>15
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,1,2,1,1]=>22
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,1,2,1,1]=>22
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,1,2,2]=>15
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,1,3,1]=>16
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,1,3,1]=>16
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,1,3,1]=>16
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,1,4]=>9
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,2,1,1,1]=>23
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,2,1,2]=>16
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,2,2,1]=>17
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,2,2,1]=>17
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,2,3]=>10
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,2,1,1,1]=>23
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,2,1,2]=>16
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,2,1,1,1]=>23
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,2,1,1,1]=>23
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,2,1,2]=>16
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,2,2,1]=>17
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,2,2,1]=>17
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,2,2,1]=>17
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,2,3]=>10
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,3,1,1]=>18
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,2]=>11
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,3,1,1]=>18
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,3,1,1]=>18
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,3,2]=>11
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,3,1,1]=>18
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,3,1,1]=>18
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,3,1,1]=>18
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,3,2]=>11
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,1]=>12
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,4,1]=>12
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,4,1]=>12
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,4,1]=>12
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,5]=>5
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1]=>27
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,2]=>20
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,1,1,2,1]=>21
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,1,1,2,1]=>21
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,1,1,3]=>14
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,1,2,1,1]=>22
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,1,2,2]=>15
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,1,2,1,1]=>22
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,1,2,1,1]=>22
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,1,2,2]=>15
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,1,3,1]=>16
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,1,3,1]=>16
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,1,3,1]=>16
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,1,4]=>9
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1]=>27
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,1,1,1,1,2]=>20
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,1,1,2,1]=>21
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,1,1,2,1]=>21
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,1,1,3]=>14
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,1,1,1,1,1,1]=>27
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,1,1,1,2]=>20
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,1,1,1,1,1]=>27
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,1,1,1,1,1]=>27
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,1,1,1,2]=>20
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,1,1,2,1]=>21
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,1,1,1,2,1]=>21
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,1,1,2,1]=>21
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,1,1,3]=>14
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,1,2,1,1]=>22
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,1,2,2]=>15
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,1,1,2,1,1]=>22
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,1,1,2,1,1]=>22
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,1,1,2,2]=>15
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,1,1,2,1,1]=>22
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,1,1,2,1,1]=>22
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,1,1,2,1,1]=>22
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,1,2,2]=>15
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,1,3,1]=>16
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,1,1,3,1]=>16
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,1,1,3,1]=>16
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,1,3,1]=>16
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,1,4]=>9
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,2,1,1,1]=>23
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,1,2,1,2]=>16
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,1,2,2,1]=>17
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,1,2,2,1]=>17
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,2,3]=>10
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,1,2,1,1,1]=>23
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,2,1,2]=>16
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,1,2,1,1,1]=>23
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,1,2,1,1,1]=>23
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,1,2,1,2]=>16
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,1,2,2,1]=>17
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,2,2,1]=>17
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,1,2,2,1]=>17
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,1,2,3]=>10
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,1,2,1,1,1]=>23
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,1,2,1,2]=>16
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,1,2,1,1,1]=>23
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,1,2,1,1,1]=>23
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,1,2,1,2]=>16
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,1,2,1,1,1]=>23
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,1,2,1,1,1]=>23
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,1,2,1,1,1]=>23
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,1,2,1,2]=>16
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,1,2,2,1]=>17
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,1,2,2,1]=>17
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,1,2,2,1]=>17
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,1,2,2,1]=>17
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,1,2,3]=>10
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,1,3,1,1]=>18
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,3,2]=>11
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,1,3,1,1]=>18
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,1,3,1,1]=>18
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,1,3,2]=>11
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,1,3,1,1]=>18
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,3,1,1]=>18
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,1,3,1,1]=>18
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,1,3,2]=>11
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,1,3,1,1]=>18
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,1,3,1,1]=>18
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,1,3,1,1]=>18
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,1,3,1,1]=>18
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,1,3,2]=>11
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,4,1]=>12
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,1,4,1]=>12
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,1,4,1]=>12
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,1,4,1]=>12
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,4,1]=>12
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,5]=>5
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,2,1,1,1,1]=>24
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[2,2,1,1,2]=>17
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[2,2,1,2,1]=>18
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[2,2,1,2,1]=>18
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[2,2,1,3]=>11
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,2,2,1,1]=>19
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]=>12
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[2,2,2,1,1]=>19
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[2,2,2,1,1]=>19
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2]=>12
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,2,3,1]=>13
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,2,3,1]=>13
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[2,2,3,1]=>13
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,2,4]=>6
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[2,2,1,1,1,1]=>24
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[2,2,1,1,2]=>17
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,2,1,2,1]=>18
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[2,2,1,2,1]=>18
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[2,2,1,3]=>11
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[2,2,1,1,1,1]=>24
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[2,2,1,1,2]=>17
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[2,2,1,1,1,1]=>24
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1,1]=>24
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[2,2,1,1,2]=>17
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[2,2,1,2,1]=>18
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[2,2,1,2,1]=>18
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[2,2,1,2,1]=>18
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[2,2,1,3]=>11
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[2,2,2,1,1]=>19
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2]=>12
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[2,2,2,1,1]=>19
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[2,2,2,1,1]=>19
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,2,2,2]=>12
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[2,2,2,1,1]=>19
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[2,2,2,1,1]=>19
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[2,2,2,1,1]=>19
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2]=>12
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[2,2,3,1]=>13
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[2,2,3,1]=>13
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[2,2,3,1]=>13
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[2,2,3,1]=>13
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,4]=>6
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[2,2,1,1,1,1]=>24
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[2,2,1,1,2]=>17
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[2,2,1,2,1]=>18
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[2,2,1,2,1]=>18
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[2,2,1,3]=>11
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[2,2,1,1,1,1]=>24
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[2,2,1,1,2]=>17
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[2,2,1,1,1,1]=>24
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[2,2,1,1,1,1]=>24
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[2,2,1,1,2]=>17
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[2,2,1,2,1]=>18
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[2,2,1,2,1]=>18
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[2,2,1,2,1]=>18
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[2,2,1,3]=>11
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[2,2,1,1,1,1]=>24
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[2,2,1,1,2]=>17
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[2,2,1,1,1,1]=>24
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[2,2,1,1,1,1]=>24
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[2,2,1,1,2]=>17
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[2,2,1,1,1,1]=>24
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[2,2,1,1,1,1]=>24
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,2,1,1,1,1]=>24
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[2,2,1,1,2]=>17
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[2,2,1,2,1]=>18
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[2,2,1,2,1]=>18
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[2,2,1,2,1]=>18
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[2,2,1,2,1]=>18
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[2,2,1,3]=>11
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[2,2,2,1,1]=>19
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[2,2,2,2]=>12
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[2,2,2,1,1]=>19
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[2,2,2,1,1]=>19
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[2,2,2,2]=>12
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[2,2,2,1,1]=>19
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[2,2,2,1,1]=>19
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[2,2,2,1,1]=>19
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[2,2,2,2]=>12
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[2,2,2,1,1]=>19
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[2,2,2,1,1]=>19
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[2,2,2,1,1]=>19
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[2,2,2,1,1]=>19
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,2,2]=>12
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[2,2,3,1]=>13
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[2,2,3,1]=>13
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[2,2,3,1]=>13
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[2,2,3,1]=>13
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,2,3,1]=>13
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,4]=>6
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,3,1,1,1]=>20
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[2,3,1,2]=>13
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,3,2,1]=>14
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[2,3,2,1]=>14
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,3,3]=>7
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[2,3,1,1,1]=>20
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[2,3,1,2]=>13
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[2,3,1,1,1]=>20
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[2,3,1,1,1]=>20
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[2,3,1,2]=>13
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[2,3,2,1]=>14
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[2,3,2,1]=>14
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[2,3,2,1]=>14
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[2,3,3]=>7
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[2,3,1,1,1]=>20
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[2,3,1,2]=>13
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[2,3,1,1,1]=>20
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[2,3,1,1,1]=>20
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[2,3,1,2]=>13
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[2,3,1,1,1]=>20
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[2,3,1,1,1]=>20
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,3,1,1,1]=>20
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[2,3,1,2]=>13
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[2,3,2,1]=>14
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[2,3,2,1]=>14
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[2,3,2,1]=>14
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[2,3,2,1]=>14
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,3,3]=>7
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[2,3,1,1,1]=>20
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[2,3,1,2]=>13
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[2,3,1,1,1]=>20
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[2,3,1,1,1]=>20
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[2,3,1,2]=>13
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[2,3,1,1,1]=>20
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[2,3,1,1,1]=>20
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[2,3,1,1,1]=>20
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[2,3,1,2]=>13
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[2,3,1,1,1]=>20
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[2,3,1,1,1]=>20
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[2,3,1,1,1]=>20
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,3,1,1,1]=>20
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,3,1,2]=>13
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[2,3,2,1]=>14
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[2,3,2,1]=>14
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[2,3,2,1]=>14
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[2,3,2,1]=>14
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,3,2,1]=>14
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,3,3]=>7
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,4,1,1]=>15
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,4,2]=>8
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[2,4,1,1]=>15
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[2,4,1,1]=>15
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[2,4,2]=>8
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[2,4,1,1]=>15
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[2,4,1,1]=>15
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[2,4,1,1]=>15
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[2,4,2]=>8
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[2,4,1,1]=>15
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[2,4,1,1]=>15
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[2,4,1,1]=>15
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[2,4,1,1]=>15
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,4,2]=>8
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[2,4,1,1]=>15
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[2,4,1,1]=>15
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[2,4,1,1]=>15
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[2,4,1,1]=>15
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,4,1,1]=>15
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,4,2]=>8
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,5,1]=>9
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[2,5,1]=>9
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[2,5,1]=>9
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[2,5,1]=>9
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,5,1]=>9
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,5,1]=>9
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,6]=>2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1]=>25
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,1,1,1,2]=>18
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,1,2,1]=>19
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,1,1,2,1]=>19
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,1,1,3]=>12
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[3,1,2,1,1]=>20
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[3,1,2,2]=>13
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,2,1,1]=>20
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[3,1,2,1,1]=>20
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,1,2,2]=>13
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,1,3,1]=>14
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,1,3,1]=>14
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,1,3,1]=>14
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,1,4]=>7
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[3,2,1,1,1]=>21
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[3,2,1,2]=>14
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,2,2,1]=>15
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,2,2,1]=>15
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,2,3]=>8
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[3,2,1,1,1]=>21
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[3,2,1,2]=>14
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[3,2,1,1,1]=>21
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,2,1,1,1]=>21
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,2,1,2]=>14
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,2,2,1]=>15
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,2,2,1]=>15
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,2,2,1]=>15
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,2,3]=>8
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[3,3,1,1]=>16
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,3,2]=>9
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,3,1,1]=>16
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,3,1,1]=>16
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,3,2]=>9
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[3,3,1,1]=>16
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,3,1,1]=>16
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,3,1,1]=>16
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,3,2]=>9
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,4,1]=>10
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,4,1]=>10
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,4,1]=>10
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,4,1]=>10
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,5]=>3
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1]=>25
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,1,1,1,2]=>18
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,1,2,1]=>19
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,1,1,2,1]=>19
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,1,1,3]=>12
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,2,1,1]=>20
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,2,2]=>13
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,2,1,1]=>20
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,1,2,1,1]=>20
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,1,2,2]=>13
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,3,1]=>14
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,1,3,1]=>14
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,1,3,1]=>14
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,4]=>7
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,1,1,1,1]=>25
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[3,1,1,1,2]=>18
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,1,2,1]=>19
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[3,1,1,2,1]=>19
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,1,1,3]=>12
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,1,1,1,1]=>25
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[3,1,1,1,2]=>18
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,1,1,1,1]=>25
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,1,1,1,1,1]=>25
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,1,1,1,2]=>18
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[3,1,1,2,1]=>19
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[3,1,1,2,1]=>19
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[3,1,1,2,1]=>19
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[3,1,1,3]=>12
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,2,1,1]=>20
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[3,1,2,2]=>13
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,2,1,1]=>20
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[3,1,2,1,1]=>20
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[3,1,2,2]=>13
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,1,1]=>20
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[3,1,2,1,1]=>20
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[3,1,2,1,1]=>20
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[3,1,2,2]=>13
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,3,1]=>14
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[3,1,3,1]=>14
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[3,1,3,1]=>14
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[3,1,3,1]=>14
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,1,4]=>7
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,1,1,1]=>21
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,1,2]=>14
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,2,1]=>15
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,2,1]=>15
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,3]=>8
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[3,2,1,1,1]=>21
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,1,2]=>14
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[3,2,1,1,1]=>21
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,1,1,1]=>21
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,1,2]=>14
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,2,1]=>15
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,2,1]=>15
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,2,1]=>15
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,3]=>8
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[3,2,1,1,1]=>21
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,2,1,2]=>14
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[3,2,1,1,1]=>21
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[3,2,1,1,1]=>21
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[3,2,1,2]=>14
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[3,2,1,1,1]=>21
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[3,2,1,1,1]=>21
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[3,2,1,1,1]=>21
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[3,2,1,2]=>14
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,2,2,1]=>15
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[3,2,2,1]=>15
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[3,2,2,1]=>15
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1]=>15
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,2,3]=>8
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[3,3,1,1]=>16
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,3,2]=>9
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[3,3,1,1]=>16
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[3,3,1,1]=>16
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[3,3,2]=>9
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[3,3,1,1]=>16
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,3,1,1]=>16
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[3,3,1,1]=>16
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,2]=>9
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,3,1,1]=>16
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[3,3,1,1]=>16
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[3,3,1,1]=>16
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[3,3,1,1]=>16
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>9
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,4,1]=>10
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[3,4,1]=>10
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[3,4,1]=>10
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,4,1]=>10
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,4,1]=>10
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,5]=>3
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1]=>25
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,1,1,1,2]=>18
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,1,1,2,1]=>19
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,1,1,2,1]=>19
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,1,1,3]=>12
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,1,2,1,1]=>20
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,1,2,2]=>13
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,1,2,1,1]=>20
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,1,2,1,1]=>20
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,1,2,2]=>13
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,1,3,1]=>14
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,1,3,1]=>14
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,1,3,1]=>14
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,1,4]=>7
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,1,1,1,1,1]=>25
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,1,1,1,2]=>18
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,1,1,2,1]=>19
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,1,1,2,1]=>19
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,1,1,3]=>12
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,1,1,1,1,1]=>25
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,1,1,1,2]=>18
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,1,1,1,1,1]=>25
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,1,1,1,1,1]=>25
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,1,1,1,2]=>18
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,1,1,2,1]=>19
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,1,1,2,1]=>19
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,1,1,2,1]=>19
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,1,1,3]=>12
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,1,2,1,1]=>20
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,1,2,2]=>13
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,1,2,1,1]=>20
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,1,2,1,1]=>20
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,1,2,2]=>13
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,1,1]=>20
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,1,2,1,1]=>20
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,1,2,1,1]=>20
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,1,2,2]=>13
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,1,3,1]=>14
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,1,3,1]=>14
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,1,3,1]=>14
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,1,3,1]=>14
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,1,4]=>7
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,1,1,1,1,1]=>25
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,1,1,1,2]=>18
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,1,1,2,1]=>19
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,1,1,2,1]=>19
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,1,1,3]=>12
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,1,1,1,1,1]=>25
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,1,1,1,2]=>18
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,1,1,1,1,1]=>25
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,1,1,1,1,1]=>25
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,1,1,1,2]=>18
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,1,1,2,1]=>19
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,1,1,2,1]=>19
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,1,1,2,1]=>19
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,1,1,3]=>12
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,1,1,1,1,1]=>25
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,1,1,1,2]=>18
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,1,1,1,1,1]=>25
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,1,1,1,1,1]=>25
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,1,1,1,2]=>18
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,1,1,1,1,1]=>25
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,1,1,1,1,1]=>25
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,1,1,1,1,1]=>25
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,1,1,1,2]=>18
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,1,1,2,1]=>19
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,1,1,2,1]=>19
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,1,1,2,1]=>19
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,1,1,2,1]=>19
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,1,1,3]=>12
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,1,2,1,1]=>20
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,1,2,2]=>13
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,1,2,1,1]=>20
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,1,2,1,1]=>20
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,1,2,2]=>13
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,1,2,1,1]=>20
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,1,2,1,1]=>20
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,1,2,1,1]=>20
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,1,2,2]=>13
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,1,2,1,1]=>20
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,1,2,1,1]=>20
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,1,2,1,1]=>20
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,1,2,1,1]=>20
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,1,2,2]=>13
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,1,3,1]=>14
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,1,3,1]=>14
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,1,3,1]=>14
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,1,3,1]=>14
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,1,3,1]=>14
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,1,4]=>7
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[3,2,1,1,1]=>21
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[3,2,1,2]=>14
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[3,2,2,1]=>15
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[3,2,2,1]=>15
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[3,2,3]=>8
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[3,2,1,1,1]=>21
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[3,2,1,2]=>14
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[3,2,1,1,1]=>21
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[3,2,1,1,1]=>21
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[3,2,1,2]=>14
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[3,2,2,1]=>15
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[3,2,2,1]=>15
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[3,2,2,1]=>15
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,2,3]=>8
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[3,2,1,1,1]=>21
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[3,2,1,2]=>14
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[3,2,1,1,1]=>21
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[3,2,1,1,1]=>21
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[3,2,1,2]=>14
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[3,2,1,1,1]=>21
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[3,2,1,1,1]=>21
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[3,2,1,1,1]=>21
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[3,2,1,2]=>14
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[3,2,2,1]=>15
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[3,2,2,1]=>15
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[3,2,2,1]=>15
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[3,2,2,1]=>15
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,2,3]=>8
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[3,2,1,1,1]=>21
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[3,2,1,2]=>14
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[3,2,1,1,1]=>21
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[3,2,1,1,1]=>21
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[3,2,1,2]=>14
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[3,2,1,1,1]=>21
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[3,2,1,1,1]=>21
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[3,2,1,1,1]=>21
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[3,2,1,2]=>14
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[3,2,1,1,1]=>21
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[3,2,1,1,1]=>21
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[3,2,1,1,1]=>21
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,2,1,1,1]=>21
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,2,1,2]=>14
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[3,2,2,1]=>15
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[3,2,2,1]=>15
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[3,2,2,1]=>15
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,2,2,1]=>15
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1]=>15
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,2,3]=>8
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[3,3,1,1]=>16
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[3,3,2]=>9
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[3,3,1,1]=>16
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[3,3,1,1]=>16
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[3,3,2]=>9
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[3,3,1,1]=>16
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[3,3,1,1]=>16
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[3,3,1,1]=>16
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3,2]=>9
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[3,3,1,1]=>16
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[3,3,1,1]=>16
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[3,3,1,1]=>16
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,3,1,1]=>16
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,2]=>9
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[3,3,1,1]=>16
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[3,3,1,1]=>16
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[3,3,1,1]=>16
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,3,1,1]=>16
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,3,1,1]=>16
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,3,2]=>9
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,4,1]=>10
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[3,4,1]=>10
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[3,4,1]=>10
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[3,4,1]=>10
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,4,1]=>10
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,4,1]=>10
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,5]=>3
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,1,1,1]=>22
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[4,1,1,2]=>15
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[4,1,2,1]=>16
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[4,1,2,1]=>16
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[4,1,3]=>9
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[4,2,1,1]=>17
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,2,2]=>10
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[4,2,1,1]=>17
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[4,2,1,1]=>17
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[4,2,2]=>10
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[4,3,1]=>11
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[4,3,1]=>11
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[4,3,1]=>11
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4]=>4
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[4,1,1,1,1]=>22
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[4,1,1,2]=>15
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[4,1,2,1]=>16
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[4,1,2,1]=>16
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[4,1,3]=>9
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[4,1,1,1,1]=>22
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[4,1,1,2]=>15
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[4,1,1,1,1]=>22
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[4,1,1,1,1]=>22
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[4,1,1,2]=>15
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[4,1,2,1]=>16
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[4,1,2,1]=>16
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[4,1,2,1]=>16
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,1,3]=>9
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[4,2,1,1]=>17
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[4,2,2]=>10
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[4,2,1,1]=>17
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[4,2,1,1]=>17
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[4,2,2]=>10
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[4,2,1,1]=>17
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[4,2,1,1]=>17
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[4,2,1,1]=>17
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,2,2]=>10
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[4,3,1]=>11
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[4,3,1]=>11
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[4,3,1]=>11
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,1]=>11
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,4]=>4
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[4,1,1,1,1]=>22
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[4,1,1,2]=>15
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[4,1,2,1]=>16
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[4,1,2,1]=>16
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[4,1,3]=>9
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[4,1,1,1,1]=>22
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[4,1,1,2]=>15
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[4,1,1,1,1]=>22
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[4,1,1,1,1]=>22
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[4,1,1,2]=>15
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[4,1,2,1]=>16
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[4,1,2,1]=>16
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[4,1,2,1]=>16
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[4,1,3]=>9
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[4,1,1,1,1]=>22
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[4,1,1,2]=>15
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[4,1,1,1,1]=>22
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[4,1,1,1,1]=>22
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[4,1,1,2]=>15
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[4,1,1,1,1]=>22
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[4,1,1,1,1]=>22
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[4,1,1,1,1]=>22
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[4,1,1,2]=>15
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,1]=>16
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[4,1,2,1]=>16
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[4,1,2,1]=>16
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[4,1,2,1]=>16
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[4,1,3]=>9
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[4,2,1,1]=>17
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[4,2,2]=>10
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[4,2,1,1]=>17
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[4,2,1,1]=>17
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[4,2,2]=>10
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[4,2,1,1]=>17
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[4,2,1,1]=>17
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[4,2,1,1]=>17
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,2,2]=>10
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[4,2,1,1]=>17
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[4,2,1,1]=>17
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,1]=>17
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[4,2,1,1]=>17
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[4,2,2]=>10
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[4,3,1]=>11
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[4,3,1]=>11
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[4,3,1]=>11
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,3,1]=>11
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[4,3,1]=>11
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[4,4]=>4
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[4,1,1,1,1]=>22
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[4,1,1,2]=>15
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[4,1,2,1]=>16
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[4,1,2,1]=>16
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[4,1,3]=>9
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[4,1,1,1,1]=>22
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[4,1,1,2]=>15
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[4,1,1,1,1]=>22
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[4,1,1,1,1]=>22
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[4,1,1,2]=>15
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[4,1,2,1]=>16
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[4,1,2,1]=>16
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[4,1,2,1]=>16
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,1,3]=>9
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[4,1,1,1,1]=>22
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[4,1,1,2]=>15
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[4,1,1,1,1]=>22
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[4,1,1,1,1]=>22
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[4,1,1,2]=>15
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[4,1,1,1,1]=>22
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[4,1,1,1,1]=>22
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[4,1,1,1,1]=>22
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[4,1,1,2]=>15
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[4,1,2,1]=>16
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[4,1,2,1]=>16
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[4,1,2,1]=>16
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[4,1,2,1]=>16
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[4,1,3]=>9
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[4,1,1,1,1]=>22
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[4,1,1,2]=>15
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[4,1,1,1,1]=>22
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[4,1,1,1,1]=>22
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[4,1,1,2]=>15
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[4,1,1,1,1]=>22
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[4,1,1,1,1]=>22
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[4,1,1,1,1]=>22
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[4,1,1,2]=>15
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[4,1,1,1,1]=>22
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[4,1,1,1,1]=>22
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[4,1,1,1,1]=>22
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,1,1,1,1]=>22
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,1,1,2]=>15
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[4,1,2,1]=>16
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[4,1,2,1]=>16
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[4,1,2,1]=>16
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[4,1,2,1]=>16
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[4,1,2,1]=>16
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[4,1,3]=>9
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[4,2,1,1]=>17
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[4,2,2]=>10
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[4,2,1,1]=>17
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[4,2,1,1]=>17
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[4,2,2]=>10
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[4,2,1,1]=>17
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[4,2,1,1]=>17
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[4,2,1,1]=>17
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,2,2]=>10
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[4,2,1,1]=>17
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[4,2,1,1]=>17
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[4,2,1,1]=>17
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[4,2,1,1]=>17
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[4,2,2]=>10
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[4,2,1,1]=>17
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[4,2,1,1]=>17
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[4,2,1,1]=>17
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1]=>17
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[4,2,1,1]=>17
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[4,2,2]=>10
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[4,3,1]=>11
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[4,3,1]=>11
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[4,3,1]=>11
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,3,1]=>11
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[4,3,1]=>11
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[4,3,1]=>11
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[4,4]=>4
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[5,1,1,1]=>18
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[5,1,2]=>11
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[5,2,1]=>12
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[5,2,1]=>12
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,3]=>5
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[5,1,1,1]=>18
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[5,1,2]=>11
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[5,1,1,1]=>18
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[5,1,1,1]=>18
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,1,2]=>11
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[5,2,1]=>12
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[5,2,1]=>12
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,2,1]=>12
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,3]=>5
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[5,1,1,1]=>18
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[5,1,2]=>11
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[5,1,1,1]=>18
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[5,1,1,1]=>18
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[5,1,2]=>11
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[5,1,1,1]=>18
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[5,1,1,1]=>18
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[5,1,1,1]=>18
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[5,1,2]=>11
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[5,2,1]=>12
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[5,2,1]=>12
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,2,1]=>12
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[5,2,1]=>12
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[5,3]=>5
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[5,1,1,1]=>18
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[5,1,2]=>11
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[5,1,1,1]=>18
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[5,1,1,1]=>18
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,1,2]=>11
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[5,1,1,1]=>18
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,1,1,1]=>18
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[5,1,1,1]=>18
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[5,1,2]=>11
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[5,1,1,1]=>18
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[5,1,1,1]=>18
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[5,1,1,1]=>18
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[5,1,1,1]=>18
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[5,1,2]=>11
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[5,2,1]=>12
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[5,2,1]=>12
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,1]=>12
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[5,2,1]=>12
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[5,2,1]=>12
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[5,3]=>5
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[5,1,1,1]=>18
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[5,1,2]=>11
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[5,1,1,1]=>18
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[5,1,1,1]=>18
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[5,1,2]=>11
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[5,1,1,1]=>18
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[5,1,1,1]=>18
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[5,1,1,1]=>18
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[5,1,2]=>11
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[5,1,1,1]=>18
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[5,1,1,1]=>18
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[5,1,1,1]=>18
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[5,1,1,1]=>18
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[5,1,2]=>11
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[5,1,1,1]=>18
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[5,1,1,1]=>18
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[5,1,1,1]=>18
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[5,1,1,1]=>18
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,1,1,1]=>18
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[5,1,2]=>11
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[5,2,1]=>12
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[5,2,1]=>12
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,2,1]=>12
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[5,2,1]=>12
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[5,2,1]=>12
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[5,2,1]=>12
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[5,3]=>5
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[6,1,1]=>13
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,2]=>6
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[6,1,1]=>13
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,1,1]=>13
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[6,2]=>6
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[6,1,1]=>13
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,1,1]=>13
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[6,1,1]=>13
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[6,2]=>6
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[6,1,1]=>13
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,1,1]=>13
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[6,1,1]=>13
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[6,1,1]=>13
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[6,2]=>6
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[6,1,1]=>13
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,1,1]=>13
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[6,1,1]=>13
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[6,1,1]=>13
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[6,1,1]=>13
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[6,2]=>6
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[6,1,1]=>13
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>13
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[6,1,1]=>13
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[6,1,1]=>13
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[6,1,1]=>13
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[6,1,1]=>13
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[6,2]=>6
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[7,1]=>7
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,1]=>7
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[7,1]=>7
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[7,1]=>7
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[7,1]=>7
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[7,1]=>7
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[7,1]=>7
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[8]=>0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[8,1]=>8
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,8]=>1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[9,1]=>9
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[7,1,1]=>15
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,7,1]=>9
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,9]=>1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[10,1]=>10
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[8,1,1]=>17
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>15
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[6,2,1]=>14
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,7,1]=>9
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,6,2]=>8
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,8,1]=>10
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,10]=>1
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0]=>[8,1,1]=>17
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0]=>[7,1,1]=>15
[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,7,1]=>9
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,6,1,1]=>16
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,8,1]=>10
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0]=>[8,1,1]=>17
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0]=>[7,1,1]=>15
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]=>[6,2,1]=>14
[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,7,1]=>9
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,6,1,1]=>16
[1,0,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[1,8,1]=>10
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,6,2]=>8
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,5,2,1]=>15
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,7,1,1]=>18
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0]=>[8,1,1]=>17
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0]=>[7,1,1]=>15
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,7,1]=>9
[1,0,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,6,1,1]=>16
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[1,8,1]=>10
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,6,1,1]=>16
[1,0,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,5,2,1]=>15
[1,0,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[1,7,1,1]=>18
[1,0,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,5,1,2]=>14
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,4,3,1]=>14
[1,0,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[1,6,2,1]=>17
[1,0,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[1,8,1,1]=>20
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0]=>[8,1,1]=>17
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[7,1,1]=>15
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,1,0]=>[6,2,1]=>14
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,7,1]=>9
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[1,8,1]=>10
[1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[1,6,1,1]=>16
[1,0,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,6,2]=>8
[1,0,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[1,7,1,1]=>18
[1,0,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[1,6,2,1]=>17
[1,0,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,4,2,2]=>13
[1,0,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[1,6,1,2]=>16
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,3,4,1]=>13
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0]=>[8,1,1]=>17
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[7,1,1]=>15
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,7,1]=>9
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,6,1,1]=>16
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[1,8,1]=>10
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,6,1,1]=>16
[1,0,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,6,1,1]=>16
[1,0,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[1,4,3,1]=>14
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,5,1,2]=>14
[1,0,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,5,2,1]=>15
[1,0,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,4,1,3]=>12
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,2,5,1]=>12
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0]=>[8,1,1]=>17
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,6,1,1]=>16
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,8,1]=>10
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,5,3,1]=>16
[1,0,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[1,4,2,2]=>13
[1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,2,5,1]=>12
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,6,1]=>11
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[8,1,1]=>17
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,8,1]=>10
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[1,6,1,1]=>16
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,5,2,1]=>15
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,6,1,1]=>16
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,3,4,1]=>13
[1,0,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,6,1]=>11
[1,0,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,2,6,1]=>13
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[2,1,5,1]=>13
[1,1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[2,1,5,1]=>13
[1,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,1,5,1]=>13
[1,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,5,1]=>13
[1,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,1,4,1]=>15
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,1,4,1]=>15
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[3,1,4,1]=>15
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[3,1,4,1]=>15
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,0]=>[6,2,1]=>14
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0]=>[6,2,1]=>14
[1,1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0,0]=>[6,2,1]=>14
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0,0]=>[6,2,1]=>14
[1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0]=>[6,2,1]=>14
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0]=>[6,2,1]=>14
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0]=>[6,2,1]=>14
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]=>[6,2,1]=>14
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[6,2,1]=>14
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0]=>[6,2,1]=>14
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0]=>[6,2,1]=>14
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[6,2,1]=>14
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[6,2,1]=>14
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[7,1,1]=>15
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0]=>[7,1,1]=>15
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,0]=>[7,1,1]=>15
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,0]=>[7,1,1]=>15
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0]=>[7,1,1]=>15
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,0]=>[7,1,1]=>15
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0]=>[7,1,1]=>15
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[7,1,1]=>15
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,0]=>[7,1,1]=>15
[1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0]=>[7,1,1]=>15
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[7,1,1]=>15
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[7,1,1]=>15
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[7,1,1]=>15
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0]=>[7,1,1]=>15
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0]=>[7,1,1]=>15
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0]=>[7,1,1]=>15
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[7,1,1]=>15
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[7,1,1]=>15
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[8,1]=>8
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[8,1]=>8
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[8,1]=>8
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[8,1]=>8
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[8,1]=>8
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[8,1]=>8
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[8,1]=>8
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,1,1]=>45
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,4,1]=>18
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,4,1]=>18
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,4,1,1,1,1]=>27
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,3,1,2,1,1]=>25
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,3,1,2,1,1]=>25
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,4,1,1,1,1]=>27
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,6,1,1]=>16
[1,0,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,3,2,1,1,1]=>26
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,4,1,1,1,1]=>27
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,5,1]=>19
[1,0,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,3,3,1,1]=>25
[1,0,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,6,1]=>11
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[3,1,1,3,1,1]=>29
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,4,1]=>18
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,6,1]=>11
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,2,5,1]=>12
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,4,1,1,1,1]=>27
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,4,1,3]=>12
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,6,1,1]=>16
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,6,2]=>8
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,5,1]=>13
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,1]=>15
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]=>[6,2,1]=>14
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,1,2,2]=>29
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,5,1]=>19
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,2,2,1,1,1,1]=>37
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,2,2,2,2]=>21
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,4,4]=>9
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,7,1]=>12
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,5,1,1,1,1]=>31
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[1,7,1,1]=>18
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,1,1,2]=>35
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,1,1,1,2,1,1]=>37
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,1,6,1]=>14
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,2,1,1,1,1,1,1]=>41
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,2,1,1,2,2]=>25
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,2,3,3]=>13
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,2,2,3]=>15
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,3,2,2]=>17
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[4,1,1,4]=>15
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[4,4,1,1]=>21
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,5]=>5
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,1,1,1,1,1,2]=>35
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[9,1]=>9
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[8,1,1]=>17
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>[10,1]=>10
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[9,1]=>9
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>[10,1]=>10
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[8,1,1]=>17
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[9,1]=>9
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[5,5]=>5
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,2,1,1,1,1,1,1]=>41
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[10,1]=>10
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1,1,1,1]=>41
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,1,1,2,1,1,1,1]=>39
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,5,1,1,1,1]=>31
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,4,1,1,1,1]=>27
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[6,2,1]=>14
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[9,1]=>9
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[9,1]=>9
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[9,1]=>9
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[9,1]=>9
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[9,1]=>9
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[2,2,2,2,1,1]=>29
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,1,1,1,1,2,1,1]=>37
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,1,1,2,1,1,1,1]=>39
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,4,1,1,2,1]=>28
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,5,1,1,1,1]=>31
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,1,2,3,1,1]=>27
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,1,1,3,1,1]=>29
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[2,2,2,2,1,1]=>29
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,1,2,1,1]=>31
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[3,3,1,1,1,1]=>33
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,0]=>[8,1,1]=>17
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,1,1,2]=>35
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,2,1,1,1]=>26
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]=>[8,1,1]=>17
[1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,7,1]=>12
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1,1,1,1]=>41
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[8,1,1]=>17
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,1,1,1,1,2,1,1]=>37
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,1,1,1,2,1,1]=>37
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,2,1,1,1,1,2]=>33
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,1,1,2]=>35
[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0]=>[10,1]=>10
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,5,1]=>13
[1,1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[4,1,1,4]=>15
[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[5,5]=>5
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[2,2,1,1,1,1,1,1]=>41
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[2,1,1,2,1,1,1,1]=>39
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>33
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,4,1,1,1,1]=>27
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0]=>[8,1,1]=>17
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,1,1,1,2,1,1]=>37
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,1,1,1,1,1,2]=>35
[1,0,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,5,1]=>12
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,1,1,3,1]=>21
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[2,2,2,2,1,1]=>29
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,2,3,1]=>19
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,1,1,2,2]=>29
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,2,1,1,1,1,1,1]=>41
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[1,4,1,1,1,1]=>27
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,2,1,1,1]=>26
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,2,2]=>13
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,6,2]=>8
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,2,3,1]=>19
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,2,5,1]=>12
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,2,2,1,1,1,1]=>37
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,1,1,2,1,1,1,1]=>39
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,5,1,1,1,1]=>31
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,1,1,1,2,1,1]=>37
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,1,2,1,1,1,1]=>39
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,1,5,1]=>13
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,1,0]=>[6,2,1]=>14
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,4,1,1,1,1]=>27
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[1,4,1,1,1,1]=>27
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0]=>[8,1,1]=>17
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0]=>[8,1,1]=>17
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0]=>[8,1,1]=>17
[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0]=>[8,1,1]=>17
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]=>[8,1,1]=>17
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,4,1]=>18
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,2,1,1,1,1,1,1]=>41
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,3,2,1,1,1]=>26
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,2,1,1,1,1,1,1]=>41
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[2,2,2,2,1,1]=>29
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[2,2,2,2,1,1]=>29
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,2,5,1]=>12
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,1,1,1,1,1,1,1,2]=>54
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[1,5,1,2]=>14
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[1,6,1,2]=>16
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,1,1,1,1,3]=>25
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[1,5,1,2]=>14
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[1,4,1,3]=>12
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>30
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,1,2,2,2]=>32
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,3,1,1,2,2]=>34
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[4,3,1,1,1,2]=>38
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[3,3,2,1,1,2]=>36
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[3,1,2,3,1,2]=>32
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[4,1,1,3,1,2]=>34
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[4,2,1,2,1,2]=>36
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,2,3,2,1,2]=>32
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,2,2,1,2]=>34
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[3,1,2,4,1,1]=>34
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[4,1,1,4,1,1]=>36
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[4,2,1,3,1,1]=>38
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,2,3,3,1,1]=>34
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,2,2,3,1,1]=>36
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[3,3,2,2,1,1]=>38
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[4,3,1,2,1,1]=>40
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[4,4,1,1,1,1]=>42
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,1,1,1,2,1,1]=>37
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,1,2,1,1,1,1]=>39
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[1,4,1,1,1,1]=>27
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1,1,1,1]=>41
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,3,1,1,2,1]=>24
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0,0]=>[8,1,1]=>17
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0,0]=>[10,1]=>10
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,5,1]=>13
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,1]=>15
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,1,6,1]=>14
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,1]=>15
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[1,4,1,1,2,1]=>28
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,5,1,1,1,1]=>31
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,3,1,1,3,1]=>25
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,4,1,1,2,1]=>28
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,5,1,1,1,1]=>31
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[2,2,2,2,1,1]=>29
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[1,7,1,1]=>18
[1,0,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,8,1]=>13
[1,0,1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,2,3,1]=>19
[1,0,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[1,4,2,2]=>13
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,1,1,2]=>35
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[1,4,1,1,1,1]=>27
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,2,1,1,1]=>26
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[1,4,1,1,2,1]=>28
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,1,2,3,1,1]=>27
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[2,2,2,2,1,1]=>29
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0,0]=>[4,3,1,2,1,1]=>40
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,3,1,1]=>38
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,1,1,4,1,1]=>36
[1,1,1,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[3,1,2,4,1,1]=>34
[1,1,1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,0,1,0,0]=>[3,3,2,2,1,1]=>38
[1,1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[3,2,2,3,1,1]=>36
[1,1,0,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,0]=>[2,2,3,3,1,1]=>34
[1,1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,1,1,3,1,1]=>29
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,1,1,1,1,3]=>25
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[4,3,1,2]=>19
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[3,2,1,1,1,2]=>29
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[4,4,1,1]=>21
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[3,2,1,2,1,1]=>31
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0]=>[3,3,1,1,1,1]=>33
[1,1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,3,1,1,3]=>30
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,0,0]=>[2,2,3,2,1,2]=>32
[1,1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[3,1,2,2,1,3]=>30
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[3,3,1,1,2,2]=>34
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0,1,1,0,0,0]=>[4,3,1,1,1,2]=>38
[1,1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[4,2,1,2,1,2]=>36
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,1,1,0,0,0]=>[3,3,2,1,1,2]=>36
[1,1,1,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0,0,1,0,0]=>[4,3,1,2,1,1]=>40
[1,1,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[4,4,1,1,1,1]=>42
[1,1,1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[4,2,1,3,1,1]=>38
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,2,1,1,2,2]=>25
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,2,1,1,2,2]=>25
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0,0]=>[10,1]=>10
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0]=>[10,1]=>10
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0,0]=>[10,1]=>10
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0]=>[10,1]=>10
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>30
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>30
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,2,2,1,2,1]=>23
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,1,2,2,1]=>22
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[2,2,2,2,1,1]=>29
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,2,1,2,1,1]=>31
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[3,3,1,1,1,1]=>33
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,1,2,2,1,2]=>25
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[3,1,1,2,1,2]=>27
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[2,2,2,1,1,2]=>27
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[3,2,1,1,1,2]=>29
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,2,2,2,2,1,1]=>42
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,3,2,1,2,1,1]=>44
[1,0,1,0,1,1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,3,3,1,1,1,1]=>46
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,1,1,2,2,2,1,1]=>44
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,2,1,1,2,2,1,1]=>46
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[2,1,2,2,1,2,1,1]=>46
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,1,2,1,2,1,1]=>48
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[2,2,2,1,1,2,1,1]=>48
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,1,1,2,1,1]=>50
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,1,1,1,1,2,1,1]=>37
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,2,1,1,1,1,1,1]=>41
[1,1,1,1,0,1,0,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,1,1,4]=>15
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,1,1,1,2]=>33
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,2,1,1,2]=>31
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,5,1,1,1,1]=>31
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[1,4,1,1,1,1]=>27
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,2,2,2,1,1]=>29
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,4,4,1]=>15
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,3,5,1]=>14
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,2,6,1]=>13
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,1,7,1]=>12
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,1,1,1,2,1,1]=>37
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,3,2,2,1,1]=>38
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,1,1,4]=>26
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,1,1,4]=>26
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,1,2,2,1,3]=>30
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,1,2,2,1,3]=>30
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,1,1,2,2,3]=>28
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[3,1,2,2,1,3]=>30
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[3,1,2,2,1,3]=>30
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,1,1,2,2,3]=>28
[1,1,1,0,0,0,1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[3,1,2,4,1,1]=>34
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[4,2,1,3,1,1]=>38
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[3,2,2,1,1,3]=>32
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,1,2,2,1,3]=>30
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,1,2,2,1,3]=>30
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,2,2,1,1,3]=>32
[1,1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[3,1,2,2,1,3]=>30
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[3,1,2,2,1,3]=>30
[1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,1,1,3,1,2]=>34
[1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,1,1,3,1,2]=>34
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[3,3,1,1,2,2]=>34
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0,0]=>[8,1,1]=>17
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,3,1,2,1,1]=>25
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,3,2,1,1,1]=>26
[1,0,1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,2,1,3,1]=>20
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,1,1,1,2,1,1]=>37
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,2,1,3,1]=>20
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,2,1,2,2,1]=>22
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,1,2,2,2]=>23
[1,1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[3,3,1,1,1,1]=>33
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,4,1,1,1,1]=>27
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,4,1,1,2,1]=>28
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,2,3,1,1]=>27
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[2,2,2,2,1,1]=>29
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,1,2,1,1]=>31
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0]=>[3,3,1,1,1,1]=>33
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Description
The major index of the composition.
The descents of a composition $[c_1,c_2,\dots,c_k]$ are the partial sums $c_1, c_1+c_2,\dots, c_1+\dots+c_{k-1}$, excluding the sum of all parts. The major index of a composition is the sum of its descents.
For details about the major index see Permutations/Descents-Major.
The descents of a composition $[c_1,c_2,\dots,c_k]$ are the partial sums $c_1, c_1+c_2,\dots, c_1+\dots+c_{k-1}$, excluding the sum of all parts. The major index of a composition is the sum of its descents.
For details about the major index see Permutations/Descents-Major.
Map
rise composition
Description
Send a Dyck path to the composition of sizes of its rises.
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