Identifier
Mp00030:
Dyck paths
—zeta map⟶
Dyck paths
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00027: Dyck paths —to partition⟶ Integer partitions
Images
=>
Cc0005;cc-rep-0Cc0005;cc-rep-1Cc0002;cc-rep-2
[1,0]=>[1,0]=>[]
[1,0,1,0]=>[1,1,0,0]=>[]
[1,1,0,0]=>[1,0,1,0]=>[1]
[1,0,1,0,1,0]=>[1,1,1,0,0,0]=>[]
[1,0,1,1,0,0]=>[1,0,1,1,0,0]=>[1,1]
[1,1,0,0,1,0]=>[1,1,0,1,0,0]=>[1]
[1,1,0,1,0,0]=>[1,1,0,0,1,0]=>[2]
[1,1,1,0,0,0]=>[1,0,1,0,1,0]=>[2,1]
[1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0]=>[]
[1,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,0]=>[1,1,1]
[1,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,0]=>[1,1]
[1,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,0]=>[2,2]
[1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,0]=>[2,2,1]
[1,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,0]=>[1]
[1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,0]=>[2,1]
[1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0]=>[2]
[1,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0]=>[3]
[1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0]=>[3,1,1]
[1,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,0]=>[2,1,1]
[1,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,0]=>[3,1]
[1,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,0]=>[3,2]
[1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0]=>[3,2,1]
[1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0]=>[]
[1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1]
[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,0]=>[1,1,1]
[1,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>[2,2,2]
[1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]=>[2,2,2,1]
[1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,0]=>[1,1]
[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,0,0]=>[2,2,1]
[1,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0]=>[2,2]
[1,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>[3,3]
[1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>[3,3,1,1]
[1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0]=>[2,2,1,1]
[1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0]=>[3,3,1]
[1,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,0]=>[3,3,2]
[1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0]=>[3,3,2,1]
[1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,0]=>[1]
[1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,0]=>[2,1,1]
[1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,0]=>[2,1]
[1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,0]=>[3,2]
[1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0]=>[3,2,1,1]
[1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,0,0]=>[2]
[1,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,0]=>[3,1]
[1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0]=>[3]
[1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0]=>[4]
[1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0]=>[4,1,1,1]
[1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0]=>[3,1,1,1]
[1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]=>[4,1,1]
[1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>[4,2,2]
[1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0]=>[4,2,2,1]
[1,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,0,0,0]=>[2,1,1,1]
[1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]=>[3,2,1]
[1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0]=>[3,1,1]
[1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0]=>[4,1]
[1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0]=>[4,2,1]
[1,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0]=>[3,2,2]
[1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,0]=>[4,2]
[1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0]=>[4,3]
[1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0]=>[4,3,1,1]
[1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0]=>[3,2,2,1]
[1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0]=>[4,2,1,1]
[1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,0]=>[4,3,1]
[1,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0]=>[4,3,2]
[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>[4,3,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,2,2,2]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[2,2,2,2,1]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,2,2,1]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[2,2,2]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,3,3]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[3,3,3,1,1]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,2,1,1]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[3,3,3,1]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[3,3,3,2]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[3,3,3,2,1]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,1,1]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[2,2,1]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[3,3,2]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[3,3,2,1,1]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[2,2]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[3,3,1]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[3,3]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,4]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[4,4,1,1,1]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[3,3,1,1,1]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[4,4,1,1]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[4,4,2,2]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[4,4,2,2,1]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[2,2,1,1,1]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[3,3,2,1]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[3,3,1,1]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[4,4,1]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[4,4,2,1]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[3,3,2,2]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[4,4,2]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[4,4,3]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[4,4,3,1,1]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[3,3,2,2,1]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[4,4,2,1,1]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[4,4,3,1]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[4,4,3,2]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[4,4,3,2,1]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,1,1]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[2,1,1]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,2]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[3,2,2,1,1]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[2,1]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[3,2,1]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[3,2]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[4,3,1,1,1]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[3,2,1,1,1]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[4,3,1,1]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[4,3,2,2]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[4,3,2,2,1]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[2]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[3,1,1]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[3,1]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[4,2]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[4,2,1,1,1]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[3]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[4,1]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[4]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[5]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[5,1,1,1,1]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[4,1,1,1,1]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[5,1,1,1]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[5,2,2,2]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[5,2,2,2,1]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[3,1,1,1,1]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[4,2,1,1]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[4,1,1,1]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[5,1,1]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[5,2,2,1]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[4,2,2,2]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[5,2,2]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[5,3,3]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[5,3,3,1,1]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[4,2,2,2,1]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[5,2,2,1,1]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[5,3,3,1]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[5,3,3,2]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[5,3,3,2,1]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,1,1,1]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[3,2,2,1]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[3,2,1,1]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[4,3,1]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[4,3,2,1]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[3,1,1,1]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[4,2,1]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[4,1,1]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[5,1]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[5,2,1,1]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[4,2,2,1]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[5,2,1]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[5,3,2]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[5,3,2,1,1]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[3,2,2,2]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[4,3,2]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[4,2,2]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[5,2]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[5,3,1]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[4,3,3]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[5,3]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[5,4]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[5,4,1,1,1]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[4,3,3,1,1]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[5,3,1,1,1]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[5,4,1,1]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[5,4,2,2]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[5,4,2,2,1]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[3,2,2,2,1]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[4,3,2,1,1]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[4,2,2,1,1]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[5,2,1,1,1]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[5,3,2,1]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[4,3,3,1]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[5,3,1,1]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[5,4,1]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[5,4,2,1]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[4,3,3,2]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[5,3,2,2]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[5,4,2]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[5,4,3]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[5,4,3,1,1]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[4,3,3,2,1]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[5,3,2,2,1]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[5,4,2,1,1]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[5,4,3,1]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[5,4,3,2]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,3,3,3]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[3,3,3,3,1,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,3,3,3,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,3,3,3,2]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[3,3,3,3,2,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,3,3,2]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[3,3,3,2,1,1]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,3,3,1]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,3,3]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,4,4]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[4,4,4,1,1,1]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[3,3,3,1,1,1]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[4,4,4,1,1]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[4,4,4,2,2]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[4,4,4,2,2,1]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1,1]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[3,3,3,2,1]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[3,3,3,1,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,4,4,1]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[4,4,4,2,1]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,3,3,2,2]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[4,4,4,2]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[4,4,4,3]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[4,4,4,3,1,1]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[3,3,3,2,2,1]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[4,4,4,2,1,1]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[4,4,4,3,1]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[4,4,4,3,2]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[4,4,4,3,2,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,3,2,2]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[3,3,2,2,1,1]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,2,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,3,2,1]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[3,3,2]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,4,3]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[4,4,3,1,1,1]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[3,3,2,1,1,1]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[4,4,3,1,1]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[4,4,3,2,2]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[4,4,3,2,2,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[3,3,1]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,4,2]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[4,4,2,1,1,1]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,4,1]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,4]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,5]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[5,5,1,1,1,1]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[4,4,1,1,1,1]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[5,5,1,1,1]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[5,5,2,2,2]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[5,5,2,2,2,1]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1,1,1]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[4,4,2,1,1]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[4,4,1,1,1]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[5,5,1,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[5,5,2,2,1]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[4,4,2,2,2]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[5,5,2,2]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[5,5,3,3]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[5,5,3,3,1,1]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[4,4,2,2,2,1]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[5,5,2,2,1,1]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[5,5,3,3,1]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[5,5,3,3,2]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[5,5,3,3,2,1]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[3,3,2,2,1]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[3,3,2,1,1]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[4,4,3,1]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[4,4,3,2,1]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1,1]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[4,4,2,1]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[4,4,1,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[5,5,1]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[5,5,2,1,1]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[4,4,2,2,1]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[5,5,2,1]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[5,5,3,2]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[5,5,3,2,1,1]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,3,2,2,2]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[4,4,3,2]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[4,4,2,2]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[5,5,2]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[5,5,3,1]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[4,4,3,3]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[5,5,3]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[5,5,4]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[5,5,4,1,1,1]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[4,4,3,3,1,1]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[5,5,3,1,1,1]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[5,5,4,1,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[5,5,4,2,2]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[5,5,4,2,2,1]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[3,3,2,2,2,1]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[4,4,3,2,1,1]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[4,4,2,2,1,1]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[5,5,2,1,1,1]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[5,5,3,2,1]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[4,4,3,3,1]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[5,5,3,1,1]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[5,5,4,1]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[5,5,4,2,1]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[4,4,3,3,2]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[5,5,3,2,2]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[5,5,4,2]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[5,5,4,3]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[5,5,4,3,1,1]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[4,4,3,3,2,1]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[5,5,3,2,2,1]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[5,5,4,2,1,1]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[5,5,4,3,1]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[5,5,4,3,2]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[5,5,4,3,2,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,2,2]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,2,2,1,1]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,1,1]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[3,2,2]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,3]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[4,3,3,1,1,1]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1,1,1]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[4,3,3,1,1]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[4,3,3,2,2]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[4,3,3,2,2,1]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,1]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,2,1]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,3,2]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[4,3,2,1,1,1]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,2]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,3,1]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[4,3]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,1,1,1]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,1,1,1]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,1,1]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[5,4,2,2,2]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[5,4,2,2,2,1]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1,1,1]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[4,3,2,1,1]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,1,1]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,1]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[5,4,2,2,1]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[4,3,2,2,2]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[5,4,2,2]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[5,4,3,3]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[5,4,3,3,1,1]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[4,3,2,2,2,1]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[5,4,2,2,1,1]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[5,4,3,3,1]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[5,4,3,3,2]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[5,4,3,3,2,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,1,1]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,2,2]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[4,2,2,1,1,1]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,1]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,2,1]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[4,2]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,3]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,1,1,1]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,1,1,1]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,1,1]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[5,3,2,2,2]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[5,3,2,2,2,1]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[3]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,1,1]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[4,1]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,2]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,1,1,1]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[4]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[5]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1,1]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1,1]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[6,2,2,2,2]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[6,2,2,2,2,1]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1,1]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,1,1]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[6,2,2,2,1]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[5,2,2,2,2]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[6,2,2,2]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[6,3,3,3]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[6,3,3,3,1,1]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[5,2,2,2,2,1]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[6,2,2,2,1,1]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[6,3,3,3,1]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[6,3,3,3,2]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[6,3,3,3,2,1]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1,1]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[4,2,2,1,1]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,1,1]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,1]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[5,3,2,2,1]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,1]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[6,1,1]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[6,2,2,1,1]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[5,2,2,2,1]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[6,2,2,1]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[6,3,3,2]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[6,3,3,2,1,1]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[4,2,2,2,2]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[5,3,2,2]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[5,2,2,2]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[6,2,2]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[6,3,3,1]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[5,3,3,3]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[6,3,3]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[6,4,4]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[6,4,4,1,1,1]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[5,3,3,3,1,1]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[6,3,3,1,1,1]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[6,4,4,1,1]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[6,4,4,2,2]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[6,4,4,2,2,1]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[4,2,2,2,2,1]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[5,3,2,2,1,1]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[5,2,2,2,1,1]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[6,2,2,1,1,1]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[6,3,3,2,1]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[5,3,3,3,1]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[6,3,3,1,1]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[6,4,4,1]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[6,4,4,2,1]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[5,3,3,3,2]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[6,3,3,2,2]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[6,4,4,2]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[6,4,4,3]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[6,4,4,3,1,1]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[5,3,3,3,2,1]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[6,3,3,2,2,1]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[6,4,4,2,1,1]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[6,4,4,3,1]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[6,4,4,3,2]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[6,4,4,3,2,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1,1]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,2,2,1]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1,1]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[4,3,3,1]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[4,3,3,2,1]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1,1]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[4,3,2,1]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,1]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[5,4,1]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[5,4,2,1,1]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,2,1]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[5,4,2,1]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,1,1]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[4,2,2,1]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,1]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[5,3,1]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[5,3,2,1,1]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[5,2,1]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[5,1,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,1,1]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,2,1,1]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,1]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[6,3,2,2]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[6,3,2,2,1,1]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[4,2,2,2,1]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[5,3,2,1]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[5,2,2,1]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[6,2,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[6,3,2,1]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[5,3,3,2]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[6,3,2]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[6,4,3]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[6,4,3,1,1,1]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[5,3,3,2,1,1]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[6,3,2,1,1,1]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[6,4,3,1,1]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,2]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,2,1]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,2,2,2]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[4,3,3,2]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,2]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[5,4,2]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[5,4,3,1]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[4,2,2,2]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[5,3,2]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[5,2,2]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,2]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,1]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[5,3,3,1]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[6,3,1]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[6,4,2]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[6,4,2,1,1,1]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[4,3,3,3]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[5,4,3]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[5,3,3]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,3]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[6,4,1]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[5,4,4]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[6,4]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[6,5]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,1,1,1]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[5,4,4,1,1,1]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,1,1,1]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,1,1]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[6,5,2,2,2]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[6,5,2,2,2,1]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[4,3,3,3,1,1]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[5,4,3,1,1,1]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[5,3,3,1,1,1]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,1,1,1]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[6,4,2,1,1]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[5,4,4,1,1]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,1,1]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,1]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[6,5,2,2,1]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[5,4,4,2,2]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[6,4,2,2,2]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[6,5,2,2]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[6,5,3,3]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[6,5,3,3,1,1]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[5,4,4,2,2,1]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[6,4,2,2,2,1]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[6,5,2,2,1,1]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[6,5,3,3,1]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[6,5,3,3,2]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[6,5,3,3,2,1]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,2,2,2,1]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[4,3,3,2,1,1]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,2,1,1]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[5,4,2,1,1,1]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,1]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[4,2,2,2,1,1]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[5,3,2,1,1,1]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,2,1,1,1]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,1,1,1]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[6,3,2,2,1]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[5,3,3,2,1]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[6,3,2,1,1]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[6,4,3,1]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,1]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[4,3,3,3,1]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[5,4,3,1,1]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[5,3,3,1,1]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,1,1]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[6,4,2,1]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[5,4,4,1]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,1]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[6,5,1]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[6,5,2,1,1]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[5,4,4,2,1]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[6,4,2,2,1]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[6,5,2,1]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[6,5,3,2]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,1,1]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[4,3,3,3,2]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,2]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[5,3,3,2,2]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[6,3,2,2,2]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[6,4,3,2]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[5,4,4,2]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[6,4,2,2]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[6,5,2]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[6,5,3,1]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[5,4,4,3]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[6,4,3,3]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[6,5,3]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[6,5,4]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[6,5,4,1,1,1]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[5,4,4,3,1,1]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[6,4,3,3,1,1]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[6,5,3,1,1,1]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[6,5,4,1,1]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,2]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,2,1]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[4,3,3,3,2,1]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,2,1]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[5,3,3,2,2,1]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[6,3,2,2,2,1]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,1,1]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[5,4,4,2,1,1]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[6,4,2,2,1,1]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[6,5,2,1,1,1]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,1]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[5,4,4,3,1]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[6,4,3,3,1]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[6,5,3,1,1]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[6,5,4,1]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,1]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[5,4,4,3,2]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[6,4,3,3,2]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,2]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[6,5,4,2]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[6,5,4,3]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,1,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[5,4,4,3,2,1]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[6,4,3,3,2,1]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,2,1]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,1,1]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,2]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,1]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,2]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,2,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,1,1]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,1,1,1]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1,1]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,1,1]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,2,2]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,2,2,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,1]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,2,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,2]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,2]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,3]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,3,1,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,2,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,2,1,1]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,3,1]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,3,2]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,3,2,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,1,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,1,1,1]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1,1,1]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,1,1]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,2,2]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,2,2,1]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,5,5]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,5,5,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,5,5,1,1,1]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[5,5,5,2,2,2]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[5,5,5,2,2,2,1]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,1,1]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,5,5,1,1]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[5,5,5,2,2,1]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,2,2]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[5,5,5,2,2]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[5,5,5,3,3]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[5,5,5,3,3,1,1]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,2,2,1]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[5,5,5,2,2,1,1]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[5,5,5,3,3,1]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[5,5,5,3,3,2]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[5,5,5,3,3,2,1]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,1]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1,1]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,1]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,2,1]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[5,5,5,1]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[5,5,5,2,1,1]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,2,1]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[5,5,5,2,1]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[5,5,5,3,2]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[5,5,5,3,2,1,1]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,2]
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,2]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,2]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[5,5,5,2]
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[5,5,5,3,1]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,3]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[5,5,5,3]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[5,5,5,4]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[5,5,5,4,1,1,1]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,3,1,1]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[5,5,5,3,1,1,1]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[5,5,5,4,1,1]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[5,5,5,4,2,2]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[5,5,5,4,2,2,1]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,2,1]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,2,1,1]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,2,1,1]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[5,5,5,2,1,1,1]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[5,5,5,3,2,1]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,3,1]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[5,5,5,3,1,1]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[5,5,5,4,1]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[5,5,5,4,2,1]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,3,2]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[5,5,5,3,2,2]
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[5,5,5,4,2]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[5,5,5,4,3]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[5,5,5,4,3,1,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,3,2,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[5,5,5,3,2,2,1]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[5,5,5,4,2,1,1]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[5,5,5,4,3,1]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[5,5,5,4,3,2]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[5,5,5,4,3,2,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2]
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,1,1]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,1,1,1]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1,1,1]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,1,1]
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,2,2]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,2,2,1]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,1,1,1]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[4,4,3]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,5,4]
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[5,5,4,1,1,1,1]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1,1,1,1]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[5,5,4,1,1,1]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[5,5,4,2,2,2]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[5,5,4,2,2,2,1]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1,1,1]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,1,1]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1,1,1]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[5,5,4,1,1]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[5,5,4,2,2,1]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,2,2]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[5,5,4,2,2]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[5,5,4,3,3]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[5,5,4,3,3,1,1]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,2,2,1]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[5,5,4,2,2,1,1]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[5,5,4,3,3,1]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[5,5,4,3,3,2]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[5,5,4,3,3,2,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1,1,1]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[5,5,3]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,5,3,1,1,1,1]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1,1,1]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,5,3,1,1,1]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2,2,2]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2,2,2,1]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[4,4,1]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,5,2]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,5,2,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[5,5,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[6,6,2,2,2,2]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[6,6,2,2,2,2,1]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1,1]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,5,2,1,1,1]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1]
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[6,6,2,2,2,1]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,2,2]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[6,6,2,2,2]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[6,6,3,3,3]
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[6,6,3,3,3,1,1]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,2,2,1]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[6,6,2,2,2,1,1]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[6,6,3,3,3,1]
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[6,6,3,3,3,2]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[6,6,3,3,3,2,1]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1,1]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1,1]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,5,3,1,1]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2,2,1]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,5,2,1,1]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1]
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[6,6,2,2,1,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,2,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[6,6,2,2,1]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[6,6,3,3,2]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[6,6,3,3,2,1,1]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,2]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2,2]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,2]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[6,6,2,2]
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[6,6,3,3,1]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,3]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[6,6,3,3]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[6,6,4,4]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[6,6,4,4,1,1,1]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,3,1,1]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[6,6,3,3,1,1,1]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[6,6,4,4,1,1]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[6,6,4,4,2,2]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[6,6,4,4,2,2,1]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,2,1]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2,2,1,1]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,2,1,1]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[6,6,2,2,1,1,1]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[6,6,3,3,2,1]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,3,1]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[6,6,3,3,1,1]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[6,6,4,4,1]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[6,6,4,4,2,1]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,3,2]
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[6,6,3,3,2,2]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[6,6,4,4,2]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[6,6,4,4,3]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[6,6,4,4,3,1,1]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,3,2,1]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[6,6,3,3,2,2,1]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[6,6,4,4,2,1,1]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[6,6,4,4,3,1]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[6,6,4,4,3,2]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[6,6,4,4,3,2,1]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,1]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,2,1]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1,1]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,1]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1,1]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[5,5,4,1]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[5,5,4,2,1,1]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,2,1]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[5,5,4,2,1]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3,2]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3,2,1,1]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[5,5,3,1]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2,1,1]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1]
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[5,5,2,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[6,6,1]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[6,6,2,1,1,1]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,1,1]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[6,6,2,1,1]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[6,6,3,2,2]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[6,6,3,2,2,1,1]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,1]
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2,1]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,1]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[6,6,2,1]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[6,6,3,2,1]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,2]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[6,6,3,2]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[6,6,4,3]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[6,6,4,3,1,1,1]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,2,1,1]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[6,6,3,2,1,1,1]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[6,6,4,3,1,1]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[6,6,4,3,2,2]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[6,6,4,3,2,2,1]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,2]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,2]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,2]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[5,5,4,2]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3,1]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[6,6,2]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[6,6,3,1,1]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,1]
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[6,6,3,1]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[6,6,4,2]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[6,6,4,2,1,1,1]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,3]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[6,6,3]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[6,6,4,1]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[5,5,4,4]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[6,6,4]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[6,6,5]
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[6,6,5,1,1,1,1]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[5,5,4,4,1,1,1]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[6,6,4,1,1,1,1]
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[6,6,5,1,1,1]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[6,6,5,2,2,2]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[6,6,5,2,2,2,1]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,3,1,1]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3,1,1,1]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,1,1,1]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[6,6,3,1,1,1,1]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[6,6,4,2,1,1]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[5,5,4,4,1,1]
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[6,6,4,1,1,1]
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[6,6,5,1,1]
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[6,6,5,2,2,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[5,5,4,4,2,2]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[6,6,4,2,2,2]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[6,6,5,2,2]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[6,6,5,3,3]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[6,6,5,3,3,1,1]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[5,5,4,4,2,2,1]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[6,6,4,2,2,2,1]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[6,6,5,2,2,1,1]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[6,6,5,3,3,1]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[6,6,5,3,3,2]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[6,6,5,3,3,2,1]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,2,1]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,2,1,1]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,2,1,1]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[5,5,4,2,1,1,1]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3,2,1]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,1,1]
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2,1,1,1]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,1,1,1]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[6,6,2,1,1,1,1]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[6,6,3,2,2,1]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,2,1]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[6,6,3,2,1,1]
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[6,6,4,3,1]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[6,6,4,3,2,1]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,3,1]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3,1,1]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,1,1]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[6,6,3,1,1,1]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[6,6,4,2,1]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[5,5,4,4,1]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[6,6,4,1,1]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[6,6,5,1]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[6,6,5,2,1,1]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[5,5,4,4,2,1]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[6,6,4,2,2,1]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[6,6,5,2,1]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[6,6,5,3,2]
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[6,6,5,3,2,1,1]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,3,2]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3,2,2]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,2,2]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[6,6,3,2,2,2]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[6,6,4,3,2]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[5,5,4,4,2]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[6,6,4,2,2]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[6,6,5,2]
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[6,6,5,3,1]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[5,5,4,4,3]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[6,6,4,3,3]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[6,6,5,3]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[6,6,5,4]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[6,6,5,4,1,1,1]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[5,5,4,4,3,1,1]
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[6,6,4,3,3,1,1]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[6,6,5,3,1,1,1]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[6,6,5,4,1,1]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[6,6,5,4,2,2]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[6,6,5,4,2,2,1]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,3,2,1]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3,2,2,1]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,2,2,1]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[6,6,3,2,2,2,1]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[6,6,4,3,2,1,1]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[5,5,4,4,2,1,1]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[6,6,4,2,2,1,1]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[6,6,5,2,1,1,1]
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[6,6,5,3,2,1]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[5,5,4,4,3,1]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[6,6,4,3,3,1]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[6,6,5,3,1,1]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[6,6,5,4,1]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[6,6,5,4,2,1]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[5,5,4,4,3,2]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[6,6,4,3,3,2]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[6,6,5,3,2,2]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[6,6,5,4,2]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[6,6,5,4,3]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[6,6,5,4,3,1,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[5,5,4,4,3,2,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[6,6,4,3,3,2,1]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[6,6,5,3,2,2,1]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[6,6,5,4,2,1,1]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[6,6,5,4,3,1]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[6,6,5,4,3,2]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[6,6,5,4,3,2,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,1,1]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,1,1,1]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1,1,1]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,1,1]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,2,2]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,2,2,1]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1]
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,1,1,1]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[4,3,3]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,4,4]
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,4,1,1,1,1]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1,1,1,1]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,4,1,1,1]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,4,2,2,2]
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,4,2,2,2,1]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1,1,1]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,1,1]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1,1,1]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,4,1,1]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,4,2,2,1]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,2,2]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,4,2,2]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,4,3,3]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,4,3,3,1,1]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,2,2,1]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,4,2,2,1,1]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,4,3,3,1]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,4,3,3,2]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,4,3,3,2,1]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,1,1,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[3,2,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[4,3,2]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[5,4,3]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1,1,1,1]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,1,1,1]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1,1,1]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,2,2]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,2,2,1]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[4,3,1]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[5,4,2]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1,1,1,1]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[5,4,1]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1,1,1]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1,1,1]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1,1]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,2,2]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,2,2,1]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1,1,1]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1,1,1]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1,1]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,2,1]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,2,2]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,2]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,3,3]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,3,3,1,1]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,2,2,1]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,2,1,1]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,3,3,1]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,3,3,2]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,3,3,2,1]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1,1,1]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,1,1]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,1,1]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1,1]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,2,1]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1,1]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1,1]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,1,1]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,2,1]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,1]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,3,2]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,3,2,1,1]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,2,2]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,2]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,2]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,3,1]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,3]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,3]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,4]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,4,1,1,1]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,3,1,1]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,3,1,1,1]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,4,1,1]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,4,2,2]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,4,2,2,1]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,2,2,1]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,2,1,1]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,2,1,1]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,1,1,1]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,3,2,1]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,3,1]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,3,1,1]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,4,1]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,4,2,1]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,3,2]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,3,2,2]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,4,2]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,4,3]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,4,3,1,1]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,3,2,1]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,3,2,2,1]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,4,2,1,1]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,4,3,1]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,4,3,2]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,4,3,2,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[2]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1,1,1]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1,1,1,1]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1,1,1]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1,1,1]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,2,2]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,2,2,1]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[4,2,1]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[5,3,2]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1,1,1,1]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[5,3,1]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1,1,1]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1,1,1]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1,1]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,2,2]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,2,2,1]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1,1,1]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1,1,1]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1,1]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,2,1]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,2,2]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,2]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,3,3]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,3,3,1,1]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,2,2,1]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,2,1,1]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,3,3,1]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,3,3,2]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,3,3,2,1]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[3]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1,1,1]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[5,2,1]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1,1,1]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1,1,1]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1,1]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,2,2]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,2,2,1]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[4]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[5]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[6]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[7]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2,2]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2,2,1]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1,1]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2,1]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,2]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,3]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,3,1,1]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,2,1]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2,1,1]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,3,1]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,3,2]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,3,2,1]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1,1]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1,1]
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,2,1]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,1,1]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,1]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,1]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,2]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,2,1,1]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,2]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,2]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2]
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,1]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,3]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[7,4,4,4]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[7,4,4,4,1,1,1]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,3,1,1]
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,1,1,1]
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[7,4,4,4,1,1]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,4,4,2,2]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,4,4,2,2,1]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,2,1]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,2,1,1]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,1,1]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,1,1,1]
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,2,1]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,3,1]
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,1,1]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[7,4,4,4,1]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,4,4,2,1]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,3,2]
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,2,2]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,4,4,2]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,4,4,3]
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,4,4,3,1,1]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,3,2,1]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,2,2,1]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,4,4,2,1,1]
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,4,4,3,1]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,4,4,3,2]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,4,4,3,2,1]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1,1]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1,1]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1,1]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,2,1]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1,1]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1,1]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,1,1]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,2,1]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,1]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,3,2]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,3,2,1,1]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,1,1]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1,1]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1,1]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2,2]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2,2,1,1]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,1]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,1]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2,1]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,2]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[7,4,4,3]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[7,4,4,3,1,1,1]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,2,1,1]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2,1,1,1]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[7,4,4,3,1,1]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,4,3,2,2]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,4,3,2,2,1]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,2]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,2]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,2]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,3,1]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1,1]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,1]
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[7,4,4,2]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[7,4,4,2,1,1,1]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,3]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,3]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[7,3,3]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,4,1]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[6,4,4,4]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[7,4,4]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[7,5,5]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[7,5,5,1,1,1,1]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[6,4,4,4,1,1,1]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,4,1,1,1,1]
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[7,5,5,1,1,1]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,5,2,2,2]
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,5,2,2,2,1]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,3,1,1]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,3,1,1,1]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,1,1,1]
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1,1,1,1]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[7,4,4,2,1,1]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[6,4,4,4,1,1]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,4,1,1,1]
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[7,5,5,1,1]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,5,2,2,1]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,4,4,2,2]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,4,2,2,2]
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,5,2,2]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,5,3,3]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,5,3,3,1,1]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,4,4,2,2,1]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,4,2,2,2,1]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,5,2,2,1,1]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,5,3,3,1]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,5,3,3,2]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,5,3,3,2,1]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,2,1]
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,2,1,1]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,2,1,1]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,1,1,1]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,3,2,1]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,1,1]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,1,1,1]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1,1,1]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1,1,1]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2,2,1]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,2,1]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2,1,1]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[7,4,4,3,1]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,4,3,2,1]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,3,1]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,3,1,1]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,1,1]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1,1,1]
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[7,4,4,2,1]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[6,4,4,4,1]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,4,1,1]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[7,5,5,1]
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[7,5,5,2,1,1]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,4,4,2,1]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,4,2,2,1]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[7,5,5,2,1]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,5,3,2]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,5,3,2,1,1]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,3,2]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,3,2,2]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,2,2]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2,2,2]
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,4,3,2]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,4,4,2]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,4,2,2]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[7,5,5,2]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[7,5,5,3,1]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,4,4,3]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,4,3,3]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[7,5,5,3]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[7,5,5,4]
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[7,5,5,4,1,1,1]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,4,4,3,1,1]
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,4,3,3,1,1]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[7,5,5,3,1,1,1]
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[7,5,5,4,1,1]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,5,4,2,2]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,5,4,2,2,1]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,3,2,1]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,3,2,2,1]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,2,2,1]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2,2,2,1]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,4,3,2,1,1]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,4,4,2,1,1]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,4,2,2,1,1]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[7,5,5,2,1,1,1]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,5,3,2,1]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,4,4,3,1]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,4,3,3,1]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[7,5,5,3,1,1]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[7,5,5,4,1]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,5,4,2,1]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,4,4,3,2]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,4,3,3,2]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,5,3,2,2]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,5,4,2]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,5,4,3]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,5,4,3,1,1]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,4,4,3,2,1]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,4,3,3,2,1]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,5,3,2,2,1]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,5,4,2,1,1]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,5,4,3,1]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,5,4,3,2]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,5,4,3,2,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,1]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1,1]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,1]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,2,1]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1,1]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,1]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1,1]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,4,1]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[5,4,4,2,1,1]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,2,1]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[5,4,4,2,1]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,4,3,2]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,4,3,2,1,1]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1,1]
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,1]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,1]
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,1,1]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[6,5,1]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,1,1]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,1,1]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,1]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,2]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,2,1,1]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,2,1]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,1]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,1]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,1]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,2]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,1,1,1]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,2,1,1]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,1,1,1]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,1,1]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,2]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,2,1]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,1,1]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[6,4,1]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1,1,1]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,1,1]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1,1]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,2]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,2,1,1]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[6,3,1]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[6,2,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1,1,1]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1,1]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1,1]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2,2]
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2,2,1,1]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1,1]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1,1]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1]
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2,1]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,2]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,3]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,3,1,1,1]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,2,1,1]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2,1,1,1]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,3,1,1]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,3,2,2]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,3,2,2,1]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,1]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,1]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,1]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,1]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[7,2,1]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,1,1,1]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,2]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[7,3,2]
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[7,4,3,1]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[6,4,4,3]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[7,4,3]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[7,5,4]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[7,5,4,1,1,1,1]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[6,4,4,3,1,1,1]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[7,4,3,1,1,1,1]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[7,5,4,1,1,1]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,2,2]
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,2,2,1]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,2,1,1]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,1,1,1]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,1,1,1]
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1,1,1,1]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,1,1]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[6,4,4,3,1,1]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[7,4,3,1,1,1]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[7,5,4,1,1]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,2,1]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,4,3,2,2]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,2,2]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,2]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,3]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,3,1,1]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,4,3,2,2,1]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,2,2,1]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,2,1,1]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,3,1]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,3,2]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,3,2,1]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,2]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,2]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,2]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[5,4,4,2]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[5,4,4,3,1]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,2]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[6,5,2]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[6,5,3,1,1]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,1]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[6,5,3,1]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,1,1,1]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[6,4,2]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1,1]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[6,3,2]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1,1]
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2,1,1,1]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,1]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[7,3,1]
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[7,4,2]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[7,5,3]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[7,5,3,1,1,1,1]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2,1,1,1]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1,1,1,1]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[7,5,3,1,1,1]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,2,2]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,2,2,1]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,3]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[5,4,4,3]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,3]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[6,5,3]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[6,4,3]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[6,3,3]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,4,1]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[7,4,1]
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[7,5,2]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[7,5,2,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[5,4,4,4]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[6,5,4]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[6,4,4]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[7,5,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[6,5,5]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,5]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[6,5,5,1,1,1,1]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1,1]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,2,2,2]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,2,2,2,1]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[5,4,4,4,1,1,1]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1,1,1,1]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,4,1,1,1,1]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1,1,1,1]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[7,5,2,1,1,1]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[6,5,5,1,1,1]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1,1,1]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1]
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,2,2,1]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,5,2,2,2]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,2,2,2]
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,2,2]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,3,3]
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,3,3,1,1]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,5,2,2,2,1]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,2,2,2,1]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,2,2,1,1]
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,3,3,1]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,3,3,2]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,3,3,2,1]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,3,1,1]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[5,4,4,3,1,1,1]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,1,1,1]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[6,5,3,1,1,1,1]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,1,1]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,1,1,1]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1,1,1,1]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1,1,1,1]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1,1,1]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2,1,1]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2,1,1]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1,1,1]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[7,5,3,1,1]
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,2,1]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[5,4,4,4,1,1]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1,1,1]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,4,1,1,1]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1,1,1]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[7,5,2,1,1]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[6,5,5,1,1]
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1,1]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,2,1,1]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,5,2,2,1]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,2,2,1]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,2,1]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,3,2]
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,3,2,1,1]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,4,4,2,2]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,2,2]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2,2,2]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2,2,2]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,2]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,5,2,2]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,2,2]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,2]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,3,1]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,5,3,3]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,3,3]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,3]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,4]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,4,1,1,1]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,5,3,3,1,1]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,3,3,1,1]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,3,1,1,1]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,4,1,1]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,4,2,2]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,4,2,2,1]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,4,4,2,2,1]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,2,2,1]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2,2,2,1]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2,2,2,1]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,2,1,1]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,5,2,2,1,1]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,2,2,1,1]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,2,1,1,1]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,3,2,1]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,5,3,3,1]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,3,3,1]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,3,1,1]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,4,1]
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,4,2,1]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,5,3,3,2]
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,3,3,2]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,3,2,2]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,4,2]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,4,3]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,4,3,1,1]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,5,3,3,2,1]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,3,3,2,1]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,3,2,2,1]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,4,2,1,1]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,4,3,1]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,4,3,2]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,4,3,2,1]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,2,1]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,2,1,1]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,2,1,1]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[5,4,4,2,1,1,1]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,4,3,2,1]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,2,1,1]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,1,1,1]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,1,1,1]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,1,1,1]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,2,1]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,2,1]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,1,1]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,1]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,1]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,1,1]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,1,1,1]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,1,1,1]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1,1,1,1]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,2,1]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1,1,1]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1,1,1,1]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1,1,1]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1,1,1,1]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2,2,1]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,2,1]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2,1,1]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,3,1]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,3,2,1]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,2,1]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,1,1]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,1,1]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1,1,1]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,1]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[6,4,4,3,1]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[7,4,3,1,1]
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[7,5,4,1]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,1,1]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,4,3,2,1]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,2,1]
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,1]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,1,1]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,3,1]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[5,4,4,3,1,1]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,1,1]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[6,5,3,1,1,1]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,1]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,1,1]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1,1,1]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1,1,1]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1,1]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2,1]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2,1]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1,1]
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[7,5,3,1]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,1,1]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[5,4,4,4,1]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1,1]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,4,1,1]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1,1]
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[7,5,2,1]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[6,5,5,1]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[7,6,1]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[7,6,2,1,1,1]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[6,5,5,2,1,1]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,2,1,1]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[7,6,2,1,1]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,2]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,2,1,1]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,4,4,2,1]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,2,1]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2,2,1]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2,2,1]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,1]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[6,5,5,2,1]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,2,1]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[7,6,2,1]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,1]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,5,3,2]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,3,2]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3]
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,1,1,1]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,5,3,2,1,1]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,3,2,1,1]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,1,1,1]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,1,1]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,2]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,2,1]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,3,2]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,4,3,2,2]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,2,2]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,2,2]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,2,2]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,2,2]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,2,2]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2,2,2]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,3,2]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,4,3,2]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,2]
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,1]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,4,4,2]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,2]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2,2]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2,2]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[6,5,5,2]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,2]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[7,6,2]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[7,6,3,1,1]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[6,5,5,3,1]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,3,1]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[7,6,3,1]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,1,1,1]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,4,4,3]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,3]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,4,3,3]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,3,3]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[6,5,5,3]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,3]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[7,6,3]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[7,6,4,1]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[6,5,5,4]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,4]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[7,6,4]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[7,6,5]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[7,6,5,1,1,1,1]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[6,5,5,4,1,1,1]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,4,1,1,1]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[7,6,4,1,1,1,1]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[7,6,5,1,1,1]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,2,2]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,2,2,1]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,4,4,3,1,1]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,3,1,1]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,4,3,3,1,1]
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,3,3,1,1]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,1,1,1]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[6,5,5,3,1,1,1]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,3,1,1,1]
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[7,6,3,1,1,1,1]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,1,1]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[6,5,5,4,1,1]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,4,1,1]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[7,6,4,1,1,1]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[7,6,5,1,1]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,2,1]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,5,4,2,2]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,4,2,2]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,2,2]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,2]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,3]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,3,1,1]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,5,4,2,2,1]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,4,2,2,1]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,2,2,1]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,2,1,1]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,3,1]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,3,2]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,3,2,1]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,3,2,1]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,4,3,2,2,1]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,2,2,1]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,2,2,1]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,1,1]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,2,2,1]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,2,2,1]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,2,2,1]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2,2,2,1]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,3,2,1,1]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,4,3,2,1,1]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,2,1,1]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,1,1,1]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,1]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,4,4,2,1,1]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,2,1,1]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2,2,1,1]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2,2,1,1]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,1,1,1]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[6,5,5,2,1,1,1]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,2,1,1,1]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[7,6,2,1,1,1,1]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,2,1]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,5,3,2,1]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,3,2,1]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,1,1]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,1]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,1]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,4,4,3,1]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,3,1]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,4,3,3,1]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,3,3,1]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,1,1]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[6,5,5,3,1,1]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,3,1,1]
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[7,6,3,1,1,1]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,1]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[6,5,5,4,1]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,4,1]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[7,6,4,1,1]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[7,6,5,1]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,1,1]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,5,4,2,1]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,4,2,1]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,2,1]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,1]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,1,1]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,4,4,3,2]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,3,2]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,4,3,3,2]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,3,3,2]
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,2]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,5,3,2,2]
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,3,2,2]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,2,2]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,5,4,2]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,4,2]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,2]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,1]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,5,4,3]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,4,3]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,3]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,1,1,1]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,5,4,3,1,1]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,4,3,1,1]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,3,1,1]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,1,1,1]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,1,1]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,2]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,2,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,4,4,3,2,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,3,2,1]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,4,3,3,2,1]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,3,3,2,1]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,2,1]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,5,3,2,2,1]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,3,2,2,1]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,2,2,1]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,1,1]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,5,4,2,1,1]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,4,2,1,1]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,2,1,1]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,1,1,1]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,1]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,5,4,3,1]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,4,3,1]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,3,1]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,1,1]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,1]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,5,4,3,2]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,4,3,2]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,3,2]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,2]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,1,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,5,4,3,2,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,4,3,2,1]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,3,2,1]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,2,1]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,1,1]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,1]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,2]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,2,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,6,5,4,3,2,1]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[7,7,6,5,4,3,2,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[8,7,7,6,5,4,3,2,1]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,6,5,4,3,2]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[7,7,6,5,4,3,2]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[8,8,7,6,5,4,3,2,1]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[9,8,8,7,6,5,4,3,2,1]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[8,7,7,6,5,4,3,2]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,6,5,4,3,1]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,6,5,4,3,1,1]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[7,7,6,5,4,3,1]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[7,7,6,5,4,3,1,1]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[8,8,7,6,5,4,3,2]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[9,9,8,7,6,5,4,3,2,1]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[10,9,9,8,7,6,5,4,3,2,1]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[8,7,7,6,5,4,3,1,1]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,6,5,4,3]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,6,5,4,2,2,1]
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[7,7,6,5,4,3]
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[8,8,7,6,5,4,3,1]
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[7,7,6,5,4,2,2,1]
[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[8,8,7,6,5,4,3,1,1]
[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[9,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,6,5,4,2,1]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[7,6,6,5,3,3,2,1]
[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[7,7,6,5,3,2,2,1]
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[7,7,6,5,4,2,1]
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[7,7,6,5,4,2,2]
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[8,8,7,6,5,4,3]
[1,0,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[9,9,8,7,6,5,4,3,1,1]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[7,6,6,4,4,3,2,1]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[8,8,7,6,5,3,2,2,1]
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[7,7,6,5,4,1]
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[7,7,6,4,4,3,2,1]
[1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[8,8,7,6,5,3,3,2,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[7,5,5,4,4,3,2,1]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,6,5,4]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[7,5,5,5,4,3,2,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,4,3,2,1]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[7,7,5,4,4,3,2,1]
[1,0,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[7,7,6,5,3,2,1]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[7,7,6,5,4]
[1,0,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[7,7,6,5,3,3,1,1]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,5,4,3,2,1]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[7,7,5,5,4,3,2,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[6,5,5,5,4,3,2,1]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[7,5,5,5,4,3,2]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[6,6,5,5,4,3,2,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,4,3,2]
[1,0,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[8,8,7,6,5,3,2,1]
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[8,8,7,6,5,4]
[1,0,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[8,8,7,6,5,3,2,1,1]
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,5,4,3,2]
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[7,7,5,5,4,3,2]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[6,6,6,5,4,3,2,1]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[8,6,6,6,5,4,3,2,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,5,4,3,2,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[6,5,5,5,4,3,2]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,4,3,1]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,4,3,1,1]
[1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[7,7,6,4,4,3]
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,5,4,3,1]
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,5,4,3,1,1]
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[6,6,6,5,4,3,2]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[8,7,6,6,5,4,3,2,1]
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[8,8,6,6,5,4,3,2,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[7,6,6,6,5,4,3,2,1]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[7,7,6,6,5,4,3,2,1]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,5,4,3,2]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[6,5,5,5,4,3,1,1]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[7,6,6,4,3,2,1]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[6,6,5,5,4,3,1,1]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,4,3]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,4,2,2,1]
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[7,7,6,5,1]
[1,0,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[7,7,6,4,3,2,1]
[1,1,0,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,5,4,2,2,1]
[1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[6,6,6,5,4,3,1,1]
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[8,7,6,6,5,4,3,2]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[7,7,7,6,5,4,3,2,1]
[]=>[]=>[]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[8]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[8,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[8,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[8,2,2,2,2,2,2]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[8,2,2,2,2,2,2,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[8,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[8,2,2,2,2,2,1]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[8,2,2,2,2,2]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,3,3,3,3]
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,3,3,3,3,1,1]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[8,2,2,2,2,2,1,1]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,3,3,3,3,1]
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,3,3,3,3,2]
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,3,3,3,3,2,1]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[8,1,1,1,1]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[8,4,4,4,4]
[1,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[8,4,4,4,4,2,2,1]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,3,3,3,2,1]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[8,4,4,4,4,1]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[8,4,4,4,4,2]
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[8,4,4,4,4,3]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,3,3,3,2,2,1]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[8,4,4,4,4,2,1,1]
[1,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[8,4,4,4,4,3,2]
[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[8,4,4,4,4,3,2,1]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0]=>[8,1,1,1]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,1,0]=>[8,3,3,3]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,5,5]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,5,5,1]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,5,5,2]
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[8,5,5,5,4]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,5,5,2,1,1,1]
[1,1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,5,5,3,2,1]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[8,4,4,4,3,3,2,1]
[1,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[8,5,5,5,4,3,2]
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[8,5,5,5,4,3,2,1]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[8,1,1]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[8,2,2,1,1,1,1]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[8,2,2,1,1]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0]=>[8,2,2,1]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[8,3,3,2,1,1]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[8,3,3,2,1]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[8,4,4,3,2]
[1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[8,4,4,3,2,1,1,1]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[8,5,5,4,2,2]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]=>[8,2,2]
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,1,0]=>[8,3,3,1]
[1,1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[8,5,5,3,1,1,1,1]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,1,0]=>[8,3,3]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,1,0]=>[8,5,5]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]=>[8,6,6]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[8,5,5,2,2,2,2]
[1,1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[8,6,6,3,3,3,2,1]
[1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[8,6,6,2,2,1,1]
[1,1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,6,4,4]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,6,4,4,2,2]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,6,4,4,2]
[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,6,4,4,3,2,1]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[8,2,2,1,1,1,1,1]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[8,4,4,3,2,1]
[1,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[8,5,5,4,3,2,1,1]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,1,0]=>[8,6,6,1]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,1,0]=>[8,6,6,2]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[8,6,6,4,2]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0,1,0]=>[8,6,6,3]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,1,0]=>[8,6,6,5]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[8,6,6,4,2,2,2]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[8,6,6,4,2,2,2,1]
[1,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[8,5,5,4,3,2,1]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[8,6,6,2,1,1,1,1]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[8,5,5,3,3,1,1]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[8,6,6,4,2,2]
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,6,5,4,2,2,1]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[8,6,6,4,2,2,1,1]
[1,1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,6,5,4,1]
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,6,5,4,3]
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,6,5,4,3,1,1]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[8,5,5,4,4,3,2,1]
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,6,5,4,2,1,1]
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,6,5,4,3,1]
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,6,5,4,3,2]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,6,5,4,3,2,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[8,1]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[8,2,1,1,1]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,1,0]=>[8,3,2,2]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[8,2,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[8,3,2,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[8,4,3,2,1]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,1,0]=>[8,4,3,2]
[1,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,1,1,1,1]
[1,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,2,2,2,1]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0]=>[8,3,2]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,2,2]
[1,1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,4]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,2,2,1,1]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,3,3,2,1]
[1,1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,4,3,1]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,4,3,2,1]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[8,2]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0]=>[8,3,1]
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,1,0]=>[8,4,2,1]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0]=>[8,4,2]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[8,5,3,1,1,1,1]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0]=>[8,3]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[8,4,1,1,1]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,1,0]=>[8,4,1]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0]=>[8,4]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0]=>[8,5]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,1,0]=>[8,6,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[8,6]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[8,7]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[8,7,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[8,7,2,2,2,2,2]
[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[8,7,2,2,2,2,2,1]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[8,6,2,2,2,2,2]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,3,3]
[1,1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[8,7,4,4,4]
[1,1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[8,7,4,4,4,2,2]
[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[8,7,4,4,4,3,2,1]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[8,3,1,1,1,1,1,1]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[8,5,2,1,1,1]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0]=>[8,7,1,1]
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,3,2,1]
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,3,2,1,1,1]
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,5]
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,5,1,1,1,1]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[8,6,4,4,4,2,2]
[1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,5,3,3,2,1]
[1,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[8,7,4,4,3,2,1]
[1,1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,5,2,1]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[8,6,4,4,4,2]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[8,7,4,4,2,2]
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[8,7,5,5,4,3,1,1]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[8,6,4,4,4,3,2,1]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[8,7,4,4,3,3,2,1]
[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[8,7,5,5,4,3,2]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[8,7,5,5,4,3,2,1]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[8,2,1,1,1,1,1,1]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[8,4,3,2,1,1]
[1,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,2,1,1]
[1,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,2,2]
[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,2,2,1]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[8,5,3,2,1]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,1,0]=>[8,6,2,1]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0]=>[8,7,1]
[1,1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[8,7,3,2,2,2]
[1,1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,2,1,1,1]
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,2,2,2,1]
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,3,3,1]
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,3,3,2,1]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[8,3,2,2,2,2,2]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,2]
[1,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,2,1,1,1]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,2]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0]=>[8,7,2]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0,1,0]=>[8,6,5,3]
[1,1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,1]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,1,0]=>[8,7,3]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,1,0]=>[8,7,4]
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0]=>[8,7,5,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]=>[8,7,5]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[8,7,6]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,2,2,2]
[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,2,2,2,1]
[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,3,3]
[1,1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,3,3,1,1]
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,3,3,2,1]
[1,1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,1,1]
[1,1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,2,1]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[8,7,4,2,2,2,2]
[1,1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,2]
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,4]
[1,1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,3,1,1,1]
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,4,2,2]
[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,4,2,2,1]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,2,2,2,1]
[1,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,2,1,1,1]
[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,3,2,1]
[1,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,3,1,1]
[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,4,2,1]
[1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,3,2,2]
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,4,3,1,1]
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,3,2,2,1]
[1,1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,4,2,1,1]
[1,1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,4,3,1]
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,4,3,2]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,4,3,2,1]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[8,3,2,2,2,2,2,1]
[1,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[8,5,4,4,3,2,1]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,2,1,1,1]
[1,1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,1]
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,2,1]
[1,1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,2,2,1]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[8,7,2,1,1,1,1,1]
[1,1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[8,7,3,2,2,2,1]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,2,2,1]
[1,1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,3,2]
[1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,3,2,1,1]
[1,1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,2,1]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[8,7,5,1,1]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,1]
[1,1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,1]
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,2,1]
[1,1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3]
[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,2,1,1,1]
[1,1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,2]
[1,1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,3,1]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[8,6,4,4,2,2]
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2]
[1,1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,3]
[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3]
[1,1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,1]
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5]
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,1,1,1,1]
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,2,2,2]
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,2,2,2,1]
[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,1,1]
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,2,2,1]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,4,2,2]
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,3]
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,3,1,1]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[8,6,5,5,4,2,2,1]
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,2,2,1,1]
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,3,1]
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,3,2]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,3,2,1]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,2,1,1]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[8,7,3,2,2,2,2,1]
[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,3,2,1]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[8,6,4,4,2,2,1,1]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,5,3,2,1]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,3,2,1]
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3,2,1]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,3,1]
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,2,1]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,1]
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,2,1,1]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[8,6,5,5,4,2,1]
[1,1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,2,2,1]
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,2,1]
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,2]
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,2,1,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,3,2]
[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3,2]
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,1]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[8,6,5,5,4,3]
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,1,1,1]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[8,6,5,5,4,3,1,1]
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,1,1,1]
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,1,1]
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,2,2]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,2,2,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[8,5,4,4,4,3,2,1]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,3,3,2,1]
[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,3,2,2,1]
[1,1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,2,2,2,1]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[8,6,5,5,4,2,1,1]
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,2,1,1,1]
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,2,1]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[8,6,5,5,4,3,1]
[1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3,3,1]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,1,1]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,1]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,2,1]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[8,6,5,5,4,3,2]
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3,3,2]
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,2,2]
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,2]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,3]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,3,1,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[8,6,5,5,4,3,2,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,4,3,2,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3,3,2,1]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,2,2,1]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,2,1,1]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,3,1]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,3,2]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,3,3]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,4,4,4,4]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,5,5,5]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[6,6,6]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[7,7]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,2]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,3,3,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,3,3,3,3,3,3]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,4,4,4,4,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,4,4,4,4,4]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,5,5,5,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,5,5,5,5]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]=>[6,6,6,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[6,6,6,6]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[7,7,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[7,7,7]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[8,8]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,2,2]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,3,3,2]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,4,4,4,4,2]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,3,3,2,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[5,5,5,5,5,5]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,1,0,0,0]=>[6,6,6,2]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[5,5,5,5,2,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[6,6,6,6,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[6,6,6,6,6]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0]=>[7,7,2]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[7,7,2,1,1,1,1,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0]=>[8,8,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[9,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[9,9]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[10]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,2,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,3,3,3,3,3,3,2]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[4,4,4,4,4,3]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,3,3,3,3,3,3,2,1]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,5,5,5,3]
[1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[4,4,4,4,4,3,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,1,0,0,0]=>[6,6,6,3]
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[4,4,4,4,4,3,2]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,1,0,0]=>[7,7,3]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[6,6,6,3,1,1,1,1]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,5,5,5,3,2,2]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,1,0,0]=>[8,8,2]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0]=>[9,2]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[9,2,1,1,1,1,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]=>[10,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,10]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,5,5,5,4]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[4,4,4,4,4,3,2,1]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,5,5,5,3,2,2,1]
[1,0,1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,5,5,5,4,2,2]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[7,7,4,1,1,1,1,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[6,6,6,3,2,2,2,1]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[6,6,6,4,2,2,2]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0]=>[9,3]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0]=>[10,2]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[9,3,2,2,2,2,2,2]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[11,1]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0]=>[6,6,6,5]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,4,4,4,4,4,3,2,1]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0]=>[7,7,5]
[1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[6,6,6,5,1,1,1,1]
[1,0,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[5,5,5,5,4,3,1]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0]=>[9,4]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[7,7,4,2,2,2,2,1]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[7,7,5,2,2,2,2]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[6,6,6,4,3,3,1]
[1,0,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[6,6,6,5,4]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[9,3,2,2,2,2,2,2,1]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[6,6,6,6,5]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0]=>[7,7,6]
[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[5,5,5,5,4,3,2]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0]=>[9,5]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[5,5,5,5,4,3,2,1]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[7,7,5,3,3,3,1]
[1,0,1,0,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[6,6,6,6,5,4]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,1,0,0]=>[7,7,6,5]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[6,6,6,6,6,5]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,1,0,0,0]=>[7,7,7,6]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[5,5,5,5,5,4,3,2]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0]=>[9,6]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[5,5,5,5,5,4,3,2,1]
[1,0,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[6,6,6,5,4,2,1,1]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,1,0,0]=>[8,8,7]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0]=>[9,7]
[1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[6,6,6,5,4,3]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,1,0,0]=>[8,8,7,6]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,3,2,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,3,2,1]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,3,2,2,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,1,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,2,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,1,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,2,2,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,2,1,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[4,4,4,4,3,2,1]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[4,4,4,4,3,3,2,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,1,1,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[3,3,3,2,1]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[4,4,4,3,2,1,1]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,1,1,1,1,1]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[4,4,4,3,2,1]
[1,0,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[5,5,5,4,3,2,1,1]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[5,5,5,4,3,2,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[5,5,5,4,3,2,2,1]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[5,5,5,4,4,3,2,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[2,2,1,1,1,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[2,2,1,1,1]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[2,2,1]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[3,3,2,1,1,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[3,3,2,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,4,3,2,1]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,4,3,2,1,1,1,1]
[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[5,5,4,3,2,2,2,1]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[3,3,2,1,1,1,1,1]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[5,5,4,3,2,2,1,1]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[5,5,4,3,3,3,2,1]
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[6,6,5,4,4,3,2,1]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[2,2,1,1,1,1,1,1]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,4,3,2,1,1]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[5,5,4,3,2,1]
[1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[6,6,5,4,3,2,2,1]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,3,2,2,2,2,2,1]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[5,5,4,4,3,2,1]
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[6,6,5,4,3,2,1]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[6,6,5,4,3,2,1,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[5,5,4,4,4,3,2,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[6,6,5,4,3,3,2,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,2,2,2,2,1,1]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,2,2,2,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[4,3,3,3,3,2,2,1]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,1,1,1]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[4,3,3,3,2,2,2,1]
[1,1,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[5,4,4,4,3,3,2,1]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[2,1,1]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[4,3,3,2,1]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[5,4,4,3,3,3,2,1]
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,5,4,4,3,2,1]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[2,1]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1,1,1,1]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,2,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,1,1,1,1]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,1,1,1,1,1]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,1,1,1]
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,3,3,2,1]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1,1,1,1,1,1]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,1,1]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,2,2,1]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,2,2,2,2,1]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,3,2,1]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,3,2,2,1]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[6,5,4,4,4,3,2,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,1,1,1,1,1,1,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,2,2,2,2,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[4,3,3,3,3,2,1]
[1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[6,5,5,4,3,2,2,1]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1,1,1,1,1]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,2,2,1]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,1]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,2,1]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,2,1,1,1]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,3,2,1]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,2,2,2,2,2,1]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[4,3,3,3,3,2,1,1]
[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[6,5,5,4,3,2,1]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,2,2,2,1,1]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,2,1,1,1]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,4,3,2,1]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,2,1,1]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[4,3,3,3,3,3,2,1]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[5,4,4,4,3,2,2,1]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[6,5,5,4,3,2,1,1]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,2,2,2,1]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,4,3,2,1,1]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,2,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[5,4,4,4,4,3,2,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[6,5,5,4,3,3,2,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,4,3,3,2,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,2,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,3,3,3,3,3,2,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,3,3,3,3,3,2,2,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,3,3,3,3,2,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,1,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[3,3,3,3,2,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,1,1,1,1,1]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[6,6,6,6,5,4,3,2,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[4,4,4,3,2,1]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,1,1,1,1,1,1]
[1,0,1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[6,6,6,5,4,3,2,2,1]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[6,6,6,5,4,3,2,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[6,6,6,5,4,3,2,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[2,2,1,1,1,1,1,1]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[2,2,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[4,4,3,2,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[5,5,4,3,2,1,1,1,1]
[1,0,1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[6,6,5,4,3,3,3,2,1]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[5,5,4,3,3,2,2,1,1]
[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[7,7,6,5,5,4,3,2,1]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[2,2,1,1,1,1,1,1,1]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[5,5,4,3,2,1]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[6,6,5,4,3,2,1]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[6,6,5,4,3,2,1,1,1]
[1,0,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[7,7,6,5,4,3,3,2,1]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[3,3,2,2,2,2,2,2,1]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[6,6,5,5,4,3,2,1]
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[7,7,6,5,4,3,2,1,1]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[7,7,6,5,4,3,2,1]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[6,6,5,5,5,4,3,2,1]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[7,7,6,5,4,4,3,2,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[2,1,1,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[3,2,2,2,2,2,2,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[2,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[4,3,3,3,3,3,2,2,1]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[2,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[5,4,4,4,4,3,3,2,1]
[1,1,0,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[6,5,5,5,4,4,3,2,1]
[1,1,0,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[7,6,6,5,5,4,3,2,1]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2,2,2,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,4,3,2,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,4,3,2,1,1,1,1,1]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[6,5,4,3,2,2,2,1]
[1,1,0,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[7,6,5,4,4,4,3,2,1]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[6,5,4,3,3,3,2,1]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[7,6,5,4,4,3,2,1]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[7,6,5,5,5,4,3,2,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,4,3,2,1,1]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[6,5,4,3,2,1,1,1]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[6,5,4,3,2,1]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[7,6,5,4,3,2,1,1]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,4,3,2,1]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[3,2,2,2,2,2,2,2,1]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[6,5,5,5,4,3,2,1]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[6,5,4,3,2,1,1,1,1]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[7,6,5,4,3,3,2,1]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[7,6,5,4,3,2,1]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[6,5,4,4,4,3,2,1]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[7,6,5,4,3,2,2,1]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,3,2,2,1]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[4,3,3,3,3,3,3,2,1]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[7,6,5,5,4,3,2,1]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,3,2,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[5,4,4,4,4,4,3,2,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[7,6,5,4,3,3,3,2,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,3,2,1,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[6,5,5,5,5,4,3,2,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,3,3,2,1]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,3,2,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[2]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[3]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[4]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[5]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[6]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[7]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[2]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[3,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[3]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[4,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[4]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[5,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[5]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[6,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[6]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[7]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[8]
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,1,1,1,1,1]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,1]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,1,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[9,8,7,1,1,1,1,1,1]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[9,8,7,1]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,2,2,2,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[9,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,3,1,1]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,3,1]
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,4,3,1,1]
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,1,1,1]
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,1]
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,4,3,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[3,2,2,2,2,2,2]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[4,2,2,2,2]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,3,2,2,2,2]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[3,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[7,6,6]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,5,5]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[5,4,4,4,4]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[4,3,3,3,3,3]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,2,2,2,2,2]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[9,7,7,6,5,4,3,2,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[9,7,6,6,5,4,3,2,1]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[10,8,7,7,6,5,4,3,2,1]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[9,7,6,6,5,4,3,2]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[6,4,4,4,3,3,2,1]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[5,3,3,3,3,2,2,1]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[4,2,2,2,2,2,1,1]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[3,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,2,2,1]
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,3,3,2,1]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,4,4,3,2,1]
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[9,8,7,5,5,4,3,2,1]
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[9,8,6,6,5,4,3,2,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]=>[7,6,5]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,5]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,1,0,0]=>[7,5,5,5]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0]=>[9,7,7]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,4,3,2]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[7,5,4,4,4,3,2,1]
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,2,2,2,1]
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,1]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,2,2]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[3,3]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]=>[2,2,2]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,3,3,3,3,3]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0]=>[5,1,1,1]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[3,2]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,1,0]=>[9,3,3]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,1,0]=>[9,2,2,2]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[9,1,1,1,1]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[8,8,7,6,5]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,1,0,0]=>[7,7,6,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[7,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[7,7,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[7,1]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[7,6]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[7,2,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[9,2,2,2,2,2,2,2,1]
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[7,3,2,2,2,2,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[9,3,3,3,3,3,3,2]
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[7,4,3,3,3,3,2]
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[9,4,4,4,4,4,3]
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[7,5,4,4,4,3]
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[9,5,5,5,5,4]
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,5,4]
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[9,6,6,6,5]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0,1,0]=>[9,7,7,6]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[9,8,7]
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[7,6,4,4,4,3,2,1]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,3,3,2,1]
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,2,2,2,1]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,1,1,1]
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,2]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,3,3,2,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[9,8,6,5,5,4,3,2,1]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,2,1,1,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[9,8,7,5,4,4,3,2,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,4,3,3,2,1]
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,3,2]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,3,2,2,1]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,2,1,1]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[4,4,4,3,3]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,3,3,2,1]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,5,3,2,2,1]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,2,1,1,1]
[1,1,1,0,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,3,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,3]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]=>[3,3]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[9,4,4,4,4,4]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,3,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[9,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[10,8,7,7,6,5,4,3,2]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[9,7,6,6,5,4,3]
[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[9,7,7,6,5,4,3]
[1,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[10,8,8,7,6,5,4,3,2]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0]=>[6,1]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0]=>[5,1]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0]=>[4,1]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[3,1]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,1,1,1]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[6,3,2,2,2,1]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[7,3,3,3,2,1]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[7,3,2,2,1]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[6,3,2,1,1]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,1]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[6,4,3,2,1,1]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[6,4,3,3,3,1,1]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[7,4,3,2,2,1]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[7,4,4,4,3,1,1]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[8,4,3,3,2,1]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[9,4,4,3,2,1]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,2,2,2,2,1]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[8,3,3,3,2,1]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[7,4,2,2,1,1]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[7,3,2,2,2,1]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[6,4,2,1,1,1]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0]=>[6,3,2,1,1,1]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[5,5,3,2,1]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[5,3,2,1]
[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[9,6,6,6,5,4,3,2,1]
[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[9,5,5,5,5,4,3,2,1]
[1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[9,4,4,4,4,4,3,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[9,3,3,3,3,3,3,2,1]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0,0]=>[6,3,3]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[9,2,2,2,2,2,2,2]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[9,3,3,3,3,3,3]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[9,5,5,5,5]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[9,6,6,6]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[9,8]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[10,1,1,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[10,2,2,2,2,2,2,2,2]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[9,3,3,3,3,3,3,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[10,3,3,3,3,3,3,3]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[9,4,4,4,4,4,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[10,4,4,4,4,4,4]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[9,5,5,5,5,1]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[10,5,5,5,5,5]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[9,6,6,6,1]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[10,6,6,6,6]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0,1,0]=>[9,7,7,1]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[10,7,7,7]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,1,0]=>[9,8,1]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,1,0]=>[10,8,8]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0]=>[10,9]
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,2,1]
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,3,2,1]
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,4,3,2,1]
[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[9,8,7,5,4,3,2,1]
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[9,8,6,5,4,3,2,1]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,7,6,5,4,3,2,1]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[8,8,6,6,4,4,2,2]
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[8,8,6,6,4,4,2]
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[8,8,6,6,4,2]
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[8,8,6,6,4,2,2,2]
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[8,8,6,6,4,2,2]
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[8,8,6,4,2,2,2,2]
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[8,8,6,4,2,2,2]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[8,8,6,4,2,2]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[8,8,6,4,2]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[8,8,6,4,4,4,2,2]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[8,8,6,4,4,4,2]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[8,8,6,4,4,2]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[8,8,6,4,4,2,2,2]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[8,8,6,4,4,2,2]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[8,6,4,4,4,4,2,2]
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[8,6,4,4,4,4,2]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[8,6,4,4,4,2]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[8,6,4,4,4,2,2,2]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[8,6,4,4,4,2,2]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[8,6,4,4,2,2]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[8,6,4,4,2]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[8,6,4,2,2,2]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[8,6,4,2,2]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[8,6,4,4,2,2,2,2]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[8,6,4,4,2,2,2]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[8,6,4,2]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[8,6,4,2,2,2,2,2]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[8,6,4,2,2,2,2]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[8,6,6,6,4,4,2,2]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[8,6,6,6,4,4,2]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[8,6,6,6,4,2]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[8,6,6,6,4,2,2,2]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[8,6,6,6,4,2,2]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[8,6,6,4,2,2,2,2]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[8,6,6,4,2,2,2]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[8,6,6,4,2,2]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[8,6,6,4,2]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[8,6,6,4,4,4,2,2]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[8,6,6,4,4,4,2]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[8,6,6,4,4,2]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[8,6,6,4,4,2,2,2]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[8,6,6,4,4,2,2]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[10,10,8,8,6,6,4,4,2,2]
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[10,10,8,8,6,6,4,4,2]
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[10,10,8,8,6,6,4,2]
[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[10,10,8,8,6,6,4,2,2,2]
[1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[10,10,8,8,6,6,4,2,2]
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[10,10,8,8,6,4,2,2,2,2]
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[10,10,8,8,6,4,2,2,2]
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[10,10,8,8,6,4,2,2]
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[10,10,8,8,6,4,2]
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[10,10,8,8,6,4,4,4,2,2]
[1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[10,10,8,8,6,4,4,4,2]
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[10,10,8,8,6,4,4,2]
[1,0,1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[10,10,8,8,6,4,4,2,2,2]
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[10,10,8,8,6,4,4,2,2]
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[10,10,8,6,4,4,4,4,2,2]
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[10,10,8,6,4,4,4,4,2]
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[10,10,8,6,4,4,4,2]
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[10,10,8,6,4,4,4,2,2,2]
[1,0,1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[10,10,8,6,4,4,4,2,2]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[10,10,8,6,4,4,2,2]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[10,10,8,6,4,4,2]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[10,10,8,6,4,2,2,2]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[10,10,8,6,4,2,2]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[10,10,8,6,4,4,2,2,2,2]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[10,10,8,6,4,4,2,2,2]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[10,10,8,6,4,2]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[10,10,8,6,4,2,2,2,2,2]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[10,10,8,6,4,2,2,2,2]
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[10,10,8,6,6,6,4,4,2,2]
[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[10,10,8,6,6,6,4,4,2]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[10,10,8,6,6,6,4,2]
[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[10,10,8,6,6,6,4,2,2,2]
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[10,10,8,6,6,6,4,2,2]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[10,10,8,6,6,4,2,2,2,2]
[1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[10,10,8,6,6,4,2,2,2]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[10,10,8,6,6,4,2,2]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[10,10,8,6,6,4,2]
[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[10,10,8,6,6,4,4,4,2,2]
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[10,10,8,6,6,4,4,4,2]
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[10,10,8,6,6,4,4,2]
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[10,10,8,6,6,4,4,2,2,2]
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[10,10,8,6,6,4,4,2,2]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[10,8,6,6,6,6,4,4,2,2]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[10,8,6,6,6,6,4,4,2]
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[10,8,6,6,6,6,4,2]
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[10,8,6,6,6,6,4,2,2,2]
[1,1,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[10,8,6,6,6,6,4,2,2]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[10,8,6,6,6,4,2,2,2,2]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[10,8,6,6,6,4,2,2,2]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[10,8,6,6,6,4,2,2]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[10,8,6,6,6,4,2]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[10,8,6,6,6,4,4,4,2,2]
[1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[10,8,6,6,6,4,4,4,2]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[10,8,6,6,6,4,4,2]
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[10,8,6,6,6,4,4,2,2,2]
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[10,8,6,6,6,4,4,2,2]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[10,8,6,6,4,4,2,2,2,2]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[10,8,6,6,4,4,2,2,2]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[10,8,6,6,4,2]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[10,8,6,6,4,2,2,2,2,2]
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[10,8,6,6,4,2,2,2,2]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[10,8,6,4,4,4,2,2,2,2]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[10,8,6,4,4,4,2,2,2]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[10,8,6,4,4,2]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[10,8,6,4,4,2,2,2,2,2]
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[10,8,6,4,4,2,2,2,2]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[10,8,6,6,4,4,2,2]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[10,8,6,6,4,2,2,2]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[10,8,6,6,4,4,2]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[10,8,6,6,4,2,2]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[10,8,6,4,2,2]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[10,8,6,4,2]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[10,8,6,4,4,4,2,2]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[10,8,6,4,4,2,2,2]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[10,8,6,4,4,4,2]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[10,8,6,4,4,2,2]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[10,8,6,6,4,4,4,4,2,2]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[10,8,6,6,4,4,4,4,2]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[10,8,6,6,4,4,4,2]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[10,8,6,6,4,4,4,2,2,2]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[10,8,6,6,4,4,4,2,2]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[10,8,6,4,2,2,2,2,2,2]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[10,8,6,4,2,2,2,2,2]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[10,8,6,4,2,2,2,2]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[10,8,6,4,2,2,2]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[10,8,6,4,4,4,4,4,2,2]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[10,8,6,4,4,4,4,4,2]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[10,8,6,4,4,4,4,2]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[10,8,6,4,4,4,4,2,2,2]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[10,8,6,4,4,4,4,2,2]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[10,8,8,8,6,6,4,4,2,2]
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[10,8,8,8,6,6,4,4,2]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[10,8,8,8,6,6,4,2]
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[10,8,8,8,6,6,4,2,2,2]
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[10,8,8,8,6,6,4,2,2]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[10,8,8,8,6,4,2,2,2,2]
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[10,8,8,8,6,4,2,2,2]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[10,8,8,8,6,4,2,2]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[10,8,8,8,6,4,2]
[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[10,8,8,8,6,4,4,4,2,2]
[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[10,8,8,8,6,4,4,4,2]
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[10,8,8,8,6,4,4,2]
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[10,8,8,8,6,4,4,2,2,2]
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[10,8,8,8,6,4,4,2,2]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[10,8,8,6,4,4,4,4,2,2]
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[10,8,8,6,4,4,4,4,2]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[10,8,8,6,4,4,4,2]
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[10,8,8,6,4,4,4,2,2,2]
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[10,8,8,6,4,4,4,2,2]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[10,8,8,6,4,4,2,2]
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[10,8,8,6,4,4,2]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[10,8,8,6,4,2,2,2]
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[10,8,8,6,4,2,2]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[10,8,8,6,4,4,2,2,2,2]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[10,8,8,6,4,4,2,2,2]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[10,8,8,6,4,2]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[10,8,8,6,4,2,2,2,2,2]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[10,8,8,6,4,2,2,2,2]
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[10,8,8,6,6,6,4,4,2,2]
[1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[10,8,8,6,6,6,4,4,2]
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[10,8,8,6,6,6,4,2]
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[10,8,8,6,6,6,4,2,2,2]
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[10,8,8,6,6,6,4,2,2]
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[10,8,8,6,6,4,2,2,2,2]
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[10,8,8,6,6,4,2,2,2]
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[10,8,8,6,6,4,2,2]
[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[10,8,8,6,6,4,2]
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[10,8,8,6,6,4,4,4,2,2]
[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[10,8,8,6,6,4,4,4,2]
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[10,8,8,6,6,4,4,2]
[1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[10,8,8,6,6,4,4,2,2,2]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[10,8,8,6,6,4,4,2,2]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,4,3,2,1]
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[9,8,7,7,6,5,4,3,2,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0]=>[8,7,7]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,1,0,0]=>[7,6,6,5]
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,2,2]
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[9,7,7,6,5,4,3,2]
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[10,8,8,7,6,5,4,3,2,1]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[11,9,8,8,7,6,5,4,3,2,1]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[9,7,6,6,5,4,3,1]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[9,7,6,6,5,4,3,1,1]
[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[9,7,7,6,5,4,3,1]
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[9,7,7,6,5,4,3,1,1]
[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[11,9,9,8,7,6,5,4,3,2,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>[2]
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[6,6,6,4,4,3,2,1]
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[5,5,5,5,3,3,2,1]
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,4,4,4,4,2,2,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,3,3,1,1]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0]=>[7,6,1]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,4]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,6,5,4,3,2,1]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[6,3,3,3,3,3]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0]=>[4,1,1]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6]
[1,1,1,0,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,3]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,2,2]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,1]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[6,5,2,2,1,1,1,1]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,0]=>[6,6,5,1]
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,2]
[1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[7,7,7,6,5,4,3,2]
[1,0,1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[6,6,6,6,5,4,3,2]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[5,4,4,4,4,3,2]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,7,6,5,4,3,2,2,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[9,8,6,5,4,3,3,2,1]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[4,3,3,3,3,2]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,3,2,2]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[7,7,1,1,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[4,4,4,3,3,3]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[9,1,1,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[2,2]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]=>[8,7]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0]=>[7,5]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,3]
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,4,3]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[9,8,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,5,5,5,4,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,2,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,3,3,2,2,2,2]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[9,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,5,5,5,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0]=>[6,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0]=>[6,6,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[6,6,6,1,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0]=>[6,6]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0]=>[6,6,6]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5]
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[6,6,6,4,3,2,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>[9]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,1,1,1,1,1]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[7,6,1,1,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[6,6]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1]
[1,1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[9,8,7,2,2,2,2,2,1]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,1]
[1,1,1,0,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,2,1,1,1,1]
[1,1,0,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[7,4,3,3,3,3,2,1]
[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,7,6,5,4,3,2,1,1]
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[9,7,6,5,5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[6,6,6,6,6,5,4,3,2]
[1,0,1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[6,6,6,4,4,3,2]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[9,8,6,5,5,3,3,2,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[7,2,2,2,2,2,2]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0]=>[6,5,5]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,2,2,2]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,4,4,4,4,2,2]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[6,6,6,4,4]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[3,2,2,2,2,2,2,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[8,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[7,2]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[6,4,4,4,3,3,1,1]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[6,5,5,5,4]
[1,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[9,8,7,4,4,4,3,2,1]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[3,3,1,1,1,1,1]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>[4,1,1,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[4,4,4,1,1,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[5,5,4,3,2,1]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0]=>[6,4,3,2]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,2]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[6,5,4,3,2]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,4,4,4,4,1,1]
[1,0,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[7,7,4,4,4,3,2,1]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[7,3,2,2,2,2,1,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[8,7,7,7,6,5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,3,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[4,3,3,3,3]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[2,2]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[3,3,1,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,3,2,1]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]=>[7,7]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0]=>[4,4]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0]=>[3,3,3]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[5,1,1,1,1]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[6,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,4,4,4,4,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,3,3,3,3,3,3,1,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,5,5,5,3,2,1]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[5,4,4,4,4,2,1]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[4,1,1,1,1,1,1]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[4,1,1,1,1,1]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[4,2]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[7,7,2,2,2,2,2]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0]=>[4,4,4]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[4,4,4,4]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0]=>[4,4,3]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[8,8,7,7,6,5,4,3,2,1]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[7,7,4,3,2,1]
[1,0,1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[6,6,6,2,2,2,2,1]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,2,2,1,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[7,3,3,2,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[7,4,3,2,1]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[6,4,3,2,1]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[6,4,3,2,1]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0,0]=>[7,4,3,2,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0,0]=>[8,4,3,2,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[9,4,3,2,1]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[6,5,3,2,1,1]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[5,5,3,2,1,1]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[5,2,2,2,2,2,2,1]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[7,3,3,3,3,3]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0]=>[8,1,1]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0]=>[7,2,2]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,1,1,1]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[6,6,4,4,4,3,2,1]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[6,6,1,1,1,1,1,1]
[1,1,0,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[9,7,7,6,2,1,1,1,1]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0,0]=>[5,4,4]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0]=>[5,5,5]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0]=>[5,2,2,2]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[5,4,4,4,4,3,1,1]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[7,4,4,4,4,3,2,1]
[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,3,2,1,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[8,8,6,5,4,3,2,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,3,1,1]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,1,0,0]=>[8,7,6,6]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[9,8,2,2,2,2,2,2]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[7,6,3,2,2,2,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[9,1,1,1,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[8,8,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,3,2,2]
[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,3,3,2]
[1,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[9,8,6,6,5,4,3,2]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[9,6,5,5,5,4,3,2,1]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[7,7,3,2,1]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[7,6,2,2,2,1]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[6,5,4,1,1,1,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[5,5,4,3,2]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[4,4,4,4,4,3,1]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[3,1,1,1,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0]=>[7,7,1,1]
[1,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,2,2,2]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,0]=>[6,6,5]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,0]=>[5,5,5,4]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[4,4,4,4,3]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,3,2]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[4,4,4,4,2,2,1]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[3,1,1,1,1,1,1,1]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0]=>[5,5,3,3]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0]=>[5,5]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[7,7,5,5,3,3,1,1]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[5,2,2,2,2,2,1]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0,1,0]=>[9,3,3,2,1]
[1,1,0,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[9,6,6,6,4,4,2,2]
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[9,8,6,6,4,4,2,2]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[8,8,4,4,4,4]
[1,0,1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[6,6,6,3,3,3,2,1]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[7,7,4,4,3,3,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[8,1,1,1,1,1,1,1,1]
[1,1,1,0,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,2,2,1]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0]=>[7,6,6,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,4,4,4,4,1,1,1]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[9,7,7,6,4,4,4,2]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[4,2,2,2,2,2,2]
[1,1,1,0,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,3,1,1]
[1,1,1,0,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,5,4,3,2,1]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,4,3,2,1,1]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[5,5,5,4,4,3,2]
[1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[9,8,4,4,4,4]
[1,1,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[9,8,4,4,4,4,2]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,2]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[6,6,6,3,2,1]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[5,5,4,4,3,3,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0]=>[6,1,1,1]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[4,3,3,3,3,3,1,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[4,4,4,4,2,1]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[5,5,5,4,4]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0]=>[4,4,2,2]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[3,3,1,1,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[2,1,1,1,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,1,0]=>[9,7,1]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,5,5,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[2,1,1,1,1,1,1,1,1,1,1]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[6,6,5,4,2,1]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[7,3,2,2,2,2,2]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[9,7,5,5,3,3,1,1]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[8,7,5,5,3,3,1,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[11,5,4,3,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0]=>[7,1]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[6,5,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0,0]=>[8,1]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[6,4,2,2,2,2,1,1]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[6,5,2,2,2,1,1,1]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0,0,0]=>[7,6,1,1,1]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]=>[9,1,1]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,4,1,1,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[7,2,1,1,1,1,1]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[9,8,4,3,2,1]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[5,5,5,2,2,2,2,1]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[6,6,3,3,3,3,2,1]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,2,2,1]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[8,7,6,4,3,2,1]
[1,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[8,8,8,7,6,5,4,3,2,1]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,3,2,2,2,2,2]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[6,4,4,4,4,3,2,1]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[5,3,3,3,3,3,2,1]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[5,3,3,3,2,2,1,1]
[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[11,10,9,8,7,6,5,4,3,1]
[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[11,10,9,8,7,6,5,4,3,2]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[9,7,5,5,5,4,3,2,1]
[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,1,1]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,3,3,2,2,1]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[7,5,5,4,3,2,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0]=>[8,7,6]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0,0]=>[6,5,5,4]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,1,1,1,1,1]
[1,1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[10,9,7,7,6,5,4,3,2,1]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[9,6,5,4,4,4,3,2,1]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[10,9,7,6,6,5,4,3,2,1]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[4,4,4,2,1]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0,0]=>[5,5,3,2,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[5,4,3,2,1]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[6,5,4,2,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[6,5,4,3,2,2,2,2]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[6,4,3,2,1]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,4,3,2]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,4,2,1]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0]=>[7,3]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[4,3,3,3,3,3,1]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[8,8,3,3,2,2,1,1]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[8,8,6,6,4,4,1,1]
[1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[7,7,6,6,4,4,1,1]
[1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[8,8,5,5,4,4,1,1]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[7,7,5,5,4,4,1,1]
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[8,8,6,6,3,3,1,1]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[7,7,6,6,3,3,1,1]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[8,8,5,5,3,3,1,1]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[7,7,5,5,3,3,1,1]
[1,0,1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[9,9,7,7,5,5,3,3,2,2]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[10,10,8,8,6,6,4,4,1,1]
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[9,9,8,8,6,6,4,4,1,1]
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[10,10,7,7,6,6,4,4,1,1]
[1,0,1,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[9,9,7,7,6,6,4,4,1,1]
[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[10,10,8,8,5,5,4,4,1,1]
[1,0,1,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[9,9,8,8,5,5,4,4,1,1]
[1,0,1,1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[10,10,7,7,5,5,4,4,1,1]
[1,0,1,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[9,9,7,7,5,5,4,4,1,1]
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[10,10,8,8,6,6,3,3,1,1]
[1,0,1,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[9,9,8,8,6,6,3,3,1,1]
[1,0,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[10,10,7,7,6,6,3,3,1,1]
[1,0,1,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[9,9,7,7,6,6,3,3,1,1]
[1,0,1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[10,10,8,8,5,5,3,3,1,1]
[1,0,1,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[9,9,8,8,5,5,3,3,1,1]
[1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[10,10,7,7,5,5,3,3,1,1]
[1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[9,9,7,7,5,5,3,3,1,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[8,7,5,4,4,4,3,2,1]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,0]=>[8,7,1]
[1,1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]=>[3,3,3]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]=>[4,4]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]=>[4,4,4]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[7,7,2,2,2,2,2,1]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[7,7,3,3,3,3]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[8,8,2,2,2,2,2,2]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[9,9,1,1,1,1,1,1,1,1]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,3,2,1,1]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,3,2,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[6,5,4,3,1,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[6,6,6,2,2,2,2]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,1]
[1,1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[9,6,6,6,5,4,3,2]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[6,4,4,4,3,2,1]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[5,5,4,3,2]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[5,5,4,4,4,3,1,1]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[7,7,6,6,5,4,3,1,1]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[6,6,5,5,4,2,1,1]
[1,0,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[6,6,6,5,4,2,2,1]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,2,1]
[1,1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[10,8,7,6,6,5,4,3,2,1]
[1,1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,7,6,5,4,3,1]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[10,8,7,6,5,4,3,2,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,7,6,5,4,3,2,2]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[10,8,7,6,5,4,3,2,1,1]
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,3,3,1,1]
[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,3,3]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0]=>[7,2,1]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0]=>[4,2,2]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[6,1,1,1,1]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[4,2,1,1,1,1,1,1]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[9,6,4,3,2,2,2]
[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[11,9,8,8,6,2,1,1]
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[6,6,6,1,1,1]
[1,1,1,0,0,1,0,0,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[10,8,5,4,4,2,1,1,1,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[5,5,4,3,1,1,1,1]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[7,6,3,3,2,1]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[6,5,4,2,2,2,1]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[6,6,5,3,3,3,1]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[7,6,5,2,2,2,2,1]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[8,7,3,3,3,2,1]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,1,1,1,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,4,3,2,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[4,4,4,4,4]
[1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[9,6,3,2,2,1,1,1]
[1,1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[11,8,7,5,5,4,2,2,2,2,1]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[5,5,3,3,3,3,2,1]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[6,3,3,3,2]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[6,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[7,2,2,2,2,2,1]
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[7,3,3,3,3,2,1]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[7,4,4,3,2,1]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[6,5,5,5,4,3]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,1,1,1,1]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,1,1,1]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[6,6,3,2,1]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[5,5,4,2,2,1,1]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[7,7,5,5,3,3,1,1,1]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[7,7,5,5,3,3,3,1,1]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0,0]=>[7,7,5,3,1]
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[11,9,7,5,3,1,1,1,1,1,1]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[2,2,1,1,1,1,1,1,1,1]
[1,1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[9,7,7,5,5,3,1,1,1]
[1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[9,6,5,5,3,3,3,1]
[1,1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[9,7,6,6,3,3,1]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,2,1]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0]=>[2,2]
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,7,6,5,4,3,2]
[1,1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,7,6,5,4,3,3,2]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[8,5,4,4,2,1,1,1]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[9,7,7,5,5,3,3,1,1]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[11,8,8,7,4,4,4,3,1,1,1]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[11,9,9,7,7,5,5,3,3,1,1]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,0]=>[4,4,2,1]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[7,7,4,4,3,1,1]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[7,7,5,5,2,1]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[7,7,5,5,3,1,1,1]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[4,4,1,1,1,1,1]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0]=>[9,2,1]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[9,5,4,3,2,1]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[4,4,4,1,1,1,1,1]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[9,5,4,4,3]
[1,0,1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[8,8,6,6,4,4,1,1,1]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0]=>[3,3,2]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,5,1]
[1,1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[9,6,4,4,2,2,2,1,1]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0,0]=>[7,5,4,4,1,1,1,1]
[1,1,0,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[8,6,5,5,5,4,3,2,1]
[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[11,10,9,8,7,6,5,4,3,1,1]
[1,1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[10,7,7,7,6,5,4,3,2,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[6,6,6,6,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,5,5,5,5,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,4,4,4,4,4,1,1,1]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[7,6,6,4,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[5,5,5,5,2,1,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[7,7,2,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[6,6,6,6,6,1,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[8,8,2,2,2,2,2,2,1]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[5,4,1,1,1,1,1,1]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[5,3,1,1,1,1,1,1]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[5,2,1,1,1,1,1,1]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0]=>[4,3]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[7,6,4,2,2]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[7,6,4,4,4,2]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,1,0,0,0]=>[9,8,6,4,2,2]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[9,8,8,6,4,4,2]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,3,3]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,2,2]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,4,4,4]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[5,5,5,5]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[7,5,5,3,3,1,1]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,1,1,1,1]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,4,2,2]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[7,7,5,3,3,1,1]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,3,3,1,1]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,1,1]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[6,6,5,5,5]
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,1,0]=>[9,5,3,2,1]
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[10,8,8,6,6,4,4,2]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,1,0]=>[9,3,2]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[9,2,2,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[10,5,4,3,2,1]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0,1,0]=>[10,4,4,3,2,1]
[1,1,0,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[6,5,4,2,2,2,2,1]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[6,4,2,2,2,1,1]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[6,4,2,2,2,2,1,1]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[8,8,5,5,4,4,3,2,1]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0]=>[6,6,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0]=>[5,2,1]
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[6,2,1,1,1,1]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0]=>[9,8,2,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0]=>[6,2,1]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0]=>[4,2,2,1]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[6,5,5,4,3,1]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[7,6,6,3,3,3]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[8,8,7,6,5,5,4,3,2,1]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[9,6,6,4,4,2,2,1,1]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[9,6,4,2,2,2,2,1,1]
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[11,10,8,4,4,2,1,1,1]
[1,1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0,0,1,0]=>[11,9,5,3,3,2,2,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[4,3,3,3,3,3]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0]=>[7,6,1,1]
[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[9,7,7,6,4,4,2,2]
[1,1,1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[9,8,7,3,3,3,3,1,1]
[1,1,1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[9,8,7,4,4,4,2,2]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[7,4,4,2,2,2,1,1]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[6,4,4,4,2,2,1,1]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[5,4,4,4,4,3,1]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[7,5,5,4,4,2,2]
[1,1,1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[11,10,7,7,4,3,2,2,1,1,1]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3]
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,4,3,2,1,1]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[9,7,6,5,4,4,3,1]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[7,7,5,5,1]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,5,5,5,1,1]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,2,2,2,2]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[6,3,2,1,1,1]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[6,4,3,2,1,1,1,1]
[1,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[7,7,5,4,3,2,1,1]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,4,3,1]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[5,5,5,5,2,2,2]
[1,0,1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[6,6,6,3,3,3,2]
[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,2,2,2,1]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[6,5,5,5,4,1]
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,2,1,1,1,1]
[1,1,1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,3,3,2,1,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[3,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[6,6,3,1,1,1]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[7,7,5,5,5,3,3,1,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[8,1,1,1,1,1,1]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,3,2,2,2]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[7,5,3,3,3,3,1]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[7,5,4,4,2]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0]=>[10,8,3,3,3,3,2,2,1,1]
[1,1,1,1,0,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,3,2,1]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,4,2,1]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[6,6,4,4,2,2,1,1]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[6,6,5,3,3,1,1]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[8,8,6,4,4,2,2,1,1]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,1,0]=>[9,3,1]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[7,7,4,4,2,1,1]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[9,7,7,5,5,2,2]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[9,7,7,4,4,2,2]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[9,6,6,4,4,2,2]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[6,5,5,4,4,1,1,1]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,1,1,0,0,0]=>[9,9,8,5,2,2,1,1,1]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[10,8,4,4,4,4,2,1,1]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[9,7,6,6,4,1,1,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[3,3,1,1,1,1,1,1,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[6,5,4,3,2,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0,0]=>[7,2,1]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0,0]=>[6,3,2,1]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[5,2,2,1,1,1]
[1,1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[10,9,8,6,6,5,4,3,2,1]
[1,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[9,6,6,6,4,3,3,1]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[9,7,7,4,2,2,2,2,1]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[4,4,1,1,1,1,1,1]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[9,7,6,4,4,2]
Map
zeta map
Description
The zeta map on Dyck paths.
The zeta map $\zeta$ is a bijection on Dyck paths of semilength $n$.
It was defined in [1, Theorem 1], see also [2, Theorem 3.15] and sends the bistatistic (area, dinv) to the bistatistic (bounce, area). It is defined by sending a Dyck path $D$ with corresponding area sequence $a=(a_1,\ldots,a_n)$ to a Dyck path as follows:
The zeta map $\zeta$ is a bijection on Dyck paths of semilength $n$.
It was defined in [1, Theorem 1], see also [2, Theorem 3.15] and sends the bistatistic (area, dinv) to the bistatistic (bounce, area). It is defined by sending a Dyck path $D$ with corresponding area sequence $a=(a_1,\ldots,a_n)$ to a Dyck path as follows:
- First, build an intermediate Dyck path consisting of $d_1$ north steps, followed by $d_1$ east steps, followed by $d_2$ north steps and $d_2$ east steps, and so on, where $d_i$ is the number of $i-1$'s within the sequence $a$.
For example, given $a=(0,1,2,2,2,3,1,2)$, we build the path
$$NE\ NNEE\ NNNNEEEE\ NE.$$ - Next, the rectangles between two consecutive peaks are filled. Observe that such the rectangle between the $k$th and the $(k+1)$st peak must be filled by $d_k$ east steps and $d_{k+1}$ north steps. In the above example, the rectangle between the second and the third peak must be filled by $2$ east and $4$ north steps, the $2$ being the number of $1$'s in $a$, and $4$ being the number of $2$'s. To fill such a rectangle, scan through the sequence a from left to right, and add east or north steps whenever you see a $k-1$ or $k$, respectively. So to fill the $2\times 4$ rectangle, we look for $1$'s and $2$'s in the sequence and see $122212$, so this rectangle gets filled with $ENNNEN$.
The complete path we obtain in thus
$$NENNENNNENEEENEE.$$
Map
to partition
Description
The cut-out partition of a Dyck path.
The partition $\lambda$ associated to a Dyck path is defined to be the complementary partition inside the staircase partition $(n-1,\ldots,2,1)$ when cutting out $D$ considered as a path from $(0,0)$ to $(n,n)$.
In other words, $\lambda_{i}$ is the number of down-steps before the $(n+1-i)$-th up-step of $D$.
This map is a bijection between Dyck paths of size $n$ and partitions inside the staircase partition $(n-1,\ldots,2,1)$.
The partition $\lambda$ associated to a Dyck path is defined to be the complementary partition inside the staircase partition $(n-1,\ldots,2,1)$ when cutting out $D$ considered as a path from $(0,0)$ to $(n,n)$.
In other words, $\lambda_{i}$ is the number of down-steps before the $(n+1-i)$-th up-step of $D$.
This map is a bijection between Dyck paths of size $n$ and partitions inside the staircase partition $(n-1,\ldots,2,1)$.
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