Identifier
Mp00228:
Dyck paths
—reflect parallelogram polyomino⟶
Dyck paths
Mp00100: Dyck paths —touch composition⟶ Integer compositions
Mp00100: Dyck paths —touch composition⟶ Integer compositions
Images
=>
Cc0005;cc-rep-0Cc0005;cc-rep-1
[1,0]=>[1,0]=>[1]
[1,0,1,0]=>[1,1,0,0]=>[2]
[1,1,0,0]=>[1,0,1,0]=>[1,1]
[1,0,1,0,1,0]=>[1,1,0,1,0,0]=>[3]
[1,0,1,1,0,0]=>[1,1,0,0,1,0]=>[2,1]
[1,1,0,0,1,0]=>[1,0,1,1,0,0]=>[1,2]
[1,1,0,1,0,0]=>[1,0,1,0,1,0]=>[1,1,1]
[1,1,1,0,0,0]=>[1,1,1,0,0,0]=>[3]
[1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,0]=>[4]
[1,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0]=>[3,1]
[1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0]=>[2,2]
[1,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,0]=>[2,1,1]
[1,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,0,0]=>[4]
[1,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0]=>[1,3]
[1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0]=>[1,2,1]
[1,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0]=>[1,1,2]
[1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0]=>[1,1,1,1]
[1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0]=>[1,3]
[1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,0]=>[4]
[1,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,0]=>[3,1]
[1,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0]=>[4]
[1,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,0]=>[4]
[1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,0]=>[5]
[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,0]=>[4,1]
[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0]=>[3,2]
[1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0]=>[3,1,1]
[1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0]=>[5]
[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,0,0]=>[2,3]
[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>[2,2,1]
[1,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0]=>[2,1,2]
[1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0]=>[2,1,1,1]
[1,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>[2,3]
[1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0]=>[5]
[1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]=>[4,1]
[1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0]=>[5]
[1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,0]=>[5]
[1,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,0]=>[1,4]
[1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,0,0,1,0]=>[1,3,1]
[1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0]=>[1,2,2]
[1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0]=>[1,2,1,1]
[1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0]=>[1,4]
[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0]=>[1,1,3]
[1,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,2,1]
[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,1,2]
[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]
[1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]=>[1,1,3]
[1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0]=>[1,4]
[1,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0]=>[1,3,1]
[1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0]=>[1,4]
[1,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0]=>[1,4]
[1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0]=>[5]
[1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,0,1,0]=>[4,1]
[1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0]=>[3,2]
[1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0]=>[3,1,1]
[1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0]=>[5]
[1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0]=>[5]
[1,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0]=>[4,1]
[1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0]=>[5]
[1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0]=>[5]
[1,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0]=>[5]
[1,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0]=>[4,1]
[1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0]=>[5]
[1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0]=>[5]
[1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0]=>[5]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[6]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[5,1]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[4,2]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[4,1,1]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[6]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[3,3]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[3,2,1]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[3,1,2]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,1,1]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[3,3]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[6]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[5,1]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[6]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[6]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,4]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,1]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,2,1,1]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,4]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,3]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,2,1]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,1,2]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,4]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,4]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[6]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[5,1]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[4,2]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[4,1,1]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[6]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[6]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[5,1]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[6]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[6]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[6]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[5,1]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[6]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[6]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[6]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,5]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,4,1]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,2]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,1,1]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,5]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,3]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,2,1]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,1,2]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,1,1,1]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,3]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,5]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,4,1]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,5]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,5]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,4]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,3,1]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,2,2]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,2,1,1]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,4]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,3]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,2,1]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,3]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,4]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,3,1]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,4]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,4]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,5]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,1]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,2]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,3,1,1]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,5]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,5]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,4,1]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,5]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,5]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,5]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,4,1]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,5]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,5]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,5]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[6]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[5,1]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[4,2]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[4,1,1]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[6]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[3,3]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[3,1,2]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,1,1]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,3]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[6]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[5,1]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[6]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[6]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[6]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[5,1]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,2]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[4,1,1]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[6]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[6]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[5,1]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[6]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[6]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[6]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[5,1]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[6]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[6]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[6]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[6]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[5,1]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[4,2]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[4,1,1]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[6]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[6]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[5,1]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[6]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[6]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[6]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[5,1]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[6]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[6]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[6]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[6]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,1]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[6]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[6]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[6]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[6]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[7]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[6,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[5,2]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[5,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[7]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[4,3]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[4,2,1]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[4,1,2]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[4,1,1,1]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[4,3]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[7]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[6,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[7]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[7]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,4]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,3,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,2]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,1]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,4]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,1,3]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,2,1]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,1,1,2]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,1,3]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,4]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,3,1]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,4]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,4]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[7]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[6,1]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[5,2]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[5,1,1]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[7]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[7]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[6,1]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[7]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[7]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[7]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[6,1]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[7]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[7]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[7]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,5]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,4,1]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,3,2]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,3,1,1]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,5]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,3]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,2,2,1]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,2,1,2]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,2,1,1,1]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,3]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,5]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,4,1]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,5]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,5]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,4]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,3,1]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,2,1,1]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,4]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,3]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,1,2,1]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,2]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,3]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,4]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,1]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,4]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,4]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,5]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,4,1]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,2]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,3,1,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,5]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,5]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,4,1]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,5]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,5]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,5]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,4,1]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,5]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,5]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,5]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[7]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[6,1]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[5,2]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[5,1,1]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[7]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[4,3]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[4,2,1]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[4,1,2]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[4,1,1,1]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[4,3]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[7]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[6,1]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[7]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[7]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[7]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[6,1]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[5,2]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[5,1,1]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[7]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[7]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[6,1]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[7]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[7]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[7]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[6,1]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[7]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[7]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[7]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[7]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[6,1]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[5,2]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[5,1,1]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[7]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[7]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[6,1]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[7]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[7]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[7]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[6,1]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[7]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[7]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[7]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[7]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[6,1]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[7]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[7]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[7]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[7]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,6]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,5,1]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,4,2]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,4,1,1]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,6]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,3]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,2,1]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,1,2]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,1,1,1]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,3]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,6]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,5,1]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,6]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,6]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,4]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,3,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,2,1,1]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,4]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,3]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,2,1,2,1]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,2]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,3]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,4]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,2,3,1]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,4]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,6]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,5,1]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,4,2]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,4,1,1]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,6]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,6]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,5,1]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,6]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,6]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,6]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,5,1]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,6]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,6]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,6]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,5]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,4,1]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,3,2]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,3,1,1]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,5]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,3]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,2,2,1]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,2,1,2]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,2,1,1,1]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,3]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,5]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,4,1]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,5]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,5]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,4]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,3,1]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,2,2]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,2,1,1]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,4]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,3]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,2,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,3]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,4]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,3,1]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,4]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,4]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,5]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,4,1]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,3,2]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,3,1,1]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,5]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,5]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,4,1]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,5]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,5]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,5]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,4,1]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,5]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,5]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,5]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,6]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,5,1]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,2]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,1,1]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,6]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,3]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,1]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,1,2]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,3,1,1,1]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,6]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,5,1]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,6]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,6]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,6]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,5,1]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,4,2]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,4,1,1]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,6]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,6]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,5,1]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,6]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,6]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,6]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,5,1]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,6]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,6]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,6]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,6]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,5,1]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,4,2]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,4,1,1]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,6]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,6]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,5,1]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,6]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,6]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,6]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,5,1]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,6]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,6]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,6]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,5,1]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,6]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,6]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,6]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,6]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[7]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[6,1]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[5,2]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[5,1,1]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[7]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[4,3]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[4,2,1]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[4,1,2]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[4,1,1,1]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[4,3]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[7]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[6,1]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[7]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[7]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,4]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,3,1]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,2]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,1]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,4]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,1,3]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,1,2,1]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,1,1,2]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,1,3]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,4]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,3,1]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,4]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,4]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[7]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[6,1]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[5,2]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[5,1,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[7]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[7]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[6,1]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[7]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[7]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[7]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[6,1]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[7]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[7]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[7]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[7]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[6,1]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[5,2]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[5,1,1]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[7]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,3]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,2,1]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,1,2]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,1,1,1]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[7]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[6,1]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[7]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[7]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[7]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[6,1]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[5,2]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[5,1,1]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[7]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[7]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[6,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[7]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[7]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[7]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[6,1]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[7]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[7]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[7]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[7]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[6,1]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[5,2]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[5,1,1]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[7]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[7]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[6,1]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[7]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[7]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[7]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[6,1]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[7]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[7]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[7]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[7]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[6,1]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[7]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[7]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[7]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[7]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[7]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[6,1]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[5,2]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[5,1,1]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[7]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,3]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[4,2,1]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[4,1,2]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[4,1,1,1]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,3]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[7]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[6,1]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[7]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[7]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[7]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[6,1]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[5,2]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[5,1,1]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[7]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[7]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[6,1]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[7]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[7]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[7]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[6,1]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[7]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[7]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[7]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[7]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[6,1]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[5,2]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[5,1,1]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[7]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[7]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[6,1]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[7]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[7]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[7]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[6,1]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[7]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[7]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[7]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[7]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[6,1]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[7]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[7]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[7]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[7]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[7]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[6,1]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,2]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,1,1]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[7]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[7]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,1]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[7]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[7]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[7]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,1]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[7]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[7]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[7]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[7]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[7]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[7]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[7]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[7]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[7]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[7]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[7]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[7]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[7]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[7,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[6,2]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[6,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[8]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[5,3]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[5,2,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[5,1,2]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[5,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[5,3]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[8]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[7,1]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[8]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[8]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[4,4]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[4,3,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[4,2,2]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[4,2,1,1]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[4,4]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[4,1,3]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[4,1,2,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[4,1,1,2]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[4,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[4,1,3]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[4,4]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[4,3,1]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,4]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[4,4]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[8]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[7,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[6,2]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[6,1,1]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[8]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[8]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[7,1]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[8]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[8]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[8]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[7,1]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[8]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[8]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[8]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,5]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[3,4,1]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[3,3,2]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[3,3,1,1]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,5]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,2,3]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,2,2,1]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[3,2,1,2]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[3,2,1,1,1]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,2,3]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,5]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,4,1]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,5]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,5]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[3,1,4]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,3,1]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[3,1,2,2]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[3,1,2,1,1]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,1,4]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,1,1,3]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,1,2,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,1,1,1,2]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,1,1,3]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,1,4]
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,1,3,1]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,1,4]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,1,4]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,5]
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,4,1]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,3,2]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[3,3,1,1]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,5]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,5]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,4,1]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,5]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,5]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,5]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[3,4,1]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,5]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,5]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,5]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[8]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[7,1]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[6,2]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[6,1,1]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[8]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[5,3]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[5,2,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[5,1,2]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[5,1,1,1]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[5,3]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[8]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[7,1]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[8]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[8]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[8]
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[7,1]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[6,2]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[6,1,1]
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[8]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[8]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[7,1]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[8]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[8]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[8]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[7,1]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[8]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[8]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[8]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[8]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[7,1]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[6,2]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[6,1,1]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[8]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[8]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[7,1]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[8]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[8]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[8]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[7,1]
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[8]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[8]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[8]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[8]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,1]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[8]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[8]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[8]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[8]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,6]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,5,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,4,2]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[2,4,1,1]
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,6]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,3]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,2,1]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,1,2]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,1,1,1]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,3]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[2,6]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[2,5,1]
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,6]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,6]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,2,4]
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[2,2,3,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,2,2,1,1]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,4]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,2,1,3]
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[2,2,1,2,1]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,2,1,1,2]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,2,1,1,1,1]
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,2,1,3]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,2,4]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,2,3,1]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,2,4]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,2,4]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,6]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[2,5,1]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,2]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,1,1]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,6]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,6]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[2,5,1]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,6]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,6]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,6]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[2,5,1]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,6]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,6]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,5]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,1]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,3,2]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,3,1,1]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,5]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,2,3]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,2,2,1]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,2,1,2]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,2,1,1,1]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,2,3]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,5]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,1]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,5]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,5]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,1,4]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,1,3,1]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,1,2,2]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,1,2,1,1]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,1,4]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,1,3]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,1,1,2,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,2]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,1,3]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,1,4]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,1,3,1]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,1,4]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,1,4]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,4,1]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,2]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,3,1,1]
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,5]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,1]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,5]
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,5]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,5]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,4,1]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,5]
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,5]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,5]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,6]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[2,5,1]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,2]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,1,1]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,6]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,3,3]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,2,1]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,3,1,2]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,1,1,1]
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,3]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,6]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[2,5,1]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,6]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,6]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,6]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[2,5,1]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,4,2]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,4,1,1]
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,6]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,6]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[2,5,1]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,6]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,6]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,6]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[2,5,1]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,6]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,6]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,6]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,6]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[2,5,1]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,4,2]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,4,1,1]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[2,6]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,6]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[2,5,1]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,6]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,6]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,6]
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[2,5,1]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[2,6]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,6]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,6]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,6]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,5,1]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,6]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,6]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,6]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,6]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[8]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[7,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[6,2]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[6,1,1]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[8]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[5,3]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[5,2,1]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[5,1,2]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[5,1,1,1]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[5,3]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[8]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[7,1]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[8]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[8]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[4,4]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[4,3,1]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[4,2,2]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[4,2,1,1]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[4,4]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[4,1,3]
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[4,1,2,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[4,1,1,2]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,1,1,1]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[4,1,3]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[4,4]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[4,3,1]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,4]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[4,4]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[8]
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[7,1]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[6,2]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[6,1,1]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[8]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[8]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[7,1]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[8]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[8]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[8]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[7,1]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[8]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[8]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[8]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[8]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[7,1]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[6,2]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[6,1,1]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[8]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[5,3]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[5,2,1]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[5,1,2]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[5,1,1,1]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,3]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[8]
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[7,1]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[8]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[8]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[8]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[7,1]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[6,2]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[6,1,1]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[8]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[8]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,1]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[8]
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[8]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[8]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,1]
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[8]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[8]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[8]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[8]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[7,1]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[6,2]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[6,1,1]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[8]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[8]
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,1]
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[8]
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[8]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[8]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[7,1]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[8]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[8]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[8]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[8]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,1]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[8]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[8]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[8]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[8]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[8]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[7,1]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[6,2]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[6,1,1]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[8]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[5,3]
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[5,2,1]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[5,1,2]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[5,1,1,1]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[5,3]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[8]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[7,1]
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[8]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[8]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[8]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[7,1]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[6,2]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[6,1,1]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[8]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[8]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,1]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[8]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[8]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[8]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[7,1]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[8]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[8]
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[8]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[8]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[7,1]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[6,2]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[6,1,1]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[8]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[8]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[7,1]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[8]
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[8]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[8]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[7,1]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[8]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[8]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[8]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[8]
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,1]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[8]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[8]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[8]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[8]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[8]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,1]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,2]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[6,1,1]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[8]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[8]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,1]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[8]
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[8]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[8]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,1]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[8]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[8]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[8]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[8]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[8]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[8]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[8]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[8]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[8]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,1]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[8]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[8]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[8]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[8]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[8]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,7]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,6,1]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,5,2]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,5,1,1]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,7]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,4,3]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,4,2,1]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,4,1,2]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,4,1,1,1]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,4,3]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,7]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,6,1]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,7]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,7]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,4]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,3,1]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,2]
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,1,1]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,4]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,1,3]
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,1,2,1]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,1,1,2]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,1,1,1,1]
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,1,3]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,4]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,3,1]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,4]
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,4]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,7]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,6,1]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,5,2]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,5,1,1]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,7]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,7]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,6,1]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,7]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,7]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,7]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,6,1]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,7]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,7]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,7]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,5]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,4,1]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,3,2]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,3,1,1]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,5]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,3]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,2,2,1]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,2,1,2]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,2,1,1,1]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,2,3]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,5]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,1]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,5]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,5]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,1,4]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,1,3,1]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,1,2,2]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,1,2,1,1]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,1,4]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,1,1,3]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,1,1,2,1]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,1,2]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,1,1,3]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,1,4]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,1,3,1]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,1,4]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,1,4]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,5]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,4,1]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,3,2]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,3,1,1]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,5]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,5]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,4,1]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,5]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,5]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,5]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,4,1]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,5]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,5]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,5]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,7]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,6,1]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,5,2]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,5,1,1]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,7]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,3]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,2,1]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,1,2]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,1,1,1]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,3]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,7]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,6,1]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,7]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,7]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,7]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,6,1]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,5,2]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,5,1,1]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,7]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,7]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,6,1]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,7]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,7]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,7]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,6,1]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,7]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,7]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,7]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,7]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,6,1]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,5,2]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,5,1,1]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,7]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,7]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,6,1]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,7]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,7]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,7]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,6,1]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,7]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,7]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,7]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,7]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,6,1]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,7]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,7]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,7]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,7]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,6]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,5,1]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,4,2]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,4,1,1]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,6]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,3,3]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,3,2,1]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,3,1,2]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,3,1,1,1]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,3,3]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,6]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,5,1]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,6]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,6]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,2,4]
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,2,3,1]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,2,2,2]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,2,2,1,1]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,2,4]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,2,1,3]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,2,1,2,1]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,2,1,1,2]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,2,1,1,1,1]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,2,1,3]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,2,4]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,2,3,1]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,2,4]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,2,4]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,6]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,5,1]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,4,2]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,4,1,1]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,6]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,6]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,5,1]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,6]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,6]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,6]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,5,1]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,6]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,6]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,6]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,5]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,4,1]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,3,2]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,3,1,1]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,5]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,2,3]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,2,2,1]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,2,1,2]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,2,1,1,1]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,2,3]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,5]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,4,1]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,5]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,5]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,4]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,3,1]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,2,2]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,2,1,1]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,4]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,3]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,3]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,4]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,3,1]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,4]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,4]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,5]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,4,1]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,3,2]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,3,1,1]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,5]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,5]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,4,1]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,5]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,5]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,5]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,4,1]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,5]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,5]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,5]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,6]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,5,1]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,4,2]
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,4,1,1]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,6]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,3,3]
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,3,2,1]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,3,1,2]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,3,1,1,1]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,3,3]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,6]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,5,1]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,6]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,6]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,6]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,5,1]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,4,2]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,4,1,1]
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,6]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,6]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,5,1]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,6]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,6]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,6]
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,5,1]
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,6]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,6]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,6]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,6]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,5,1]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,4,2]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,4,1,1]
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,6]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,6]
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,5,1]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,6]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,6]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,6]
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,5,1]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,6]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,6]
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,6]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,6]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,5,1]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,6]
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,6]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,6]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,6]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,7]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,6,1]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,5,2]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,5,1,1]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,7]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,4,3]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,4,2,1]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,4,1,2]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,4,1,1,1]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,4,3]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,7]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,6,1]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,7]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,7]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,3,4]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,3,3,1]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,2]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,1,1]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,3,4]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,3,1,3]
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,3,1,2,1]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,3,1,1,2]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,3,1,1,1,1]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,3,1,3]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,3,4]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,3,3,1]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,3,4]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,3,4]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,7]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,6,1]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,5,2]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,5,1,1]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,7]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,7]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,6,1]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,7]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,7]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,7]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,6,1]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,7]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,7]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,7]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,7]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,6,1]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,5,2]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,5,1,1]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,7]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,4,3]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,4,2,1]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,4,1,2]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,4,1,1,1]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,4,3]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,7]
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,6,1]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,7]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,7]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,7]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,6,1]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,5,2]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,5,1,1]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,7]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,7]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,6,1]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,7]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,7]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,7]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,6,1]
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,7]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,7]
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,7]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,7]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,6,1]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,5,2]
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,5,1,1]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,7]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,7]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,6,1]
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,7]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,7]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,7]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,6,1]
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,7]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,7]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,7]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,7]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,6,1]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,7]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,7]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,7]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,7]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,7]
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,6,1]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,5,2]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,5,1,1]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,7]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,4,3]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,4,2,1]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,4,1,2]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,4,1,1,1]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,4,3]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,7]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,6,1]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,7]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,7]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,7]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,6,1]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,5,2]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,5,1,1]
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,7]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,7]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,6,1]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,7]
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,7]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,7]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,6,1]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,7]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,7]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,7]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,7]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,6,1]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,5,2]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,5,1,1]
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,7]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,7]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,6,1]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,7]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,7]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,7]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,6,1]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,7]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,7]
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,7]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,7]
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,6,1]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,7]
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,7]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,7]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,7]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,7]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,6,1]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,5,2]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,5,1,1]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,7]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,7]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,6,1]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,7]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,7]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,7]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,6,1]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,7]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,7]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,7]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,7]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,6,1]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,7]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,7]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,7]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,7]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,7]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,6,1]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,7]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,7]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,7]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,7]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,7]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[8]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[7,1]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[6,2]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[6,1,1]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[8]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[5,3]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[5,2,1]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[5,1,2]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[5,1,1,1]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[5,3]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[8]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[7,1]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[8]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[8]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[4,4]
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[4,3,1]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[4,2,2]
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[4,2,1,1]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[4,4]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[4,1,3]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[4,1,2,1]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[4,1,1,2]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[4,1,1,1,1]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[4,1,3]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[4,4]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[4,3,1]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,4]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[4,4]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[8]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[7,1]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[6,2]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[6,1,1]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[8]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[8]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[7,1]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[8]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[8]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[8]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[7,1]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[8]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[8]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[8]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,5]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[3,4,1]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[3,3,2]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[3,3,1,1]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,5]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,2,3]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,2,2,1]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[3,2,1,2]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[3,2,1,1,1]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,2,3]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,5]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,4,1]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,5]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,5]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[3,1,4]
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,3,1]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[3,1,2,2]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[3,1,2,1,1]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,1,4]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,1,1,3]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,1,2,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,1,1,1,2]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,1,1,3]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,1,4]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,1,3,1]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,1,4]
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,1,4]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,5]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,4,1]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,3,2]
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[3,3,1,1]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,5]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,5]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,4,1]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,5]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,5]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,5]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[3,4,1]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,5]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,5]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,5]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[8]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[7,1]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[6,2]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[6,1,1]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[8]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[5,3]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[5,2,1]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[5,1,2]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[5,1,1,1]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[5,3]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[8]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[7,1]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[8]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[8]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[8]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[7,1]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[6,2]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[6,1,1]
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[8]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[8]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[7,1]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[8]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[8]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[8]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[7,1]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[8]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[8]
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[8]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[8]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[7,1]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[6,2]
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[6,1,1]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[8]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[8]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[7,1]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[8]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[8]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[8]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[7,1]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[8]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[8]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[8]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[8]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,1]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[8]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[8]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[8]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[8]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[8]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[7,1]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[6,2]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[6,1,1]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[8]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[5,3]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[5,2,1]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[5,1,2]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[5,1,1,1]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[5,3]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[8]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[7,1]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[8]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[8]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[4,4]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[4,3,1]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,2,2]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[4,2,1,1]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[4,4]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[4,1,3]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[4,1,2,1]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[4,1,1,2]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,1,1,1]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[4,1,3]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[4,4]
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[4,3,1]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[4,4]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[8]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[7,1]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[6,2]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[6,1,1]
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[8]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[8]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[7,1]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[8]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[8]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[8]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[7,1]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[8]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[8]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[8]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[8]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[7,1]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[6,2]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[6,1,1]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[8]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[5,3]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[5,2,1]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[5,1,2]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[5,1,1,1]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[5,3]
[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]=>[8]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[7,1]
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[8]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[8]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[8]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[7,1]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[6,2]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[6,1,1]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[8]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[8]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[7,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[8]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[8]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[8]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[7,1]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[8]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[8]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[8]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[8]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[7,1]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[6,2]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[6,1,1]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[8]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[8]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[7,1]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[8]
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[8]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[8]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[7,1]
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[8]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[8]
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[8]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[8]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[7,1]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[8]
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[8]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[8]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[8]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[8]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[7,1]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[6,2]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[6,1,1]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[8]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[5,3]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[5,2,1]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[5,1,2]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[5,1,1,1]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[5,3]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[8]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[7,1]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[8]
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[8]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[8]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[7,1]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[6,2]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[6,1,1]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[8]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[8]
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[7,1]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[8]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[8]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[8]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[7,1]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[8]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[8]
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[8]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[8]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[7,1]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[6,2]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[6,1,1]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[8]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[8]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[7,1]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[8]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[8]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[8]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[7,1]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[8]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[8]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[8]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[8]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[7,1]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[8]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[8]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[8]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[8]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[8]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[7,1]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[6,2]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[6,1,1]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[8]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[8]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[7,1]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[8]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[8]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[8]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[7,1]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[8]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[8]
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[8]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[8]
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[8]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[8]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[8]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[8]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[8]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[7,1]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[8]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[8]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[8]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[8]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[8]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[8]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[7,1]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[6,2]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[6,1,1]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[8]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[5,3]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[5,2,1]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[5,1,2]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[5,1,1,1]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[5,3]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[8]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[7,1]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[8]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[8]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[4,4]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[4,3,1]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[4,2,2]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[4,2,1,1]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[4,4]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[4,1,3]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[4,1,2,1]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[4,1,1,2]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,1,1,1]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[4,1,3]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[4,4]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[4,3,1]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,4]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[4,4]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[8]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[7,1]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[6,2]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[6,1,1]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[8]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[8]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[7,1]
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[8]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[8]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[8]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[7,1]
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[8]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[8]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[8]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[8]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[7,1]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[6,2]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[6,1,1]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[8]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[5,3]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[5,2,1]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[5,1,2]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[5,1,1,1]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,3]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[8]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[7,1]
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[8]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[8]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[8]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[7,1]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[6,2]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[6,1,1]
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[8]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[8]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,1]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[8]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[8]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[8]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,1]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[8]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[8]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[8]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[8]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[7,1]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[6,2]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[6,1,1]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[8]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[8]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,1]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[8]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[8]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[8]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[7,1]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[8]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[8]
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[8]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[8]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,1]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[8]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[8]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[8]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[8]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[8]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[7,1]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[6,2]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[6,1,1]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[8]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[5,3]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[5,2,1]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[5,1,2]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[5,1,1,1]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[5,3]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[8]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[7,1]
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[8]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[8]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[8]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[7,1]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[6,2]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[6,1,1]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[8]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[8]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,1]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[8]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[8]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[8]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[7,1]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[8]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[8]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[8]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[8]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[7,1]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[6,2]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[6,1,1]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[8]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[8]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[7,1]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[8]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[8]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[8]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[7,1]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[8]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[8]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[8]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[8]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,1]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[8]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[8]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[8]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[8]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[8]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,1]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,2]
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[6,1,1]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[8]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[8]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,1]
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[8]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[8]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[8]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,1]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[8]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[8]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[8]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[8]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[8]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[8]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[8]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[8]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[8]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,1]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[8]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[8]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[8]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[8]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[8]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[8]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[7,1]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[6,2]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[6,1,1]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[8]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[5,3]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[5,2,1]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[5,1,2]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[5,1,1,1]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,3]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[8]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[7,1]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[8]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[8]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[8]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[7,1]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[6,2]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[6,1,1]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[8]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[8]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[7,1]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[8]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[8]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[8]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[7,1]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[8]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[8]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[8]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[8]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[7,1]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[6,2]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[6,1,1]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[8]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[8]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[7,1]
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[8]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[8]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[8]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[7,1]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[8]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[8]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[8]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[8]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,1]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[8]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[8]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[8]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[8]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[8]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,1]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,2]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[6,1,1]
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[8]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[8]
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,1]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[8]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[8]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[8]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,1]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[8]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[8]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[8]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[8]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[8]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[8]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[8]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[8]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[8]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,1]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[8]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[8]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[8]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[8]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[8]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[8]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[7,1]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[6,2]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[6,1,1]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[8]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[8]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[7,1]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[8]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[8]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[8]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[7,1]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[8]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[8]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[8]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[8]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[8]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[8]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[8]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[8]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[8]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[7,1]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[8]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[8]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[8]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[8]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[8]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[8]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[7,1]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[8]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[8]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[8]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[8]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[8]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[8]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[9]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[9]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[10]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[9]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[9]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[10]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0]=>[11]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0]=>[9]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0]=>[9]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[9]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[9]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[11]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>[11]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0]=>[10]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[9]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[9]
[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[9]
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[10]
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[9]
[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[10]
[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[11]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[10]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0]=>[9]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[9]
[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[9]
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[9]
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[10]
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[9]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0,0]=>[9]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0]=>[9]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[9]
[1,0,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[9]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[7,2]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,8]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[8,1]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[8,1]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[9]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,8]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,7]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[9]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,1,0,0]=>[7,2]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[9]
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[9]
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,7]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[9]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0]=>[8,2]
[1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,7]
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,8]
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,8]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,0]=>[10]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0]=>[9,1]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0]=>[9]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[9]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,1,0]=>[8,1]
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[9]
[1,0,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[9]
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,8]
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,9]
[1,0,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,8]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[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]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,3]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,1,3,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,4]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,1,4]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,3,1,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,5]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,4,1]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,5]
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,5]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,4,1]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,5]
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,5]
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,5]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,3,1,1,1]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,3,3]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,4,1,1]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,5,1]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,6]
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,6]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,5,1]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,6]
[1,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,6]
[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,6]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,3,1,1,1,1]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,4,1,1,1]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,4,1,1,1]
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,5,1,1]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,7]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,7]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,6,1]
[1,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,7]
[1,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,7]
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,7]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,1,1,1,1,1]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,3,3,1,1]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,5,1,1,1]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,4,1,1,1,1]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,4,1,3]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,4,4]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,8]
[1,1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[1,8]
[1,1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,8]
[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,8]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,4,1,1,1,1]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,4,4]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,5,1,1,1]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,6,1,1]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,7,1]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,8]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,8]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,5,1,1,1]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,8]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,8]
[1,1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,8]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,8]
[1,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,8]
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,8]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[1,6,1,1]
[1,1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,8]
[1,1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,8]
[1,1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,8]
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,8]
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,8]
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,8]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,7,1]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,8]
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,8]
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,8]
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,8]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,8]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[3,1,1,1,3]
[1,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[3,1,1,4]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[3,6]
[1,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,6]
[1,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,6]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,1,1]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[9]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,1,1,1,1]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[4,1,1,3]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[4,1,4]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,5]
[1,1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[9]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[5,1,1,1,1]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,4]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[8,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[9]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[9]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[9]
[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[9]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[7,1,1]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[8,1]
[1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[9]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[8,1]
[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[9]
[1,1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[9]
[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[9]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[9]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[9]
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[9]
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[9]
[1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[9]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[6,1,1,1]
[1,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[9]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[9]
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[9]
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[9]
[1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[9]
[1,1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[9]
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[9]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[8,1]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[9]
[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[9]
[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[9]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[9]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,1,1,1,1]
[1,1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[4,5]
[1,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5]
[1,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[9]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[5,1,1,1,1]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[9]
[1,1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[9]
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[9]
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[9]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[5,1,1,1,1]
[1,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[9]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[6,1,1,1]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[7,1,1]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[9]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[7,1,1]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[8,1]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[9]
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[9]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[8,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[9]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[9]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[9]
[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[9]
[1,1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[9]
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[9]
[1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[9]
[1,1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[9]
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[9]
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[9]
[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[9]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[8,1]
[1,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[9]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[9]
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[9]
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[9]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[8,1]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[9]
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[9]
[1,1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[9]
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[9]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[9]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[5,1,1,1,1]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,4]
[1,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0]=>[5,4]
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[9]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,1,0]=>[8,1]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[9]
[1,1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,0]=>[9]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0]=>[9]
[1,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0,0]=>[9]
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0]=>[9]
[1,1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0]=>[9]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0,0]=>[9]
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]=>[9]
[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0]=>[9]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,1,0]=>[8,1]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0]=>[9]
[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0]=>[9]
[1,1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0]=>[9]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0]=>[9]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[9]
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[9]
[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]=>[9]
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0]=>[9]
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[9]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0]=>[7,1,1]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0]=>[9]
[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]=>[9]
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0]=>[9]
[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0]=>[9]
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[9]
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]=>[9]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[8,1]
[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0]=>[9]
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[9]
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0]=>[9]
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[9]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[9]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0]=>[6,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]=>[6,3]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,0]=>[9]
[1,1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,0]=>[9]
[1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0]=>[9]
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0]=>[9]
[1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0,0]=>[9]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0]=>[9]
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0]=>[9]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0]=>[8,1]
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0]=>[9]
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0]=>[9]
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[9]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0]=>[9]
[1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0]=>[9]
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0]=>[9]
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0]=>[9]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[8,1]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[9]
[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0]=>[9]
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[9]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[9]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0]=>[9]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0]=>[8,1]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0]=>[9]
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0]=>[9]
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>[9]
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[9]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[9]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[7,1,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[9]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0]=>[8,1]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0]=>[8,1]
[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]=>[9]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[8,1]
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[9]
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[9]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0]=>[8,1]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[9]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0]=>[9]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[9]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[8,1]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[9]
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[9]
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[9]
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[9]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[9]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[9]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[8,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0]=>[9]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0]=>[9]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[9]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0]=>[9]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[9]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[9]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[7,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[6,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[5,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[10]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[8,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[8,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[7,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[7,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[6,1,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[6,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[5,1,1,1,1,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[5,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,1,1,1,1,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[11]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[10,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[10]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[9,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[9,1]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[8,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[9]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[8,1]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[6,1,1,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,1,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[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]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[11]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[10]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[10]
[1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[9]
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[9]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[6,1,1,1]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[7,1,1]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[8,1]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[7,1,1]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,1,1,1,1,1]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,1,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[10]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[9]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[9]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[10]
[1,0,1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[9]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[7,1,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,1,1]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[8,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[10]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[7,1,1]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[8,1]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[8,1]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[5,1,1,1,1,1]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[8,1]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[9]
[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[9]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[8,1]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[8,1]
[1,0,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[9]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[9]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[10]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[6,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[11]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[9,1]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[10]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[9,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[7,2]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[6,3]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[6,2,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[9]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[5,4]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[5,3,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[5,2,2]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[9]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[8,1]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[9]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[4,5]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[4,2,2,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[9]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[9]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[3,6]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[3,5,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,2,2]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[9]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[9]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,7]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,6,1]
[1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,7]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,2,5]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,3]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,2,2,2,1]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,2,5]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[9]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[5,2,2]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[9]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[9]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[9]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,8]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,7,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,6,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,8]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,5,3]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,8]
[1,1,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,8]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,4,4]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,2,1]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,6]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2,2]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,8]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,8]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[7,2]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[9]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[4,2,2,1]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[9]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,1]
[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[9]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[5,2,2]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[9]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0,0]=>[9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[8,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[7,3]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[7,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[10]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[6,4]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[6,2,2]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[10]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[5,2,2,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[10]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[4,5,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[4,2,4]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[4,2,2,2]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[10]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[10]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,2,2,2,1]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[10]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[10]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,8]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,7,1]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,2,6]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,2,2,4]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2,2]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,4]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,5,2,1]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[10]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[5,2,2,1]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[10]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,9]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,8,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,7,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,9]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,9]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,9]
[1,1,0,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,9]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,2,3]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,2,2,2,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,2,5]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,9]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[10]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[8,2]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[4,2,2,2]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[10]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,1]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[5,5]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[10]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0]=>[10]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[10]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,7]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,6]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,5]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,1,4]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,3]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,1,2]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,8]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,8]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,7]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,7]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,6]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,6]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,5]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,5]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,4]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,1,4]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,1,3]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,1,1,2]
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[10]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[10]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,10]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,6,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,1,3]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[10]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[10]
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>[11]
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]=>[10]
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0]=>[10]
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]=>[11]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,7,1,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,5,1,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,6,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[9]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[9]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[9]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[9]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[9]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,9]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[9,1]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]=>[10,1]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0]=>[9,1]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0]=>[6,3]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,0]=>[5,4]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[3,6]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[10]
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[10]
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[10]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[10]
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[10]
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[10]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,8]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,9]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0]=>[11]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,7]
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[9]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,0]=>[9]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,1,5]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[3,1,5]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[6,1,1,2]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,4,1]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,1,5]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,3,1,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[3,1,1,1,1,2]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,1,1,3]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,2,1]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,1,4]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,1,1,4]
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,5]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,5]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,9]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[10]
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,6]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0]=>[7,1,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[10]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,0]=>[9]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[10]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[10]
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[9]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[10]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[10]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[3,3,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,1,0]=>[6,2,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[5,1,1,2]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,4,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[5,1,2,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,3,1,1,1]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[10,1]
[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,9]
[1,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,10]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,2,2]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,2,3]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,2,4]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,2,5]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,4,2,2]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,6,2]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,8]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,2,1]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,2,2,2,1]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,4,2,2,1]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,4,2,1]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,2,2]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[4,2,2,1]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,2,2,2,2]
[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,8]
[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,7]
[1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,6]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,5]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,3,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,1,4]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,5]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[10]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,1,1,3]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,1,5]
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0]=>[10]
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0]=>[10]
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[2,8]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[4,2,4]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[10]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[8,2]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[12]
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,2,8]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[8,2,1,1]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[12]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[11]
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,10]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[9]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[9]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[10]
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[10]
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,9]
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,10]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0]=>[11,1]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]=>[9,1]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0]=>[9,1]
[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,9]
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,9]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,9]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,7,1]
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,6]
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[6,3]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,1,1,1,1]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[5,1,1,1,1]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,7]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[10]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[5,1,1,1,1]
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[10]
[1,1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,9]
[1,1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,9]
[1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[10]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]=>[9]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[9]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]=>[7,1,1]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[8,1]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[1,7,1,1]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,5,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[9]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[9]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,3,1,1,1,1,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,6]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1,1,1]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,2,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[10]
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[11]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[9,2]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[9]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,4,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,2,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[6,1,2]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,3,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,1,1,1,2,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,1,1,1,3]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[3,1,1,1,1,1,2]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,5,1]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[4,5]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[10]
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[10]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[1,10]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[9]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[2,6,1]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,6,2]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[9]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[10,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,1,1,1,2]
[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0,0]=>[11]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0]=>[10]
[1,1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[10]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,2,4]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[6,2,1]
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,7]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,8]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,1,2]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[3,1,2,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,1,1,2,1,1]
[1,1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[10]
[1,1,0,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,6]
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[10]
[1,0,1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,6]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,3,2]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,5]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,2,1,2]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,5]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[10]
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0,0]=>[10]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[9]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,5,1,2]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,4,1,2]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,4]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,7]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[10]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,1,2,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,2,1,1]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[7,1,1]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[10]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[6,3]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,1,0,0]=>[5,1,3]
[1,0,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,7]
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,7]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,2,2,1,1]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[4,2,2,1]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[5,2,2]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[11]
[1,1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[10]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[5,3,1]
[1,0,1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,1,7]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[9]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[9]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[5,4]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[4,1,4]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,7]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,1,1,2]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,1,1,5]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,3,4]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,2,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[9]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,5]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[3,1,5]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[9,1]
[1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[10]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,2,1,4]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,1,1,4]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[3,1,1,1,3]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[4,1,1,3]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[9]
[1,1,0,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,8]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,1,1,1,1,2,1]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,1,1,3,1]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,2,2]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[5,2,2]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[6,2,1]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,2,2,2,1]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[5,2,2]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,8]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,8]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,7]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,7]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[3,1,1,1,1,1,2]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[4,1,1,1,2]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[2,7]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,1,1,4]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,3,2]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,3,1,1,2]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[3,1,1,1,1,2]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,4,1,1]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,3,1,1,1,2]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]=>[10]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[9]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[8,1,1]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,7]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[9]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[7,2]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[9]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]=>[6,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,1,1,3,1]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,1,1,3,1]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[9]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,1,1,1,3]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,1,1,2]
[1,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[10]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,1,0]=>[8,1,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[7,1,1,1]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,2,4,1]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,6,1]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[8,1]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,2,2,3,1]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,8,1]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,2,4,1,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,2,2,3,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,2,2,2,1,1]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[10]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[9]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,9]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0,1,0]=>[7,1,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[7,1,1]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,1,1,1]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,2,1,1,1,1]
[1,1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[10]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,8]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,3,1,1,1,1]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,2,1,1,1,1,1]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[3,2,1,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[4,2,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[5,2,1,1]
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[3,4,2]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,3]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[9]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,1,1,1,2]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,7]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,1,1,3]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[2,6,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,1,1,4]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,1,3,1]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[5,1,1,2]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[8,1]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,7,1]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[9]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[9]
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[10]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[10]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,7]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,4,2,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[3,1,1,1,3]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,5,1,1,1,1]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[9]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[4,4,1]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[5,4,1]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[1,8,1]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[9]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,4,2,2,1]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,6,2,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,2,2,2,2,1]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,2,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,1,2,2]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,5]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,4,2]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,2,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,1,1,3]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,4,2]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,1,1,1,1,2]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,1,1,1,2]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,4,1]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,1,5]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[9]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0]=>[9,1,1]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[5,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[9,1]
[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]=>[12]
[1,1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[1,10]
[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[10]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[7,2]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[5,2,2]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[4,1,1,3]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0,0]=>[11]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0]=>[7,2]
[1,1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[1,10]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,10]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,1,1,2,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,1,1,1,2,1]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,2,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,9,1]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,9]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[5,1,1,1,1]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,1,1,1,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,8,1]
[1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,1,1,4]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,1,1,1,3,1]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,1,5]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,1,1,1,4]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,2,4,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,2,2,3]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,2,3,2,2]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[10]
[1,1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[10]
[1,1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[10]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]=>[10]
[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[10]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,1,1,2,1]
[1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0]=>[11]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,2,5]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,6]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,9]
[1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[9,1]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[9,1]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,11]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[3,9]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[9,3]
[1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[11,1]
[1,0,1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[4,5]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,4,1]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[6,2,1]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[6,2,1]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[4,2,2,2]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[9]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[6,2,1,1]
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,2,6]
[1,0,1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,9]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0]=>[10]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0,0]=>[11]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0,0]=>[11]
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[10]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0,0]=>[11]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0]=>[11]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,6,2]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,2,2,2]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,2,2]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[2,6,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,6,2]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,8]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[5,2,2]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[10]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[1,8]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,2,1,1]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[3,1,4,1]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[4,1,1,1,1,2]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,6,1]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,2,2,1,1,1]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[1,6,3]
[1,1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[11,1]
[1,1,1,0,0,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[12]
[1,0,1,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0,0]=>[12]
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,1,1,0,0,0]=>[1,11]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,4,1]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,8]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2,2,2]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[7,2]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,1,2,3]
[1,1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]=>[10]
[1,1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0]=>[10]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[1,9,1]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[9]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,1,0,0]=>[7,2]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[8,1]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[6,2,1]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,2,1,1,1,1,1]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[6,2,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,2,2,1,1,1]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[1,6,2]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,5,1,1]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[2,7,1]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,2,2,2]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,2,2,2]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,7,1]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[8,1]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,2,2,1]
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[12]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[4,1,1,4]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,4,1,1,1,1]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,1,0,0]=>[5,1,1,2]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,0]=>[9]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,2,1,1,3]
[1,1,0,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,1,1,4]
[1,1,0,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,1,5]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[12]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0]=>[11]
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0]=>[10]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[5,2,2]
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0]=>[10]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,11]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,4,2,1]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[4,2,2,1]
[1,0,1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,6]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,2,6]
[1,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0]=>[10]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[9]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[10]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[8,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[3,4,1,1]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,4,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,2,2,1]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,2,2,2,1]
[1,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[11]
[1,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,7]
Map
reflect parallelogram polyomino
Description
Reflect the corresponding parallelogram polyomino, such that the first column becomes the first row.
Let $D$ be a Dyck path of semilength $n$. The parallelogram polyomino $\gamma(D)$ is defined as follows: let $\tilde D = d_0 d_1 \dots d_{2n+1}$ be the Dyck path obtained by prepending an up step and appending a down step to $D$. Then, the upper path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with even indices, and the lower path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with odd indices.
Let $D$ be a Dyck path of semilength $n$. The parallelogram polyomino $\gamma(D)$ is defined as follows: let $\tilde D = d_0 d_1 \dots d_{2n+1}$ be the Dyck path obtained by prepending an up step and appending a down step to $D$. Then, the upper path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with even indices, and the lower path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with odd indices.
Map
touch composition
Description
Sends a Dyck path to its touch composition given by the composition of lengths of its touch points.
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