Identifier
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00032: Dyck paths —inverse zeta map⟶ Dyck paths
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Images
=>
Cc0005;cc-rep-0Cc0005;cc-rep-1Cc0005;cc-rep-2Cc0002;cc-rep-3Cc0005;cc-rep-4
[1,0]=>[1,1,0,0]=>[1,0,1,0]=>[1]=>[1,0,1,0] [1,0,1,0]=>[1,1,0,1,0,0]=>[1,1,0,0,1,0]=>[2]=>[1,1,0,0,1,0] [1,1,0,0]=>[1,1,1,0,0,0]=>[1,0,1,0,1,0]=>[2,1]=>[1,0,1,0,1,0] [1,0,1,0,1,0]=>[1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0]=>[2,2]=>[1,1,0,0,1,1,0,0] [1,0,1,1,0,0]=>[1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0]=>[3,1,1]=>[1,0,1,1,0,0,1,0] [1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,0]=>[3,1]=>[1,1,0,1,0,0,1,0] [1,1,0,1,0,0]=>[1,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,0]=>[3,2]=>[1,1,0,0,1,0,1,0] [1,1,1,0,0,0]=>[1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0]=>[3,2,1]=>[1,0,1,0,1,0,1,0] [1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>[3,3]=>[1,1,1,0,0,0,1,1,0,0] [1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>[3,3,1,1]=>[1,0,1,1,0,0,1,1,0,0] [1,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,0]=>[4,2]=>[1,1,1,0,0,1,0,0,1,0] [1,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,0]=>[3,3,2]=>[1,1,0,0,1,0,1,1,0,0] [1,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0]=>[4,2,2,1]=>[1,0,1,0,1,1,0,0,1,0] [1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,0]=>[3,2,2]=>[1,1,0,0,1,1,0,1,0,0] [1,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0]=>[4,2,1,1]=>[1,0,1,1,0,1,0,0,1,0] [1,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0]=>[3,3,1]=>[1,1,0,1,0,0,1,1,0,0] [1,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>[4,2,2]=>[1,1,0,0,1,1,0,0,1,0] [1,1,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0]=>[4,3,1,1]=>[1,0,1,1,0,0,1,0,1,0] [1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0]=>[4,2,1]=>[1,1,0,1,0,1,0,0,1,0] [1,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,0]=>[4,3,1]=>[1,1,0,1,0,0,1,0,1,0] [1,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0]=>[4,3,2]=>[1,1,0,0,1,0,1,0,1,0] [1,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>[4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0] [1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,3,3]=>[1,1,1,0,0,0,1,1,1,0,0,0] [1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[4,4,1,1,1]=>[1,0,1,1,1,0,0,0,1,1,0,0] [1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[5,2,2]=>[1,1,1,0,0,1,1,0,0,0,1,0] [1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[4,4,3]=>[1,1,1,0,0,0,1,0,1,1,0,0] [1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[4,4,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0] [1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[4,2,2,2]=>[1,1,0,0,1,1,1,0,0,1,0,0] [1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[5,3,1,1,1]=>[1,0,1,1,1,0,0,1,0,0,1,0] [1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[4,4,1,1]=>[1,1,0,1,1,0,0,0,1,1,0,0] [1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[5,3,3]=>[1,1,1,0,0,0,1,1,0,0,1,0] [1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[4,4,3,1,1]=>[1,0,1,1,0,0,1,0,1,1,0,0] [1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[5,3,1,1]=>[1,1,0,1,1,0,0,1,0,0,1,0] [1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[5,4,2]=>[1,1,1,0,0,1,0,0,1,0,1,0] [1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[4,4,3,2]=>[1,1,0,0,1,0,1,0,1,1,0,0] [1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[5,3,3,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0] [1,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[4,4,1]=>[1,1,1,0,1,0,0,0,1,1,0,0] [1,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[4,3,3,1,1]=>[1,0,1,1,0,0,1,1,0,1,0,0] [1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[5,3,1]=>[1,1,1,0,1,0,0,1,0,0,1,0] [1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[4,3,3,2]=>[1,1,0,0,1,0,1,1,0,1,0,0] [1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[5,3,2,2,1]=>[1,0,1,0,1,1,0,1,0,0,1,0] [1,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[4,3,3]=>[1,1,1,0,0,0,1,1,0,1,0,0] [1,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[4,4,2,1,1]=>[1,0,1,1,0,1,0,0,1,1,0,0] [1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[4,4,2]=>[1,1,1,0,0,1,0,0,1,1,0,0] [1,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[4,4,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0] [1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[5,3,3,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0] [1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[5,3,2]=>[1,1,1,0,0,1,0,1,0,0,1,0] [1,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[4,4,3,1]=>[1,1,0,1,0,0,1,0,1,1,0,0] [1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[5,3,3,2]=>[1,1,0,0,1,0,1,1,0,0,1,0] [1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[5,4,2,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,0] [1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[4,3,2,2]=>[1,1,0,0,1,1,0,1,0,1,0,0] [1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[5,3,2,1,1]=>[1,0,1,1,0,1,0,1,0,0,1,0] [1,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[4,3,3,1]=>[1,1,0,1,0,0,1,1,0,1,0,0] [1,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[5,3,2,2]=>[1,1,0,0,1,1,0,1,0,0,1,0] [1,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[5,4,2,1,1]=>[1,0,1,1,0,1,0,0,1,0,1,0] [1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[4,4,2,1]=>[1,1,0,1,0,1,0,0,1,1,0,0] [1,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[5,3,3,1]=>[1,1,0,1,0,0,1,1,0,0,1,0] [1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[5,4,2,2]=>[1,1,0,0,1,1,0,0,1,0,1,0] [1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[5,4,3,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0] [1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[5,3,2,1]=>[1,1,0,1,0,1,0,1,0,0,1,0] [1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[5,4,2,1]=>[1,1,0,1,0,1,0,0,1,0,1,0] [1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[5,4,3,1]=>[1,1,0,1,0,0,1,0,1,0,1,0] [1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[5,4,3,2]=>[1,1,0,0,1,0,1,0,1,0,1,0] [1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0] [1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,4,4]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0] [1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[4,4,4,1,1,1]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0] [1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[6,3,3]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0] [1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[4,4,4,3]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0] [1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[5,5,2,2,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0] [1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[4,4,2,2,2]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0] [1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[6,3,3,1,1,1]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0] [1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[4,4,4,1,1]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0] [1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[6,3,3,3]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0] [1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[5,5,4,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0] [1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[6,3,3,1,1]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0] [1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[6,5,2,2]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0] [1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[5,5,4,3]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0] [1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[5,5,3,3,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0] [1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[5,5,2]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0] [1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[5,3,3,3,1,1]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0] [1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[6,4,2]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0] [1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[5,3,3,3,2]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0] [1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[6,4,2,2,2,1]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0] [1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[4,4,3,3]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0] [1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[5,5,2,2,1,1]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0] [1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[4,4,4,2]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0] [1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[5,5,2,2,2]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0] [1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[6,4,4,1,1,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0] [1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[6,3,3,2]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0] [1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[5,5,4,1,1]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0] [1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[6,4,4,3]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0] [1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[5,5,4,2,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0] [1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[5,3,3,2,2]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0] [1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[6,4,2,2,1,1]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0] [1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[5,3,3,3,1]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0] [1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[6,4,2,2,2]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0] [1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[6,5,3,1,1,1]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0] [1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[5,5,2,2,1]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0] [1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[6,4,4,1,1]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0] [1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[6,5,3,3]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0] [1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[5,5,4,3,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0] [1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[6,4,2,2,1]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0] [1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[6,5,3,1,1]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0] [1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[6,5,4,2]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0] [1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[5,5,4,3,2]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0] [1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[6,4,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0] [1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[4,3,3,3]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0] [1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[5,5,2,1,1,1]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0] [1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[6,3,2,2]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0] [1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[5,5,4,1]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0] [1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[5,4,4,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0] [1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[5,3,2,2,2]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0] [1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[6,4,2,1,1,1]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0] [1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[5,5,2,1,1]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0] [1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[6,4,4,1]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0] [1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[5,4,4,3,1,1]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0] [1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[6,4,2,1,1]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0] [1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[6,5,3,1]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0] [1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[5,4,4,3,2]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0] [1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[6,4,3,3,2,1]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0] [1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,4,4,1]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0] [1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[5,4,4,1,1,1]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0] [1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[6,3,3,1]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0] [1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[5,4,4,3]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0] [1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[5,5,3,2,2,1]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0] [1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[5,3,3,3]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0] [1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[5,5,3,1,1,1]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0] [1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[5,5,2,2]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0] [1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[5,5,3,3]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0] [1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[5,5,3,3,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0] [1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[6,4,2,2]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0] [1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[5,5,4,2]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0] [1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[5,5,3,3,2]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0] [1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[6,4,4,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0] [1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[5,4,2,2,2]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0] [1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[6,4,3,1,1,1]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0] [1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[5,4,4,1,1]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0] [1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[6,4,3,3]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0] [1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[5,5,4,2,1,1]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0] [1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[5,5,3,1,1]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0] [1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[6,4,4,2]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0] [1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[5,5,4,2,2]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0] [1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[6,4,4,3,1,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0] [1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[6,4,3,1,1]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0] [1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[6,5,3,2]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0] [1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[5,5,4,3,1]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0] [1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[6,4,4,3,2]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0] [1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[6,5,3,3,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0] [1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[5,5,2,1]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0] [1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[5,4,3,3,1,1]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0] [1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[6,4,2,1]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0] [1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[5,4,3,3,2]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0] [1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,2,1]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0] [1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[5,4,4,1]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0] [1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[5,4,4,2,1,1]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0] [1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[5,5,3,1]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0] [1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[5,4,4,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0] [1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[6,4,3,3,1,1]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0] [1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[6,4,3,1]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0] [1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[5,4,4,3,1]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0] [1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[6,4,3,3,2]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0] [1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,2,1]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0] [1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[5,4,3,3]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0] [1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[5,5,3,2,1,1]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0] [1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[5,4,4,2]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0] [1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[5,5,3,2,2]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0] [1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[6,4,4,2,1,1]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0] [1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[5,5,3,2]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0] [1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[5,5,3,3,1]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0] [1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[6,4,4,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0] [1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[6,5,3,3,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0] [1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[6,4,3,2]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0] [1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[5,5,4,2,1]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0] [1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[6,4,4,3,1]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0] [1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[6,5,3,3,2]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0] [1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0] [1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,2]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0] [1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,1,1]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0] [1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[5,4,3,3,1]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0] [1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,2]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0] [1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,1,1]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0] [1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[5,4,4,2,1]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0] [1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[6,4,3,3,1]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0] [1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,2]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0] [1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,1,1]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0] [1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[5,5,3,2,1]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0] [1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[6,4,4,2,1]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0] [1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[6,5,3,3,1]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0] [1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,2]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0] [1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0] [1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,1]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0] [1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,1]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0] [1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,1]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0] [1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,1]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0] [1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0] [1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0] [1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] [1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] [1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[6,6,2,2]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,2]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[6,6,5,4,3]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] [1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[6,6,4,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,3]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2,2]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,5,5,1,1]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,4,1,1]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[6,6,5,3,3,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[6,6,3,1,1]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] [1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[7,5,3,1,1]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] [1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[6,6,5,4,2,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] [1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[6,6,5,4,3,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[6,6,5,4,3,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] [1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[5,5,5,1]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] [1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,4,1]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] [1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,4,4,3]=>[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] [1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[6,6,3,1]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] [1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[7,5,3,1]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] [1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,5,4,2,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] [1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,5,4,3,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] [1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,5,4,3,2]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] [1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[5,4,4,4]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[5,5,5,2,1,1,1]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] [1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,3]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] [1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[6,5,5,4,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] [1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,5,4,3]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] [1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[5,5,5,2]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] [1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[7,4,4,2]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] [1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[6,6,3,2]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] [1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[6,6,5,4,2,1,1]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[6,6,5,4,3,1]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] [1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,5,4,3,2]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,3]=>[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] [1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[6,6,5,2,1]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,4,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] [1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,1]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] [1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,4,3,2]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] [1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,1,1,1]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,5,4,2,1,1]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] [1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,5,4,3,1]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] [1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,2,2]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] [1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,4,3,2]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] [1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[6,6,3,2,1]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] [1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,3,2]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] [1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[6,6,4,2,1]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,1]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,1]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] [1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[6,6,5,3,2,1]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] [1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,2]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[6,6,4,3,2,1]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] [1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] [1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,1]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] [1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,1]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] [1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,1]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,1]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] [1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] [1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,5,5,5]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[7,7,5,5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,2]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[7,7,6,5,4,3,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,2]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[7,7,6,5,4,3,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[5,4,4,4,4]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,6,5,4,3,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,6,5,4,3,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,5,5,5,1]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[7,7,6,5,4,3,1]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,6,5,4,3,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] [1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[7,7,6,5,3,2,1]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,3,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[7,7,4,3,2,1]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0] [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,2,2,1]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,3,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,2]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,2,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,2,2]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,2,1,1]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,2,2]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[7,7,5,4,3,2,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,2,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,3,2,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,2,1]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,3,1]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,3,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,7,6,5,4,3,2,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[8,8,7,6,5,4,3,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] [1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[8,7,7,6,5,4,3,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] []=>[1,0]=>[1,0]=>[]=>[] [1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[9,8,6,5,5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[9,8,7,5,5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,3,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,5,5,5,5]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[6,6,6,6,6]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[9,7,5,3,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[9,7,6,5,5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,4,3,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
Map
prime Dyck path
Description
Return the Dyck path obtained by adding an initial up and a final down step.
Map
inverse zeta map
Description
The inverse zeta map on Dyck paths.
See its inverse, the zeta map Mp00030zeta map, for the definition and details.
Map
to partition
Description
The cut-out partition of a Dyck path.
The partition $\lambda$ associated to a Dyck path is defined to be the complementary partition inside the staircase partition $(n-1,\ldots,2,1)$ when cutting out $D$ considered as a path from $(0,0)$ to $(n,n)$.
In other words, $\lambda_{i}$ is the number of down-steps before the $(n+1-i)$-th up-step of $D$.
This map is a bijection between Dyck paths of size $n$ and partitions inside the staircase partition $(n-1,\ldots,2,1)$.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.