Identifier
Mp00201: Dyck paths —Ringel⟶ Permutations
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Images
=>
Cc0005;cc-rep-0Cc0002;cc-rep-2
[1,0]=>[2,1]=>[1,1] [1,0,1,0]=>[3,1,2]=>[2,1] [1,1,0,0]=>[2,3,1]=>[2,1] [1,0,1,0,1,0]=>[4,1,2,3]=>[3,1] [1,0,1,1,0,0]=>[3,1,4,2]=>[2,2] [1,1,0,0,1,0]=>[2,4,1,3]=>[2,2] [1,1,0,1,0,0]=>[4,3,1,2]=>[2,1,1] [1,1,1,0,0,0]=>[2,3,4,1]=>[3,1] [1,0,1,0,1,0,1,0]=>[5,1,2,3,4]=>[4,1] [1,0,1,0,1,1,0,0]=>[4,1,2,5,3]=>[3,2] [1,0,1,1,0,0,1,0]=>[3,1,5,2,4]=>[3,2] [1,0,1,1,0,1,0,0]=>[5,1,4,2,3]=>[3,1,1] [1,0,1,1,1,0,0,0]=>[3,1,4,5,2]=>[3,2] [1,1,0,0,1,0,1,0]=>[2,5,1,3,4]=>[3,2] [1,1,0,0,1,1,0,0]=>[2,4,1,5,3]=>[3,2] [1,1,0,1,0,0,1,0]=>[5,3,1,2,4]=>[3,1,1] [1,1,0,1,0,1,0,0]=>[5,4,1,2,3]=>[3,1,1] [1,1,0,1,1,0,0,0]=>[4,3,1,5,2]=>[2,2,1] [1,1,1,0,0,0,1,0]=>[2,3,5,1,4]=>[3,2] [1,1,1,0,0,1,0,0]=>[2,5,4,1,3]=>[2,2,1] [1,1,1,0,1,0,0,0]=>[5,3,4,1,2]=>[2,2,1] [1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>[4,1] [1,0,1,0,1,0,1,0,1,0]=>[6,1,2,3,4,5]=>[5,1] [1,0,1,0,1,0,1,1,0,0]=>[5,1,2,3,6,4]=>[4,2] [1,0,1,0,1,1,0,0,1,0]=>[4,1,2,6,3,5]=>[4,2] [1,0,1,0,1,1,0,1,0,0]=>[6,1,2,5,3,4]=>[4,1,1] [1,0,1,0,1,1,1,0,0,0]=>[4,1,2,5,6,3]=>[4,2] [1,0,1,1,0,0,1,0,1,0]=>[3,1,6,2,4,5]=>[4,2] [1,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,6,4]=>[3,3] [1,0,1,1,0,1,0,0,1,0]=>[6,1,4,2,3,5]=>[4,1,1] [1,0,1,1,0,1,0,1,0,0]=>[6,1,5,2,3,4]=>[4,1,1] [1,0,1,1,0,1,1,0,0,0]=>[5,1,4,2,6,3]=>[3,2,1] [1,0,1,1,1,0,0,0,1,0]=>[3,1,4,6,2,5]=>[3,3] [1,0,1,1,1,0,0,1,0,0]=>[3,1,6,5,2,4]=>[3,2,1] [1,0,1,1,1,0,1,0,0,0]=>[6,1,4,5,2,3]=>[3,2,1] [1,0,1,1,1,1,0,0,0,0]=>[3,1,4,5,6,2]=>[4,2] [1,1,0,0,1,0,1,0,1,0]=>[2,6,1,3,4,5]=>[4,2] [1,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,6,4]=>[3,3] [1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,5]=>[3,3] [1,1,0,0,1,1,0,1,0,0]=>[2,6,1,5,3,4]=>[3,2,1] [1,1,0,0,1,1,1,0,0,0]=>[2,4,1,5,6,3]=>[4,2] [1,1,0,1,0,0,1,0,1,0]=>[6,3,1,2,4,5]=>[4,1,1] [1,1,0,1,0,0,1,1,0,0]=>[5,3,1,2,6,4]=>[3,2,1] [1,1,0,1,0,1,0,0,1,0]=>[6,4,1,2,3,5]=>[4,1,1] [1,1,0,1,0,1,0,1,0,0]=>[5,6,1,2,3,4]=>[4,2] [1,1,0,1,0,1,1,0,0,0]=>[5,4,1,2,6,3]=>[3,2,1] [1,1,0,1,1,0,0,0,1,0]=>[4,3,1,6,2,5]=>[3,2,1] [1,1,0,1,1,0,0,1,0,0]=>[6,3,1,5,2,4]=>[3,2,1] [1,1,0,1,1,0,1,0,0,0]=>[6,4,1,5,2,3]=>[3,2,1] [1,1,0,1,1,1,0,0,0,0]=>[4,3,1,5,6,2]=>[3,2,1] [1,1,1,0,0,0,1,0,1,0]=>[2,3,6,1,4,5]=>[4,2] [1,1,1,0,0,0,1,1,0,0]=>[2,3,5,1,6,4]=>[4,2] [1,1,1,0,0,1,0,0,1,0]=>[2,6,4,1,3,5]=>[3,2,1] [1,1,1,0,0,1,0,1,0,0]=>[2,6,5,1,3,4]=>[3,2,1] [1,1,1,0,0,1,1,0,0,0]=>[2,5,4,1,6,3]=>[3,2,1] [1,1,1,0,1,0,0,0,1,0]=>[6,3,4,1,2,5]=>[3,2,1] [1,1,1,0,1,0,0,1,0,0]=>[6,3,5,1,2,4]=>[3,2,1] [1,1,1,0,1,0,1,0,0,0]=>[6,5,4,1,2,3]=>[3,1,1,1] [1,1,1,0,1,1,0,0,0,0]=>[5,3,4,1,6,2]=>[3,2,1] [1,1,1,1,0,0,0,0,1,0]=>[2,3,4,6,1,5]=>[4,2] [1,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,1,4]=>[3,2,1] [1,1,1,1,0,0,1,0,0,0]=>[2,6,4,5,1,3]=>[3,2,1] [1,1,1,1,0,1,0,0,0,0]=>[6,3,4,5,1,2]=>[3,2,1] [1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>[5,1] [1,0,1,0,1,0,1,0,1,0,1,0]=>[7,1,2,3,4,5,6]=>[6,1] [1,0,1,0,1,0,1,0,1,1,0,0]=>[6,1,2,3,4,7,5]=>[5,2] [1,0,1,0,1,0,1,1,0,0,1,0]=>[5,1,2,3,7,4,6]=>[5,2] [1,0,1,0,1,0,1,1,0,1,0,0]=>[7,1,2,3,6,4,5]=>[5,1,1] [1,0,1,0,1,0,1,1,1,0,0,0]=>[5,1,2,3,6,7,4]=>[5,2] [1,0,1,0,1,1,0,0,1,0,1,0]=>[4,1,2,7,3,5,6]=>[5,2] [1,0,1,0,1,1,0,0,1,1,0,0]=>[4,1,2,6,3,7,5]=>[4,3] [1,0,1,0,1,1,0,1,0,0,1,0]=>[7,1,2,5,3,4,6]=>[5,1,1] [1,0,1,0,1,1,0,1,0,1,0,0]=>[7,1,2,6,3,4,5]=>[5,1,1] [1,0,1,0,1,1,0,1,1,0,0,0]=>[6,1,2,5,3,7,4]=>[4,2,1] [1,0,1,0,1,1,1,0,0,0,1,0]=>[4,1,2,5,7,3,6]=>[4,3] [1,0,1,0,1,1,1,0,0,1,0,0]=>[4,1,2,7,6,3,5]=>[4,2,1] [1,0,1,0,1,1,1,0,1,0,0,0]=>[7,1,2,5,6,3,4]=>[4,2,1] [1,0,1,0,1,1,1,1,0,0,0,0]=>[4,1,2,5,6,7,3]=>[5,2] [1,0,1,1,0,0,1,0,1,0,1,0]=>[3,1,7,2,4,5,6]=>[5,2] [1,0,1,1,0,0,1,0,1,1,0,0]=>[3,1,6,2,4,7,5]=>[4,3] [1,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,6]=>[4,3] [1,0,1,1,0,0,1,1,0,1,0,0]=>[3,1,7,2,6,4,5]=>[4,2,1] [1,0,1,1,0,0,1,1,1,0,0,0]=>[3,1,5,2,6,7,4]=>[4,3] [1,0,1,1,0,1,0,0,1,0,1,0]=>[7,1,4,2,3,5,6]=>[5,1,1] [1,0,1,1,0,1,0,0,1,1,0,0]=>[6,1,4,2,3,7,5]=>[4,2,1] [1,0,1,1,0,1,0,1,0,0,1,0]=>[7,1,5,2,3,4,6]=>[5,1,1] [1,0,1,1,0,1,0,1,0,1,0,0]=>[6,1,7,2,3,4,5]=>[5,2] [1,0,1,1,0,1,0,1,1,0,0,0]=>[6,1,5,2,3,7,4]=>[4,2,1] [1,0,1,1,0,1,1,0,0,0,1,0]=>[5,1,4,2,7,3,6]=>[4,2,1] [1,0,1,1,0,1,1,0,0,1,0,0]=>[7,1,4,2,6,3,5]=>[4,2,1] [1,0,1,1,0,1,1,0,1,0,0,0]=>[7,1,5,2,6,3,4]=>[4,2,1] [1,0,1,1,0,1,1,1,0,0,0,0]=>[5,1,4,2,6,7,3]=>[4,2,1] [1,0,1,1,1,0,0,0,1,0,1,0]=>[3,1,4,7,2,5,6]=>[4,3] [1,0,1,1,1,0,0,0,1,1,0,0]=>[3,1,4,6,2,7,5]=>[4,3] [1,0,1,1,1,0,0,1,0,0,1,0]=>[3,1,7,5,2,4,6]=>[4,2,1] [1,0,1,1,1,0,0,1,0,1,0,0]=>[3,1,7,6,2,4,5]=>[4,2,1] [1,0,1,1,1,0,0,1,1,0,0,0]=>[3,1,6,5,2,7,4]=>[3,3,1] [1,0,1,1,1,0,1,0,0,0,1,0]=>[7,1,4,5,2,3,6]=>[4,2,1] [1,0,1,1,1,0,1,0,0,1,0,0]=>[7,1,4,6,2,3,5]=>[4,2,1] [1,0,1,1,1,0,1,0,1,0,0,0]=>[7,1,6,5,2,3,4]=>[4,1,1,1] [1,0,1,1,1,0,1,1,0,0,0,0]=>[6,1,4,5,2,7,3]=>[4,2,1] [1,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,5,7,2,6]=>[4,3] [1,0,1,1,1,1,0,0,0,1,0,0]=>[3,1,4,7,6,2,5]=>[3,3,1] [1,0,1,1,1,1,0,0,1,0,0,0]=>[3,1,7,5,6,2,4]=>[3,3,1] [1,0,1,1,1,1,0,1,0,0,0,0]=>[7,1,4,5,6,2,3]=>[4,2,1] [1,0,1,1,1,1,1,0,0,0,0,0]=>[3,1,4,5,6,7,2]=>[5,2] [1,1,0,0,1,0,1,0,1,0,1,0]=>[2,7,1,3,4,5,6]=>[5,2] [1,1,0,0,1,0,1,0,1,1,0,0]=>[2,6,1,3,4,7,5]=>[4,3] [1,1,0,0,1,0,1,1,0,0,1,0]=>[2,5,1,3,7,4,6]=>[4,3] [1,1,0,0,1,0,1,1,0,1,0,0]=>[2,7,1,3,6,4,5]=>[4,2,1] [1,1,0,0,1,0,1,1,1,0,0,0]=>[2,5,1,3,6,7,4]=>[4,3] [1,1,0,0,1,1,0,0,1,0,1,0]=>[2,4,1,7,3,5,6]=>[4,3] [1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,7,5]=>[4,3] [1,1,0,0,1,1,0,1,0,0,1,0]=>[2,7,1,5,3,4,6]=>[4,2,1] [1,1,0,0,1,1,0,1,0,1,0,0]=>[2,7,1,6,3,4,5]=>[4,2,1] [1,1,0,0,1,1,0,1,1,0,0,0]=>[2,6,1,5,3,7,4]=>[3,3,1] [1,1,0,0,1,1,1,0,0,0,1,0]=>[2,4,1,5,7,3,6]=>[4,3] [1,1,0,0,1,1,1,0,0,1,0,0]=>[2,4,1,7,6,3,5]=>[3,3,1] [1,1,0,0,1,1,1,0,1,0,0,0]=>[2,7,1,5,6,3,4]=>[3,3,1] [1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4,1,5,6,7,3]=>[5,2] [1,1,0,1,0,0,1,0,1,0,1,0]=>[7,3,1,2,4,5,6]=>[5,1,1] [1,1,0,1,0,0,1,0,1,1,0,0]=>[6,3,1,2,4,7,5]=>[4,2,1] [1,1,0,1,0,0,1,1,0,0,1,0]=>[5,3,1,2,7,4,6]=>[4,2,1] [1,1,0,1,0,0,1,1,0,1,0,0]=>[7,3,1,2,6,4,5]=>[4,2,1] [1,1,0,1,0,0,1,1,1,0,0,0]=>[5,3,1,2,6,7,4]=>[4,2,1] [1,1,0,1,0,1,0,0,1,0,1,0]=>[7,4,1,2,3,5,6]=>[5,1,1] [1,1,0,1,0,1,0,0,1,1,0,0]=>[6,4,1,2,3,7,5]=>[4,2,1] [1,1,0,1,0,1,0,1,0,0,1,0]=>[5,7,1,2,3,4,6]=>[5,2] [1,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,1,2,3,4,5]=>[5,1,1] [1,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,1,2,3,7,4]=>[4,3] [1,1,0,1,0,1,1,0,0,0,1,0]=>[5,4,1,2,7,3,6]=>[4,2,1] [1,1,0,1,0,1,1,0,0,1,0,0]=>[7,4,1,2,6,3,5]=>[4,2,1] [1,1,0,1,0,1,1,0,1,0,0,0]=>[5,7,1,2,6,3,4]=>[4,2,1] [1,1,0,1,0,1,1,1,0,0,0,0]=>[5,4,1,2,6,7,3]=>[4,2,1] [1,1,0,1,1,0,0,0,1,0,1,0]=>[4,3,1,7,2,5,6]=>[4,2,1] [1,1,0,1,1,0,0,0,1,1,0,0]=>[4,3,1,6,2,7,5]=>[3,3,1] [1,1,0,1,1,0,0,1,0,0,1,0]=>[7,3,1,5,2,4,6]=>[4,2,1] [1,1,0,1,1,0,0,1,0,1,0,0]=>[7,3,1,6,2,4,5]=>[4,2,1] [1,1,0,1,1,0,0,1,1,0,0,0]=>[6,3,1,5,2,7,4]=>[3,3,1] [1,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,1,5,2,3,6]=>[4,2,1] [1,1,0,1,1,0,1,0,0,1,0,0]=>[7,4,1,6,2,3,5]=>[4,2,1] [1,1,0,1,1,0,1,0,1,0,0,0]=>[6,7,1,5,2,3,4]=>[4,2,1] [1,1,0,1,1,0,1,1,0,0,0,0]=>[6,4,1,5,2,7,3]=>[3,3,1] [1,1,0,1,1,1,0,0,0,0,1,0]=>[4,3,1,5,7,2,6]=>[3,3,1] [1,1,0,1,1,1,0,0,0,1,0,0]=>[4,3,1,7,6,2,5]=>[3,2,2] [1,1,0,1,1,1,0,0,1,0,0,0]=>[7,3,1,5,6,2,4]=>[3,3,1] [1,1,0,1,1,1,0,1,0,0,0,0]=>[7,4,1,5,6,2,3]=>[3,3,1] [1,1,0,1,1,1,1,0,0,0,0,0]=>[4,3,1,5,6,7,2]=>[4,2,1] [1,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,7,1,4,5,6]=>[5,2] [1,1,1,0,0,0,1,0,1,1,0,0]=>[2,3,6,1,4,7,5]=>[4,3] [1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,5,1,7,4,6]=>[4,3] [1,1,1,0,0,0,1,1,0,1,0,0]=>[2,3,7,1,6,4,5]=>[4,2,1] [1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,5,1,6,7,4]=>[5,2] [1,1,1,0,0,1,0,0,1,0,1,0]=>[2,7,4,1,3,5,6]=>[4,2,1] [1,1,1,0,0,1,0,0,1,1,0,0]=>[2,6,4,1,3,7,5]=>[3,3,1] [1,1,1,0,0,1,0,1,0,0,1,0]=>[2,7,5,1,3,4,6]=>[4,2,1] [1,1,1,0,0,1,0,1,0,1,0,0]=>[2,6,7,1,3,4,5]=>[4,3] [1,1,1,0,0,1,0,1,1,0,0,0]=>[2,6,5,1,3,7,4]=>[3,3,1] [1,1,1,0,0,1,1,0,0,0,1,0]=>[2,5,4,1,7,3,6]=>[3,3,1] [1,1,1,0,0,1,1,0,0,1,0,0]=>[2,7,4,1,6,3,5]=>[3,3,1] [1,1,1,0,0,1,1,0,1,0,0,0]=>[2,7,5,1,6,3,4]=>[3,3,1] [1,1,1,0,0,1,1,1,0,0,0,0]=>[2,5,4,1,6,7,3]=>[4,2,1] [1,1,1,0,1,0,0,0,1,0,1,0]=>[7,3,4,1,2,5,6]=>[4,2,1] [1,1,1,0,1,0,0,0,1,1,0,0]=>[6,3,4,1,2,7,5]=>[3,3,1] [1,1,1,0,1,0,0,1,0,0,1,0]=>[7,3,5,1,2,4,6]=>[4,2,1] [1,1,1,0,1,0,0,1,0,1,0,0]=>[6,3,7,1,2,4,5]=>[4,2,1] [1,1,1,0,1,0,0,1,1,0,0,0]=>[6,3,5,1,2,7,4]=>[3,3,1] [1,1,1,0,1,0,1,0,0,0,1,0]=>[7,5,4,1,2,3,6]=>[4,1,1,1] [1,1,1,0,1,0,1,0,0,1,0,0]=>[6,7,4,1,2,3,5]=>[4,2,1] [1,1,1,0,1,0,1,0,1,0,0,0]=>[6,7,5,1,2,3,4]=>[4,2,1] [1,1,1,0,1,0,1,1,0,0,0,0]=>[6,5,4,1,2,7,3]=>[3,2,1,1] [1,1,1,0,1,1,0,0,0,0,1,0]=>[5,3,4,1,7,2,6]=>[3,3,1] [1,1,1,0,1,1,0,0,0,1,0,0]=>[7,3,4,1,6,2,5]=>[3,3,1] [1,1,1,0,1,1,0,0,1,0,0,0]=>[7,3,5,1,6,2,4]=>[3,3,1] [1,1,1,0,1,1,0,1,0,0,0,0]=>[7,5,4,1,6,2,3]=>[3,2,1,1] [1,1,1,0,1,1,1,0,0,0,0,0]=>[5,3,4,1,6,7,2]=>[4,2,1] [1,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,4,7,1,5,6]=>[5,2] [1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,4,6,1,7,5]=>[5,2] [1,1,1,1,0,0,0,1,0,0,1,0]=>[2,3,7,5,1,4,6]=>[4,2,1] [1,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,7,6,1,4,5]=>[4,2,1] [1,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,6,5,1,7,4]=>[4,2,1] [1,1,1,1,0,0,1,0,0,0,1,0]=>[2,7,4,5,1,3,6]=>[4,2,1] [1,1,1,1,0,0,1,0,0,1,0,0]=>[2,7,4,6,1,3,5]=>[3,3,1] [1,1,1,1,0,0,1,0,1,0,0,0]=>[2,7,6,5,1,3,4]=>[3,2,1,1] [1,1,1,1,0,0,1,1,0,0,0,0]=>[2,6,4,5,1,7,3]=>[4,2,1] [1,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,4,5,1,2,6]=>[4,2,1] [1,1,1,1,0,1,0,0,0,1,0,0]=>[7,3,4,6,1,2,5]=>[3,3,1] [1,1,1,1,0,1,0,0,1,0,0,0]=>[7,3,6,5,1,2,4]=>[3,2,1,1] [1,1,1,1,0,1,0,1,0,0,0,0]=>[7,6,4,5,1,2,3]=>[3,2,1,1] [1,1,1,1,0,1,1,0,0,0,0,0]=>[6,3,4,5,1,7,2]=>[4,2,1] [1,1,1,1,1,0,0,0,0,0,1,0]=>[2,3,4,5,7,1,6]=>[5,2] [1,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,4,7,6,1,5]=>[4,2,1] [1,1,1,1,1,0,0,0,1,0,0,0]=>[2,3,7,5,6,1,4]=>[4,2,1] [1,1,1,1,1,0,0,1,0,0,0,0]=>[2,7,4,5,6,1,3]=>[4,2,1] [1,1,1,1,1,0,1,0,0,0,0,0]=>[7,3,4,5,6,1,2]=>[4,2,1] [1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1]=>[6,1] [1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[8,1,2,3,4,5,6,7]=>[7,1] [1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[7,1,2,3,4,5,8,6]=>[6,2] [1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[6,1,2,3,4,8,5,7]=>[6,2] [1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[8,1,2,3,4,7,5,6]=>[6,1,1] [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[6,1,2,3,4,7,8,5]=>[6,2] [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[5,1,2,3,8,4,6,7]=>[6,2] [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[5,1,2,3,7,4,8,6]=>[5,3] [1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[8,1,2,3,6,4,5,7]=>[6,1,1] [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[8,1,2,3,7,4,5,6]=>[6,1,1] [1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[7,1,2,3,6,4,8,5]=>[5,2,1] [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[5,1,2,3,6,8,4,7]=>[5,3] [1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[5,1,2,3,8,7,4,6]=>[5,2,1] [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[8,1,2,3,6,7,4,5]=>[5,2,1] [1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[5,1,2,3,6,7,8,4]=>[6,2] [1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[4,1,2,8,3,5,6,7]=>[6,2] [1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[4,1,2,7,3,5,8,6]=>[5,3] [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[4,1,2,6,3,8,5,7]=>[5,3] [1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[4,1,2,8,3,7,5,6]=>[5,2,1] [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[4,1,2,6,3,7,8,5]=>[5,3] [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[8,1,2,5,3,4,6,7]=>[6,1,1] [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[7,1,2,5,3,4,8,6]=>[5,2,1] [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[8,1,2,6,3,4,5,7]=>[6,1,1] [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[7,1,2,8,3,4,5,6]=>[6,2] [1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[7,1,2,6,3,4,8,5]=>[5,2,1] [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[6,1,2,5,3,8,4,7]=>[5,2,1] [1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[8,1,2,5,3,7,4,6]=>[5,2,1] [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[8,1,2,6,3,7,4,5]=>[5,2,1] [1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[6,1,2,5,3,7,8,4]=>[5,2,1] [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[4,1,2,5,8,3,6,7]=>[5,3] [1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[4,1,2,5,7,3,8,6]=>[5,3] [1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[4,1,2,8,6,3,5,7]=>[5,2,1] [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[4,1,2,8,7,3,5,6]=>[5,2,1] [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[4,1,2,7,6,3,8,5]=>[4,3,1] [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[8,1,2,5,6,3,4,7]=>[5,2,1] [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[8,1,2,5,7,3,4,6]=>[5,2,1] [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[8,1,2,7,6,3,4,5]=>[5,1,1,1] [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[7,1,2,5,6,3,8,4]=>[5,2,1] [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[4,1,2,5,6,8,3,7]=>[5,3] [1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[4,1,2,5,8,7,3,6]=>[4,3,1] [1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[4,1,2,8,6,7,3,5]=>[4,3,1] [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[8,1,2,5,6,7,3,4]=>[5,2,1] [1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[4,1,2,5,6,7,8,3]=>[6,2] [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,8,2,4,5,6,7]=>[6,2] [1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[3,1,7,2,4,5,8,6]=>[5,3] [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,6,2,4,8,5,7]=>[5,3] [1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[3,1,8,2,4,7,5,6]=>[5,2,1] [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[3,1,6,2,4,7,8,5]=>[5,3] [1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,5,2,8,4,6,7]=>[5,3] [1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,8,6]=>[4,4] [1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,8,2,6,4,5,7]=>[5,2,1] [1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[3,1,8,2,7,4,5,6]=>[5,2,1] [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[3,1,7,2,6,4,8,5]=>[4,3,1] [1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,5,2,6,8,4,7]=>[4,4] [1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[3,1,5,2,8,7,4,6]=>[4,3,1] [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[3,1,8,2,6,7,4,5]=>[4,3,1] [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,5,2,6,7,8,4]=>[5,3] [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[8,1,4,2,3,5,6,7]=>[6,1,1] [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[7,1,4,2,3,5,8,6]=>[5,2,1] [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[6,1,4,2,3,8,5,7]=>[5,2,1] [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[8,1,4,2,3,7,5,6]=>[5,2,1] [1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[6,1,4,2,3,7,8,5]=>[5,2,1] [1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[8,1,5,2,3,4,6,7]=>[6,1,1] [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[7,1,5,2,3,4,8,6]=>[5,2,1] [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[6,1,8,2,3,4,5,7]=>[6,2] [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[8,1,7,2,3,4,5,6]=>[6,1,1] [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[6,1,7,2,3,4,8,5]=>[5,3] [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[6,1,5,2,3,8,4,7]=>[5,2,1] [1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[8,1,5,2,3,7,4,6]=>[5,2,1] [1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[6,1,8,2,3,7,4,5]=>[5,2,1] [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[6,1,5,2,3,7,8,4]=>[5,2,1] [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[5,1,4,2,8,3,6,7]=>[5,2,1] [1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[5,1,4,2,7,3,8,6]=>[4,3,1] [1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[8,1,4,2,6,3,5,7]=>[5,2,1] [1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[8,1,4,2,7,3,5,6]=>[5,2,1] [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[7,1,4,2,6,3,8,5]=>[4,3,1] [1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[8,1,5,2,6,3,4,7]=>[5,2,1] [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[8,1,5,2,7,3,4,6]=>[5,2,1] [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[7,1,8,2,6,3,4,5]=>[5,2,1] [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[7,1,5,2,6,3,8,4]=>[4,3,1] [1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[5,1,4,2,6,8,3,7]=>[4,3,1] [1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[5,1,4,2,8,7,3,6]=>[4,2,2] [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[8,1,4,2,6,7,3,5]=>[4,3,1] [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[8,1,5,2,6,7,3,4]=>[4,3,1] [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[5,1,4,2,6,7,8,3]=>[5,2,1] [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,4,8,2,5,6,7]=>[5,3] [1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[3,1,4,7,2,5,8,6]=>[4,4] [1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,4,6,2,8,5,7]=>[4,4] [1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[3,1,4,8,2,7,5,6]=>[4,3,1] [1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[3,1,4,6,2,7,8,5]=>[5,3] [1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,8,5,2,4,6,7]=>[5,2,1] [1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[3,1,7,5,2,4,8,6]=>[4,3,1] [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[3,1,8,6,2,4,5,7]=>[5,2,1] [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[3,1,7,8,2,4,5,6]=>[5,3] [1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[3,1,7,6,2,4,8,5]=>[4,3,1] [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[3,1,6,5,2,8,4,7]=>[4,3,1] [1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[3,1,8,5,2,7,4,6]=>[4,3,1] [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[3,1,8,6,2,7,4,5]=>[4,3,1] [1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[3,1,6,5,2,7,8,4]=>[4,3,1] [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[8,1,4,5,2,3,6,7]=>[5,2,1] [1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[7,1,4,5,2,3,8,6]=>[4,3,1] [1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[8,1,4,6,2,3,5,7]=>[5,2,1] [1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[7,1,4,8,2,3,5,6]=>[5,2,1] [1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[7,1,4,6,2,3,8,5]=>[4,3,1] [1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[8,1,6,5,2,3,4,7]=>[5,1,1,1] [1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[7,1,8,5,2,3,4,6]=>[5,2,1] [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[7,1,8,6,2,3,4,5]=>[5,2,1] [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[7,1,6,5,2,3,8,4]=>[4,2,1,1] [1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[6,1,4,5,2,8,3,7]=>[4,3,1] [1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[8,1,4,5,2,7,3,6]=>[4,3,1] [1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[8,1,4,6,2,7,3,5]=>[4,3,1] [1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[8,1,6,5,2,7,3,4]=>[4,2,1,1] [1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[6,1,4,5,2,7,8,3]=>[5,2,1] [1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[3,1,4,5,8,2,6,7]=>[5,3] [1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[3,1,4,5,7,2,8,6]=>[5,3] [1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[3,1,4,8,6,2,5,7]=>[4,3,1] [1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[3,1,4,8,7,2,5,6]=>[4,3,1] [1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[3,1,4,7,6,2,8,5]=>[4,3,1] [1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[3,1,8,5,6,2,4,7]=>[4,3,1] [1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[3,1,8,5,7,2,4,6]=>[4,3,1] [1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[3,1,8,7,6,2,4,5]=>[4,2,1,1] [1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[3,1,7,5,6,2,8,4]=>[4,3,1] [1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[8,1,4,5,6,2,3,7]=>[5,2,1] [1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[8,1,4,5,7,2,3,6]=>[4,3,1] [1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[8,1,4,7,6,2,3,5]=>[4,2,1,1] [1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[8,1,7,5,6,2,3,4]=>[4,2,1,1] [1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[7,1,4,5,6,2,8,3]=>[5,2,1] [1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[3,1,4,5,6,8,2,7]=>[5,3] [1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[3,1,4,5,8,7,2,6]=>[4,3,1] [1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[3,1,4,8,6,7,2,5]=>[4,3,1] [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,8,5,6,7,2,4]=>[4,3,1] [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[8,1,4,5,6,7,2,3]=>[5,2,1] [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,1,4,5,6,7,8,2]=>[6,2] [1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,8,1,3,4,5,6,7]=>[6,2] [1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,7,1,3,4,5,8,6]=>[5,3] [1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,6,1,3,4,8,5,7]=>[5,3] [1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,8,1,3,4,7,5,6]=>[5,2,1] [1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,6,1,3,4,7,8,5]=>[5,3] [1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,5,1,3,8,4,6,7]=>[5,3] [1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,7,4,8,6]=>[4,4] [1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,8,1,3,6,4,5,7]=>[5,2,1] [1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,8,1,3,7,4,5,6]=>[5,2,1] [1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,7,1,3,6,4,8,5]=>[4,3,1] [1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,5,1,3,6,8,4,7]=>[4,4] [1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,5,1,3,8,7,4,6]=>[4,3,1] [1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,8,1,3,6,7,4,5]=>[4,3,1] [1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,5,1,3,6,7,8,4]=>[5,3] [1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,4,1,8,3,5,6,7]=>[5,3] [1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,4,1,7,3,5,8,6]=>[4,4] [1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,7]=>[4,4] [1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,4,1,8,3,7,5,6]=>[4,3,1] [1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,1,6,3,7,8,5]=>[5,3] [1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,8,1,5,3,4,6,7]=>[5,2,1] [1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,7,1,5,3,4,8,6]=>[4,3,1] [1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,8,1,6,3,4,5,7]=>[5,2,1] [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,7,1,8,3,4,5,6]=>[5,3] [1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,7,1,6,3,4,8,5]=>[4,3,1] [1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,6,1,5,3,8,4,7]=>[4,3,1] [1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,8,1,5,3,7,4,6]=>[4,3,1] [1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,6,1,5,3,7,8,4]=>[4,3,1] [1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,4,1,5,8,3,6,7]=>[5,3] [1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,5,7,3,8,6]=>[5,3] [1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,4,1,8,6,3,5,7]=>[4,3,1] [1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,4,1,8,7,3,5,6]=>[4,3,1] [1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,4,1,7,6,3,8,5]=>[4,3,1] [1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,8,1,5,6,3,4,7]=>[4,3,1] [1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,8,1,5,7,3,4,6]=>[4,3,1] [1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,8,1,7,6,3,4,5]=>[4,2,1,1] [1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,7,1,5,6,3,8,4]=>[4,3,1] [1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,4,1,5,6,8,3,7]=>[5,3] [1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,4,1,5,8,7,3,6]=>[4,3,1] [1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,4,1,8,6,7,3,5]=>[4,3,1] [1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,8,1,5,6,7,3,4]=>[4,3,1] [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,4,1,5,6,7,8,3]=>[6,2] [1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,3,1,2,4,5,6,7]=>[6,1,1] [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[7,3,1,2,4,5,8,6]=>[5,2,1] [1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[6,3,1,2,4,8,5,7]=>[5,2,1] [1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[8,3,1,2,4,7,5,6]=>[5,2,1] [1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[6,3,1,2,4,7,8,5]=>[5,2,1] [1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[5,3,1,2,8,4,6,7]=>[5,2,1] [1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[5,3,1,2,7,4,8,6]=>[4,3,1] [1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[8,3,1,2,6,4,5,7]=>[5,2,1] [1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[8,3,1,2,7,4,5,6]=>[5,2,1] [1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[7,3,1,2,6,4,8,5]=>[4,3,1] [1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[5,3,1,2,6,8,4,7]=>[4,3,1] [1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[5,3,1,2,8,7,4,6]=>[4,2,2] [1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[8,3,1,2,6,7,4,5]=>[4,3,1] [1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,3,1,2,6,7,8,4]=>[5,2,1] [1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[8,4,1,2,3,5,6,7]=>[6,1,1] [1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[7,4,1,2,3,5,8,6]=>[5,2,1] [1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[6,4,1,2,3,8,5,7]=>[5,2,1] [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[8,4,1,2,3,7,5,6]=>[5,2,1] [1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[6,4,1,2,3,7,8,5]=>[5,2,1] [1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[5,8,1,2,3,4,6,7]=>[6,2] [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[5,7,1,2,3,4,8,6]=>[5,3] [1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,1,2,3,4,5,7]=>[6,1,1] [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,1,2,3,4,5,6]=>[6,1,1] [1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[7,6,1,2,3,4,8,5]=>[5,2,1] [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[5,6,1,2,3,8,4,7]=>[5,3] [1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[5,8,1,2,3,7,4,6]=>[5,2,1] [1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[8,6,1,2,3,7,4,5]=>[5,2,1] [1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[5,6,1,2,3,7,8,4]=>[5,3] [1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[5,4,1,2,8,3,6,7]=>[5,2,1] [1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[5,4,1,2,7,3,8,6]=>[4,3,1] [1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[8,4,1,2,6,3,5,7]=>[5,2,1] [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[8,4,1,2,7,3,5,6]=>[5,2,1] [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[7,4,1,2,6,3,8,5]=>[4,3,1] [1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[5,8,1,2,6,3,4,7]=>[5,2,1] [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[5,8,1,2,7,3,4,6]=>[5,2,1] [1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[8,7,1,2,6,3,4,5]=>[5,1,1,1] [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[5,7,1,2,6,3,8,4]=>[4,3,1] [1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[5,4,1,2,6,8,3,7]=>[4,3,1] [1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[5,4,1,2,8,7,3,6]=>[4,2,2] [1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[8,4,1,2,6,7,3,5]=>[4,3,1] [1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[5,8,1,2,6,7,3,4]=>[4,3,1] [1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[5,4,1,2,6,7,8,3]=>[5,2,1] [1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[4,3,1,8,2,5,6,7]=>[5,2,1] [1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[4,3,1,7,2,5,8,6]=>[4,3,1] [1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[4,3,1,6,2,8,5,7]=>[4,3,1] [1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[4,3,1,8,2,7,5,6]=>[4,2,2] [1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[4,3,1,6,2,7,8,5]=>[4,3,1] [1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[8,3,1,5,2,4,6,7]=>[5,2,1] [1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[7,3,1,5,2,4,8,6]=>[4,3,1] [1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[8,3,1,6,2,4,5,7]=>[5,2,1] [1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[7,3,1,8,2,4,5,6]=>[5,2,1] [1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[7,3,1,6,2,4,8,5]=>[4,3,1] [1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[6,3,1,5,2,8,4,7]=>[4,3,1] [1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[8,3,1,5,2,7,4,6]=>[4,3,1] [1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[8,3,1,6,2,7,4,5]=>[4,3,1] [1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[6,3,1,5,2,7,8,4]=>[4,3,1] [1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[8,4,1,5,2,3,6,7]=>[5,2,1] [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[7,4,1,5,2,3,8,6]=>[4,3,1] [1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[8,4,1,6,2,3,5,7]=>[5,2,1] [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[7,4,1,8,2,3,5,6]=>[5,2,1] [1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[7,4,1,6,2,3,8,5]=>[4,3,1] [1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[6,8,1,5,2,3,4,7]=>[5,2,1] [1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[8,7,1,5,2,3,4,6]=>[5,1,1,1] [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[8,7,1,6,2,3,4,5]=>[5,1,1,1] [1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[6,7,1,5,2,3,8,4]=>[4,3,1] [1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[6,4,1,5,2,8,3,7]=>[4,3,1] [1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[8,4,1,5,2,7,3,6]=>[4,3,1] [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[8,4,1,6,2,7,3,5]=>[4,3,1] [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[6,8,1,5,2,7,3,4]=>[4,2,2] [1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[6,4,1,5,2,7,8,3]=>[4,3,1] [1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[4,3,1,5,8,2,6,7]=>[4,3,1] [1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,1,5,7,2,8,6]=>[4,3,1] [1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[4,3,1,8,6,2,5,7]=>[4,2,2] [1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[4,3,1,8,7,2,5,6]=>[4,2,2] [1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[4,3,1,7,6,2,8,5]=>[3,3,2] [1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[8,3,1,5,6,2,4,7]=>[4,3,1] [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[8,3,1,5,7,2,4,6]=>[4,3,1] [1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[8,3,1,7,6,2,4,5]=>[4,2,1,1] [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[7,3,1,5,6,2,8,4]=>[4,3,1] [1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[8,4,1,5,6,2,3,7]=>[4,3,1] [1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[8,4,1,5,7,2,3,6]=>[4,3,1] [1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[8,4,1,7,6,2,3,5]=>[4,2,1,1] [1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[7,8,1,5,6,2,3,4]=>[4,2,2] [1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[7,4,1,5,6,2,8,3]=>[4,3,1] [1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[4,3,1,5,6,8,2,7]=>[4,3,1] [1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[4,3,1,5,8,7,2,6]=>[3,3,2] [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[4,3,1,8,6,7,2,5]=>[3,3,2] [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[8,3,1,5,6,7,2,4]=>[4,3,1] [1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[8,4,1,5,6,7,2,3]=>[4,3,1] [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[4,3,1,5,6,7,8,2]=>[5,2,1] [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,3,8,1,4,5,6,7]=>[6,2] [1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[2,3,7,1,4,5,8,6]=>[5,3] [1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[2,3,6,1,4,8,5,7]=>[5,3] [1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[2,3,8,1,4,7,5,6]=>[5,2,1] [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[2,3,6,1,4,7,8,5]=>[5,3] [1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,3,5,1,8,4,6,7]=>[5,3] [1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,3,5,1,7,4,8,6]=>[5,3] [1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[2,3,8,1,6,4,5,7]=>[5,2,1] [1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[2,3,8,1,7,4,5,6]=>[5,2,1] [1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,3,7,1,6,4,8,5]=>[4,3,1] [1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,3,5,1,6,8,4,7]=>[5,3] [1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,3,5,1,8,7,4,6]=>[4,3,1] [1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[2,3,8,1,6,7,4,5]=>[4,3,1] [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,5,1,6,7,8,4]=>[6,2] [1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[2,8,4,1,3,5,6,7]=>[5,2,1] [1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[2,7,4,1,3,5,8,6]=>[4,3,1] [1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,6,4,1,3,8,5,7]=>[4,3,1] [1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[2,8,4,1,3,7,5,6]=>[4,3,1] [1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[2,6,4,1,3,7,8,5]=>[4,3,1] [1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[2,8,5,1,3,4,6,7]=>[5,2,1] [1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[2,7,5,1,3,4,8,6]=>[4,3,1] [1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[2,6,8,1,3,4,5,7]=>[5,3] [1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,8,7,1,3,4,5,6]=>[5,2,1] [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[2,6,7,1,3,4,8,5]=>[4,4] [1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[2,6,5,1,3,8,4,7]=>[4,3,1] [1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[2,8,5,1,3,7,4,6]=>[4,3,1] [1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[2,6,8,1,3,7,4,5]=>[4,3,1] [1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[2,6,5,1,3,7,8,4]=>[4,3,1] [1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[2,5,4,1,8,3,6,7]=>[4,3,1] [1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,5,4,1,7,3,8,6]=>[4,3,1] [1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[2,8,4,1,6,3,5,7]=>[4,3,1] [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[2,8,4,1,7,3,5,6]=>[4,3,1] [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,7,4,1,6,3,8,5]=>[4,3,1] [1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[2,8,5,1,6,3,4,7]=>[4,3,1] [1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[2,8,5,1,7,3,4,6]=>[4,3,1] [1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[2,7,8,1,6,3,4,5]=>[4,3,1] [1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[2,7,5,1,6,3,8,4]=>[4,3,1] [1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[2,5,4,1,6,8,3,7]=>[4,3,1] [1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[2,5,4,1,8,7,3,6]=>[3,3,2] [1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[2,8,4,1,6,7,3,5]=>[4,3,1] [1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[2,8,5,1,6,7,3,4]=>[4,3,1] [1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,5,4,1,6,7,8,3]=>[5,2,1] [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[8,3,4,1,2,5,6,7]=>[5,2,1] [1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[7,3,4,1,2,5,8,6]=>[4,3,1] [1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[6,3,4,1,2,8,5,7]=>[4,3,1] [1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[8,3,4,1,2,7,5,6]=>[4,3,1] [1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[6,3,4,1,2,7,8,5]=>[4,3,1] [1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[8,3,5,1,2,4,6,7]=>[5,2,1] [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[7,3,5,1,2,4,8,6]=>[4,3,1] [1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[6,3,8,1,2,4,5,7]=>[5,2,1] [1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[8,3,7,1,2,4,5,6]=>[5,2,1] [1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[6,3,7,1,2,4,8,5]=>[4,3,1] [1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[6,3,5,1,2,8,4,7]=>[4,3,1] [1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[8,3,5,1,2,7,4,6]=>[4,3,1] [1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[6,3,8,1,2,7,4,5]=>[4,2,2] [1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[6,3,5,1,2,7,8,4]=>[4,3,1] [1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[8,5,4,1,2,3,6,7]=>[5,1,1,1] [1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[7,5,4,1,2,3,8,6]=>[4,2,1,1] [1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[6,8,4,1,2,3,5,7]=>[5,2,1] [1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[8,7,4,1,2,3,5,6]=>[5,1,1,1] [1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[6,7,4,1,2,3,8,5]=>[4,3,1] [1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[6,8,5,1,2,3,4,7]=>[5,2,1] [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[8,7,5,1,2,3,4,6]=>[5,1,1,1] [1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,7,8,1,2,3,4,5]=>[5,3] [1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[6,7,5,1,2,3,8,4]=>[4,3,1] [1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[6,5,4,1,2,8,3,7]=>[4,2,1,1] [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[8,5,4,1,2,7,3,6]=>[4,2,1,1] [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[6,8,4,1,2,7,3,5]=>[4,2,2] [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[6,8,5,1,2,7,3,4]=>[4,2,2] [1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[6,5,4,1,2,7,8,3]=>[4,2,1,1] [1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[5,3,4,1,8,2,6,7]=>[4,3,1] [1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[5,3,4,1,7,2,8,6]=>[4,3,1] [1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[8,3,4,1,6,2,5,7]=>[4,3,1] [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[8,3,4,1,7,2,5,6]=>[4,3,1] [1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[7,3,4,1,6,2,8,5]=>[4,3,1] [1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[8,3,5,1,6,2,4,7]=>[4,3,1] [1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[8,3,5,1,7,2,4,6]=>[4,3,1] [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[7,3,8,1,6,2,4,5]=>[4,2,2] [1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[7,3,5,1,6,2,8,4]=>[4,3,1] [1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[8,5,4,1,6,2,3,7]=>[4,2,1,1] [1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[8,5,4,1,7,2,3,6]=>[4,2,1,1] [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[7,8,4,1,6,2,3,5]=>[4,2,2] [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[7,8,5,1,6,2,3,4]=>[4,2,2] [1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[7,5,4,1,6,2,8,3]=>[3,3,1,1] [1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[5,3,4,1,6,8,2,7]=>[4,3,1] [1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[5,3,4,1,8,7,2,6]=>[3,3,2] [1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[8,3,4,1,6,7,2,5]=>[4,3,1] [1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[8,3,5,1,6,7,2,4]=>[4,3,1] [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[8,5,4,1,6,7,2,3]=>[3,3,1,1] [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[5,3,4,1,6,7,8,2]=>[5,2,1] [1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,3,4,8,1,5,6,7]=>[6,2] [1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[2,3,4,7,1,5,8,6]=>[5,3] [1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,3,4,6,1,8,5,7]=>[5,3] [1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[2,3,4,8,1,7,5,6]=>[5,2,1] [1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,6,1,7,8,5]=>[6,2] [1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[2,3,8,5,1,4,6,7]=>[5,2,1] [1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[2,3,7,5,1,4,8,6]=>[4,3,1] [1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[2,3,8,6,1,4,5,7]=>[5,2,1] [1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[2,3,7,8,1,4,5,6]=>[5,3] [1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[2,3,7,6,1,4,8,5]=>[4,3,1] [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[2,3,6,5,1,8,4,7]=>[4,3,1] [1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[2,3,8,5,1,7,4,6]=>[4,3,1] [1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[2,3,8,6,1,7,4,5]=>[4,3,1] [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[2,3,6,5,1,7,8,4]=>[5,2,1] [1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[2,8,4,5,1,3,6,7]=>[5,2,1] [1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[2,7,4,5,1,3,8,6]=>[4,3,1] [1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[2,8,4,6,1,3,5,7]=>[4,3,1] [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[2,7,4,8,1,3,5,6]=>[4,3,1] [1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[2,7,4,6,1,3,8,5]=>[4,3,1] [1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[2,8,6,5,1,3,4,7]=>[4,2,1,1] [1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[2,7,8,5,1,3,4,6]=>[4,3,1] [1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,7,8,6,1,3,4,5]=>[4,3,1] [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[2,7,6,5,1,3,8,4]=>[3,3,1,1] [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[2,6,4,5,1,8,3,7]=>[4,3,1] [1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[2,8,4,5,1,7,3,6]=>[4,3,1] [1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[2,8,4,6,1,7,3,5]=>[4,3,1] [1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[2,8,6,5,1,7,3,4]=>[3,3,1,1] [1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,6,4,5,1,7,8,3]=>[5,2,1] [1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[8,3,4,5,1,2,6,7]=>[5,2,1] [1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[7,3,4,5,1,2,8,6]=>[4,3,1] [1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[8,3,4,6,1,2,5,7]=>[4,3,1] [1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[7,3,4,8,1,2,5,6]=>[4,3,1] [1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[7,3,4,6,1,2,8,5]=>[4,3,1] [1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[8,3,6,5,1,2,4,7]=>[4,2,1,1] [1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[7,3,8,5,1,2,4,6]=>[4,2,2] [1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[7,3,8,6,1,2,4,5]=>[4,2,2] [1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[7,3,6,5,1,2,8,4]=>[3,3,1,1] [1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[8,6,4,5,1,2,3,7]=>[4,2,1,1] [1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[7,8,4,5,1,2,3,6]=>[4,2,2] [1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[7,8,4,6,1,2,3,5]=>[4,2,2] [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[7,8,6,5,1,2,3,4]=>[4,2,1,1] [1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[7,6,4,5,1,2,8,3]=>[3,3,1,1] [1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[6,3,4,5,1,8,2,7]=>[4,3,1] [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[8,3,4,5,1,7,2,6]=>[4,3,1] [1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[8,3,4,6,1,7,2,5]=>[4,3,1] [1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[8,3,6,5,1,7,2,4]=>[3,3,1,1] [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[8,6,4,5,1,7,2,3]=>[3,3,1,1] [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[6,3,4,5,1,7,8,2]=>[5,2,1] [1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,3,4,5,8,1,6,7]=>[6,2] [1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,7,1,8,6]=>[6,2] [1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[2,3,4,8,6,1,5,7]=>[5,2,1] [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[2,3,4,8,7,1,5,6]=>[5,2,1] [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[2,3,4,7,6,1,8,5]=>[5,2,1] [1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[2,3,8,5,6,1,4,7]=>[5,2,1] [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[2,3,8,5,7,1,4,6]=>[4,3,1] [1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[2,3,8,7,6,1,4,5]=>[4,2,1,1] [1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[2,3,7,5,6,1,8,4]=>[5,2,1] [1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[2,8,4,5,6,1,3,7]=>[5,2,1] [1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[2,8,4,5,7,1,3,6]=>[4,3,1] [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[2,8,4,7,6,1,3,5]=>[3,3,1,1] [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[2,8,7,5,6,1,3,4]=>[3,3,1,1] [1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,7,4,5,6,1,8,3]=>[5,2,1] [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,1,2,7]=>[5,2,1] [1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[8,3,4,5,7,1,2,6]=>[4,3,1] [1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[8,3,4,7,6,1,2,5]=>[3,3,1,1] [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[8,3,7,5,6,1,2,4]=>[3,3,1,1] [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[8,7,4,5,6,1,2,3]=>[3,3,1,1] [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[7,3,4,5,6,1,8,2]=>[5,2,1] [1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,8,1,7]=>[6,2] [1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[2,3,4,5,8,7,1,6]=>[5,2,1] [1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[2,3,4,8,6,7,1,5]=>[5,2,1] [1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[2,3,8,5,6,7,1,4]=>[5,2,1] [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,8,4,5,6,7,1,3]=>[5,2,1] [1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[8,3,4,5,6,7,1,2]=>[5,2,1] [1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1]=>[7,1] [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,1,2,3,4,5,6,7,8]=>[8,1] [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[8,1,2,3,4,5,6,9,7]=>[7,2] [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[7,1,2,3,4,5,9,6,8]=>[7,2] [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[9,1,2,3,4,5,8,6,7]=>[7,1,1] [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[7,1,2,3,4,5,8,9,6]=>[7,2] [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[6,1,2,3,4,9,5,7,8]=>[7,2] [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[6,1,2,3,4,8,5,9,7]=>[6,3] [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[9,1,2,3,4,7,5,6,8]=>[7,1,1] [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[9,1,2,3,4,8,5,6,7]=>[7,1,1] [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[8,1,2,3,4,7,5,9,6]=>[6,2,1] [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[6,1,2,3,4,7,9,5,8]=>[6,3] [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[6,1,2,3,4,9,8,5,7]=>[6,2,1] [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[9,1,2,3,4,7,8,5,6]=>[6,2,1] [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[6,1,2,3,4,7,8,9,5]=>[7,2] [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[5,1,2,3,9,4,6,7,8]=>[7,2] [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[5,1,2,3,8,4,6,9,7]=>[6,3] [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[8,1,2,3,9,4,5,6,7]=>[7,2] [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[5,1,2,3,9,8,4,6,7]=>[6,2,1] [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[9,1,2,3,6,8,4,5,7]=>[6,2,1] [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[5,1,2,3,6,9,8,4,7]=>[5,3,1] [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[5,1,2,3,6,7,8,9,4]=>[7,2] [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[4,1,2,8,3,5,6,9,7]=>[6,3] [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[4,1,2,9,3,5,8,6,7]=>[6,2,1] [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[4,1,2,9,3,8,5,6,7]=>[6,2,1] [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[9,1,2,8,3,4,5,6,7]=>[7,1,1] [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[7,1,2,8,3,4,5,9,6]=>[6,3] [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[4,1,2,5,9,3,6,7,8]=>[6,3] [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[4,1,2,8,9,3,5,6,7]=>[6,3] [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[8,1,2,5,9,3,4,6,7]=>[6,2,1] [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[8,1,2,9,6,3,4,5,7]=>[6,2,1] [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[4,1,2,5,9,8,3,6,7]=>[5,3,1] [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[9,1,2,8,6,7,3,4,5]=>[5,2,1,1] [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[4,1,2,5,6,7,9,3,8]=>[6,3] [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,1,2,9,6,7,8,3,5]=>[5,3,1] [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[9,1,2,5,6,7,8,3,4]=>[6,2,1] [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,1,2,5,6,7,8,9,3]=>[7,2] [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,9,2,4,5,6,7,8]=>[7,2] [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,1,8,2,4,5,6,9,7]=>[6,3] [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,1,9,2,4,5,8,6,7]=>[6,2,1] [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[8,1,4,2,3,5,6,9,7]=>[6,2,1] [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[9,1,4,2,3,5,8,6,7]=>[6,2,1] [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[6,1,4,2,3,7,8,9,5]=>[6,2,1] [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,1,8,2,3,4,5,6,7]=>[7,1,1] [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[8,1,7,2,3,4,5,9,6]=>[6,2,1] [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,1,4,9,2,5,6,7,8]=>[6,3] [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,1,4,9,2,5,8,6,7]=>[5,3,1] [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,1,9,8,2,4,5,6,7]=>[6,2,1] [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[9,1,4,5,2,3,6,7,8]=>[6,2,1] [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[7,1,4,5,2,3,8,9,6]=>[5,3,1] [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[7,1,4,9,2,3,5,6,8]=>[6,2,1] [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[9,1,4,8,2,3,5,6,7]=>[6,2,1] [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[9,1,6,5,2,3,4,7,8]=>[6,1,1,1] [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[7,1,9,6,2,3,4,5,8]=>[6,2,1] [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[9,1,8,6,2,3,4,5,7]=>[6,1,1,1] [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[7,1,8,9,2,3,4,5,6]=>[6,3] [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[3,1,4,8,9,2,5,6,7]=>[5,4] [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[3,1,8,9,7,2,4,5,6]=>[5,3,1] [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[8,1,4,5,6,2,3,9,7]=>[5,3,1] [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[8,1,4,9,7,2,3,5,6]=>[5,2,2] [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[8,1,9,5,6,2,3,4,7]=>[5,2,2] [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[8,1,9,7,6,2,3,4,5]=>[5,2,1,1] [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[7,1,4,5,6,2,8,9,3]=>[6,2,1] [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[3,1,4,5,6,9,2,7,8]=>[6,3] [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[3,1,4,5,6,8,2,9,7]=>[6,3] [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[3,1,4,9,8,7,2,5,6]=>[4,3,1,1] [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,1,9,8,6,7,2,4,5]=>[4,3,1,1] [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[9,1,4,5,6,7,2,3,8]=>[6,2,1] [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[9,1,4,8,6,7,2,3,5]=>[4,3,1,1] [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[9,1,8,5,6,7,2,3,4]=>[4,3,1,1] [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[8,1,4,5,6,7,2,9,3]=>[6,2,1] [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,9,2,8]=>[6,3] [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[3,1,4,9,6,7,8,2,5]=>[5,3,1] [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,9,5,6,7,8,2,4]=>[5,3,1] [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[9,1,4,5,6,7,8,2,3]=>[6,2,1] [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,1,4,5,6,7,8,9,2]=>[7,2] [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,9,1,3,4,5,6,7,8]=>[7,2] [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,8,1,3,4,5,6,9,7]=>[6,3] [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,7,1,3,4,5,9,6,8]=>[6,3] [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,9,1,3,4,5,8,6,7]=>[6,2,1] [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,7,1,3,4,5,8,9,6]=>[6,3] [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,6,1,3,4,9,5,7,8]=>[6,3] [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,9,1,3,4,8,5,6,7]=>[6,2,1] [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,8,1,3,9,4,5,6,7]=>[6,3] [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,9,1,3,8,7,4,5,6]=>[5,2,1,1] [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,9,1,3,6,7,8,4,5]=>[5,3,1] [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,5,1,3,6,7,8,9,4]=>[6,3] [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,8,5,9,7]=>[5,4] [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,9,1,8,3,4,5,6,7]=>[6,2,1] [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,7,1,6,3,4,8,9,5]=>[5,3,1] [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,1,5,3,7,8,9,4]=>[5,3,1] [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,1,5,9,3,6,7,8]=>[6,3] [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,1,8,9,3,5,6,7]=>[5,4] [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,8,1,9,7,3,4,5,6]=>[5,3,1] [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,9,1,8,6,7,3,4,5]=>[4,3,1,1] [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1,5,6,7,9,3,8]=>[6,3] [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,4,1,5,6,9,8,3,7]=>[5,3,1] [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,9,1,5,6,7,8,3,4]=>[5,3,1] [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,4,1,5,6,7,8,9,3]=>[7,2] [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,3,1,2,4,5,6,7,8]=>[7,1,1] [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[8,3,1,2,4,5,6,9,7]=>[6,2,1] [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[9,3,1,2,4,5,8,6,7]=>[6,2,1] [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[6,3,1,2,4,7,8,9,5]=>[6,2,1] [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[9,3,1,2,6,7,8,4,5]=>[5,3,1] [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,3,1,2,6,7,8,9,4]=>[6,2,1] [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[9,4,1,2,3,5,6,7,8]=>[7,1,1] [1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[7,4,1,2,3,5,8,9,6]=>[6,2,1] [1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[6,4,1,2,3,7,8,9,5]=>[6,2,1] [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[5,9,1,2,3,4,6,7,8]=>[7,2] [1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[5,8,1,2,3,4,6,9,7]=>[6,3] [1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[5,7,1,2,3,4,8,9,6]=>[6,3] [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[9,6,1,2,3,4,5,7,8]=>[7,1,1] [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[8,6,1,2,3,4,5,9,7]=>[6,2,1] [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,7,1,2,3,4,5,6,8]=>[7,1,1] [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,9,1,2,3,4,5,6,7]=>[7,2] [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[8,7,1,2,3,4,5,9,6]=>[6,2,1] [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[9,6,1,2,3,4,8,5,7]=>[6,2,1] [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[9,7,1,2,3,4,8,5,6]=>[6,2,1] [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[7,6,1,2,3,4,8,9,5]=>[6,2,1] [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[5,9,1,2,3,8,4,6,7]=>[6,2,1] [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[9,8,1,2,3,7,4,5,6]=>[6,1,1,1] [1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[8,6,1,2,3,7,4,9,5]=>[5,3,1] [1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[9,6,1,2,3,7,8,4,5]=>[5,3,1] [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[5,6,1,2,3,7,8,9,4]=>[6,3] [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[5,4,1,2,9,3,6,7,8]=>[6,2,1] [1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[8,4,1,2,9,3,5,6,7]=>[6,2,1] [1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[5,8,1,2,9,3,4,6,7]=>[6,3] [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[9,7,1,2,6,3,8,4,5]=>[5,2,1,1] [1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[9,8,1,2,6,7,3,4,5]=>[5,2,1,1] [1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[5,4,1,2,6,7,9,3,8]=>[5,3,1] [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[5,4,1,2,6,7,8,9,3]=>[6,2,1] [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[4,3,1,9,2,5,6,7,8]=>[6,2,1] [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[9,3,1,8,2,4,5,6,7]=>[6,2,1] [1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[9,4,1,8,2,3,5,6,7]=>[6,2,1] [1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[6,9,1,5,2,3,4,7,8]=>[6,2,1] [1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[9,7,1,6,2,3,4,5,8]=>[6,1,1,1] [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[8,7,1,9,2,3,4,5,6]=>[6,2,1] [1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[8,7,1,6,2,3,4,9,5]=>[5,2,1,1] [1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[9,8,1,6,2,7,3,4,5]=>[5,2,1,1] [1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[9,8,1,7,6,2,3,4,5]=>[5,1,1,1,1] [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[4,3,1,5,6,8,2,9,7]=>[5,3,1] [1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[4,3,1,5,9,8,2,6,7]=>[4,3,2] [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,3,1,5,8,7,2,9,6]=>[4,3,2] [1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[8,9,1,5,6,7,2,3,4]=>[4,3,2] [1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[4,3,1,5,6,7,9,2,8]=>[5,3,1] [1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[4,3,1,5,6,9,8,2,7]=>[4,3,2] [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[9,3,1,5,6,7,8,2,4]=>[5,3,1] [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[9,4,1,5,6,7,8,2,3]=>[5,3,1] [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,3,1,5,6,7,8,9,2]=>[6,2,1] [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,9,1,4,5,6,7,8]=>[7,2] [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,8,1,4,5,6,9,7]=>[6,3] [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,9,1,4,5,8,6,7]=>[6,2,1] [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,3,9,1,4,7,8,5,6]=>[5,3,1] [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,9,1,8,7,4,5,6]=>[5,2,1,1] [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,8,1,6,7,4,9,5]=>[5,3,1] [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>[6,3] [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,9,1,6,7,8,4,5]=>[5,3,1] [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,5,1,6,7,8,9,4]=>[7,2] [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,9,4,1,3,5,6,7,8]=>[6,2,1] [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,6,4,1,3,7,8,9,5]=>[5,3,1] [1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,9,5,1,3,4,6,7,8]=>[6,2,1] [1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,6,9,1,3,4,5,7,8]=>[6,3] [1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,9,7,1,3,4,5,6,8]=>[6,2,1] [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,9,8,1,3,4,5,6,7]=>[6,2,1] [1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,6,7,1,3,4,8,9,5]=>[5,4] [1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,9,4,1,6,3,5,7,8]=>[5,3,1] [1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,8,4,1,9,3,5,6,7]=>[5,3,1] [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,9,4,1,6,3,8,5,7]=>[4,4,1] [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,9,8,1,7,3,4,5,6]=>[5,2,1,1] [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,9,5,1,6,7,8,3,4]=>[5,3,1] [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[9,3,4,1,2,5,6,7,8]=>[6,2,1] [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[6,3,4,1,2,7,8,9,5]=>[5,3,1] [1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[9,3,7,1,2,4,5,6,8]=>[6,2,1] [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[9,3,8,1,2,4,5,6,7]=>[6,2,1] [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[9,5,4,1,2,3,6,7,8]=>[6,1,1,1] [1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[8,5,4,1,2,3,6,9,7]=>[5,2,1,1] [1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[6,9,4,1,2,3,5,7,8]=>[6,2,1] [1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[6,8,4,1,2,3,5,9,7]=>[5,3,1] [1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[9,7,4,1,2,3,5,6,8]=>[6,1,1,1] [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[9,8,4,1,2,3,5,6,7]=>[6,1,1,1] [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[6,9,5,1,2,3,4,7,8]=>[6,2,1] [1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[6,8,5,1,2,3,4,9,7]=>[5,3,1] [1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[8,7,5,1,2,3,4,9,6]=>[5,2,1,1] [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[6,7,9,1,2,3,4,5,8]=>[6,3] [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,9,8,1,2,3,4,5,7]=>[6,2,1] [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[9,7,8,1,2,3,4,5,6]=>[6,2,1] [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[6,7,8,1,2,3,4,9,5]=>[5,4] [1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[6,5,4,1,2,8,3,9,7]=>[4,3,1,1] [1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[7,8,9,1,6,2,3,4,5]=>[5,3,1] [1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[7,8,5,1,6,2,3,9,4]=>[4,3,2] [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,3,4,1,6,8,2,9,7]=>[5,3,1] [1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[9,3,4,1,8,7,2,5,6]=>[4,3,1,1] [1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[8,3,4,1,6,7,2,9,5]=>[5,3,1] [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[8,5,4,1,6,7,2,9,3]=>[4,3,1,1] [1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,3,4,1,9,7,8,2,6]=>[4,3,2] [1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[9,3,5,1,6,7,8,2,4]=>[5,3,1] [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[9,5,4,1,6,7,8,2,3]=>[4,3,1,1] [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[5,3,4,1,6,7,8,9,2]=>[6,2,1] [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,9,1,5,6,7,8]=>[7,2] [1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[2,3,4,9,1,5,8,6,7]=>[6,2,1] [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[2,3,4,9,1,7,8,5,6]=>[5,3,1] [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,6,1,7,8,9,5]=>[7,2] [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[2,3,9,5,1,4,6,7,8]=>[6,2,1] [1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[2,3,9,6,1,4,5,7,8]=>[6,2,1] [1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[2,3,7,9,1,4,5,6,8]=>[6,3] [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[2,3,9,8,1,4,5,6,7]=>[6,2,1] [1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[2,3,9,5,1,7,4,6,8]=>[5,3,1] [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[2,3,9,6,1,7,8,4,5]=>[5,3,1] [1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[2,9,4,5,1,3,6,7,8]=>[6,2,1] [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[2,7,4,5,1,3,8,9,6]=>[5,3,1] [1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[2,9,8,6,1,3,4,5,7]=>[5,2,1,1] [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[2,7,8,9,1,3,4,5,6]=>[5,4] [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[2,8,9,6,1,7,3,4,5]=>[4,3,2] [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[2,9,6,5,1,7,8,3,4]=>[4,3,1,1] [1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[7,3,4,5,1,2,8,9,6]=>[5,3,1] [1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[9,3,4,8,1,2,5,6,7]=>[5,3,1] [1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[7,3,4,8,1,2,5,9,6]=>[4,4,1] [1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[7,3,8,9,1,2,4,5,6]=>[5,3,1] [1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[9,8,4,5,1,2,3,6,7]=>[5,2,1,1] [1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[7,8,4,6,1,2,3,9,5]=>[4,3,2] [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[9,8,6,5,1,2,3,4,7]=>[5,1,1,1,1] [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[7,8,9,6,1,2,3,4,5]=>[5,3,1] [1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[7,8,6,5,1,2,3,9,4]=>[4,3,1,1] [1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[8,3,9,6,1,7,2,4,5]=>[4,3,2] [1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[8,3,6,5,1,7,2,9,4]=>[4,3,1,1] [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[8,6,4,5,1,7,2,9,3]=>[4,3,1,1] [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[6,3,4,5,1,7,9,2,8]=>[5,3,1] [1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,3,4,5,1,9,8,2,7]=>[4,3,2] [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[9,3,4,6,1,7,8,2,5]=>[5,3,1] [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[6,3,4,5,1,7,8,9,2]=>[6,2,1] [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[2,3,4,5,9,1,6,7,8]=>[7,2] [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[2,3,4,5,8,1,6,9,7]=>[6,3] [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[2,3,4,5,9,1,8,6,7]=>[6,2,1] [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,7,1,8,9,6]=>[7,2] [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[2,3,4,9,6,1,5,7,8]=>[6,2,1] [1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[2,3,4,9,7,1,5,6,8]=>[6,2,1] [1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[2,3,4,9,6,1,8,5,7]=>[5,3,1] [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[2,3,4,9,7,1,8,5,6]=>[5,3,1] [1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[2,3,9,5,6,1,4,7,8]=>[6,2,1] [1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[2,3,8,5,6,1,4,9,7]=>[5,3,1] [1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[2,3,9,5,6,1,8,4,7]=>[5,3,1] [1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[2,8,4,5,6,1,3,9,7]=>[5,3,1] [1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[2,8,9,5,7,1,3,4,6]=>[4,3,2] [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[2,8,9,7,6,1,3,4,5]=>[4,3,1,1] [1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[2,9,7,5,6,1,8,3,4]=>[4,3,1,1] [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[8,3,4,5,6,1,2,9,7]=>[5,3,1] [1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[8,3,4,7,6,1,2,9,5]=>[4,3,1,1] [1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[8,3,9,7,6,1,2,4,5]=>[4,2,2,1] [1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[8,3,7,5,6,1,2,9,4]=>[4,3,1,1] [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[9,7,4,5,6,1,2,3,8]=>[4,3,1,1] [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[8,9,4,5,6,1,2,3,7]=>[4,3,2] [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[8,9,7,5,6,1,2,3,4]=>[4,2,2,1] [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[8,7,4,5,6,1,2,9,3]=>[4,3,1,1] [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,3,4,5,6,1,9,2,8]=>[5,3,1] [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[9,3,4,5,6,1,8,2,7]=>[5,3,1] [1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[9,3,7,5,6,1,8,2,4]=>[4,3,1,1] [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[7,3,4,5,6,1,8,9,2]=>[6,2,1] [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[2,3,4,5,6,9,1,7,8]=>[7,2] [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,8,1,9,7]=>[7,2] [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[2,3,4,5,9,7,1,6,8]=>[6,2,1] [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[2,3,4,5,9,8,1,6,7]=>[6,2,1] [1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[2,3,4,9,6,7,1,5,8]=>[6,2,1] [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[2,3,9,5,6,7,1,4,8]=>[6,2,1] [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[2,3,9,5,6,8,1,4,7]=>[5,3,1] [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[2,9,4,5,6,7,1,3,8]=>[6,2,1] [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[2,9,4,5,6,8,1,3,7]=>[5,3,1] [1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[2,9,4,5,8,7,1,3,6]=>[4,3,1,1] [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[2,9,4,8,6,7,1,3,5]=>[4,3,1,1] [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[2,9,8,5,6,7,1,3,4]=>[4,3,1,1] [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,8,4,5,6,7,1,9,3]=>[6,2,1] [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[9,3,4,5,6,7,1,2,8]=>[6,2,1] [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[9,3,4,5,6,8,1,2,7]=>[5,3,1] [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[9,8,4,5,6,7,1,2,3]=>[4,3,1,1] [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[8,3,4,5,6,7,1,9,2]=>[6,2,1] [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,7,9,1,8]=>[7,2] [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[2,3,4,5,6,9,8,1,7]=>[6,2,1] [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[2,3,4,5,9,7,8,1,6]=>[6,2,1] [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[2,3,4,9,6,7,8,1,5]=>[6,2,1] [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[2,3,9,5,6,7,8,1,4]=>[6,2,1] [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[2,9,4,5,6,7,8,1,3]=>[6,2,1] [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[9,3,4,5,6,7,8,1,2]=>[6,2,1] [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,1]=>[8,1] [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,7,8,10,1,9]=>[8,2] [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,1,4,5,6,7,8,9,10,2]=>[8,2] [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,7,8,9,11,1,10]=>[9,2] [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[10,3,4,5,6,7,8,1,2,9]=>[7,2,1] [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[10,1,4,5,6,7,8,9,2,3]=>[7,2,1] [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[3,1,4,5,6,7,8,9,10,11,2]=>[9,2] [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,7,8,9,10,12,1,11]=>[10,2] [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[11,3,4,5,6,7,8,9,1,2,10]=>[8,2,1] [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[2,10,4,5,6,7,8,1,3,9]=>[7,2,1] [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[8,3,4,5,6,7,1,10,2,9]=>[6,3,1] [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[3,1,10,5,6,7,8,9,2,4]=>[6,3,1] [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[9,1,4,5,6,7,8,2,10,3]=>[7,2,1] [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[11,1,4,5,6,7,8,9,10,2,3]=>[8,2,1] [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[3,1,4,5,6,7,8,9,10,11,12,2]=>[10,2] [1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[10,1,9,5,6,7,8,2,3,4]=>[5,3,1,1] [1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[3,1,11,5,6,7,8,9,10,2,4]=>[7,3,1] [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0]=>[2,3,4,10,6,7,8,1,5,9]=>[7,2,1] [1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[11,1,10,5,6,7,8,9,2,3,4]=>[6,3,1,1] [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0]=>[2,3,4,5,10,7,8,1,6,9]=>[7,2,1] [1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,1,10,9,6,7,8,2,4,5]=>[4,4,1,1] [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[2,3,4,5,6,10,8,1,7,9]=>[7,2,1] [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[4,3,1,5,6,7,8,10,2,9]=>[6,3,1] [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,7,9,1,10,8]=>[8,2] [1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[9,1,10,8,6,7,2,3,4,5]=>[5,2,2,1] [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,4,1,5,6,7,8,9,10,3]=>[8,2] [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[2,3,4,5,6,7,10,1,8,9]=>[8,2] [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,8,10,2,9]=>[7,3] [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[9,3,4,5,6,7,1,2,10,8]=>[6,3,1] [1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[10,1,11,9,6,7,8,2,3,4,5]=>[5,3,2,1] [1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,10,1,5,6,7,8,9,3,4]=>[6,3,1] [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,1,2,5,6,7,8,9,10,3]=>[8,2] [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,7,8,10,1,11,9]=>[9,2] [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,4,1,5,6,7,8,9,10,11,3]=>[9,2] [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[2,3,4,5,6,7,8,11,1,9,10]=>[9,2] [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,8,9,11,2,10]=>[8,3] [1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[3,1,9,10,8,7,2,4,5,6]=>[5,3,1,1] []=>[1]=>[1] [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[10,9,1,2,3,4,5,6,7,8]=>[8,1,1] [1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[8,9,1,2,3,4,5,6,10,7]=>[7,3] [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[10,7,1,2,3,4,5,9,6,8]=>[7,2,1] [1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[8,10,1,2,3,4,5,9,6,7]=>[7,2,1] [1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[8,7,1,2,3,4,5,9,10,6]=>[7,2,1] [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[10,6,1,2,3,4,9,5,7,8]=>[7,2,1] [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[10,7,1,2,3,4,9,5,6,8]=>[7,2,1] [1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[9,10,1,2,3,4,8,5,6,7]=>[7,2,1] [1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[9,7,1,2,3,4,8,5,10,6]=>[6,3,1] [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[7,6,1,2,3,4,10,9,5,8]=>[6,2,2] [1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[10,7,1,2,3,4,8,9,5,6]=>[6,3,1] [1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[10,9,1,2,3,7,8,4,5,6]=>[6,2,1,1] [1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[5,6,1,2,3,7,8,9,10,4]=>[7,3] [1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[10,9,1,2,8,7,3,4,5,6]=>[6,1,1,1,1] [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[10,3,1,9,2,4,5,6,7,8]=>[7,2,1] [1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[10,8,1,9,2,3,4,5,6,7]=>[7,2,1] [1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[9,8,1,10,7,2,3,4,5,6]=>[6,2,1,1] [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[4,3,1,5,6,7,10,9,2,8]=>[5,3,2] [1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[10,3,1,5,6,7,8,9,2,4]=>[6,3,1] [1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[10,4,1,5,6,7,8,9,2,3]=>[6,3,1] [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[4,3,1,5,6,7,8,9,10,2]=>[7,2,1] [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,9,10,1,3,4,5,6,7,8]=>[7,3] [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,3,10,1,2,4,5,6,7,8]=>[7,2,1] [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[10,7,9,1,2,3,4,5,6,8]=>[7,2,1] [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[10,9,8,1,2,3,4,5,6,7]=>[7,1,1,1] [1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[6,7,8,1,2,3,4,9,10,5]=>[6,4] [1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[7,8,9,1,6,2,3,4,10,5]=>[5,4,1] [1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[5,3,4,1,6,10,8,9,2,7]=>[5,3,2] [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[5,3,4,1,6,7,8,9,10,2]=>[7,2,1] [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,10,5,1,7,4,9,6,8]=>[5,4,1] [1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[2,7,8,9,1,3,4,5,10,6]=>[5,5] [1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,8,9,10,1,7,3,4,5,6]=>[5,4,1] [1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[10,8,4,9,1,2,3,5,6,7]=>[6,2,1,1] [1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[7,8,9,5,1,2,3,4,10,6]=>[5,4,1] [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[7,8,9,10,1,2,3,4,5,6]=>[6,4] [1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[7,8,9,6,1,2,3,4,10,5]=>[5,4,1] [1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[10,3,4,5,1,7,8,9,2,6]=>[6,3,1] [1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[6,3,4,5,1,7,8,9,10,2]=>[7,2,1] [1,1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0,0]=>[2,3,10,5,6,1,8,9,4,7]=>[6,3,1] [1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0]=>[2,8,9,10,6,1,3,4,5,7]=>[5,4,1] [1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[2,8,9,10,7,1,3,4,5,6]=>[5,4,1] [1,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0,0]=>[8,3,4,9,10,1,2,5,6,7]=>[5,4,1] [1,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0]=>[8,9,4,5,10,1,2,3,6,7]=>[5,3,2] [1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[8,9,7,5,6,1,2,3,10,4]=>[4,3,2,1] [1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[9,7,4,5,6,1,8,2,10,3]=>[5,3,1,1] [1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>[10,3,4,7,6,1,8,9,2,5]=>[5,3,1,1] [1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[7,3,4,5,6,1,8,9,10,2]=>[7,2,1] [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,0]=>[2,3,4,5,10,7,1,9,6,8]=>[6,3,1] [1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[2,9,10,8,6,7,1,3,4,5]=>[4,3,2,1] [1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]=>[2,10,8,5,6,7,1,9,3,4]=>[5,3,1,1] [1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]=>[9,3,8,5,6,7,1,2,10,4]=>[5,3,1,1] [1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[9,8,4,5,6,7,1,2,10,3]=>[5,3,1,1] [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[10,3,4,5,6,7,1,9,2,8]=>[6,3,1] [1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[10,3,8,5,6,7,1,9,2,4]=>[5,3,1,1] [1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[8,3,4,5,6,7,1,9,10,2]=>[7,2,1] [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[2,10,4,5,6,7,9,1,3,8]=>[6,3,1] [1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[2,10,4,9,6,7,8,1,3,5]=>[5,3,1,1] [1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[2,10,9,5,6,7,8,1,3,4]=>[5,3,1,1] [1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[2,9,4,5,6,7,8,1,10,3]=>[7,2,1] [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[10,3,4,5,6,7,9,1,2,8]=>[6,3,1] [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[10,9,4,5,6,7,8,1,2,3]=>[5,3,1,1] [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[9,3,4,5,6,7,8,1,10,2]=>[7,2,1] [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[2,3,4,5,6,7,10,9,1,8]=>[7,2,1] [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[2,3,4,5,6,10,8,9,1,7]=>[7,2,1] [1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[2,3,4,5,10,7,8,9,1,6]=>[7,2,1] [1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[2,3,4,10,6,7,8,9,1,5]=>[7,2,1] [1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[2,3,10,5,6,7,8,9,1,4]=>[7,2,1] [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[2,10,4,5,6,7,8,9,1,3]=>[7,2,1] [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[10,3,4,5,6,7,8,9,1,2]=>[7,2,1] [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,10,1]=>[9,1] [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,1,2,3,4,5,6,7,8,9]=>[9,1] [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[9,1,2,3,4,5,6,7,10,8]=>[8,2] [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[10,1,2,3,4,5,6,9,7,8]=>[8,1,1] [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[10,1,2,3,4,5,9,6,7,8]=>[8,1,1] [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[9,1,2,3,4,10,5,6,7,8]=>[8,2] [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[10,1,2,3,9,4,5,6,7,8]=>[8,1,1] [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[10,1,2,9,3,4,5,6,7,8]=>[8,1,1] [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,1,10,2,3,4,5,6,7,8]=>[8,2] [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[11,1,2,3,4,5,6,7,8,9,10]=>[10,1] [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[10,1,2,3,4,5,6,7,8,11,9]=>[9,2] [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[8,1,2,3,4,5,6,9,10,7]=>[8,2] [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[11,1,2,3,4,5,6,7,10,8,9]=>[9,1,1] [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[7,1,2,3,4,5,10,9,6,8]=>[7,2,1] [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[11,1,2,3,4,5,6,10,7,8,9]=>[9,1,1] [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[6,1,2,3,4,10,9,5,7,8]=>[7,2,1] [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[10,1,2,3,4,5,11,6,7,8,9]=>[9,2] [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[5,1,2,3,9,10,4,6,7,8]=>[7,3] [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[11,1,2,3,4,10,5,6,7,8,9]=>[9,1,1] [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[4,1,2,10,9,3,5,6,7,8]=>[7,2,1] [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[11,1,2,3,10,4,5,6,7,8,9]=>[9,1,1] [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,1,10,9,2,4,5,6,7,8]=>[7,2,1] [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[10,1,2,11,3,4,5,6,7,8,9]=>[9,2] [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[11,1,10,2,3,4,5,6,7,8,9]=>[9,1,1] [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[11,10,1,2,3,4,5,6,7,8,9]=>[9,1,1] [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[12,1,2,3,4,5,6,7,8,9,10,11]=>[11,1] [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[11,1,2,3,4,5,6,7,8,9,12,10]=>[10,2] [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[12,1,2,3,4,5,6,7,8,11,9,10]=>[10,1,1] [1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[7,1,2,3,4,5,8,9,10,6]=>[8,2] [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,11,10,1,3,4,5,6,7,8,9]=>[8,2,1] [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[11,12,1,2,3,4,5,6,7,8,9,10]=>[10,2] [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[10,1,2,9,6,3,4,5,7,8]=>[7,1,1,1] [1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[6,1,2,3,4,7,8,9,10,5]=>[8,2] [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[7,1,10,9,2,3,4,5,6,8]=>[7,2,1] [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[11,10,5,1,2,3,4,6,7,8,9]=>[8,1,1,1] [1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[10,1,8,9,2,3,4,5,6,7]=>[7,2,1] [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[5,1,2,3,6,7,8,9,10,4]=>[8,2] [1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[8,1,9,10,7,2,3,4,5,6]=>[6,3,1] [1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[11,1,10,9,2,3,4,5,6,7,8]=>[8,1,1,1] [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[10,11,8,1,2,3,4,5,6,7,9]=>[8,2,1] [1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[8,1,9,10,11,2,3,4,5,6,7]=>[7,4] [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[7,1,2,3,4,5,9,6,10,8]=>[7,3] [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[5,1,2,3,10,4,6,7,8,9]=>[8,2] [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,2,10,3,5,6,7,8,9]=>[8,2] [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[3,1,9,2,4,5,6,7,10,8]=>[7,3] [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,10,4,6,7,8,9]=>[7,3] [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,10,2,5,6,7,8,9]=>[7,3] [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[3,1,4,5,6,7,9,2,10,8]=>[7,3] [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,10,1,3,4,5,6,7,8,9]=>[8,2] [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,9,1,3,4,5,6,7,10,8]=>[7,3] [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,8,1,3,4,5,6,10,7,9]=>[7,3] [1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,5,1,3,6,7,8,9,10,4]=>[7,3] [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,10,7,9]=>[5,5] [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,4,1,5,6,7,8,10,3,9]=>[7,3] [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,10,1,4,5,6,7,8,9]=>[8,2] [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,5,1,6,7,8,9,10,4]=>[8,2] [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,10,1,5,6,7,8,9]=>[8,2] [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,6,1,7,8,9,10,5]=>[8,2] [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,10,1,6,7,8,9]=>[8,2] [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,6]=>[8,2] [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[2,3,4,5,6,10,1,7,8,9]=>[8,2] [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,8,1,9,10,7]=>[8,2] [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[7,1,2,3,4,5,11,6,8,9,10]=>[9,2] [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,11,1,3,4,5,6,7,8,9,10]=>[9,2] [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,10,1,3,4,5,6,7,8,11,9]=>[8,3] [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,11,1,4,5,6,7,8,9,10]=>[9,2] [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,5,1,6,7,8,9,10,11,4]=>[9,2] [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,11,1,5,6,7,8,9,10]=>[9,2] [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,6,1,7,8,9,10,11,5]=>[9,2] [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,11,1,6,7,8,9,10]=>[9,2] [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,11,6]=>[9,2] [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,11,1,7,8,9,10]=>[9,2] [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,6,8,1,9,10,11,7]=>[9,2] [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,11,1,8,9,10]=>[9,2] [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,7,9,1,10,11,8]=>[9,2] [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,10,11,1]=>[10,1] [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,3,1,2,4,5,6,7,8,9]=>[8,1,1] [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[5,10,1,2,3,4,6,7,8,9]=>[8,2] [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[10,7,1,2,3,4,5,6,8,9]=>[8,1,1] [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,10,1,2,3,4,5,6,7,9]=>[8,2] [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,3,1,10,2,5,6,7,8,9]=>[7,2,1] [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[11,9,1,2,3,4,5,6,7,8,10]=>[9,1,1] [1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[8,9,10,7,6,1,2,3,4,11,5]=>[5,4,1,1] [1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[2,9,10,11,8,7,1,3,4,5,6]=>[5,4,1,1] [1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[8,9,10,11,7,1,2,3,4,5,12,6]=>[6,5,1] [1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[7,8,9,10,1,2,3,4,5,11,6]=>[6,5] [1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[2,8,9,10,11,1,3,4,5,6,7]=>[6,5] [1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[2,9,10,11,12,8,1,3,4,5,6,7]=>[6,5,1] [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,12,1,3,4,5,6,7,8,9,10,11]=>[10,2] [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,10,1,3,4,5,6,9,7,8]=>[7,2,1] [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[10,9,1,2,3,4,5,6,7,11,8]=>[8,2,1] [1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[10,3,4,5,6,7,8,9,1,11,2]=>[8,2,1] [1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[2,11,4,5,6,7,8,9,10,1,3]=>[8,2,1] [1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]=>[11,3,4,5,6,7,8,9,10,1,12,2]=>[9,2,1] [1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[10,9,4,5,6,7,8,1,2,11,3]=>[6,3,1,1] [1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[2,11,10,5,6,7,8,9,1,3,4]=>[6,3,1,1] [1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>[2,12,4,5,6,7,8,9,10,11,1,3]=>[9,2,1] [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,11,1,3,4,5,6,7,10,8,9]=>[8,2,1] [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[10,3,1,2,4,5,6,9,7,8]=>[7,2,1] [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[3,1,10,2,4,5,6,9,7,8]=>[7,2,1] [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[9,3,1,2,4,5,6,7,10,8]=>[7,2,1] [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[10,7,8,1,2,3,4,5,6,9]=>[7,2,1] [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[6,7,10,1,2,3,4,5,8,9]=>[7,3] [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[6,10,5,1,2,3,4,7,8,9]=>[7,2,1] [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[10,5,4,1,2,3,6,7,8,9]=>[7,1,1,1] [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[10,3,4,1,2,5,6,7,8,9]=>[7,2,1] [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[4,3,1,5,6,7,8,9,10,11,2]=>[8,2,1] [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[2,3,4,5,6,7,8,11,10,1,9]=>[8,2,1] [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>[2,3,4,5,6,7,8,9,12,11,1,10]=>[9,2,1] [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[11,3,4,5,6,7,8,10,1,2,9]=>[7,3,1] [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]=>[2,3,4,5,10,7,1,6,8,9]=>[7,2,1] [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,10,6,1,5,7,8,9]=>[7,2,1] [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,10,5,1,4,6,7,8,9]=>[7,2,1] [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,10,4,1,3,5,6,7,8,9]=>[7,2,1] [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[11,3,4,5,6,7,8,9,10,1,2]=>[8,2,1] [1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[9,3,4,5,6,7,8,1,10,11,2]=>[8,2,1] [1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[8,3,4,5,6,7,1,9,10,11,2]=>[8,2,1] [1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[7,3,4,5,6,1,8,9,10,11,2]=>[8,2,1] [1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[6,3,4,5,1,7,8,9,10,11,2]=>[8,2,1] [1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[5,3,4,1,6,7,8,9,10,11,2]=>[8,2,1] [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[6,7,9,1,2,3,4,5,10,8]=>[6,4] [1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,8,1,9,10,3,4,5,6,7]=>[6,4] [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[8,7,1,10,2,3,4,5,6,9]=>[7,2,1] [1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[10,11,1,9,2,3,4,5,6,7,8]=>[8,2,1] [1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[12,3,4,5,6,7,8,9,10,11,1,2]=>[9,2,1] [1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[5,3,1,2,6,7,8,9,10,4]=>[7,2,1] [1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[6,3,4,1,2,7,8,9,10,5]=>[6,3,1] [1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[7,3,4,5,1,2,8,9,10,6]=>[6,3,1] [1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]=>[8,3,4,5,6,1,2,9,10,7]=>[6,3,1] [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[10,1,5,2,3,4,6,7,8,9]=>[8,1,1] [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[10,1,2,5,3,4,6,7,8,9]=>[8,1,1] [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[11,1,2,3,4,5,8,6,7,9,10]=>[9,1,1] [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[11,1,2,3,4,5,9,6,7,8,10]=>[9,1,1] [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[5,9,1,2,3,4,6,7,10,8]=>[7,3] [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,10,1,5,3,4,6,7,8,9]=>[7,2,1] [1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[11,10,1,5,2,3,4,6,7,8,9]=>[8,1,1,1] [1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[5,11,1,2,10,3,4,6,7,8,9]=>[8,2,1] [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[5,11,1,2,3,10,4,6,7,8,9]=>[8,2,1] [1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[9,1,10,11,8,7,2,3,4,5,6]=>[6,3,1,1] [1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[3,1,8,9,10,2,4,5,6,7]=>[6,4] [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,10,8,1,3,4,5,6,7,9]=>[7,2,1] [1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[9,1,8,2,3,4,5,6,10,7]=>[7,2,1] [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[9,7,1,2,3,4,5,6,10,8]=>[7,2,1] [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,10,1,9,3,4,5,6,7,8]=>[7,2,1] [1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[8,6,1,2,3,4,5,9,10,7]=>[7,2,1] [1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[8,9,1,2,3,4,5,6,10,11,7]=>[8,3] [1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,7,1,2,3,4,8,9,10,6]=>[7,3] [1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[8,11,1,2,3,4,5,9,10,6,7]=>[7,3,1] [1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[10,4,1,2,3,7,8,9,5,6]=>[6,3,1] [1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[10,11,1,2,3,4,8,9,5,6,7]=>[7,2,2] [1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[10,3,1,2,9,7,8,4,5,6]=>[5,3,1,1] [1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[10,11,1,2,3,9,8,4,5,6,7]=>[7,2,1,1] [1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,9,1,10,8,7,3,4,5,6]=>[5,3,1,1] [1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[10,9,1,2,11,8,3,4,5,6,7]=>[7,2,1,1] [1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[9,8,1,10,11,2,3,4,5,6,7]=>[7,3,1] [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[11,8,9,10,1,2,3,4,5,6,7]=>[7,3,1] [1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,6,1,5,3,7,8,9,10,4]=>[6,3,1] [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[5,3,4,1,6,7,9,2,10,8]=>[6,3,1] [1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,8,1,6,7,4,9,10,5]=>[6,3,1] [1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[6,3,4,5,1,8,2,9,10,7]=>[6,3,1] [1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,4,10,1,7,8,9,5,6]=>[6,3,1] [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[2,3,4,5,6,10,1,9,7,8]=>[7,2,1] [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[2,3,4,5,6,7,11,9,10,1,8]=>[8,2,1] [1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0]=>[2,3,4,5,10,1,8,9,6,7]=>[6,3,1] [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[2,3,4,5,6,11,8,9,10,1,7]=>[8,2,1] [1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[2,3,4,5,11,7,8,9,10,1,6]=>[8,2,1] [1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,3,10,1,6,7,8,9,4,5]=>[6,3,1] [1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[2,3,4,11,6,7,8,9,10,1,5]=>[8,2,1] [1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[2,3,11,5,6,7,8,9,10,1,4]=>[8,2,1] [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[4,1,2,10,3,5,9,6,7,8]=>[7,2,1] [1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[2,10,4,5,6,7,8,9,1,11,3]=>[8,2,1] [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,10,11,12,1]=>[11,1] [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[6,1,10,2,3,4,5,9,7,8]=>[7,2,1] [1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[8,9,10,11,12,1,2,3,4,5,6,7]=>[7,5] [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[2,10,4,1,6,3,8,5,7,9]=>[5,4,1] [1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,1,0]=>[2,3,4,10,6,7,1,5,8,9]=>[7,2,1] [1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0,1,0]=>[2,3,10,5,6,1,4,7,8,9]=>[7,2,1]
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.
Map
Robinson-Schensted tableau shape
Description
Sends a permutation to its Robinson-Schensted tableau shape.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to the shape of its corresponding insertion and recording tableau.