Identifier
Mp00024: Dyck paths to 321-avoiding permutationPermutations
Mp00108: Permutations cycle type Integer partitions
Images
=>
Cc0005;cc-rep-0Cc0002;cc-rep-2
[1,0]=>[1]=>[1] [1,0,1,0]=>[2,1]=>[2] [1,1,0,0]=>[1,2]=>[1,1] [1,0,1,0,1,0]=>[2,1,3]=>[2,1] [1,0,1,1,0,0]=>[2,3,1]=>[3] [1,1,0,0,1,0]=>[3,1,2]=>[3] [1,1,0,1,0,0]=>[1,3,2]=>[2,1] [1,1,1,0,0,0]=>[1,2,3]=>[1,1,1] [1,0,1,0,1,0,1,0]=>[2,1,4,3]=>[2,2] [1,0,1,0,1,1,0,0]=>[2,4,1,3]=>[4] [1,0,1,1,0,0,1,0]=>[2,1,3,4]=>[2,1,1] [1,0,1,1,0,1,0,0]=>[2,3,1,4]=>[3,1] [1,0,1,1,1,0,0,0]=>[2,3,4,1]=>[4] [1,1,0,0,1,0,1,0]=>[3,1,4,2]=>[4] [1,1,0,0,1,1,0,0]=>[3,4,1,2]=>[2,2] [1,1,0,1,0,0,1,0]=>[3,1,2,4]=>[3,1] [1,1,0,1,0,1,0,0]=>[1,3,2,4]=>[2,1,1] [1,1,0,1,1,0,0,0]=>[1,3,4,2]=>[3,1] [1,1,1,0,0,0,1,0]=>[4,1,2,3]=>[4] [1,1,1,0,0,1,0,0]=>[1,4,2,3]=>[3,1] [1,1,1,0,1,0,0,0]=>[1,2,4,3]=>[2,1,1] [1,1,1,1,0,0,0,0]=>[1,2,3,4]=>[1,1,1,1] [1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,5]=>[2,2,1] [1,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,5]=>[4,1] [1,0,1,0,1,1,0,0,1,0]=>[2,1,4,5,3]=>[3,2] [1,0,1,0,1,1,0,1,0,0]=>[2,4,1,5,3]=>[5] [1,0,1,0,1,1,1,0,0,0]=>[2,4,5,1,3]=>[3,2] [1,0,1,1,0,0,1,0,1,0]=>[2,1,5,3,4]=>[3,2] [1,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,4]=>[5] [1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,4]=>[2,2,1] [1,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,4]=>[3,2] [1,0,1,1,0,1,1,0,0,0]=>[2,3,5,1,4]=>[5] [1,0,1,1,1,0,0,0,1,0]=>[2,1,3,4,5]=>[2,1,1,1] [1,0,1,1,1,0,0,1,0,0]=>[2,3,1,4,5]=>[3,1,1] [1,0,1,1,1,0,1,0,0,0]=>[2,3,4,1,5]=>[4,1] [1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>[5] [1,1,0,0,1,0,1,0,1,0]=>[3,1,4,2,5]=>[4,1] [1,1,0,0,1,0,1,1,0,0]=>[3,4,1,2,5]=>[2,2,1] [1,1,0,0,1,1,0,0,1,0]=>[3,1,4,5,2]=>[5] [1,1,0,0,1,1,0,1,0,0]=>[3,4,1,5,2]=>[3,2] [1,1,0,0,1,1,1,0,0,0]=>[3,4,5,1,2]=>[5] [1,1,0,1,0,0,1,0,1,0]=>[3,1,5,2,4]=>[5] [1,1,0,1,0,0,1,1,0,0]=>[3,5,1,2,4]=>[3,2] [1,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,4]=>[3,2] [1,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4]=>[2,2,1] [1,1,0,1,0,1,1,0,0,0]=>[1,3,5,2,4]=>[4,1] [1,1,0,1,1,0,0,0,1,0]=>[3,1,2,4,5]=>[3,1,1] [1,1,0,1,1,0,0,1,0,0]=>[1,3,2,4,5]=>[2,1,1,1] [1,1,0,1,1,0,1,0,0,0]=>[1,3,4,2,5]=>[3,1,1] [1,1,0,1,1,1,0,0,0,0]=>[1,3,4,5,2]=>[4,1] [1,1,1,0,0,0,1,0,1,0]=>[4,1,5,2,3]=>[3,2] [1,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,3]=>[5] [1,1,1,0,0,1,0,0,1,0]=>[4,1,2,5,3]=>[5] [1,1,1,0,0,1,0,1,0,0]=>[1,4,2,5,3]=>[4,1] [1,1,1,0,0,1,1,0,0,0]=>[1,4,5,2,3]=>[2,2,1] [1,1,1,0,1,0,0,0,1,0]=>[4,1,2,3,5]=>[4,1] [1,1,1,0,1,0,0,1,0,0]=>[1,4,2,3,5]=>[3,1,1] [1,1,1,0,1,0,1,0,0,0]=>[1,2,4,3,5]=>[2,1,1,1] [1,1,1,0,1,1,0,0,0,0]=>[1,2,4,5,3]=>[3,1,1] [1,1,1,1,0,0,0,0,1,0]=>[5,1,2,3,4]=>[5] [1,1,1,1,0,0,0,1,0,0]=>[1,5,2,3,4]=>[4,1] [1,1,1,1,0,0,1,0,0,0]=>[1,2,5,3,4]=>[3,1,1] [1,1,1,1,0,1,0,0,0,0]=>[1,2,3,5,4]=>[2,1,1,1] [1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5]=>[1,1,1,1,1] [1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,6,5]=>[2,2,2] [1,0,1,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,6,5]=>[4,2] [1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,4,6,3,5]=>[4,2] [1,0,1,0,1,0,1,1,0,1,0,0]=>[2,4,1,6,3,5]=>[6] [1,0,1,0,1,0,1,1,1,0,0,0]=>[2,4,6,1,3,5]=>[3,3] [1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>[2,2,1,1] [1,0,1,0,1,1,0,0,1,1,0,0]=>[2,4,1,3,5,6]=>[4,1,1] [1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>[3,2,1] [1,0,1,0,1,1,0,1,0,1,0,0]=>[2,4,1,5,3,6]=>[5,1] [1,0,1,0,1,1,0,1,1,0,0,0]=>[2,4,5,1,3,6]=>[3,2,1] [1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,4,5,6,3]=>[4,2] [1,0,1,0,1,1,1,0,0,1,0,0]=>[2,4,1,5,6,3]=>[6] [1,0,1,0,1,1,1,0,1,0,0,0]=>[2,4,5,1,6,3]=>[3,3] [1,0,1,0,1,1,1,1,0,0,0,0]=>[2,4,5,6,1,3]=>[6] [1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,5,3,6,4]=>[4,2] [1,0,1,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,6,4]=>[6] [1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,5,6,3,4]=>[2,2,2] [1,0,1,1,0,0,1,1,0,1,0,0]=>[2,5,1,6,3,4]=>[4,2] [1,0,1,1,0,0,1,1,1,0,0,0]=>[2,5,6,1,3,4]=>[6] [1,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,5,3,4,6]=>[3,2,1] [1,0,1,1,0,1,0,0,1,1,0,0]=>[2,5,1,3,4,6]=>[5,1] [1,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,3,5,4,6]=>[2,2,1,1] [1,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,4,6]=>[3,2,1] [1,0,1,1,0,1,0,1,1,0,0,0]=>[2,3,5,1,4,6]=>[5,1] [1,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,3,5,6,4]=>[3,2,1] [1,0,1,1,0,1,1,0,0,1,0,0]=>[2,3,1,5,6,4]=>[3,3] [1,0,1,1,0,1,1,0,1,0,0,0]=>[2,3,5,1,6,4]=>[6] [1,0,1,1,0,1,1,1,0,0,0,0]=>[2,3,5,6,1,4]=>[4,2] [1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,6,3,4,5]=>[4,2] [1,0,1,1,1,0,0,0,1,1,0,0]=>[2,6,1,3,4,5]=>[6] [1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,3,6,4,5]=>[3,2,1] [1,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,1,6,4,5]=>[3,3] [1,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,6,1,4,5]=>[6] [1,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,3,4,6,5]=>[2,2,1,1] [1,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,1,4,6,5]=>[3,2,1] [1,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,4,1,6,5]=>[4,2] [1,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,4,6,1,5]=>[6] [1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,3,4,5,6]=>[2,1,1,1,1] [1,0,1,1,1,1,0,0,0,1,0,0]=>[2,3,1,4,5,6]=>[3,1,1,1] [1,0,1,1,1,1,0,0,1,0,0,0]=>[2,3,4,1,5,6]=>[4,1,1] [1,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,4,5,1,6]=>[5,1] [1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>[6] [1,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,6,5]=>[4,2] [1,1,0,0,1,0,1,0,1,1,0,0]=>[3,4,1,2,6,5]=>[2,2,2] [1,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,4,6,2,5]=>[6] [1,1,0,0,1,0,1,1,0,1,0,0]=>[3,4,1,6,2,5]=>[4,2] [1,1,0,0,1,0,1,1,1,0,0,0]=>[3,4,6,1,2,5]=>[6] [1,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,4,2,5,6]=>[4,1,1] [1,1,0,0,1,1,0,0,1,1,0,0]=>[3,4,1,2,5,6]=>[2,2,1,1] [1,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,4,5,2,6]=>[5,1] [1,1,0,0,1,1,0,1,0,1,0,0]=>[3,4,1,5,2,6]=>[3,2,1] [1,1,0,0,1,1,0,1,1,0,0,0]=>[3,4,5,1,2,6]=>[5,1] [1,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,4,5,6,2]=>[6] [1,1,0,0,1,1,1,0,0,1,0,0]=>[3,4,1,5,6,2]=>[4,2] [1,1,0,0,1,1,1,0,1,0,0,0]=>[3,4,5,1,6,2]=>[6] [1,1,0,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,1,2]=>[3,3] [1,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,5,2,6,4]=>[6] [1,1,0,1,0,0,1,0,1,1,0,0]=>[3,5,1,2,6,4]=>[4,2] [1,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,5,6,2,4]=>[4,2] [1,1,0,1,0,0,1,1,0,1,0,0]=>[3,5,1,6,2,4]=>[2,2,2] [1,1,0,1,0,0,1,1,1,0,0,0]=>[3,5,6,1,2,4]=>[4,2] [1,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,5,2,4,6]=>[5,1] [1,1,0,1,0,1,0,0,1,1,0,0]=>[3,5,1,2,4,6]=>[3,2,1] [1,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,4,6]=>[3,2,1] [1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,6]=>[2,2,1,1] [1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,5,2,4,6]=>[4,1,1] [1,1,0,1,0,1,1,0,0,0,1,0]=>[3,1,2,5,6,4]=>[3,3] [1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,2,5,6,4]=>[3,2,1] [1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,5,2,6,4]=>[5,1] [1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,5,6,2,4]=>[3,2,1] [1,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,6,2,4,5]=>[6] [1,1,0,1,1,0,0,0,1,1,0,0]=>[3,6,1,2,4,5]=>[4,2] [1,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,2,6,4,5]=>[3,3] [1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,2,6,4,5]=>[3,2,1] [1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,6,2,4,5]=>[5,1] [1,1,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,4,6,5]=>[3,2,1] [1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,2,4,6,5]=>[2,2,1,1] [1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,4,2,6,5]=>[3,2,1] [1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,4,6,2,5]=>[5,1] [1,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,2,4,5,6]=>[3,1,1,1] [1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,2,4,5,6]=>[2,1,1,1,1] [1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,4,2,5,6]=>[3,1,1,1] [1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,4,5,2,6]=>[4,1,1] [1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,4,5,6,2]=>[5,1] [1,1,1,0,0,0,1,0,1,0,1,0]=>[4,1,5,2,6,3]=>[3,3] [1,1,1,0,0,0,1,0,1,1,0,0]=>[4,5,1,2,6,3]=>[6] [1,1,1,0,0,0,1,1,0,0,1,0]=>[4,1,5,6,2,3]=>[6] [1,1,1,0,0,0,1,1,0,1,0,0]=>[4,5,1,6,2,3]=>[4,2] [1,1,1,0,0,0,1,1,1,0,0,0]=>[4,5,6,1,2,3]=>[2,2,2] [1,1,1,0,0,1,0,0,1,0,1,0]=>[4,1,5,2,3,6]=>[3,2,1] [1,1,1,0,0,1,0,0,1,1,0,0]=>[4,5,1,2,3,6]=>[5,1] [1,1,1,0,0,1,0,1,0,0,1,0]=>[4,1,2,5,3,6]=>[5,1] [1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,5,3,6]=>[4,1,1] [1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,5,2,3,6]=>[2,2,1,1] [1,1,1,0,0,1,1,0,0,0,1,0]=>[4,1,2,5,6,3]=>[6] [1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,5,6,3]=>[5,1] [1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,5,2,6,3]=>[3,2,1] [1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,5,6,2,3]=>[5,1] [1,1,1,0,1,0,0,0,1,0,1,0]=>[4,1,6,2,3,5]=>[3,3] [1,1,1,0,1,0,0,0,1,1,0,0]=>[4,6,1,2,3,5]=>[6] [1,1,1,0,1,0,0,1,0,0,1,0]=>[4,1,2,6,3,5]=>[6] [1,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,2,6,3,5]=>[5,1] [1,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,6,2,3,5]=>[3,2,1] [1,1,1,0,1,0,1,0,0,0,1,0]=>[4,1,2,3,6,5]=>[4,2] [1,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,2,3,6,5]=>[3,2,1] [1,1,1,0,1,0,1,0,1,0,0,0]=>[1,2,4,3,6,5]=>[2,2,1,1] [1,1,1,0,1,0,1,1,0,0,0,0]=>[1,2,4,6,3,5]=>[4,1,1] [1,1,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,3,5,6]=>[4,1,1] [1,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,2,3,5,6]=>[3,1,1,1] [1,1,1,0,1,1,0,0,1,0,0,0]=>[1,2,4,3,5,6]=>[2,1,1,1,1] [1,1,1,0,1,1,0,1,0,0,0,0]=>[1,2,4,5,3,6]=>[3,1,1,1] [1,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,4,5,6,3]=>[4,1,1] [1,1,1,1,0,0,0,0,1,0,1,0]=>[5,1,6,2,3,4]=>[6] [1,1,1,1,0,0,0,0,1,1,0,0]=>[5,6,1,2,3,4]=>[3,3] [1,1,1,1,0,0,0,1,0,0,1,0]=>[5,1,2,6,3,4]=>[4,2] [1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,2,6,3,4]=>[3,2,1] [1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,6,2,3,4]=>[5,1] [1,1,1,1,0,0,1,0,0,0,1,0]=>[5,1,2,3,6,4]=>[6] [1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,2,3,6,4]=>[5,1] [1,1,1,1,0,0,1,0,1,0,0,0]=>[1,2,5,3,6,4]=>[4,1,1] [1,1,1,1,0,0,1,1,0,0,0,0]=>[1,2,5,6,3,4]=>[2,2,1,1] [1,1,1,1,0,1,0,0,0,0,1,0]=>[5,1,2,3,4,6]=>[5,1] [1,1,1,1,0,1,0,0,0,1,0,0]=>[1,5,2,3,4,6]=>[4,1,1] [1,1,1,1,0,1,0,0,1,0,0,0]=>[1,2,5,3,4,6]=>[3,1,1,1] [1,1,1,1,0,1,0,1,0,0,0,0]=>[1,2,3,5,4,6]=>[2,1,1,1,1] [1,1,1,1,0,1,1,0,0,0,0,0]=>[1,2,3,5,6,4]=>[3,1,1,1] [1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5]=>[6] [1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,2,3,4,5]=>[5,1] [1,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,6,3,4,5]=>[4,1,1] [1,1,1,1,1,0,0,1,0,0,0,0]=>[1,2,3,6,4,5]=>[3,1,1,1] [1,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,3,4,6,5]=>[2,1,1,1,1] [1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,5,6]=>[1,1,1,1,1,1] [1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,7]=>[2,2,2,1] [1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,6,5,7]=>[4,2,1] [1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,4,6,3,5,7]=>[4,2,1] [1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,4,1,6,3,5,7]=>[6,1] [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,4,6,1,3,5,7]=>[3,3,1] [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,6,7,5]=>[3,2,2] [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,4,1,3,6,7,5]=>[4,3] [1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,4,6,3,7,5]=>[5,2] [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,4,1,6,3,7,5]=>[7] [1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,4,6,1,3,7,5]=>[4,3] [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,4,6,7,3,5]=>[3,2,2] [1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,4,1,6,7,3,5]=>[5,2] [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,4,6,1,7,3,5]=>[3,2,2] [1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,4,6,7,1,3,5]=>[5,2] [1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,7,5,6]=>[3,2,2] [1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,4,1,3,7,5,6]=>[4,3] [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,7,3,5,6]=>[5,2] [1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,4,1,7,3,5,6]=>[7] [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,7,1,3,5,6]=>[4,3] [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,3,5,7,6]=>[2,2,2,1] [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[2,4,1,3,5,7,6]=>[4,2,1] [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,3,7,6]=>[3,2,2] [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,4,1,5,3,7,6]=>[5,2] [1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,4,5,1,3,7,6]=>[3,2,2] [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,5,7,3,6]=>[5,2] [1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[2,4,1,5,7,3,6]=>[7] [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,4,5,1,7,3,6]=>[4,3] [1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,4,5,7,1,3,6]=>[7] [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>[2,2,1,1,1] [1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,3,5,6,7]=>[4,1,1,1] [1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,4,5,3,6,7]=>[3,2,1,1] [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,4,1,5,3,6,7]=>[5,1,1] [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,4,5,1,3,6,7]=>[3,2,1,1] [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,4,5,6,3,7]=>[4,2,1] [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,4,1,5,6,3,7]=>[6,1] [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,4,5,1,6,3,7]=>[3,3,1] [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,4,5,6,1,3,7]=>[6,1] [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,5,6,7,3]=>[5,2] [1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[2,4,1,5,6,7,3]=>[7] [1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[2,4,5,1,6,7,3]=>[4,3] [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,4,5,6,1,7,3]=>[7] [1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,4,5,6,7,1,3]=>[4,3] [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,5,3,6,4,7]=>[4,2,1] [1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,5,1,3,6,4,7]=>[6,1] [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,5,6,3,4,7]=>[2,2,2,1] [1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,5,1,6,3,4,7]=>[4,2,1] [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,5,6,1,3,4,7]=>[6,1] [1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,5,3,6,7,4]=>[5,2] [1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,6,7,4]=>[7] [1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,5,6,3,7,4]=>[3,2,2] [1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,5,1,6,3,7,4]=>[4,3] [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,5,6,1,3,7,4]=>[7] [1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,6,7,3,4]=>[5,2] [1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,5,1,6,7,3,4]=>[7] [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,5,6,1,7,3,4]=>[5,2] [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,5,6,7,1,3,4]=>[3,2,2] [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,5,3,7,4,6]=>[5,2] [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,7,4,6]=>[7] [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,5,7,3,4,6]=>[3,2,2] [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[2,5,1,7,3,4,6]=>[4,3] [1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,5,7,1,3,4,6]=>[7] [1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[2,1,5,3,4,7,6]=>[3,2,2] [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,5,1,3,4,7,6]=>[5,2] [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,3,5,4,7,6]=>[2,2,2,1] [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,4,7,6]=>[3,2,2] [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,5,1,4,7,6]=>[5,2] [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,3,5,7,4,6]=>[4,2,1] [1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,1,5,7,4,6]=>[4,3] [1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,1,7,4,6]=>[7] [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,5,7,1,4,6]=>[4,3] [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,5,3,4,6,7]=>[3,2,1,1] [1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,5,1,3,4,6,7]=>[5,1,1] [1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[2,1,3,5,4,6,7]=>[2,2,1,1,1] [1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,1,5,4,6,7]=>[3,2,1,1] [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,1,4,6,7]=>[5,1,1] [1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[2,1,3,5,6,4,7]=>[3,2,1,1] [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,1,5,6,4,7]=>[3,3,1] [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,1,6,4,7]=>[6,1] [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,5,6,1,4,7]=>[4,2,1] [1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,3,5,6,7,4]=>[4,2,1] [1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,1,5,6,7,4]=>[4,3] [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,5,1,6,7,4]=>[7] [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,5,6,1,7,4]=>[4,3] [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,5,6,7,1,4]=>[7] [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,6,3,7,4,5]=>[3,2,2] [1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,6,1,3,7,4,5]=>[5,2] [1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,1,6,7,3,4,5]=>[5,2] [1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,6,1,7,3,4,5]=>[7] [1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,6,7,1,3,4,5]=>[4,3] [1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[2,1,6,3,4,7,5]=>[5,2] [1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,6,1,3,4,7,5]=>[7] [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[2,1,3,6,4,7,5]=>[4,2,1] [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,1,6,4,7,5]=>[4,3] [1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,3,6,1,4,7,5]=>[7] [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[2,1,3,6,7,4,5]=>[2,2,2,1] [1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,1,6,7,4,5]=>[3,2,2] [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,6,1,7,4,5]=>[5,2] [1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,6,7,1,4,5]=>[7] [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,1,6,3,4,5,7]=>[4,2,1] [1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,6,1,3,4,5,7]=>[6,1] [1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[2,1,3,6,4,5,7]=>[3,2,1,1] [1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,3,1,6,4,5,7]=>[3,3,1] [1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[2,3,6,1,4,5,7]=>[6,1] [1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[2,1,3,4,6,5,7]=>[2,2,1,1,1] [1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,3,1,4,6,5,7]=>[3,2,1,1] [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,4,1,6,5,7]=>[4,2,1] [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[2,3,4,6,1,5,7]=>[6,1] [1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[2,1,3,4,6,7,5]=>[3,2,1,1] [1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,3,1,4,6,7,5]=>[3,3,1] [1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,3,4,1,6,7,5]=>[4,3] [1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,4,6,1,7,5]=>[7] [1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,4,6,7,1,5]=>[5,2] [1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,1,7,3,4,5,6]=>[5,2] [1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,7,1,3,4,5,6]=>[7] [1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[2,1,3,7,4,5,6]=>[4,2,1] [1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,1,7,4,5,6]=>[4,3] [1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,7,1,4,5,6]=>[7] [1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[2,1,3,4,7,5,6]=>[3,2,1,1] [1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,3,1,4,7,5,6]=>[3,3,1] [1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,3,4,1,7,5,6]=>[4,3] [1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,4,7,1,5,6]=>[7] [1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[2,1,3,4,5,7,6]=>[2,2,1,1,1] [1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,3,1,4,5,7,6]=>[3,2,1,1] [1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,3,4,1,5,7,6]=>[4,2,1] [1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,4,5,1,7,6]=>[5,2] [1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,4,5,7,1,6]=>[7] [1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7]=>[2,1,1,1,1,1] [1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,1,4,5,6,7]=>[3,1,1,1,1] [1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,3,4,1,5,6,7]=>[4,1,1,1] [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,3,4,5,1,6,7]=>[5,1,1] [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,3,4,5,6,1,7]=>[6,1] [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1]=>[7] [1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,6,5,7]=>[4,2,1] [1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,4,1,2,6,5,7]=>[2,2,2,1] [1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,4,6,2,5,7]=>[6,1] [1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,4,1,6,2,5,7]=>[4,2,1] [1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,4,6,1,2,5,7]=>[6,1] [1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[3,1,4,2,6,7,5]=>[4,3] [1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[3,4,1,2,6,7,5]=>[3,2,2] [1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,4,6,2,7,5]=>[7] [1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[3,4,1,6,2,7,5]=>[5,2] [1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,4,6,1,2,7,5]=>[7] [1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,1,4,6,7,2,5]=>[5,2] [1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,4,1,6,7,2,5]=>[3,2,2] [1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,4,6,1,7,2,5]=>[5,2] [1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,4,6,7,1,2,5]=>[7] [1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[3,1,4,2,7,5,6]=>[4,3] [1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[3,4,1,2,7,5,6]=>[3,2,2] [1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,4,7,2,5,6]=>[7] [1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,4,1,7,2,5,6]=>[5,2] [1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,4,7,1,2,5,6]=>[7] [1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[3,1,4,2,5,7,6]=>[4,2,1] [1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[3,4,1,2,5,7,6]=>[2,2,2,1] [1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[3,1,4,5,2,7,6]=>[5,2] [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,4,1,5,2,7,6]=>[3,2,2] [1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,4,5,1,2,7,6]=>[5,2] [1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,1,4,5,7,2,6]=>[7] [1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,4,1,5,7,2,6]=>[5,2] [1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,4,5,1,7,2,6]=>[7] [1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,4,5,7,1,2,6]=>[4,3] [1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[3,1,4,2,5,6,7]=>[4,1,1,1] [1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,4,1,2,5,6,7]=>[2,2,1,1,1] [1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,1,4,5,2,6,7]=>[5,1,1] [1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,4,1,5,2,6,7]=>[3,2,1,1] [1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,4,5,1,2,6,7]=>[5,1,1] [1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[3,1,4,5,6,2,7]=>[6,1] [1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,4,1,5,6,2,7]=>[4,2,1] [1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,4,5,1,6,2,7]=>[6,1] [1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,4,5,6,1,2,7]=>[3,3,1] [1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,5,6,7,2]=>[7] [1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,4,1,5,6,7,2]=>[5,2] [1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,4,5,1,6,7,2]=>[7] [1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,4,5,6,1,7,2]=>[4,3] [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,1,2]=>[7] [1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,6,4,7]=>[6,1] [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,5,1,2,6,4,7]=>[4,2,1] [1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,5,6,2,4,7]=>[4,2,1] [1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,5,1,6,2,4,7]=>[2,2,2,1] [1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,5,6,1,2,4,7]=>[4,2,1] [1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,5,2,6,7,4]=>[7] [1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,5,1,2,6,7,4]=>[5,2] [1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,5,6,2,7,4]=>[4,3] [1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,5,1,6,2,7,4]=>[3,2,2] [1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,5,6,1,2,7,4]=>[5,2] [1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,5,6,7,2,4]=>[7] [1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,5,1,6,7,2,4]=>[5,2] [1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,5,6,1,7,2,4]=>[7] [1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,5,6,7,1,2,4]=>[5,2] [1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,5,2,7,4,6]=>[7] [1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[3,5,1,2,7,4,6]=>[5,2] [1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,5,7,2,4,6]=>[4,3] [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[3,5,1,7,2,4,6]=>[3,2,2] [1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,5,7,1,2,4,6]=>[5,2] [1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,5,2,4,7,6]=>[5,2] [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[3,5,1,2,4,7,6]=>[3,2,2] [1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,4,7,6]=>[3,2,2] [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,7,6]=>[2,2,2,1] [1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,5,2,4,7,6]=>[4,2,1] [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[3,1,2,5,7,4,6]=>[4,3] [1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,2,5,7,4,6]=>[4,2,1] [1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,5,2,7,4,6]=>[6,1] [1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,5,7,2,4,6]=>[3,3,1] [1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,5,2,4,6,7]=>[5,1,1] [1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[3,5,1,2,4,6,7]=>[3,2,1,1] [1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,2,5,4,6,7]=>[3,2,1,1] [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,2,5,4,6,7]=>[2,2,1,1,1] [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,2,4,6,7]=>[4,1,1,1] [1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,5,6,4,7]=>[3,3,1] [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,2,5,6,4,7]=>[3,2,1,1] [1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,2,6,4,7]=>[5,1,1] [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,6,2,4,7]=>[3,2,1,1] [1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,2,5,6,7,4]=>[4,3] [1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,2,5,6,7,4]=>[4,2,1] [1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,5,2,6,7,4]=>[6,1] [1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,5,6,2,7,4]=>[3,3,1] [1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,5,6,7,2,4]=>[6,1] [1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,6,2,7,4,5]=>[5,2] [1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[3,6,1,2,7,4,5]=>[3,2,2] [1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,6,7,2,4,5]=>[7] [1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,6,1,7,2,4,5]=>[5,2] [1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,6,7,1,2,4,5]=>[7] [1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,6,2,4,7,5]=>[7] [1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,6,1,2,4,7,5]=>[5,2] [1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[3,1,2,6,4,7,5]=>[4,3] [1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,3,2,6,4,7,5]=>[4,2,1] [1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,6,2,4,7,5]=>[6,1] [1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,1,2,6,7,4,5]=>[3,2,2] [1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,6,7,4,5]=>[2,2,2,1] [1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,6,2,7,4,5]=>[4,2,1] [1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,6,7,2,4,5]=>[6,1] [1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[3,1,6,2,4,5,7]=>[6,1] [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,6,1,2,4,5,7]=>[4,2,1] [1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[3,1,2,6,4,5,7]=>[3,3,1] [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,3,2,6,4,5,7]=>[3,2,1,1] [1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,6,2,4,5,7]=>[5,1,1] [1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[3,1,2,4,6,5,7]=>[3,2,1,1] [1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,3,2,4,6,5,7]=>[2,2,1,1,1] [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,4,2,6,5,7]=>[3,2,1,1] [1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,3,4,6,2,5,7]=>[5,1,1] [1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,1,2,4,6,7,5]=>[3,3,1] [1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,2,4,6,7,5]=>[3,2,1,1] [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,4,2,6,7,5]=>[3,3,1] [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,4,6,2,7,5]=>[6,1] [1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,4,6,7,2,5]=>[4,2,1] [1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[3,1,7,2,4,5,6]=>[7] [1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,7,1,2,4,5,6]=>[5,2] [1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[3,1,2,7,4,5,6]=>[4,3] [1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,3,2,7,4,5,6]=>[4,2,1] [1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,3,7,2,4,5,6]=>[6,1] [1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[3,1,2,4,7,5,6]=>[3,3,1] [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,3,2,4,7,5,6]=>[3,2,1,1] [1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,3,4,2,7,5,6]=>[3,3,1] [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,3,4,7,2,5,6]=>[6,1] [1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,1,2,4,5,7,6]=>[3,2,1,1] [1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,3,2,4,5,7,6]=>[2,2,1,1,1] [1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,3,4,2,5,7,6]=>[3,2,1,1] [1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,3,4,5,2,7,6]=>[4,2,1] [1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,3,4,5,7,2,6]=>[6,1] [1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,1,2,4,5,6,7]=>[3,1,1,1,1] [1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,3,2,4,5,6,7]=>[2,1,1,1,1,1] [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,3,4,2,5,6,7]=>[3,1,1,1,1] [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,3,4,5,2,6,7]=>[4,1,1,1] [1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,3,4,5,6,2,7]=>[5,1,1] [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,4,5,6,7,2]=>[6,1] [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,5,2,6,3,7]=>[3,3,1] [1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[4,5,1,2,6,3,7]=>[6,1] [1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[4,1,5,6,2,3,7]=>[6,1] [1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[4,5,1,6,2,3,7]=>[4,2,1] [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[4,5,6,1,2,3,7]=>[2,2,2,1] [1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[4,1,5,2,6,7,3]=>[4,3] [1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[4,5,1,2,6,7,3]=>[7] [1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[4,1,5,6,2,7,3]=>[7] [1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[4,5,1,6,2,7,3]=>[5,2] [1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[4,5,6,1,2,7,3]=>[3,2,2] [1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[4,1,5,6,7,2,3]=>[4,3] [1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[4,5,1,6,7,2,3]=>[7] [1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[4,5,6,1,7,2,3]=>[5,2] [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,1,2,3]=>[7] [1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[4,1,5,2,7,3,6]=>[4,3] [1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[4,5,1,2,7,3,6]=>[7] [1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[4,1,5,7,2,3,6]=>[7] [1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[4,5,1,7,2,3,6]=>[5,2] [1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[4,5,7,1,2,3,6]=>[3,2,2] [1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[4,1,5,2,3,7,6]=>[3,2,2] [1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[4,5,1,2,3,7,6]=>[5,2] [1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[4,1,2,5,3,7,6]=>[5,2] [1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,4,2,5,3,7,6]=>[4,2,1] [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,4,5,2,3,7,6]=>[2,2,2,1] [1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[4,1,2,5,7,3,6]=>[7] [1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,4,2,5,7,3,6]=>[6,1] [1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,4,5,2,7,3,6]=>[4,2,1] [1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,4,5,7,2,3,6]=>[6,1] [1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[4,1,5,2,3,6,7]=>[3,2,1,1] [1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,3,6,7]=>[5,1,1] [1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[4,1,2,5,3,6,7]=>[5,1,1] [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,4,2,5,3,6,7]=>[4,1,1,1] [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,5,2,3,6,7]=>[2,2,1,1,1] [1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[4,1,2,5,6,3,7]=>[6,1] [1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,4,2,5,6,3,7]=>[5,1,1] [1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,4,5,2,6,3,7]=>[3,2,1,1] [1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,4,5,6,2,3,7]=>[5,1,1] [1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[4,1,2,5,6,7,3]=>[7] [1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,4,2,5,6,7,3]=>[6,1] [1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,4,5,2,6,7,3]=>[4,2,1] [1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,4,5,6,2,7,3]=>[6,1] [1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,4,5,6,7,2,3]=>[3,3,1] [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[4,1,6,2,7,3,5]=>[3,2,2] [1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[4,6,1,2,7,3,5]=>[5,2] [1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[4,1,6,7,2,3,5]=>[5,2] [1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,6,1,7,2,3,5]=>[7] [1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,6,7,1,2,3,5]=>[5,2] [1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[4,1,6,2,3,7,5]=>[4,3] [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[4,6,1,2,3,7,5]=>[7] [1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[4,1,2,6,3,7,5]=>[7] [1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,6,3,7,5]=>[6,1] [1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,4,6,2,3,7,5]=>[4,2,1] [1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[4,1,2,6,7,3,5]=>[5,2] [1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,6,7,3,5]=>[4,2,1] [1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,4,6,2,7,3,5]=>[2,2,2,1] [1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,4,6,7,2,3,5]=>[4,2,1] [1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[4,1,6,2,3,5,7]=>[3,3,1] [1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[4,6,1,2,3,5,7]=>[6,1] [1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[4,1,2,6,3,5,7]=>[6,1] [1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,4,2,6,3,5,7]=>[5,1,1] [1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,4,6,2,3,5,7]=>[3,2,1,1] [1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[4,1,2,3,6,5,7]=>[4,2,1] [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,4,2,3,6,5,7]=>[3,2,1,1] [1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,2,4,3,6,5,7]=>[2,2,1,1,1] [1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,2,4,6,3,5,7]=>[4,1,1,1] [1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,3,6,7,5]=>[4,3] [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,4,2,3,6,7,5]=>[3,3,1] [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,2,4,3,6,7,5]=>[3,2,1,1] [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,2,4,6,3,7,5]=>[5,1,1] [1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,2,4,6,7,3,5]=>[3,2,1,1] [1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[4,1,7,2,3,5,6]=>[4,3] [1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[4,7,1,2,3,5,6]=>[7] [1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[4,1,2,7,3,5,6]=>[7] [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,4,2,7,3,5,6]=>[6,1] [1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,4,7,2,3,5,6]=>[4,2,1] [1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[4,1,2,3,7,5,6]=>[4,3] [1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,4,2,3,7,5,6]=>[3,3,1] [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,2,4,3,7,5,6]=>[3,2,1,1] [1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,2,4,7,3,5,6]=>[5,1,1] [1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[4,1,2,3,5,7,6]=>[4,2,1] [1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,4,2,3,5,7,6]=>[3,2,1,1] [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,2,4,3,5,7,6]=>[2,2,1,1,1] [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,2,4,5,3,7,6]=>[3,2,1,1] [1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,2,4,5,7,3,6]=>[5,1,1] [1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[4,1,2,3,5,6,7]=>[4,1,1,1] [1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,4,2,3,5,6,7]=>[3,1,1,1,1] [1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,2,4,3,5,6,7]=>[2,1,1,1,1,1] [1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,2,4,5,3,6,7]=>[3,1,1,1,1] [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,2,4,5,6,3,7]=>[4,1,1,1] [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,5,6,7,3]=>[5,1,1] [1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[5,1,6,2,7,3,4]=>[5,2] [1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[5,6,1,2,7,3,4]=>[7] [1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[5,1,6,7,2,3,4]=>[3,2,2] [1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[5,6,1,7,2,3,4]=>[5,2] [1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,6,7,1,2,3,4]=>[7] [1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[5,1,6,2,3,7,4]=>[7] [1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[5,6,1,2,3,7,4]=>[4,3] [1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[5,1,2,6,3,7,4]=>[4,3] [1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,5,2,6,3,7,4]=>[3,3,1] [1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,5,6,2,3,7,4]=>[6,1] [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[5,1,2,6,7,3,4]=>[7] [1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,5,2,6,7,3,4]=>[6,1] [1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,5,6,2,7,3,4]=>[4,2,1] [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,5,6,7,2,3,4]=>[2,2,2,1] [1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[5,1,6,2,3,4,7]=>[6,1] [1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[5,6,1,2,3,4,7]=>[3,3,1] [1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[5,1,2,6,3,4,7]=>[4,2,1] [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,5,2,6,3,4,7]=>[3,2,1,1] [1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,5,6,2,3,4,7]=>[5,1,1] [1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[5,1,2,3,6,4,7]=>[6,1] [1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,5,2,3,6,4,7]=>[5,1,1] [1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,2,5,3,6,4,7]=>[4,1,1,1] [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,2,5,6,3,4,7]=>[2,2,1,1,1] [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[5,1,2,3,6,7,4]=>[7] [1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,5,2,3,6,7,4]=>[6,1] [1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,2,5,3,6,7,4]=>[5,1,1] [1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,2,5,6,3,7,4]=>[3,2,1,1] [1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,2,5,6,7,3,4]=>[5,1,1] [1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[5,1,7,2,3,4,6]=>[7] [1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[5,7,1,2,3,4,6]=>[4,3] [1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[5,1,2,7,3,4,6]=>[4,3] [1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,5,2,7,3,4,6]=>[3,3,1] [1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,5,7,2,3,4,6]=>[6,1] [1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[5,1,2,3,7,4,6]=>[7] [1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,5,2,3,7,4,6]=>[6,1] [1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,2,5,3,7,4,6]=>[5,1,1] [1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,2,5,7,3,4,6]=>[3,2,1,1] [1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[5,1,2,3,4,7,6]=>[5,2] [1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,5,2,3,4,7,6]=>[4,2,1] [1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,2,5,3,4,7,6]=>[3,2,1,1] [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,2,3,5,4,7,6]=>[2,2,1,1,1] [1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,2,3,5,7,4,6]=>[4,1,1,1] [1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[5,1,2,3,4,6,7]=>[5,1,1] [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,5,2,3,4,6,7]=>[4,1,1,1] [1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,2,5,3,4,6,7]=>[3,1,1,1,1] [1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,2,3,5,4,6,7]=>[2,1,1,1,1,1] [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,2,3,5,6,4,7]=>[3,1,1,1,1] [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,2,3,5,6,7,4]=>[4,1,1,1] [1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[6,1,7,2,3,4,5]=>[4,3] [1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,7,1,2,3,4,5]=>[7] [1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[6,1,2,7,3,4,5]=>[7] [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,6,2,7,3,4,5]=>[6,1] [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,6,7,2,3,4,5]=>[3,3,1] [1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,1,2,3,7,4,5]=>[5,2] [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,6,2,3,7,4,5]=>[4,2,1] [1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,2,6,3,7,4,5]=>[3,2,1,1] [1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,2,6,7,3,4,5]=>[5,1,1] [1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,1,2,3,4,7,5]=>[7] [1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,6,2,3,4,7,5]=>[6,1] [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,2,6,3,4,7,5]=>[5,1,1] [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,2,3,6,4,7,5]=>[4,1,1,1] [1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,2,3,6,7,4,5]=>[2,2,1,1,1] [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,7]=>[6,1] [1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,6,2,3,4,5,7]=>[5,1,1] [1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,2,6,3,4,5,7]=>[4,1,1,1] [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,2,3,6,4,5,7]=>[3,1,1,1,1] [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,2,3,4,6,5,7]=>[2,1,1,1,1,1] [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,2,3,4,6,7,5]=>[3,1,1,1,1] [1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6]=>[7] [1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,7,2,3,4,5,6]=>[6,1] [1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,2,7,3,4,5,6]=>[5,1,1] [1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,2,3,7,4,5,6]=>[4,1,1,1] [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,2,3,4,7,5,6]=>[3,1,1,1,1] [1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,2,3,4,5,7,6]=>[2,1,1,1,1,1] [1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7]=>[1,1,1,1,1,1,1] [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,8,7]=>[2,2,2,2] [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,7,5,8,6]=>[4,4] [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,7,8,5,6]=>[2,2,2,2] [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,4,5,6,7,1,8,3]=>[4,4] [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,5,6,3,4,8,7]=>[2,2,2,2] [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,5,1,7,3,4,8,6]=>[4,4] [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,5,7,3,8,4,6]=>[2,2,2,2] [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,3,5,6,1,7,8,4]=>[4,4] [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[2,6,7,1,3,4,8,5]=>[4,4] [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,1,6,7,8,3,4,5]=>[2,2,2,2] [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[2,3,4,1,6,7,8,5]=>[4,4] [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[2,3,1,4,5,7,8,6]=>[3,3,1,1] [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,8,7]=>[2,2,1,1,1,1] [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[3,4,1,2,6,5,8,7]=>[2,2,2,2] [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[3,1,4,2,6,8,5,7]=>[4,4] [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,4,1,2,7,8,5,6]=>[2,2,2,2] [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,8,1,2]=>[4,4] [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,5,1,6,2,4,8,7]=>[2,2,2,2] [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,5,6,2,8,4,7]=>[4,4] [1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,5,1,7,2,8,4,6]=>[2,2,2,2] [1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,3,5,6,2,7,4,8]=>[3,3,1,1] [1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,6,7,1,2,8,4,5]=>[4,4] [1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,6,1,7,8,2,4,5]=>[2,2,2,2] [1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,3,4,2,6,7,5,8]=>[3,3,1,1] [1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,3,2,4,5,7,6,8]=>[2,2,1,1,1,1] [1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[3,1,2,4,5,8,6,7]=>[3,3,1,1] [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[4,5,6,1,2,3,8,7]=>[2,2,2,2] [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[4,1,5,6,8,2,3,7]=>[4,4] [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[4,5,7,1,2,8,3,6]=>[2,2,2,2] [1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[4,5,1,7,8,2,3,6]=>[4,4] [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,4,5,6,7,2,3,8]=>[3,3,1,1] [1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[4,6,7,1,8,2,3,5]=>[2,2,2,2] [1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,2,4,3,6,5,7,8]=>[2,2,1,1,1,1] [1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,4,2,3,7,5,6,8]=>[3,3,1,1] [1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[4,1,2,3,8,5,6,7]=>[4,4] [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,1,2,3,4]=>[2,2,2,2] [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,2,5,6,3,4,7,8]=>[2,2,1,1,1,1] [1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,5,2,7,3,4,6,8]=>[3,3,1,1] [1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[5,1,2,8,3,4,6,7]=>[4,4] [1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[1,6,7,2,3,4,5,8]=>[3,3,1,1] [1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[6,1,8,2,3,4,5,7]=>[4,4] [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[7,8,1,2,3,4,5,6]=>[4,4] [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8]=>[1,1,1,1,1,1,1,1]
Map
to 321-avoiding permutation
Description
Sends a Dyck path to a 321-avoiding permutation.
This bijection defined in [3, pp. 60] and in [2, Section 3.1].
It is shown in [1] that it sends the number of centered tunnels to the number of fixed points, the number of right tunnels to the number of exceedences, and the semilength plus the height of the middle point to 2 times the length of the longest increasing subsequence.
Map
cycle type
Description
The cycle type of a permutation as a partition.