Identifier
Mp00023: Dyck paths to non-crossing permutationPermutations
Mp00073: Permutations major-index to inversion-number bijectionPermutations
Mp00235: Permutations descent views to invisible inversion bottomsPermutations
Mp00108: Permutations cycle type Integer partitions
Images
=>
Cc0005;cc-rep-0Cc0002;cc-rep-4
[1,0]=>[1]=>[1]=>[1]=>[1] [1,0,1,0]=>[1,2]=>[1,2]=>[1,2]=>[1,1] [1,1,0,0]=>[2,1]=>[2,1]=>[2,1]=>[2] [1,0,1,0,1,0]=>[1,2,3]=>[1,2,3]=>[1,2,3]=>[1,1,1] [1,0,1,1,0,0]=>[1,3,2]=>[2,3,1]=>[3,2,1]=>[2,1] [1,1,0,0,1,0]=>[2,1,3]=>[2,1,3]=>[2,1,3]=>[2,1] [1,1,0,1,0,0]=>[2,3,1]=>[3,1,2]=>[3,1,2]=>[3] [1,1,1,0,0,0]=>[3,2,1]=>[3,2,1]=>[2,3,1]=>[3] [1,0,1,0,1,0,1,0]=>[1,2,3,4]=>[1,2,3,4]=>[1,2,3,4]=>[1,1,1,1] [1,0,1,0,1,1,0,0]=>[1,2,4,3]=>[2,3,4,1]=>[4,2,3,1]=>[2,1,1] [1,0,1,1,0,0,1,0]=>[1,3,2,4]=>[2,3,1,4]=>[3,2,1,4]=>[2,1,1] [1,0,1,1,0,1,0,0]=>[1,3,4,2]=>[2,4,1,3]=>[4,2,1,3]=>[3,1] [1,0,1,1,1,0,0,0]=>[1,4,3,2]=>[3,4,2,1]=>[2,4,3,1]=>[3,1] [1,1,0,0,1,0,1,0]=>[2,1,3,4]=>[2,1,3,4]=>[2,1,3,4]=>[2,1,1] [1,1,0,0,1,1,0,0]=>[2,1,4,3]=>[3,2,4,1]=>[4,3,2,1]=>[2,2] [1,1,0,1,0,0,1,0]=>[2,3,1,4]=>[3,1,2,4]=>[3,1,2,4]=>[3,1] [1,1,0,1,0,1,0,0]=>[2,3,4,1]=>[4,1,2,3]=>[4,1,2,3]=>[4] [1,1,0,1,1,0,0,0]=>[2,4,3,1]=>[4,2,3,1]=>[3,4,2,1]=>[4] [1,1,1,0,0,0,1,0]=>[3,2,1,4]=>[3,2,1,4]=>[2,3,1,4]=>[3,1] [1,1,1,0,0,1,0,0]=>[3,2,4,1]=>[4,2,1,3]=>[2,4,1,3]=>[4] [1,1,1,0,1,0,0,0]=>[4,2,3,1]=>[4,1,3,2]=>[4,3,1,2]=>[4] [1,1,1,1,0,0,0,0]=>[4,3,2,1]=>[4,3,2,1]=>[2,3,4,1]=>[4] [1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[1,1,1,1,1] [1,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,4]=>[2,3,4,5,1]=>[5,2,3,4,1]=>[2,1,1,1] [1,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5]=>[2,3,4,1,5]=>[4,2,3,1,5]=>[2,1,1,1] [1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,3]=>[2,3,5,1,4]=>[5,2,3,1,4]=>[3,1,1] [1,0,1,0,1,1,1,0,0,0]=>[1,2,5,4,3]=>[3,4,5,2,1]=>[2,5,3,4,1]=>[3,1,1] [1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,5]=>[2,3,1,4,5]=>[3,2,1,4,5]=>[2,1,1,1] [1,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4]=>[3,4,2,5,1]=>[5,4,3,2,1]=>[2,2,1] [1,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,5]=>[2,4,1,3,5]=>[4,2,1,3,5]=>[3,1,1] [1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,2]=>[2,5,1,3,4]=>[5,2,1,3,4]=>[4,1] [1,0,1,1,0,1,1,0,0,0]=>[1,3,5,4,2]=>[3,5,2,4,1]=>[4,5,3,2,1]=>[4,1] [1,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,5]=>[3,4,2,1,5]=>[2,4,3,1,5]=>[3,1,1] [1,0,1,1,1,0,0,1,0,0]=>[1,4,3,5,2]=>[3,5,2,1,4]=>[2,5,3,1,4]=>[4,1] [1,0,1,1,1,0,1,0,0,0]=>[1,5,3,4,2]=>[3,5,1,4,2]=>[5,4,3,1,2]=>[4,1] [1,0,1,1,1,1,0,0,0,0]=>[1,5,4,3,2]=>[4,5,3,2,1]=>[2,3,5,4,1]=>[4,1] [1,1,0,0,1,0,1,0,1,0]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[2,1,1,1] [1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4]=>[3,2,4,5,1]=>[5,3,2,4,1]=>[2,2,1] [1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,5]=>[3,2,4,1,5]=>[4,3,2,1,5]=>[2,2,1] [1,1,0,0,1,1,0,1,0,0]=>[2,1,4,5,3]=>[3,2,5,1,4]=>[5,3,2,1,4]=>[3,2] [1,1,0,0,1,1,1,0,0,0]=>[2,1,5,4,3]=>[4,3,5,2,1]=>[2,5,4,3,1]=>[3,2] [1,1,0,1,0,0,1,0,1,0]=>[2,3,1,4,5]=>[3,1,2,4,5]=>[3,1,2,4,5]=>[3,1,1] [1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,4]=>[4,2,3,5,1]=>[5,4,2,3,1]=>[3,2] [1,1,0,1,0,1,0,0,1,0]=>[2,3,4,1,5]=>[4,1,2,3,5]=>[4,1,2,3,5]=>[4,1] [1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,1]=>[5,1,2,3,4]=>[5,1,2,3,4]=>[5] [1,1,0,1,0,1,1,0,0,0]=>[2,3,5,4,1]=>[5,2,3,4,1]=>[4,5,2,3,1]=>[5] [1,1,0,1,1,0,0,0,1,0]=>[2,4,3,1,5]=>[4,2,3,1,5]=>[3,4,2,1,5]=>[4,1] [1,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,1]=>[5,2,3,1,4]=>[3,5,2,1,4]=>[5] [1,1,0,1,1,0,1,0,0,0]=>[2,5,3,4,1]=>[5,2,1,4,3]=>[2,5,4,1,3]=>[5] [1,1,0,1,1,1,0,0,0,0]=>[2,5,4,3,1]=>[5,3,4,2,1]=>[2,4,5,3,1]=>[5] [1,1,1,0,0,0,1,0,1,0]=>[3,2,1,4,5]=>[3,2,1,4,5]=>[2,3,1,4,5]=>[3,1,1] [1,1,1,0,0,0,1,1,0,0]=>[3,2,1,5,4]=>[4,3,2,5,1]=>[5,3,4,2,1]=>[3,2] [1,1,1,0,0,1,0,0,1,0]=>[3,2,4,1,5]=>[4,2,1,3,5]=>[2,4,1,3,5]=>[4,1] [1,1,1,0,0,1,0,1,0,0]=>[3,2,4,5,1]=>[5,2,1,3,4]=>[2,5,1,3,4]=>[5] [1,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,1]=>[5,3,2,4,1]=>[4,3,5,2,1]=>[5] [1,1,1,0,1,0,0,0,1,0]=>[4,2,3,1,5]=>[4,1,3,2,5]=>[4,3,1,2,5]=>[4,1] [1,1,1,0,1,0,0,1,0,0]=>[4,2,3,5,1]=>[5,1,3,2,4]=>[5,3,1,2,4]=>[5] [1,1,1,0,1,0,1,0,0,0]=>[5,2,3,4,1]=>[5,1,2,4,3]=>[5,1,4,2,3]=>[5] [1,1,1,0,1,1,0,0,0,0]=>[5,2,4,3,1]=>[5,2,4,3,1]=>[3,4,5,1,2]=>[5] [1,1,1,1,0,0,0,0,1,0]=>[4,3,2,1,5]=>[4,3,2,1,5]=>[2,3,4,1,5]=>[4,1] [1,1,1,1,0,0,0,1,0,0]=>[4,3,2,5,1]=>[5,3,2,1,4]=>[2,3,5,1,4]=>[5] [1,1,1,1,0,0,1,0,0,0]=>[5,3,2,4,1]=>[5,3,1,4,2]=>[3,5,4,2,1]=>[5] [1,1,1,1,0,1,0,0,0,0]=>[5,3,4,2,1]=>[5,4,1,3,2]=>[4,3,1,5,2]=>[5] [1,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[2,3,4,5,1]=>[5] [1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[1,1,1,1,1,1] [1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,6,5]=>[2,3,4,5,6,1]=>[6,2,3,4,5,1]=>[2,1,1,1,1] [1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,4,6]=>[2,3,4,5,1,6]=>[5,2,3,4,1,6]=>[2,1,1,1,1] [1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,4]=>[2,3,4,6,1,5]=>[6,2,3,4,1,5]=>[3,1,1,1] [1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,6,5,4]=>[3,4,5,6,2,1]=>[2,6,3,4,5,1]=>[3,1,1,1] [1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,5,6]=>[2,3,4,1,5,6]=>[4,2,3,1,5,6]=>[2,1,1,1,1] [1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5]=>[3,4,5,2,6,1]=>[6,5,3,4,2,1]=>[2,2,1,1] [1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,3,6]=>[2,3,5,1,4,6]=>[5,2,3,1,4,6]=>[3,1,1,1] [1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,5,6,3]=>[2,3,6,1,4,5]=>[6,2,3,1,4,5]=>[4,1,1] [1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,5,3]=>[3,4,6,2,5,1]=>[5,6,3,4,2,1]=>[4,1,1] [1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,5,4,3,6]=>[3,4,5,2,1,6]=>[2,5,3,4,1,6]=>[3,1,1,1] [1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,5,4,6,3]=>[3,4,6,2,1,5]=>[2,6,3,4,1,5]=>[4,1,1] [1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,6,4,5,3]=>[3,4,6,1,5,2]=>[6,5,3,4,1,2]=>[4,1,1] [1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,6,5,4,3]=>[4,5,6,3,2,1]=>[2,3,6,4,5,1]=>[4,1,1] [1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,4,5,6]=>[2,3,1,4,5,6]=>[3,2,1,4,5,6]=>[2,1,1,1,1] [1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,5]=>[3,4,2,5,6,1]=>[6,4,3,2,5,1]=>[2,2,1,1] [1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,6]=>[3,4,2,5,1,6]=>[5,4,3,2,1,6]=>[2,2,1,1] [1,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,6,4]=>[3,4,2,6,1,5]=>[6,4,3,2,1,5]=>[3,2,1] [1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,6,5,4]=>[4,5,3,6,2,1]=>[2,6,5,4,3,1]=>[3,2,1] [1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,4,2,5,6]=>[2,4,1,3,5,6]=>[4,2,1,3,5,6]=>[3,1,1,1] [1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,4,2,6,5]=>[3,5,2,4,6,1]=>[6,5,3,2,4,1]=>[3,2,1] [1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,2,6]=>[2,5,1,3,4,6]=>[5,2,1,3,4,6]=>[4,1,1] [1,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,2]=>[2,6,1,3,4,5]=>[6,2,1,3,4,5]=>[5,1] [1,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,4,6,5,2]=>[3,6,2,4,5,1]=>[5,6,3,2,4,1]=>[5,1] [1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,4,2,6]=>[3,5,2,4,1,6]=>[4,5,3,2,1,6]=>[4,1,1] [1,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,4,6,2]=>[3,6,2,4,1,5]=>[4,6,3,2,1,5]=>[5,1] [1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,6,4,5,2]=>[3,6,2,1,5,4]=>[2,6,3,5,1,4]=>[5,1] [1,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,6,5,4,2]=>[4,6,3,5,2,1]=>[2,5,6,4,3,1]=>[5,1] [1,0,1,1,1,0,0,0,1,0,1,0]=>[1,4,3,2,5,6]=>[3,4,2,1,5,6]=>[2,4,3,1,5,6]=>[3,1,1,1] [1,0,1,1,1,0,0,0,1,1,0,0]=>[1,4,3,2,6,5]=>[4,5,3,2,6,1]=>[6,3,5,4,2,1]=>[3,2,1] [1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,3,5,2,6]=>[3,5,2,1,4,6]=>[2,5,3,1,4,6]=>[4,1,1] [1,0,1,1,1,0,0,1,0,1,0,0]=>[1,4,3,5,6,2]=>[3,6,2,1,4,5]=>[2,6,3,1,4,5]=>[5,1] [1,0,1,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,2]=>[4,6,3,2,5,1]=>[5,3,6,4,2,1]=>[5,1] [1,0,1,1,1,0,1,0,0,0,1,0]=>[1,5,3,4,2,6]=>[3,5,1,4,2,6]=>[5,4,3,1,2,6]=>[4,1,1] [1,0,1,1,1,0,1,0,0,1,0,0]=>[1,5,3,4,6,2]=>[3,6,1,4,2,5]=>[6,4,3,1,2,5]=>[5,1] [1,0,1,1,1,0,1,0,1,0,0,0]=>[1,6,3,4,5,2]=>[3,6,1,2,5,4]=>[6,1,3,5,2,4]=>[5,1] [1,0,1,1,1,0,1,1,0,0,0,0]=>[1,6,3,5,4,2]=>[4,6,2,5,3,1]=>[3,5,6,4,1,2]=>[5,1] [1,0,1,1,1,1,0,0,0,0,1,0]=>[1,5,4,3,2,6]=>[4,5,3,2,1,6]=>[2,3,5,4,1,6]=>[4,1,1] [1,0,1,1,1,1,0,0,0,1,0,0]=>[1,5,4,3,6,2]=>[4,6,3,2,1,5]=>[2,3,6,4,1,5]=>[5,1] [1,0,1,1,1,1,0,0,1,0,0,0]=>[1,6,4,3,5,2]=>[4,6,3,1,5,2]=>[3,6,5,4,2,1]=>[5,1] [1,0,1,1,1,1,0,1,0,0,0,0]=>[1,6,4,5,3,2]=>[4,6,5,1,3,2]=>[5,3,1,4,6,2]=>[5,1] [1,0,1,1,1,1,1,0,0,0,0,0]=>[1,6,5,4,3,2]=>[5,6,4,3,2,1]=>[2,3,4,6,5,1]=>[5,1] [1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[2,1,1,1,1] [1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,6,5]=>[3,2,4,5,6,1]=>[6,3,2,4,5,1]=>[2,2,1,1] [1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,4,6]=>[3,2,4,5,1,6]=>[5,3,2,4,1,6]=>[2,2,1,1] [1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,3,5,6,4]=>[3,2,4,6,1,5]=>[6,3,2,4,1,5]=>[3,2,1] [1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,6,5,4]=>[4,3,5,6,2,1]=>[2,6,4,3,5,1]=>[3,2,1] [1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>[3,2,4,1,5,6]=>[4,3,2,1,5,6]=>[2,2,1,1] [1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5]=>[4,3,5,2,6,1]=>[6,5,4,3,2,1]=>[2,2,2] [1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>[3,2,5,1,4,6]=>[5,3,2,1,4,6]=>[3,2,1] [1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,6,3]=>[3,2,6,1,4,5]=>[6,3,2,1,4,5]=>[4,2] [1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,5,3]=>[4,3,6,2,5,1]=>[5,6,4,3,2,1]=>[4,2] [1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,4,3,6]=>[4,3,5,2,1,6]=>[2,5,4,3,1,6]=>[3,2,1] [1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,4,6,3]=>[4,3,6,2,1,5]=>[2,6,4,3,1,5]=>[4,2] [1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,6,4,5,3]=>[4,3,6,1,5,2]=>[6,5,4,3,1,2]=>[4,2] [1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,5,4,3]=>[5,4,6,3,2,1]=>[2,3,6,5,4,1]=>[4,2] [1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,1,4,5,6]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>[3,1,1,1] [1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,5]=>[4,2,3,5,6,1]=>[6,4,2,3,5,1]=>[3,2,1] [1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,6]=>[4,2,3,5,1,6]=>[5,4,2,3,1,6]=>[3,2,1] [1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,6,4]=>[4,2,3,6,1,5]=>[6,4,2,3,1,5]=>[3,3] [1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,1,6,5,4]=>[5,3,4,6,2,1]=>[2,6,5,3,4,1]=>[3,3] [1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,1,5,6]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>[4,1,1] [1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,1,6,5]=>[5,2,3,4,6,1]=>[6,5,2,3,4,1]=>[4,2] [1,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>[5,1] [1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>[6] [1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,5,1]=>[6,2,3,4,5,1]=>[5,6,2,3,4,1]=>[6] [1,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,5,4,1,6]=>[5,2,3,4,1,6]=>[4,5,2,3,1,6]=>[5,1] [1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,4,6,1]=>[6,2,3,4,1,5]=>[4,6,2,3,1,5]=>[6] [1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,6,4,5,1]=>[6,2,3,1,5,4]=>[3,6,2,5,1,4]=>[6] [1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,5,4,1]=>[6,3,4,5,2,1]=>[2,5,6,3,4,1]=>[6] [1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,3,1,5,6]=>[4,2,3,1,5,6]=>[3,4,2,1,5,6]=>[4,1,1] [1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,3,1,6,5]=>[5,3,4,2,6,1]=>[6,4,5,3,2,1]=>[4,2] [1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,3,5,1,6]=>[5,2,3,1,4,6]=>[3,5,2,1,4,6]=>[5,1] [1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,5,6,1]=>[6,2,3,1,4,5]=>[3,6,2,1,4,5]=>[6] [1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,1]=>[6,3,4,2,5,1]=>[5,4,6,3,2,1]=>[6] [1,1,0,1,1,0,1,0,0,0,1,0]=>[2,5,3,4,1,6]=>[5,2,1,4,3,6]=>[2,5,4,1,3,6]=>[5,1] [1,1,0,1,1,0,1,0,0,1,0,0]=>[2,5,3,4,6,1]=>[6,2,1,4,3,5]=>[2,6,4,1,3,5]=>[6] [1,1,0,1,1,0,1,0,1,0,0,0]=>[2,6,3,4,5,1]=>[6,2,1,3,5,4]=>[2,6,1,5,3,4]=>[6] [1,1,0,1,1,0,1,1,0,0,0,0]=>[2,6,3,5,4,1]=>[6,3,2,5,4,1]=>[4,3,5,6,1,2]=>[6] [1,1,0,1,1,1,0,0,0,0,1,0]=>[2,5,4,3,1,6]=>[5,3,4,2,1,6]=>[2,4,5,3,1,6]=>[5,1] [1,1,0,1,1,1,0,0,0,1,0,0]=>[2,5,4,3,6,1]=>[6,3,4,2,1,5]=>[2,4,6,3,1,5]=>[6] [1,1,0,1,1,1,0,0,1,0,0,0]=>[2,6,4,3,5,1]=>[6,3,4,1,5,2]=>[4,5,6,3,1,2]=>[6] [1,1,0,1,1,1,0,1,0,0,0,0]=>[2,6,4,5,3,1]=>[6,3,5,1,4,2]=>[5,4,6,1,3,2]=>[6] [1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,5,4,3,1]=>[6,4,5,3,2,1]=>[2,3,5,6,4,1]=>[6] [1,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,1,4,5,6]=>[3,2,1,4,5,6]=>[2,3,1,4,5,6]=>[3,1,1,1] [1,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,1,4,6,5]=>[4,3,2,5,6,1]=>[6,3,4,2,5,1]=>[3,2,1] [1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,6]=>[4,3,2,5,1,6]=>[5,3,4,2,1,6]=>[3,2,1] [1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1,5,6,4]=>[4,3,2,6,1,5]=>[6,3,4,2,1,5]=>[3,3] [1,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,1,6,5,4]=>[5,4,3,6,2,1]=>[2,6,4,5,3,1]=>[3,3] [1,1,1,0,0,1,0,0,1,0,1,0]=>[3,2,4,1,5,6]=>[4,2,1,3,5,6]=>[2,4,1,3,5,6]=>[4,1,1] [1,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,6,5]=>[5,3,2,4,6,1]=>[6,3,5,2,4,1]=>[4,2] [1,1,1,0,0,1,0,1,0,0,1,0]=>[3,2,4,5,1,6]=>[5,2,1,3,4,6]=>[2,5,1,3,4,6]=>[5,1] [1,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,1]=>[6,2,1,3,4,5]=>[2,6,1,3,4,5]=>[6] [1,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,4,6,5,1]=>[6,3,2,4,5,1]=>[5,3,6,2,4,1]=>[6] [1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,1,6]=>[5,3,2,4,1,6]=>[4,3,5,2,1,6]=>[5,1] [1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,6,1]=>[6,3,2,4,1,5]=>[4,3,6,2,1,5]=>[6] [1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,6,4,5,1]=>[6,3,2,1,5,4]=>[2,3,6,5,1,4]=>[6] [1,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,6,5,4,1]=>[6,4,3,5,2,1]=>[2,5,4,6,3,1]=>[6] [1,1,1,0,1,0,0,0,1,0,1,0]=>[4,2,3,1,5,6]=>[4,1,3,2,5,6]=>[4,3,1,2,5,6]=>[4,1,1] [1,1,1,0,1,0,0,0,1,1,0,0]=>[4,2,3,1,6,5]=>[5,2,4,3,6,1]=>[6,5,4,2,3,1]=>[4,2] [1,1,1,0,1,0,0,1,0,0,1,0]=>[4,2,3,5,1,6]=>[5,1,3,2,4,6]=>[5,3,1,2,4,6]=>[5,1] [1,1,1,0,1,0,0,1,0,1,0,0]=>[4,2,3,5,6,1]=>[6,1,3,2,4,5]=>[6,3,1,2,4,5]=>[6] [1,1,1,0,1,0,0,1,1,0,0,0]=>[4,2,3,6,5,1]=>[6,2,4,3,5,1]=>[5,6,4,2,3,1]=>[6] [1,1,1,0,1,0,1,0,0,0,1,0]=>[5,2,3,4,1,6]=>[5,1,2,4,3,6]=>[5,1,4,2,3,6]=>[5,1] [1,1,1,0,1,0,1,0,0,1,0,0]=>[5,2,3,4,6,1]=>[6,1,2,4,3,5]=>[6,1,4,2,3,5]=>[6] [1,1,1,0,1,0,1,0,1,0,0,0]=>[6,2,3,4,5,1]=>[6,1,2,3,5,4]=>[6,1,2,5,3,4]=>[6] [1,1,1,0,1,0,1,1,0,0,0,0]=>[6,2,3,5,4,1]=>[6,2,3,5,4,1]=>[4,5,1,6,3,2]=>[6] [1,1,1,0,1,1,0,0,0,0,1,0]=>[5,2,4,3,1,6]=>[5,2,4,3,1,6]=>[3,4,5,1,2,6]=>[5,1] [1,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,4,3,6,1]=>[6,2,4,3,1,5]=>[3,4,6,1,2,5]=>[6] [1,1,1,0,1,1,0,0,1,0,0,0]=>[6,2,4,3,5,1]=>[6,2,4,1,5,3]=>[4,6,5,2,1,3]=>[6] [1,1,1,0,1,1,0,1,0,0,0,0]=>[6,2,4,5,3,1]=>[6,2,5,1,4,3]=>[5,6,4,1,2,3]=>[6] [1,1,1,0,1,1,1,0,0,0,0,0]=>[6,2,5,4,3,1]=>[6,3,5,4,2,1]=>[2,4,5,6,1,3]=>[6] [1,1,1,1,0,0,0,0,1,0,1,0]=>[4,3,2,1,5,6]=>[4,3,2,1,5,6]=>[2,3,4,1,5,6]=>[4,1,1] [1,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,2,1,6,5]=>[5,4,3,2,6,1]=>[6,3,4,5,2,1]=>[4,2] [1,1,1,1,0,0,0,1,0,0,1,0]=>[4,3,2,5,1,6]=>[5,3,2,1,4,6]=>[2,3,5,1,4,6]=>[5,1] [1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3,2,5,6,1]=>[6,3,2,1,4,5]=>[2,3,6,1,4,5]=>[6] [1,1,1,1,0,0,0,1,1,0,0,0]=>[4,3,2,6,5,1]=>[6,4,3,2,5,1]=>[5,3,4,6,2,1]=>[6] [1,1,1,1,0,0,1,0,0,0,1,0]=>[5,3,2,4,1,6]=>[5,3,1,4,2,6]=>[3,5,4,2,1,6]=>[5,1] [1,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,2,4,6,1]=>[6,3,1,4,2,5]=>[3,6,4,2,1,5]=>[6] [1,1,1,1,0,0,1,0,1,0,0,0]=>[6,3,2,4,5,1]=>[6,3,1,2,5,4]=>[3,1,6,5,2,4]=>[6] [1,1,1,1,0,0,1,1,0,0,0,0]=>[6,3,2,5,4,1]=>[6,4,2,5,3,1]=>[3,5,4,6,1,2]=>[6] [1,1,1,1,0,1,0,0,0,0,1,0]=>[5,3,4,2,1,6]=>[5,4,1,3,2,6]=>[4,3,1,5,2,6]=>[5,1] [1,1,1,1,0,1,0,0,0,1,0,0]=>[5,3,4,2,6,1]=>[6,4,1,3,2,5]=>[4,3,1,6,2,5]=>[6] [1,1,1,1,0,1,0,0,1,0,0,0]=>[6,3,4,2,5,1]=>[6,4,1,2,5,3]=>[4,1,6,5,3,2]=>[6] [1,1,1,1,0,1,0,1,0,0,0,0]=>[6,3,4,5,2,1]=>[6,5,1,2,4,3]=>[5,1,4,2,6,3]=>[6] [1,1,1,1,0,1,1,0,0,0,0,0]=>[6,3,5,4,2,1]=>[6,5,2,4,3,1]=>[3,4,5,1,6,2]=>[6] [1,1,1,1,1,0,0,0,0,0,1,0]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[2,3,4,5,1,6]=>[5,1] [1,1,1,1,1,0,0,0,0,1,0,0]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[2,3,4,6,1,5]=>[6] [1,1,1,1,1,0,0,0,1,0,0,0]=>[6,4,3,2,5,1]=>[6,4,3,1,5,2]=>[3,4,6,5,1,2]=>[6] [1,1,1,1,1,0,0,1,0,0,0,0]=>[6,4,3,5,2,1]=>[6,5,3,1,4,2]=>[3,5,4,2,6,1]=>[6] [1,1,1,1,1,0,1,0,0,0,0,0]=>[6,5,3,4,2,1]=>[6,5,1,4,3,2]=>[5,3,4,1,6,2]=>[6] [1,1,1,1,1,1,0,0,0,0,0,0]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6] [1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[1,1,1,1,1,1,1] [1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,7,6]=>[2,3,4,5,6,7,1]=>[7,2,3,4,5,6,1]=>[2,1,1,1,1,1] [1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,7]=>[2,3,4,5,6,1,7]=>[6,2,3,4,5,1,7]=>[2,1,1,1,1,1] [1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,6,7,5]=>[2,3,4,5,7,1,6]=>[7,2,3,4,5,1,6]=>[3,1,1,1,1] [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,7,6,5]=>[3,4,5,6,7,2,1]=>[2,7,3,4,5,6,1]=>[3,1,1,1,1] [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,6,7]=>[2,3,4,5,1,6,7]=>[5,2,3,4,1,6,7]=>[2,1,1,1,1,1] [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6]=>[3,4,5,6,2,7,1]=>[7,6,3,4,5,2,1]=>[2,2,1,1,1] [1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,5,6,4,7]=>[2,3,4,6,1,5,7]=>[6,2,3,4,1,5,7]=>[3,1,1,1,1] [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,4]=>[2,3,4,7,1,5,6]=>[7,2,3,4,1,5,6]=>[4,1,1,1] [1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,5,7,6,4]=>[3,4,5,7,2,6,1]=>[6,7,3,4,5,2,1]=>[4,1,1,1] [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,6,5,4,7]=>[3,4,5,6,2,1,7]=>[2,6,3,4,5,1,7]=>[3,1,1,1,1] [1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,6,5,7,4]=>[3,4,5,7,2,1,6]=>[2,7,3,4,5,1,6]=>[4,1,1,1] [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,7,5,6,4]=>[3,4,5,7,1,6,2]=>[7,6,3,4,5,1,2]=>[4,1,1,1] [1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,7,6,5,4]=>[4,5,6,7,3,2,1]=>[2,3,7,4,5,6,1]=>[4,1,1,1] [1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7]=>[2,3,4,1,5,6,7]=>[4,2,3,1,5,6,7]=>[2,1,1,1,1,1] [1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,5,7,6]=>[3,4,5,2,6,7,1]=>[7,5,3,4,2,6,1]=>[2,2,1,1,1] [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,7]=>[3,4,5,2,6,1,7]=>[6,5,3,4,2,1,7]=>[2,2,1,1,1] [1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,4,3,6,7,5]=>[3,4,5,2,7,1,6]=>[7,5,3,4,2,1,6]=>[3,2,1,1] [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,7,6,5]=>[4,5,6,3,7,2,1]=>[2,7,6,4,5,3,1]=>[3,2,1,1] [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,3,6,7]=>[2,3,5,1,4,6,7]=>[5,2,3,1,4,6,7]=>[3,1,1,1,1] [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,4,5,3,7,6]=>[3,4,6,2,5,7,1]=>[7,6,3,4,2,5,1]=>[3,2,1,1] [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,4,5,6,3,7]=>[2,3,6,1,4,5,7]=>[6,2,3,1,4,5,7]=>[4,1,1,1] [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,3]=>[2,3,7,1,4,5,6]=>[7,2,3,1,4,5,6]=>[5,1,1] [1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,7,6,3]=>[3,4,7,2,5,6,1]=>[6,7,3,4,2,5,1]=>[5,1,1] [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,6,5,3,7]=>[3,4,6,2,5,1,7]=>[5,6,3,4,2,1,7]=>[4,1,1,1] [1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,4,6,5,7,3]=>[3,4,7,2,5,1,6]=>[5,7,3,4,2,1,6]=>[5,1,1] [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,4,7,5,6,3]=>[3,4,7,2,1,6,5]=>[2,7,3,4,6,1,5]=>[5,1,1] [1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,4,7,6,5,3]=>[4,5,7,3,6,2,1]=>[2,6,7,4,5,3,1]=>[5,1,1] [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,5,4,3,6,7]=>[3,4,5,2,1,6,7]=>[2,5,3,4,1,6,7]=>[3,1,1,1,1] [1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,5,4,3,7,6]=>[4,5,6,3,2,7,1]=>[7,3,6,4,5,2,1]=>[3,2,1,1] [1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,5,4,6,3,7]=>[3,4,6,2,1,5,7]=>[2,6,3,4,1,5,7]=>[4,1,1,1] [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,5,4,6,7,3]=>[3,4,7,2,1,5,6]=>[2,7,3,4,1,5,6]=>[5,1,1] [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,5,4,7,6,3]=>[4,5,7,3,2,6,1]=>[6,3,7,4,5,2,1]=>[5,1,1] [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,6,4,5,3,7]=>[3,4,6,1,5,2,7]=>[6,5,3,4,1,2,7]=>[4,1,1,1] [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,6,4,5,7,3]=>[3,4,7,1,5,2,6]=>[7,5,3,4,1,2,6]=>[5,1,1] [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,7,4,5,6,3]=>[3,4,7,1,2,6,5]=>[7,1,3,4,6,2,5]=>[5,1,1] [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,7,4,6,5,3]=>[4,5,7,2,6,3,1]=>[3,6,7,4,5,1,2]=>[5,1,1] [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,6,5,4,3,7]=>[4,5,6,3,2,1,7]=>[2,3,6,4,5,1,7]=>[4,1,1,1] [1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,6,5,4,7,3]=>[4,5,7,3,2,1,6]=>[2,3,7,4,5,1,6]=>[5,1,1] [1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,7,5,4,6,3]=>[4,5,7,3,1,6,2]=>[3,7,6,4,5,2,1]=>[5,1,1] [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,7,5,6,4,3]=>[4,5,7,6,1,3,2]=>[6,3,1,4,5,7,2]=>[5,1,1] [1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,7,6,5,4,3]=>[5,6,7,4,3,2,1]=>[2,3,4,7,5,6,1]=>[5,1,1] [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7]=>[2,3,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[2,1,1,1,1,1] [1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,7,6]=>[3,4,2,5,6,7,1]=>[7,4,3,2,5,6,1]=>[2,2,1,1,1] [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,7]=>[3,4,2,5,6,1,7]=>[6,4,3,2,5,1,7]=>[2,2,1,1,1] [1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,6,7,5]=>[3,4,2,5,7,1,6]=>[7,4,3,2,5,1,6]=>[3,2,1,1] [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,7,6,5]=>[4,5,3,6,7,2,1]=>[2,7,5,4,3,6,1]=>[3,2,1,1] [1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,6,7]=>[3,4,2,5,1,6,7]=>[5,4,3,2,1,6,7]=>[2,2,1,1,1] [1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6]=>[4,5,3,6,2,7,1]=>[7,6,5,4,3,2,1]=>[2,2,2,1] [1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,5,6,4,7]=>[3,4,2,6,1,5,7]=>[6,4,3,2,1,5,7]=>[3,2,1,1] [1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,4]=>[3,4,2,7,1,5,6]=>[7,4,3,2,1,5,6]=>[4,2,1] [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,5,7,6,4]=>[4,5,3,7,2,6,1]=>[6,7,5,4,3,2,1]=>[4,2,1] [1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,6,5,4,7]=>[4,5,3,6,2,1,7]=>[2,6,5,4,3,1,7]=>[3,2,1,1] [1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,5,7,4]=>[4,5,3,7,2,1,6]=>[2,7,5,4,3,1,6]=>[4,2,1] [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,7,5,6,4]=>[4,5,3,7,1,6,2]=>[7,6,5,4,3,1,2]=>[4,2,1] [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,7,6,5,4]=>[5,6,4,7,3,2,1]=>[2,3,7,6,5,4,1]=>[4,2,1] [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7]=>[2,4,1,3,5,6,7]=>[4,2,1,3,5,6,7]=>[3,1,1,1,1] [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5,7,6]=>[3,5,2,4,6,7,1]=>[7,5,3,2,4,6,1]=>[3,2,1,1] [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,7]=>[3,5,2,4,6,1,7]=>[6,5,3,2,4,1,7]=>[3,2,1,1] [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,2,6,7,5]=>[3,5,2,4,7,1,6]=>[7,5,3,2,4,1,6]=>[3,3,1] [1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,2,7,6,5]=>[4,6,3,5,7,2,1]=>[2,7,6,4,3,5,1]=>[3,3,1] [1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,2,6,7]=>[2,5,1,3,4,6,7]=>[5,2,1,3,4,6,7]=>[4,1,1,1] [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6]=>[3,6,2,4,5,7,1]=>[7,6,3,2,4,5,1]=>[4,2,1] [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,2,7]=>[2,6,1,3,4,5,7]=>[6,2,1,3,4,5,7]=>[5,1,1] [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,2]=>[2,7,1,3,4,5,6]=>[7,2,1,3,4,5,6]=>[6,1] [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,7,6,2]=>[3,7,2,4,5,6,1]=>[6,7,3,2,4,5,1]=>[6,1] [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,6,5,2,7]=>[3,6,2,4,5,1,7]=>[5,6,3,2,4,1,7]=>[5,1,1] [1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,6,5,7,2]=>[3,7,2,4,5,1,6]=>[5,7,3,2,4,1,6]=>[6,1] [1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,7,5,6,2]=>[3,7,2,4,1,6,5]=>[4,7,3,2,6,1,5]=>[6,1] [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,7,6,5,2]=>[4,7,3,5,6,2,1]=>[2,6,7,4,3,5,1]=>[6,1] [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,3,5,4,2,6,7]=>[3,5,2,4,1,6,7]=>[4,5,3,2,1,6,7]=>[4,1,1,1] [1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,5,4,2,7,6]=>[4,6,3,5,2,7,1]=>[7,5,6,4,3,2,1]=>[4,2,1] [1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,5,4,6,2,7]=>[3,6,2,4,1,5,7]=>[4,6,3,2,1,5,7]=>[5,1,1] [1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,5,4,6,7,2]=>[3,7,2,4,1,5,6]=>[4,7,3,2,1,5,6]=>[6,1] [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,4,7,6,2]=>[4,7,3,5,2,6,1]=>[6,5,7,4,3,2,1]=>[6,1] [1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,6,4,5,2,7]=>[3,6,2,1,5,4,7]=>[2,6,3,5,1,4,7]=>[5,1,1] [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,6,4,5,7,2]=>[3,7,2,1,5,4,6]=>[2,7,3,5,1,4,6]=>[6,1] [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,7,4,5,6,2]=>[3,7,2,1,4,6,5]=>[2,7,3,1,6,4,5]=>[6,1] [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,7,4,6,5,2]=>[4,7,3,2,6,5,1]=>[5,3,6,4,7,1,2]=>[6,1] [1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,6,5,4,2,7]=>[4,6,3,5,2,1,7]=>[2,5,6,4,3,1,7]=>[5,1,1] [1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,6,5,4,7,2]=>[4,7,3,5,2,1,6]=>[2,5,7,4,3,1,6]=>[6,1] [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,7,5,4,6,2]=>[4,7,3,5,1,6,2]=>[5,6,7,4,3,1,2]=>[6,1] [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,7,5,6,4,2]=>[4,7,3,6,1,5,2]=>[6,5,7,4,1,3,2]=>[6,1] [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,7,6,5,4,2]=>[5,7,4,6,3,2,1]=>[2,3,6,7,5,4,1]=>[6,1] [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7]=>[3,4,2,1,5,6,7]=>[2,4,3,1,5,6,7]=>[3,1,1,1,1] [1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,3,2,5,7,6]=>[4,5,3,2,6,7,1]=>[7,3,5,4,2,6,1]=>[3,2,1,1] [1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,3,2,6,5,7]=>[4,5,3,2,6,1,7]=>[6,3,5,4,2,1,7]=>[3,2,1,1] [1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,3,2,6,7,5]=>[4,5,3,2,7,1,6]=>[7,3,5,4,2,1,6]=>[3,3,1] [1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,3,2,7,6,5]=>[5,6,4,3,7,2,1]=>[2,7,4,6,5,3,1]=>[3,3,1] [1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,3,5,2,6,7]=>[3,5,2,1,4,6,7]=>[2,5,3,1,4,6,7]=>[4,1,1,1] [1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,3,5,2,7,6]=>[4,6,3,2,5,7,1]=>[7,3,6,4,2,5,1]=>[4,2,1] [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,3,5,6,2,7]=>[3,6,2,1,4,5,7]=>[2,6,3,1,4,5,7]=>[5,1,1] [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,3,5,6,7,2]=>[3,7,2,1,4,5,6]=>[2,7,3,1,4,5,6]=>[6,1] [1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,3,5,7,6,2]=>[4,7,3,2,5,6,1]=>[6,3,7,4,2,5,1]=>[6,1] [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,3,6,5,2,7]=>[4,6,3,2,5,1,7]=>[5,3,6,4,2,1,7]=>[5,1,1] [1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,3,6,5,7,2]=>[4,7,3,2,5,1,6]=>[5,3,7,4,2,1,6]=>[6,1] [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,3,7,5,6,2]=>[4,7,3,2,1,6,5]=>[2,3,7,4,6,1,5]=>[6,1] [1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,3,7,6,5,2]=>[5,7,4,3,6,2,1]=>[2,6,4,7,5,3,1]=>[6,1] [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,5,3,4,2,6,7]=>[3,5,1,4,2,6,7]=>[5,4,3,1,2,6,7]=>[4,1,1,1] [1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,5,3,4,2,7,6]=>[4,6,2,5,3,7,1]=>[7,6,5,4,2,3,1]=>[4,2,1] [1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,5,3,4,6,2,7]=>[3,6,1,4,2,5,7]=>[6,4,3,1,2,5,7]=>[5,1,1] [1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,5,3,4,6,7,2]=>[3,7,1,4,2,5,6]=>[7,4,3,1,2,5,6]=>[6,1] [1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,5,3,4,7,6,2]=>[4,7,2,5,3,6,1]=>[6,7,5,4,2,3,1]=>[6,1] [1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,6,3,4,5,2,7]=>[3,6,1,2,5,4,7]=>[6,1,3,5,2,4,7]=>[5,1,1] [1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,6,3,4,5,7,2]=>[3,7,1,2,5,4,6]=>[7,1,3,5,2,4,6]=>[6,1] [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,7,3,4,5,6,2]=>[3,7,1,2,4,6,5]=>[7,1,3,2,6,4,5]=>[6,1] [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,7,3,4,6,5,2]=>[4,7,2,3,6,5,1]=>[5,6,1,4,7,3,2]=>[6,1] [1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,6,3,5,4,2,7]=>[4,6,2,5,3,1,7]=>[3,5,6,4,1,2,7]=>[5,1,1] [1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,6,3,5,4,7,2]=>[4,7,2,5,3,1,6]=>[3,5,7,4,1,2,6]=>[6,1] [1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,7,3,5,4,6,2]=>[4,7,2,5,1,6,3]=>[5,7,6,4,2,1,3]=>[6,1] [1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,7,3,5,6,4,2]=>[4,7,2,6,1,5,3]=>[6,7,5,4,1,2,3]=>[6,1] [1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,7,3,6,5,4,2]=>[5,7,3,6,4,2,1]=>[2,4,6,7,5,1,3]=>[6,1] [1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,5,4,3,2,6,7]=>[4,5,3,2,1,6,7]=>[2,3,5,4,1,6,7]=>[4,1,1,1] [1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,5,4,3,2,7,6]=>[5,6,4,3,2,7,1]=>[7,3,4,6,5,2,1]=>[4,2,1] [1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,5,4,3,6,2,7]=>[4,6,3,2,1,5,7]=>[2,3,6,4,1,5,7]=>[5,1,1] [1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,4,3,6,7,2]=>[4,7,3,2,1,5,6]=>[2,3,7,4,1,5,6]=>[6,1] [1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,4,3,7,6,2]=>[5,7,4,3,2,6,1]=>[6,3,4,7,5,2,1]=>[6,1] [1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,6,4,3,5,2,7]=>[4,6,3,1,5,2,7]=>[3,6,5,4,2,1,7]=>[5,1,1] [1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,6,4,3,5,7,2]=>[4,7,3,1,5,2,6]=>[3,7,5,4,2,1,6]=>[6,1] [1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,7,4,3,5,6,2]=>[4,7,3,1,2,6,5]=>[3,1,7,4,6,2,5]=>[6,1] [1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,7,4,3,6,5,2]=>[5,7,4,2,6,3,1]=>[3,6,4,7,5,1,2]=>[6,1] [1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,6,4,5,3,2,7]=>[4,6,5,1,3,2,7]=>[5,3,1,4,6,2,7]=>[5,1,1] [1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,6,4,5,3,7,2]=>[4,7,5,1,3,2,6]=>[5,3,1,4,7,2,6]=>[6,1] [1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,7,4,5,3,6,2]=>[4,7,5,1,2,6,3]=>[5,1,7,4,6,3,2]=>[6,1] [1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,7,4,5,6,3,2]=>[4,7,6,1,2,5,3]=>[6,1,5,4,2,7,3]=>[6,1] [1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,7,4,6,5,3,2]=>[5,7,6,2,4,3,1]=>[3,4,6,1,5,7,2]=>[6,1] [1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,6,5,4,3,2,7]=>[5,6,4,3,2,1,7]=>[2,3,4,6,5,1,7]=>[5,1,1] [1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,5,4,3,7,2]=>[5,7,4,3,2,1,6]=>[2,3,4,7,5,1,6]=>[6,1] [1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,7,5,4,3,6,2]=>[5,7,4,3,1,6,2]=>[3,4,7,6,5,1,2]=>[6,1] [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,7,5,4,6,3,2]=>[5,7,6,3,1,4,2]=>[3,6,4,2,5,7,1]=>[6,1] [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,7,6,4,5,3,2]=>[5,7,6,1,4,3,2]=>[6,3,4,1,5,7,2]=>[6,1] [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,7,6,5,4,3,2]=>[6,7,5,4,3,2,1]=>[2,3,4,5,7,6,1]=>[6,1] [1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[2,1,1,1,1,1] [1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,7,6]=>[3,2,4,5,6,7,1]=>[7,3,2,4,5,6,1]=>[2,2,1,1,1] [1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,7]=>[3,2,4,5,6,1,7]=>[6,3,2,4,5,1,7]=>[2,2,1,1,1] [1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,6,7,5]=>[3,2,4,5,7,1,6]=>[7,3,2,4,5,1,6]=>[3,2,1,1] [1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,7,6,5]=>[4,3,5,6,7,2,1]=>[2,7,4,3,5,6,1]=>[3,2,1,1] [1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,6,7]=>[3,2,4,5,1,6,7]=>[5,3,2,4,1,6,7]=>[2,2,1,1,1] [1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,5,4,7,6]=>[4,3,5,6,2,7,1]=>[7,6,4,3,5,2,1]=>[2,2,2,1] [1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,6,4,7]=>[3,2,4,6,1,5,7]=>[6,3,2,4,1,5,7]=>[3,2,1,1] [1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,5,6,7,4]=>[3,2,4,7,1,5,6]=>[7,3,2,4,1,5,6]=>[4,2,1] [1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,3,5,7,6,4]=>[4,3,5,7,2,6,1]=>[6,7,4,3,5,2,1]=>[4,2,1] [1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,6,5,4,7]=>[4,3,5,6,2,1,7]=>[2,6,4,3,5,1,7]=>[3,2,1,1] [1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,6,5,7,4]=>[4,3,5,7,2,1,6]=>[2,7,4,3,5,1,6]=>[4,2,1] [1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,7,5,6,4]=>[4,3,5,7,1,6,2]=>[7,6,4,3,5,1,2]=>[4,2,1] [1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,7,6,5,4]=>[5,4,6,7,3,2,1]=>[2,3,7,5,4,6,1]=>[4,2,1] [1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>[3,2,4,1,5,6,7]=>[4,3,2,1,5,6,7]=>[2,2,1,1,1] [1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,5,7,6]=>[4,3,5,2,6,7,1]=>[7,5,4,3,2,6,1]=>[2,2,2,1] [1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,7]=>[4,3,5,2,6,1,7]=>[6,5,4,3,2,1,7]=>[2,2,2,1] [1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,3,6,7,5]=>[4,3,5,2,7,1,6]=>[7,5,4,3,2,1,6]=>[3,2,2] [1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,7,6,5]=>[5,4,6,3,7,2,1]=>[2,7,6,5,4,3,1]=>[3,2,2] [1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,5,3,6,7]=>[3,2,5,1,4,6,7]=>[5,3,2,1,4,6,7]=>[3,2,1,1] [1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,3,7,6]=>[4,3,6,2,5,7,1]=>[7,6,4,3,2,5,1]=>[3,2,2] [1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,6,3,7]=>[3,2,6,1,4,5,7]=>[6,3,2,1,4,5,7]=>[4,2,1] [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,3]=>[3,2,7,1,4,5,6]=>[7,3,2,1,4,5,6]=>[5,2] [1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,7,6,3]=>[4,3,7,2,5,6,1]=>[6,7,4,3,2,5,1]=>[5,2] [1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,6,5,3,7]=>[4,3,6,2,5,1,7]=>[5,6,4,3,2,1,7]=>[4,2,1] [1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,4,6,5,7,3]=>[4,3,7,2,5,1,6]=>[5,7,4,3,2,1,6]=>[5,2] [1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,4,7,5,6,3]=>[4,3,7,2,1,6,5]=>[2,7,4,3,6,1,5]=>[5,2] [1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,4,7,6,5,3]=>[5,4,7,3,6,2,1]=>[2,6,7,5,4,3,1]=>[5,2] [1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,5,4,3,6,7]=>[4,3,5,2,1,6,7]=>[2,5,4,3,1,6,7]=>[3,2,1,1] [1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,5,4,3,7,6]=>[5,4,6,3,2,7,1]=>[7,3,6,5,4,2,1]=>[3,2,2] [1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,4,6,3,7]=>[4,3,6,2,1,5,7]=>[2,6,4,3,1,5,7]=>[4,2,1] [1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,4,6,7,3]=>[4,3,7,2,1,5,6]=>[2,7,4,3,1,5,6]=>[5,2] [1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,4,7,6,3]=>[5,4,7,3,2,6,1]=>[6,3,7,5,4,2,1]=>[5,2] [1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,6,4,5,3,7]=>[4,3,6,1,5,2,7]=>[6,5,4,3,1,2,7]=>[4,2,1] [1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,6,4,5,7,3]=>[4,3,7,1,5,2,6]=>[7,5,4,3,1,2,6]=>[5,2] [1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,7,4,5,6,3]=>[4,3,7,1,2,6,5]=>[7,1,4,3,6,2,5]=>[5,2] [1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,7,4,6,5,3]=>[5,4,7,2,6,3,1]=>[3,6,7,5,4,1,2]=>[5,2] [1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,6,5,4,3,7]=>[5,4,6,3,2,1,7]=>[2,3,6,5,4,1,7]=>[4,2,1] [1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,6,5,4,7,3]=>[5,4,7,3,2,1,6]=>[2,3,7,5,4,1,6]=>[5,2] [1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,7,5,4,6,3]=>[5,4,7,3,1,6,2]=>[3,7,6,5,4,2,1]=>[5,2] [1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,7,5,6,4,3]=>[5,4,7,6,1,3,2]=>[6,3,1,5,4,7,2]=>[5,2] [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,7,6,5,4,3]=>[6,5,7,4,3,2,1]=>[2,3,4,7,6,5,1]=>[5,2] [1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7]=>[3,1,2,4,5,6,7]=>[3,1,2,4,5,6,7]=>[3,1,1,1,1] [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,7,6]=>[4,2,3,5,6,7,1]=>[7,4,2,3,5,6,1]=>[3,2,1,1] [1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,1,4,6,5,7]=>[4,2,3,5,6,1,7]=>[6,4,2,3,5,1,7]=>[3,2,1,1] [1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,6,7,5]=>[4,2,3,5,7,1,6]=>[7,4,2,3,5,1,6]=>[3,3,1] [1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,7,6,5]=>[5,3,4,6,7,2,1]=>[2,7,5,3,4,6,1]=>[3,3,1] [1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,4,6,7]=>[4,2,3,5,1,6,7]=>[5,4,2,3,1,6,7]=>[3,2,1,1] [1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6]=>[5,3,4,6,2,7,1]=>[7,6,5,3,4,2,1]=>[3,2,2] [1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,1,5,6,4,7]=>[4,2,3,6,1,5,7]=>[6,4,2,3,1,5,7]=>[3,3,1] [1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,4]=>[4,2,3,7,1,5,6]=>[7,4,2,3,1,5,6]=>[4,3] [1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,1,5,7,6,4]=>[5,3,4,7,2,6,1]=>[6,7,5,3,4,2,1]=>[4,3] [1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1,6,5,4,7]=>[5,3,4,6,2,1,7]=>[2,6,5,3,4,1,7]=>[3,3,1] [1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,5,7,4]=>[5,3,4,7,2,1,6]=>[2,7,5,3,4,1,6]=>[4,3] [1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1,7,5,6,4]=>[5,3,4,7,1,6,2]=>[7,6,5,3,4,1,2]=>[4,3] [1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,7,6,5,4]=>[6,4,5,7,3,2,1]=>[2,3,7,6,4,5,1]=>[4,3] [1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7]=>[4,1,2,3,5,6,7]=>[4,1,2,3,5,6,7]=>[4,1,1,1] [1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,4,1,5,7,6]=>[5,2,3,4,6,7,1]=>[7,5,2,3,4,6,1]=>[4,2,1] [1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,7]=>[5,2,3,4,6,1,7]=>[6,5,2,3,4,1,7]=>[4,2,1] [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,1,6,7,5]=>[5,2,3,4,7,1,6]=>[7,5,2,3,4,1,6]=>[4,3] [1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,7,6,5]=>[6,3,4,5,7,2,1]=>[2,7,6,3,4,5,1]=>[4,3] [1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,1,6,7]=>[5,1,2,3,4,6,7]=>[5,1,2,3,4,6,7]=>[5,1,1] [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6]=>[6,2,3,4,5,7,1]=>[7,6,2,3,4,5,1]=>[5,2] [1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>[6,1,2,3,4,5,7]=>[6,1] [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>[7,1,2,3,4,5,6]=>[7] [1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,7,6,1]=>[7,2,3,4,5,6,1]=>[6,7,2,3,4,5,1]=>[7] [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,6,5,1,7]=>[6,2,3,4,5,1,7]=>[5,6,2,3,4,1,7]=>[6,1] [1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,6,5,7,1]=>[7,2,3,4,5,1,6]=>[5,7,2,3,4,1,6]=>[7] [1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,7,5,6,1]=>[7,2,3,4,1,6,5]=>[4,7,2,3,6,1,5]=>[7] [1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,7,6,5,1]=>[7,3,4,5,6,2,1]=>[2,6,7,3,4,5,1]=>[7] [1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,5,4,1,6,7]=>[5,2,3,4,1,6,7]=>[4,5,2,3,1,6,7]=>[5,1,1] [1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,3,5,4,1,7,6]=>[6,3,4,5,2,7,1]=>[7,5,6,3,4,2,1]=>[5,2] [1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,5,4,6,1,7]=>[6,2,3,4,1,5,7]=>[4,6,2,3,1,5,7]=>[6,1] [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,5,4,6,7,1]=>[7,2,3,4,1,5,6]=>[4,7,2,3,1,5,6]=>[7] [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,4,7,6,1]=>[7,3,4,5,2,6,1]=>[6,5,7,3,4,2,1]=>[7] [1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,6,4,5,1,7]=>[6,2,3,1,5,4,7]=>[3,6,2,5,1,4,7]=>[6,1] [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,6,4,5,7,1]=>[7,2,3,1,5,4,6]=>[3,7,2,5,1,4,6]=>[7] [1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,7,4,5,6,1]=>[7,2,3,1,4,6,5]=>[3,7,2,1,6,4,5]=>[7] [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,7,4,6,5,1]=>[7,3,4,2,6,5,1]=>[5,4,6,1,7,2,3]=>[7] [1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,6,5,4,1,7]=>[6,3,4,5,2,1,7]=>[2,5,6,3,4,1,7]=>[6,1] [1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,4,7,1]=>[7,3,4,5,2,1,6]=>[2,5,7,3,4,1,6]=>[7] [1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,7,5,4,6,1]=>[7,3,4,5,1,6,2]=>[5,6,7,3,4,1,2]=>[7] [1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,7,5,6,4,1]=>[7,3,4,6,1,5,2]=>[6,5,7,3,1,4,2]=>[7] [1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,7,6,5,4,1]=>[7,4,5,6,3,2,1]=>[2,3,6,7,4,5,1]=>[7] [1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7]=>[4,2,3,1,5,6,7]=>[3,4,2,1,5,6,7]=>[4,1,1,1] [1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,4,3,1,5,7,6]=>[5,3,4,2,6,7,1]=>[7,4,5,3,2,6,1]=>[4,2,1] [1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,4,3,1,6,5,7]=>[5,3,4,2,6,1,7]=>[6,4,5,3,2,1,7]=>[4,2,1] [1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,3,1,6,7,5]=>[5,3,4,2,7,1,6]=>[7,4,5,3,2,1,6]=>[4,3] [1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,3,1,7,6,5]=>[6,4,5,3,7,2,1]=>[2,7,5,6,4,3,1]=>[4,3] [1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,3,5,1,6,7]=>[5,2,3,1,4,6,7]=>[3,5,2,1,4,6,7]=>[5,1,1] [1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,3,5,1,7,6]=>[6,3,4,2,5,7,1]=>[7,4,6,3,2,5,1]=>[5,2] [1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,4,3,5,6,1,7]=>[6,2,3,1,4,5,7]=>[3,6,2,1,4,5,7]=>[6,1] [1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,1]=>[7,2,3,1,4,5,6]=>[3,7,2,1,4,5,6]=>[7] [1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,4,3,5,7,6,1]=>[7,3,4,2,5,6,1]=>[6,4,7,3,2,5,1]=>[7] [1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,4,3,6,5,1,7]=>[6,3,4,2,5,1,7]=>[5,4,6,3,2,1,7]=>[6,1] [1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,3,6,5,7,1]=>[7,3,4,2,5,1,6]=>[5,4,7,3,2,1,6]=>[7] [1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,3,7,5,6,1]=>[7,3,4,2,1,6,5]=>[2,4,7,3,6,1,5]=>[7] [1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,3,7,6,5,1]=>[7,4,5,3,6,2,1]=>[2,6,5,7,4,3,1]=>[7] [1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,5,3,4,1,6,7]=>[5,2,1,4,3,6,7]=>[2,5,4,1,3,6,7]=>[5,1,1] [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,5,3,4,1,7,6]=>[6,3,2,5,4,7,1]=>[7,3,6,5,2,4,1]=>[5,2] [1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,5,3,4,6,1,7]=>[6,2,1,4,3,5,7]=>[2,6,4,1,3,5,7]=>[6,1] [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,5,3,4,6,7,1]=>[7,2,1,4,3,5,6]=>[2,7,4,1,3,5,6]=>[7] [1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,5,3,4,7,6,1]=>[7,3,2,5,4,6,1]=>[6,3,7,5,2,4,1]=>[7] [1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,6,3,4,5,1,7]=>[6,2,1,3,5,4,7]=>[2,6,1,5,3,4,7]=>[6,1] [1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,6,3,4,5,7,1]=>[7,2,1,3,5,4,6]=>[2,7,1,5,3,4,6]=>[7] [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,7,3,4,5,6,1]=>[7,2,1,3,4,6,5]=>[2,7,1,3,6,4,5]=>[7] [1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,7,3,4,6,5,1]=>[7,3,2,4,6,5,1]=>[5,3,6,1,7,4,2]=>[7] [1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,6,3,5,4,1,7]=>[6,3,2,5,4,1,7]=>[4,3,5,6,1,2,7]=>[6,1] [1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,6,3,5,4,7,1]=>[7,3,2,5,4,1,6]=>[4,3,5,7,1,2,6]=>[7] [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,7,3,5,4,6,1]=>[7,3,2,5,1,6,4]=>[5,3,7,6,2,1,4]=>[7] [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,7,3,5,6,4,1]=>[7,3,2,6,1,5,4]=>[6,3,7,5,1,2,4]=>[7] [1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,7,3,6,5,4,1]=>[7,4,3,6,5,2,1]=>[2,5,4,6,7,1,3]=>[7] [1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,5,4,3,1,6,7]=>[5,3,4,2,1,6,7]=>[2,4,5,3,1,6,7]=>[5,1,1] [1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,5,4,3,1,7,6]=>[6,4,5,3,2,7,1]=>[7,3,5,6,4,2,1]=>[5,2] [1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,5,4,3,6,1,7]=>[6,3,4,2,1,5,7]=>[2,4,6,3,1,5,7]=>[6,1] [1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,5,4,3,6,7,1]=>[7,3,4,2,1,5,6]=>[2,4,7,3,1,5,6]=>[7] [1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,5,4,3,7,6,1]=>[7,4,5,3,2,6,1]=>[6,3,5,7,4,2,1]=>[7] [1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,6,4,3,5,1,7]=>[6,3,4,1,5,2,7]=>[4,5,6,3,1,2,7]=>[6,1] [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,6,4,3,5,7,1]=>[7,3,4,1,5,2,6]=>[4,5,7,3,1,2,6]=>[7] [1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,7,4,3,5,6,1]=>[7,3,4,1,2,6,5]=>[4,1,7,3,6,2,5]=>[7] [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,7,4,3,6,5,1]=>[7,4,5,2,6,3,1]=>[3,6,5,7,4,1,2]=>[7] [1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,6,4,5,3,1,7]=>[6,3,5,1,4,2,7]=>[5,4,6,1,3,2,7]=>[6,1] [1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,6,4,5,3,7,1]=>[7,3,5,1,4,2,6]=>[5,4,7,1,3,2,6]=>[7] [1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,7,4,5,3,6,1]=>[7,3,5,1,2,6,4]=>[5,1,7,6,3,2,4]=>[7] [1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,7,4,5,6,3,1]=>[7,3,6,1,2,5,4]=>[6,1,7,5,2,3,4]=>[7] [1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,7,4,6,5,3,1]=>[7,4,6,2,5,3,1]=>[3,5,6,7,1,4,2]=>[7] [1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,6,5,4,3,1,7]=>[6,4,5,3,2,1,7]=>[2,3,5,6,4,1,7]=>[6,1] [1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,6,5,4,3,7,1]=>[7,4,5,3,2,1,6]=>[2,3,5,7,4,1,6]=>[7] [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,7,5,4,3,6,1]=>[7,4,5,3,1,6,2]=>[3,5,6,7,4,2,1]=>[7] [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,7,5,4,6,3,1]=>[7,4,6,3,1,5,2]=>[3,6,5,7,2,4,1]=>[7] [1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,7,6,4,5,3,1]=>[7,4,6,1,5,3,2]=>[6,3,5,7,1,4,2]=>[7] [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,7,6,5,4,3,1]=>[7,5,6,4,3,2,1]=>[2,3,4,6,7,5,1]=>[7] [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[2,3,1,4,5,6,7]=>[3,1,1,1,1] [1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,2,1,4,5,7,6]=>[4,3,2,5,6,7,1]=>[7,3,4,2,5,6,1]=>[3,2,1,1] [1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,2,1,4,6,5,7]=>[4,3,2,5,6,1,7]=>[6,3,4,2,5,1,7]=>[3,2,1,1] [1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,2,1,4,6,7,5]=>[4,3,2,5,7,1,6]=>[7,3,4,2,5,1,6]=>[3,3,1] [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,7,6,5]=>[5,4,3,6,7,2,1]=>[2,7,4,5,3,6,1]=>[3,3,1] [1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,5,4,6,7]=>[4,3,2,5,1,6,7]=>[5,3,4,2,1,6,7]=>[3,2,1,1] [1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,1,5,4,7,6]=>[5,4,3,6,2,7,1]=>[7,6,4,5,3,2,1]=>[3,2,2] [1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,5,6,4,7]=>[4,3,2,6,1,5,7]=>[6,3,4,2,1,5,7]=>[3,3,1] [1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,4]=>[4,3,2,7,1,5,6]=>[7,3,4,2,1,5,6]=>[4,3] [1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,1,5,7,6,4]=>[5,4,3,7,2,6,1]=>[6,7,4,5,3,2,1]=>[4,3] [1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,2,1,6,5,4,7]=>[5,4,3,6,2,1,7]=>[2,6,4,5,3,1,7]=>[3,3,1] [1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,2,1,6,5,7,4]=>[5,4,3,7,2,1,6]=>[2,7,4,5,3,1,6]=>[4,3] [1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,2,1,7,5,6,4]=>[5,4,3,7,1,6,2]=>[7,6,4,5,3,1,2]=>[4,3] [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,2,1,7,6,5,4]=>[6,5,4,7,3,2,1]=>[2,3,7,5,6,4,1]=>[4,3] [1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7]=>[4,2,1,3,5,6,7]=>[2,4,1,3,5,6,7]=>[4,1,1,1] [1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,2,4,1,5,7,6]=>[5,3,2,4,6,7,1]=>[7,3,5,2,4,6,1]=>[4,2,1] [1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,2,4,1,6,5,7]=>[5,3,2,4,6,1,7]=>[6,3,5,2,4,1,7]=>[4,2,1] [1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,2,4,1,6,7,5]=>[5,3,2,4,7,1,6]=>[7,3,5,2,4,1,6]=>[4,3] [1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,2,4,1,7,6,5]=>[6,4,3,5,7,2,1]=>[2,7,4,6,3,5,1]=>[4,3] [1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,2,4,5,1,6,7]=>[5,2,1,3,4,6,7]=>[2,5,1,3,4,6,7]=>[5,1,1] [1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,2,4,5,1,7,6]=>[6,3,2,4,5,7,1]=>[7,3,6,2,4,5,1]=>[5,2] [1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,2,4,5,6,1,7]=>[6,2,1,3,4,5,7]=>[2,6,1,3,4,5,7]=>[6,1] [1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,1]=>[7,2,1,3,4,5,6]=>[2,7,1,3,4,5,6]=>[7] [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,2,4,5,7,6,1]=>[7,3,2,4,5,6,1]=>[6,3,7,2,4,5,1]=>[7] [1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,2,4,6,5,1,7]=>[6,3,2,4,5,1,7]=>[5,3,6,2,4,1,7]=>[6,1] [1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,2,4,6,5,7,1]=>[7,3,2,4,5,1,6]=>[5,3,7,2,4,1,6]=>[7] [1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,2,4,7,5,6,1]=>[7,3,2,4,1,6,5]=>[4,3,7,2,6,1,5]=>[7] [1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,2,4,7,6,5,1]=>[7,4,3,5,6,2,1]=>[2,6,4,7,3,5,1]=>[7] [1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,5,4,1,6,7]=>[5,3,2,4,1,6,7]=>[4,3,5,2,1,6,7]=>[5,1,1] [1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,5,4,1,7,6]=>[6,4,3,5,2,7,1]=>[7,5,4,6,3,2,1]=>[5,2] [1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,5,4,6,1,7]=>[6,3,2,4,1,5,7]=>[4,3,6,2,1,5,7]=>[6,1] [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,5,4,6,7,1]=>[7,3,2,4,1,5,6]=>[4,3,7,2,1,5,6]=>[7] [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,7,6,1]=>[7,4,3,5,2,6,1]=>[6,5,4,7,3,2,1]=>[7] [1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,6,4,5,1,7]=>[6,3,2,1,5,4,7]=>[2,3,6,5,1,4,7]=>[6,1] [1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,6,4,5,7,1]=>[7,3,2,1,5,4,6]=>[2,3,7,5,1,4,6]=>[7] [1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,7,4,5,6,1]=>[7,3,2,1,4,6,5]=>[2,3,7,1,6,4,5]=>[7] [1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,7,4,6,5,1]=>[7,4,3,2,6,5,1]=>[5,3,4,6,7,1,2]=>[7] [1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,2,6,5,4,1,7]=>[6,4,3,5,2,1,7]=>[2,5,4,6,3,1,7]=>[6,1] [1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,2,6,5,4,7,1]=>[7,4,3,5,2,1,6]=>[2,5,4,7,3,1,6]=>[7] [1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,2,7,5,4,6,1]=>[7,4,3,5,1,6,2]=>[5,6,4,7,3,1,2]=>[7] [1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,7,5,6,4,1]=>[7,4,3,6,1,5,2]=>[6,5,4,7,1,3,2]=>[7] [1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,2,7,6,5,4,1]=>[7,5,4,6,3,2,1]=>[2,3,6,5,7,4,1]=>[7] [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[4,2,3,1,5,6,7]=>[4,1,3,2,5,6,7]=>[4,3,1,2,5,6,7]=>[4,1,1,1] [1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[4,2,3,1,5,7,6]=>[5,2,4,3,6,7,1]=>[7,5,4,2,3,6,1]=>[4,2,1] [1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[4,2,3,1,6,5,7]=>[5,2,4,3,6,1,7]=>[6,5,4,2,3,1,7]=>[4,2,1] [1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,2,3,1,6,7,5]=>[5,2,4,3,7,1,6]=>[7,5,4,2,3,1,6]=>[4,3] [1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,2,3,1,7,6,5]=>[6,3,5,4,7,2,1]=>[2,7,6,5,3,4,1]=>[4,3] [1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[4,2,3,5,1,6,7]=>[5,1,3,2,4,6,7]=>[5,3,1,2,4,6,7]=>[5,1,1] [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[4,2,3,5,1,7,6]=>[6,2,4,3,5,7,1]=>[7,6,4,2,3,5,1]=>[5,2] [1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[4,2,3,5,6,1,7]=>[6,1,3,2,4,5,7]=>[6,3,1,2,4,5,7]=>[6,1] [1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[4,2,3,5,6,7,1]=>[7,1,3,2,4,5,6]=>[7,3,1,2,4,5,6]=>[7] [1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[4,2,3,5,7,6,1]=>[7,2,4,3,5,6,1]=>[6,7,4,2,3,5,1]=>[7] [1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[4,2,3,6,5,1,7]=>[6,2,4,3,5,1,7]=>[5,6,4,2,3,1,7]=>[6,1] [1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[4,2,3,6,5,7,1]=>[7,2,4,3,5,1,6]=>[5,7,4,2,3,1,6]=>[7] [1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[4,2,3,7,5,6,1]=>[7,2,4,3,1,6,5]=>[3,4,7,1,6,2,5]=>[7] [1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,2,3,7,6,5,1]=>[7,3,5,4,6,2,1]=>[2,6,7,5,3,4,1]=>[7] [1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[5,2,3,4,1,6,7]=>[5,1,2,4,3,6,7]=>[5,1,4,2,3,6,7]=>[5,1,1] [1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[5,2,3,4,1,7,6]=>[6,2,3,5,4,7,1]=>[7,6,2,5,3,4,1]=>[5,2] [1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[5,2,3,4,6,1,7]=>[6,1,2,4,3,5,7]=>[6,1,4,2,3,5,7]=>[6,1] [1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[5,2,3,4,6,7,1]=>[7,1,2,4,3,5,6]=>[7,1,4,2,3,5,6]=>[7] [1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[5,2,3,4,7,6,1]=>[7,2,3,5,4,6,1]=>[6,7,2,5,3,4,1]=>[7] [1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[6,2,3,4,5,1,7]=>[6,1,2,3,5,4,7]=>[6,1,2,5,3,4,7]=>[6,1] [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,2,3,4,5,7,1]=>[7,1,2,3,5,4,6]=>[7,1,2,5,3,4,6]=>[7] [1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[7,2,3,4,5,6,1]=>[7,1,2,3,4,6,5]=>[7,1,2,3,6,4,5]=>[7] [1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[7,2,3,4,6,5,1]=>[7,2,3,4,6,5,1]=>[5,6,1,3,7,4,2]=>[7] [1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[6,2,3,5,4,1,7]=>[6,2,3,5,4,1,7]=>[4,5,1,6,3,2,7]=>[6,1] [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,2,3,5,4,7,1]=>[7,2,3,5,4,1,6]=>[4,5,1,7,3,2,6]=>[7] [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[7,2,3,5,4,6,1]=>[7,2,3,5,1,6,4]=>[5,7,2,6,3,1,4]=>[7] [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[7,2,3,5,6,4,1]=>[7,2,3,6,1,5,4]=>[6,7,2,5,1,3,4]=>[7] [1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[7,2,3,6,5,4,1]=>[7,3,4,6,5,2,1]=>[2,5,6,1,7,4,3]=>[7] [1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[5,2,4,3,1,6,7]=>[5,2,4,3,1,6,7]=>[3,4,5,1,2,6,7]=>[5,1,1] [1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[5,2,4,3,1,7,6]=>[6,3,5,4,2,7,1]=>[7,4,5,6,2,3,1]=>[5,2] [1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[5,2,4,3,6,1,7]=>[6,2,4,3,1,5,7]=>[3,4,6,1,2,5,7]=>[6,1] [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[5,2,4,3,6,7,1]=>[7,2,4,3,1,5,6]=>[3,4,7,1,2,5,6]=>[7] [1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,2,4,3,7,6,1]=>[7,3,5,4,2,6,1]=>[6,4,5,7,2,3,1]=>[7] [1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[6,2,4,3,5,1,7]=>[6,2,4,1,5,3,7]=>[4,6,5,2,1,3,7]=>[6,1] [1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,2,4,3,5,7,1]=>[7,2,4,1,5,3,6]=>[4,7,5,2,1,3,6]=>[7] [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[7,2,4,3,5,6,1]=>[7,2,4,1,3,6,5]=>[4,7,1,2,6,3,5]=>[7] [1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[7,2,4,3,6,5,1]=>[7,3,5,2,6,4,1]=>[4,6,5,7,1,3,2]=>[7] [1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[6,2,4,5,3,1,7]=>[6,2,5,1,4,3,7]=>[5,6,4,1,2,3,7]=>[6,1] [1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,2,4,5,3,7,1]=>[7,2,5,1,4,3,6]=>[5,7,4,1,2,3,6]=>[7] [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[7,2,4,5,3,6,1]=>[7,2,5,1,3,6,4]=>[5,7,1,6,2,3,4]=>[7] [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[7,2,4,5,6,3,1]=>[7,2,6,1,3,5,4]=>[6,7,1,5,3,2,4]=>[7] [1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[7,2,4,6,5,3,1]=>[7,3,6,2,5,4,1]=>[4,5,6,7,3,1,2]=>[7] [1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[6,2,5,4,3,1,7]=>[6,3,5,4,2,1,7]=>[2,4,5,6,1,3,7]=>[6,1] [1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,5,4,3,7,1]=>[7,3,5,4,2,1,6]=>[2,4,5,7,1,3,6]=>[7] [1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[7,2,5,4,3,6,1]=>[7,3,5,4,1,6,2]=>[4,5,6,7,1,2,3]=>[7] [1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[7,2,5,4,6,3,1]=>[7,3,6,4,1,5,2]=>[4,6,5,7,2,1,3]=>[7] [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[7,2,6,4,5,3,1]=>[7,3,6,1,5,4,2]=>[6,4,5,7,1,2,3]=>[7] [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[7,2,6,5,4,3,1]=>[7,4,6,5,3,2,1]=>[2,3,5,6,7,1,4]=>[7] [1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>[2,3,4,1,5,6,7]=>[4,1,1,1] [1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,3,2,1,5,7,6]=>[5,4,3,2,6,7,1]=>[7,3,4,5,2,6,1]=>[4,2,1] [1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,3,2,1,6,5,7]=>[5,4,3,2,6,1,7]=>[6,3,4,5,2,1,7]=>[4,2,1] [1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,3,2,1,6,7,5]=>[5,4,3,2,7,1,6]=>[7,3,4,5,2,1,6]=>[4,3] [1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3,2,1,7,6,5]=>[6,5,4,3,7,2,1]=>[2,7,4,5,6,3,1]=>[4,3] [1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,3,2,5,1,6,7]=>[5,3,2,1,4,6,7]=>[2,3,5,1,4,6,7]=>[5,1,1] [1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,3,2,5,1,7,6]=>[6,4,3,2,5,7,1]=>[7,3,4,6,2,5,1]=>[5,2] [1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,3,2,5,6,1,7]=>[6,3,2,1,4,5,7]=>[2,3,6,1,4,5,7]=>[6,1] [1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,1]=>[7,3,2,1,4,5,6]=>[2,3,7,1,4,5,6]=>[7] [1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,3,2,5,7,6,1]=>[7,4,3,2,5,6,1]=>[6,3,4,7,2,5,1]=>[7] [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,3,2,6,5,1,7]=>[6,4,3,2,5,1,7]=>[5,3,4,6,2,1,7]=>[6,1] [1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,3,2,6,5,7,1]=>[7,4,3,2,5,1,6]=>[5,3,4,7,2,1,6]=>[7] [1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,2,7,5,6,1]=>[7,4,3,2,1,6,5]=>[2,3,4,7,6,1,5]=>[7] [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3,2,7,6,5,1]=>[7,5,4,3,6,2,1]=>[2,6,4,5,7,3,1]=>[7] [1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[5,3,2,4,1,6,7]=>[5,3,1,4,2,6,7]=>[3,5,4,2,1,6,7]=>[5,1,1] [1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[5,3,2,4,1,7,6]=>[6,4,2,5,3,7,1]=>[7,4,6,5,3,2,1]=>[5,2] [1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[5,3,2,4,6,1,7]=>[6,3,1,4,2,5,7]=>[3,6,4,2,1,5,7]=>[6,1] [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[5,3,2,4,6,7,1]=>[7,3,1,4,2,5,6]=>[3,7,4,2,1,5,6]=>[7] [1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,3,2,4,7,6,1]=>[7,4,2,5,3,6,1]=>[6,4,7,5,3,2,1]=>[7] [1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[6,3,2,4,5,1,7]=>[6,3,1,2,5,4,7]=>[3,1,6,5,2,4,7]=>[6,1] [1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,3,2,4,5,7,1]=>[7,3,1,2,5,4,6]=>[3,1,7,5,2,4,6]=>[7] [1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[7,3,2,4,5,6,1]=>[7,3,1,2,4,6,5]=>[3,1,7,2,6,4,5]=>[7] [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[7,3,2,4,6,5,1]=>[7,4,2,3,6,5,1]=>[5,4,1,6,7,3,2]=>[7] [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[6,3,2,5,4,1,7]=>[6,4,2,5,3,1,7]=>[3,5,4,6,1,2,7]=>[6,1] [1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,2,5,4,7,1]=>[7,4,2,5,3,1,6]=>[3,5,4,7,1,2,6]=>[7] [1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[7,3,2,5,4,6,1]=>[7,4,2,5,1,6,3]=>[5,4,7,6,3,1,2]=>[7] [1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[7,3,2,5,6,4,1]=>[7,4,2,6,1,5,3]=>[6,4,7,5,1,3,2]=>[7] [1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[7,3,2,6,5,4,1]=>[7,5,3,6,4,2,1]=>[2,4,6,5,7,1,3]=>[7] [1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[5,3,4,2,1,6,7]=>[5,4,1,3,2,6,7]=>[4,3,1,5,2,6,7]=>[5,1,1] [1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[5,3,4,2,1,7,6]=>[6,5,2,4,3,7,1]=>[7,5,4,2,6,3,1]=>[5,2] [1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[5,3,4,2,6,1,7]=>[6,4,1,3,2,5,7]=>[4,3,1,6,2,5,7]=>[6,1] [1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[5,3,4,2,6,7,1]=>[7,4,1,3,2,5,6]=>[4,3,1,7,2,5,6]=>[7] [1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,3,4,2,7,6,1]=>[7,5,2,4,3,6,1]=>[6,5,4,2,7,3,1]=>[7] [1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[6,3,4,2,5,1,7]=>[6,4,1,2,5,3,7]=>[4,1,6,5,3,2,7]=>[6,1] [1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,3,4,2,5,7,1]=>[7,4,1,2,5,3,6]=>[4,1,7,5,3,2,6]=>[7] [1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[7,3,4,2,5,6,1]=>[7,4,1,2,3,6,5]=>[4,1,2,7,6,3,5]=>[7] [1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[7,3,4,2,6,5,1]=>[7,5,2,3,6,4,1]=>[4,6,1,5,7,3,2]=>[7] [1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[6,3,4,5,2,1,7]=>[6,5,1,2,4,3,7]=>[5,1,4,2,6,3,7]=>[6,1] [1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,4,5,2,7,1]=>[7,5,1,2,4,3,6]=>[5,1,4,2,7,3,6]=>[7] [1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[7,3,4,5,2,6,1]=>[7,5,1,2,3,6,4]=>[5,1,2,7,6,4,3]=>[7] [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[7,3,4,5,6,2,1]=>[7,6,1,2,3,5,4]=>[6,1,2,5,3,7,4]=>[7] [1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[7,3,4,6,5,2,1]=>[7,6,2,3,5,4,1]=>[4,5,1,6,3,7,2]=>[7] [1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[6,3,5,4,2,1,7]=>[6,5,2,4,3,1,7]=>[3,4,5,1,6,2,7]=>[6,1] [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,3,5,4,2,7,1]=>[7,5,2,4,3,1,6]=>[3,4,5,1,7,2,6]=>[7] [1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[7,3,5,4,2,6,1]=>[7,5,2,4,1,6,3]=>[4,5,7,3,6,1,2]=>[7] [1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[7,3,5,4,6,2,1]=>[7,6,2,4,1,5,3]=>[4,6,5,2,1,7,3]=>[7] [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[7,3,6,4,5,2,1]=>[7,6,2,1,5,4,3]=>[2,6,4,5,1,7,3]=>[7] [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[7,3,6,5,4,2,1]=>[7,6,3,5,4,2,1]=>[2,4,5,6,1,7,3]=>[7] [1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>[2,3,4,5,1,6,7]=>[5,1,1] [1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,4,3,2,1,7,6]=>[6,5,4,3,2,7,1]=>[7,3,4,5,6,2,1]=>[5,2] [1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[5,4,3,2,6,1,7]=>[6,4,3,2,1,5,7]=>[2,3,4,6,1,5,7]=>[6,1] [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4,3,2,6,7,1]=>[7,4,3,2,1,5,6]=>[2,3,4,7,1,5,6]=>[7] [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,4,3,2,7,6,1]=>[7,5,4,3,2,6,1]=>[6,3,4,5,7,2,1]=>[7] [1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,4,3,2,5,1,7]=>[6,4,3,1,5,2,7]=>[3,4,6,5,1,2,7]=>[6,1] [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,3,2,5,7,1]=>[7,4,3,1,5,2,6]=>[3,4,7,5,1,2,6]=>[7] [1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[7,4,3,2,5,6,1]=>[7,4,3,1,2,6,5]=>[3,1,4,7,6,2,5]=>[7] [1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[7,4,3,2,6,5,1]=>[7,5,4,2,6,3,1]=>[3,6,4,5,7,1,2]=>[7] [1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,4,3,5,2,1,7]=>[6,5,3,1,4,2,7]=>[3,5,4,2,6,1,7]=>[6,1] [1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,4,3,5,2,7,1]=>[7,5,3,1,4,2,6]=>[3,5,4,2,7,1,6]=>[7] [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[7,4,3,5,2,6,1]=>[7,5,3,1,2,6,4]=>[3,1,5,7,6,4,2]=>[7] [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[7,4,3,5,6,2,1]=>[7,6,3,1,2,5,4]=>[3,1,6,5,2,7,4]=>[7] [1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[7,4,3,6,5,2,1]=>[7,6,4,2,5,3,1]=>[3,5,4,6,1,7,2]=>[7] [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,5,3,4,2,1,7]=>[6,5,1,4,3,2,7]=>[5,3,4,1,6,2,7]=>[6,1] [1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,5,3,4,2,7,1]=>[7,5,1,4,3,2,6]=>[5,3,4,1,7,2,6]=>[7] [1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[7,5,3,4,2,6,1]=>[7,5,1,4,2,6,3]=>[5,4,7,3,6,2,1]=>[7] [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[7,5,3,4,6,2,1]=>[7,6,1,4,2,5,3]=>[6,4,5,1,2,7,3]=>[7] [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[7,6,3,4,5,2,1]=>[7,6,1,2,5,4,3]=>[6,1,4,5,2,7,3]=>[7] [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[7,6,3,5,4,2,1]=>[7,6,2,5,4,3,1]=>[3,4,5,6,2,7,1]=>[7] [1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,1] [1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[2,3,4,5,7,1,6]=>[7] [1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[7,5,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[3,4,5,7,6,2,1]=>[7] [1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[7,5,4,3,6,2,1]=>[7,6,4,3,1,5,2]=>[3,4,6,5,1,7,2]=>[7] [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[7,6,4,3,5,2,1]=>[7,6,4,1,5,3,2]=>[4,3,6,5,2,7,1]=>[7] [1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[7,6,4,5,3,2,1]=>[7,6,5,1,4,3,2]=>[5,3,4,1,6,7,2]=>[7] [1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7] [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[1,1,1,1,1,1,1,1] [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7]=>[5,4,6,3,7,2,8,1]=>[8,7,6,5,4,3,2,1]=>[2,2,2,2]
Map
to non-crossing permutation
Description
Sends a Dyck path $D$ with valley at positions $\{(i_1,j_1),\ldots,(i_k,j_k)\}$ to the unique non-crossing permutation $\pi$ having descents $\{i_1,\ldots,i_k\}$ and whose inverse has descents $\{j_1,\ldots,j_k\}$.
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
Map
major-index to inversion-number bijection
Description
Return the permutation whose Lehmer code equals the major code of the preimage.
This map sends the major index to the number of inversions.
Map
descent views to invisible inversion bottoms
Description
Return a permutation whose multiset of invisible inversion bottoms is the multiset of descent views of the given permutation.
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
  • the multiset of descent views in $\pi$ is the multiset of invisible inversion bottoms in $\chi(\pi)$,
  • the set of left-to-right maximima of $\pi$ is the set of maximal elements in the cycles of $\chi(\pi)$,
  • the set of global ascent of $\pi$ is the set of global ascent of $\chi(\pi)$,
  • the set of maximal elements in the decreasing runs of $\pi$ is the set of deficiency positions of $\chi(\pi)$, and
  • the set of minimal elements in the decreasing runs of $\pi$ is the set of deficiency values of $\chi(\pi)$.
Map
cycle type
Description
The cycle type of a permutation as a partition.