Identifier
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00108: Permutations —cycle type⟶ Integer partitions
Images
=>
Cc0005;cc-rep-0Cc0002;cc-rep-3
[1,0]=>[1]=>[1]=>[1] [1,0,1,0]=>[2,1]=>[2,1]=>[2] [1,1,0,0]=>[1,2]=>[1,2]=>[1,1] [1,0,1,0,1,0]=>[3,2,1]=>[2,3,1]=>[3] [1,0,1,1,0,0]=>[2,3,1]=>[3,2,1]=>[2,1] [1,1,0,0,1,0]=>[3,1,2]=>[3,1,2]=>[3] [1,1,0,1,0,0]=>[2,1,3]=>[2,1,3]=>[2,1] [1,1,1,0,0,0]=>[1,2,3]=>[1,2,3]=>[1,1,1] [1,0,1,0,1,0,1,0]=>[4,3,2,1]=>[2,3,4,1]=>[4] [1,0,1,0,1,1,0,0]=>[3,4,2,1]=>[2,4,3,1]=>[3,1] [1,0,1,1,0,0,1,0]=>[4,2,3,1]=>[3,4,2,1]=>[4] [1,0,1,1,0,1,0,0]=>[3,2,4,1]=>[4,3,2,1]=>[2,2] [1,0,1,1,1,0,0,0]=>[2,3,4,1]=>[4,2,3,1]=>[2,1,1] [1,1,0,0,1,0,1,0]=>[4,3,1,2]=>[3,1,4,2]=>[4] [1,1,0,0,1,1,0,0]=>[3,4,1,2]=>[4,1,3,2]=>[3,1] [1,1,0,1,0,0,1,0]=>[4,2,1,3]=>[2,4,1,3]=>[4] [1,1,0,1,0,1,0,0]=>[3,2,1,4]=>[2,3,1,4]=>[3,1] [1,1,0,1,1,0,0,0]=>[2,3,1,4]=>[3,2,1,4]=>[2,1,1] [1,1,1,0,0,0,1,0]=>[4,1,2,3]=>[4,1,2,3]=>[4] [1,1,1,0,0,1,0,0]=>[3,1,2,4]=>[3,1,2,4]=>[3,1] [1,1,1,0,1,0,0,0]=>[2,1,3,4]=>[2,1,3,4]=>[2,1,1] [1,1,1,1,0,0,0,0]=>[1,2,3,4]=>[1,2,3,4]=>[1,1,1,1] [1,0,1,0,1,0,1,0,1,0]=>[5,4,3,2,1]=>[2,3,4,5,1]=>[5] [1,0,1,0,1,0,1,1,0,0]=>[4,5,3,2,1]=>[2,3,5,4,1]=>[4,1] [1,0,1,0,1,1,0,0,1,0]=>[5,3,4,2,1]=>[2,4,5,3,1]=>[5] [1,0,1,0,1,1,0,1,0,0]=>[4,3,5,2,1]=>[2,5,4,3,1]=>[3,2] [1,0,1,0,1,1,1,0,0,0]=>[3,4,5,2,1]=>[2,5,3,4,1]=>[3,1,1] [1,0,1,1,0,0,1,0,1,0]=>[5,4,2,3,1]=>[3,4,2,5,1]=>[5] [1,0,1,1,0,0,1,1,0,0]=>[4,5,2,3,1]=>[3,5,2,4,1]=>[4,1] [1,0,1,1,0,1,0,0,1,0]=>[5,3,2,4,1]=>[4,3,5,2,1]=>[5] [1,0,1,1,0,1,0,1,0,0]=>[4,3,2,5,1]=>[5,3,4,2,1]=>[3,2] [1,0,1,1,0,1,1,0,0,0]=>[3,4,2,5,1]=>[5,4,3,2,1]=>[2,2,1] [1,0,1,1,1,0,0,0,1,0]=>[5,2,3,4,1]=>[4,5,2,3,1]=>[5] [1,0,1,1,1,0,0,1,0,0]=>[4,2,3,5,1]=>[5,4,2,3,1]=>[3,2] [1,0,1,1,1,0,1,0,0,0]=>[3,2,4,5,1]=>[5,3,2,4,1]=>[2,2,1] [1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>[5,2,3,4,1]=>[2,1,1,1] [1,1,0,0,1,0,1,0,1,0]=>[5,4,3,1,2]=>[3,1,4,5,2]=>[5] [1,1,0,0,1,0,1,1,0,0]=>[4,5,3,1,2]=>[3,1,5,4,2]=>[4,1] [1,1,0,0,1,1,0,0,1,0]=>[5,3,4,1,2]=>[4,1,5,3,2]=>[5] [1,1,0,0,1,1,0,1,0,0]=>[4,3,5,1,2]=>[5,1,4,3,2]=>[3,2] [1,1,0,0,1,1,1,0,0,0]=>[3,4,5,1,2]=>[5,1,3,4,2]=>[3,1,1] [1,1,0,1,0,0,1,0,1,0]=>[5,4,2,1,3]=>[2,4,1,5,3]=>[5] [1,1,0,1,0,0,1,1,0,0]=>[4,5,2,1,3]=>[2,5,1,4,3]=>[4,1] [1,1,0,1,0,1,0,0,1,0]=>[5,3,2,1,4]=>[2,3,5,1,4]=>[5] [1,1,0,1,0,1,0,1,0,0]=>[4,3,2,1,5]=>[2,3,4,1,5]=>[4,1] [1,1,0,1,0,1,1,0,0,0]=>[3,4,2,1,5]=>[2,4,3,1,5]=>[3,1,1] [1,1,0,1,1,0,0,0,1,0]=>[5,2,3,1,4]=>[3,5,2,1,4]=>[5] [1,1,0,1,1,0,0,1,0,0]=>[4,2,3,1,5]=>[3,4,2,1,5]=>[4,1] [1,1,0,1,1,0,1,0,0,0]=>[3,2,4,1,5]=>[4,3,2,1,5]=>[2,2,1] [1,1,0,1,1,1,0,0,0,0]=>[2,3,4,1,5]=>[4,2,3,1,5]=>[2,1,1,1] [1,1,1,0,0,0,1,0,1,0]=>[5,4,1,2,3]=>[4,1,2,5,3]=>[5] [1,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[4,1] [1,1,1,0,0,1,0,0,1,0]=>[5,3,1,2,4]=>[3,1,5,2,4]=>[5] [1,1,1,0,0,1,0,1,0,0]=>[4,3,1,2,5]=>[3,1,4,2,5]=>[4,1] [1,1,1,0,0,1,1,0,0,0]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[3,1,1] [1,1,1,0,1,0,0,0,1,0]=>[5,2,1,3,4]=>[2,5,1,3,4]=>[5] [1,1,1,0,1,0,0,1,0,0]=>[4,2,1,3,5]=>[2,4,1,3,5]=>[4,1] [1,1,1,0,1,0,1,0,0,0]=>[3,2,1,4,5]=>[2,3,1,4,5]=>[3,1,1] [1,1,1,0,1,1,0,0,0,0]=>[2,3,1,4,5]=>[3,2,1,4,5]=>[2,1,1,1] [1,1,1,1,0,0,0,0,1,0]=>[5,1,2,3,4]=>[5,1,2,3,4]=>[5] [1,1,1,1,0,0,0,1,0,0]=>[4,1,2,3,5]=>[4,1,2,3,5]=>[4,1] [1,1,1,1,0,0,1,0,0,0]=>[3,1,2,4,5]=>[3,1,2,4,5]=>[3,1,1] [1,1,1,1,0,1,0,0,0,0]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[2,1,1,1] [1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[1,1,1,1,1] [1,0,1,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6] [1,0,1,0,1,0,1,0,1,1,0,0]=>[5,6,4,3,2,1]=>[2,3,4,6,5,1]=>[5,1] [1,0,1,0,1,0,1,1,0,0,1,0]=>[6,4,5,3,2,1]=>[2,3,5,6,4,1]=>[6] [1,0,1,0,1,0,1,1,0,1,0,0]=>[5,4,6,3,2,1]=>[2,3,6,5,4,1]=>[4,2] [1,0,1,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,2,1]=>[2,3,6,4,5,1]=>[4,1,1] [1,0,1,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,2,1]=>[2,4,5,3,6,1]=>[6] [1,0,1,0,1,1,0,0,1,1,0,0]=>[5,6,3,4,2,1]=>[2,4,6,3,5,1]=>[5,1] [1,0,1,0,1,1,0,1,0,0,1,0]=>[6,4,3,5,2,1]=>[2,5,4,6,3,1]=>[6] [1,0,1,0,1,1,0,1,0,1,0,0]=>[5,4,3,6,2,1]=>[2,6,4,5,3,1]=>[3,3] [1,0,1,0,1,1,0,1,1,0,0,0]=>[4,5,3,6,2,1]=>[2,6,5,4,3,1]=>[3,2,1] [1,0,1,0,1,1,1,0,0,0,1,0]=>[6,3,4,5,2,1]=>[2,5,6,3,4,1]=>[6] [1,0,1,0,1,1,1,0,0,1,0,0]=>[5,3,4,6,2,1]=>[2,6,5,3,4,1]=>[3,3] [1,0,1,0,1,1,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>[2,6,4,3,5,1]=>[3,2,1] [1,0,1,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,2,1]=>[2,6,3,4,5,1]=>[3,1,1,1] [1,0,1,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,3,1]=>[3,4,2,5,6,1]=>[6] [1,0,1,1,0,0,1,0,1,1,0,0]=>[5,6,4,2,3,1]=>[3,4,2,6,5,1]=>[5,1] [1,0,1,1,0,0,1,1,0,0,1,0]=>[6,4,5,2,3,1]=>[3,5,2,6,4,1]=>[6] [1,0,1,1,0,0,1,1,0,1,0,0]=>[5,4,6,2,3,1]=>[3,6,2,5,4,1]=>[4,2] [1,0,1,1,0,0,1,1,1,0,0,0]=>[4,5,6,2,3,1]=>[3,6,2,4,5,1]=>[4,1,1] [1,0,1,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,4,1]=>[4,3,5,2,6,1]=>[6] [1,0,1,1,0,1,0,0,1,1,0,0]=>[5,6,3,2,4,1]=>[4,3,6,2,5,1]=>[5,1] [1,0,1,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,5,1]=>[5,3,4,6,2,1]=>[6] [1,0,1,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,6,1]=>[6,3,4,5,2,1]=>[4,2] [1,0,1,1,0,1,0,1,1,0,0,0]=>[4,5,3,2,6,1]=>[6,3,5,4,2,1]=>[3,2,1] [1,0,1,1,0,1,1,0,0,0,1,0]=>[6,3,4,2,5,1]=>[5,4,6,3,2,1]=>[6] [1,0,1,1,0,1,1,0,0,1,0,0]=>[5,3,4,2,6,1]=>[6,4,5,3,2,1]=>[4,2] [1,0,1,1,0,1,1,0,1,0,0,0]=>[4,3,5,2,6,1]=>[6,5,4,3,2,1]=>[2,2,2] [1,0,1,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,6,1]=>[6,5,3,4,2,1]=>[2,2,1,1] [1,0,1,1,1,0,0,0,1,0,1,0]=>[6,5,2,3,4,1]=>[4,5,2,3,6,1]=>[6] [1,0,1,1,1,0,0,0,1,1,0,0]=>[5,6,2,3,4,1]=>[4,6,2,3,5,1]=>[5,1] [1,0,1,1,1,0,0,1,0,0,1,0]=>[6,4,2,3,5,1]=>[5,4,2,6,3,1]=>[6] [1,0,1,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,6,1]=>[6,4,2,5,3,1]=>[4,2] [1,0,1,1,1,0,0,1,1,0,0,0]=>[4,5,2,3,6,1]=>[6,5,2,4,3,1]=>[3,2,1] [1,0,1,1,1,0,1,0,0,0,1,0]=>[6,3,2,4,5,1]=>[5,3,6,2,4,1]=>[6] [1,0,1,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,6,1]=>[6,3,5,2,4,1]=>[4,2] [1,0,1,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,6,1]=>[6,3,4,2,5,1]=>[3,2,1] [1,0,1,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,6,1]=>[6,4,3,2,5,1]=>[2,2,1,1] [1,0,1,1,1,1,0,0,0,0,1,0]=>[6,2,3,4,5,1]=>[5,6,2,3,4,1]=>[6] [1,0,1,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,6,1]=>[6,5,2,3,4,1]=>[4,2] [1,0,1,1,1,1,0,0,1,0,0,0]=>[4,2,3,5,6,1]=>[6,4,2,3,5,1]=>[3,2,1] [1,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,6,1]=>[6,3,2,4,5,1]=>[2,2,1,1] [1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>[6,2,3,4,5,1]=>[2,1,1,1,1] [1,1,0,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,1,2]=>[3,1,4,5,6,2]=>[6] [1,1,0,0,1,0,1,0,1,1,0,0]=>[5,6,4,3,1,2]=>[3,1,4,6,5,2]=>[5,1] [1,1,0,0,1,0,1,1,0,0,1,0]=>[6,4,5,3,1,2]=>[3,1,5,6,4,2]=>[6] [1,1,0,0,1,0,1,1,0,1,0,0]=>[5,4,6,3,1,2]=>[3,1,6,5,4,2]=>[4,2] [1,1,0,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,1,2]=>[3,1,6,4,5,2]=>[4,1,1] [1,1,0,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,1,2]=>[4,1,5,3,6,2]=>[6] [1,1,0,0,1,1,0,0,1,1,0,0]=>[5,6,3,4,1,2]=>[4,1,6,3,5,2]=>[5,1] [1,1,0,0,1,1,0,1,0,0,1,0]=>[6,4,3,5,1,2]=>[5,1,4,6,3,2]=>[6] [1,1,0,0,1,1,0,1,0,1,0,0]=>[5,4,3,6,1,2]=>[6,1,4,5,3,2]=>[3,3] [1,1,0,0,1,1,0,1,1,0,0,0]=>[4,5,3,6,1,2]=>[6,1,5,4,3,2]=>[3,2,1] [1,1,0,0,1,1,1,0,0,0,1,0]=>[6,3,4,5,1,2]=>[5,1,6,3,4,2]=>[6] [1,1,0,0,1,1,1,0,0,1,0,0]=>[5,3,4,6,1,2]=>[6,1,5,3,4,2]=>[3,3] [1,1,0,0,1,1,1,0,1,0,0,0]=>[4,3,5,6,1,2]=>[6,1,4,3,5,2]=>[3,2,1] [1,1,0,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,1,2]=>[6,1,3,4,5,2]=>[3,1,1,1] [1,1,0,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,1,3]=>[2,4,1,5,6,3]=>[6] [1,1,0,1,0,0,1,0,1,1,0,0]=>[5,6,4,2,1,3]=>[2,4,1,6,5,3]=>[5,1] [1,1,0,1,0,0,1,1,0,0,1,0]=>[6,4,5,2,1,3]=>[2,5,1,6,4,3]=>[6] [1,1,0,1,0,0,1,1,0,1,0,0]=>[5,4,6,2,1,3]=>[2,6,1,5,4,3]=>[4,2] [1,1,0,1,0,0,1,1,1,0,0,0]=>[4,5,6,2,1,3]=>[2,6,1,4,5,3]=>[4,1,1] [1,1,0,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,1,4]=>[2,3,5,1,6,4]=>[6] [1,1,0,1,0,1,0,0,1,1,0,0]=>[5,6,3,2,1,4]=>[2,3,6,1,5,4]=>[5,1] [1,1,0,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,1,5]=>[2,3,4,6,1,5]=>[6] [1,1,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,1,6]=>[2,3,4,5,1,6]=>[5,1] [1,1,0,1,0,1,0,1,1,0,0,0]=>[4,5,3,2,1,6]=>[2,3,5,4,1,6]=>[4,1,1] [1,1,0,1,0,1,1,0,0,0,1,0]=>[6,3,4,2,1,5]=>[2,4,6,3,1,5]=>[6] [1,1,0,1,0,1,1,0,0,1,0,0]=>[5,3,4,2,1,6]=>[2,4,5,3,1,6]=>[5,1] [1,1,0,1,0,1,1,0,1,0,0,0]=>[4,3,5,2,1,6]=>[2,5,4,3,1,6]=>[3,2,1] [1,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,1,6]=>[2,5,3,4,1,6]=>[3,1,1,1] [1,1,0,1,1,0,0,0,1,0,1,0]=>[6,5,2,3,1,4]=>[3,5,2,1,6,4]=>[6] [1,1,0,1,1,0,0,0,1,1,0,0]=>[5,6,2,3,1,4]=>[3,6,2,1,5,4]=>[5,1] [1,1,0,1,1,0,0,1,0,0,1,0]=>[6,4,2,3,1,5]=>[3,4,2,6,1,5]=>[6] [1,1,0,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,1,6]=>[3,4,2,5,1,6]=>[5,1] [1,1,0,1,1,0,0,1,1,0,0,0]=>[4,5,2,3,1,6]=>[3,5,2,4,1,6]=>[4,1,1] [1,1,0,1,1,0,1,0,0,0,1,0]=>[6,3,2,4,1,5]=>[4,3,6,2,1,5]=>[6] [1,1,0,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,1,6]=>[4,3,5,2,1,6]=>[5,1] [1,1,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,1,6]=>[5,3,4,2,1,6]=>[3,2,1] [1,1,0,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,1,6]=>[5,4,3,2,1,6]=>[2,2,1,1] [1,1,0,1,1,1,0,0,0,0,1,0]=>[6,2,3,4,1,5]=>[4,6,2,3,1,5]=>[6] [1,1,0,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,1,6]=>[4,5,2,3,1,6]=>[5,1] [1,1,0,1,1,1,0,0,1,0,0,0]=>[4,2,3,5,1,6]=>[5,4,2,3,1,6]=>[3,2,1] [1,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,1,6]=>[5,3,2,4,1,6]=>[2,2,1,1] [1,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,1,6]=>[5,2,3,4,1,6]=>[2,1,1,1,1] [1,1,1,0,0,0,1,0,1,0,1,0]=>[6,5,4,1,2,3]=>[4,1,2,5,6,3]=>[6] [1,1,1,0,0,0,1,0,1,1,0,0]=>[5,6,4,1,2,3]=>[4,1,2,6,5,3]=>[5,1] [1,1,1,0,0,0,1,1,0,0,1,0]=>[6,4,5,1,2,3]=>[5,1,2,6,4,3]=>[6] [1,1,1,0,0,0,1,1,0,1,0,0]=>[5,4,6,1,2,3]=>[6,1,2,5,4,3]=>[4,2] [1,1,1,0,0,0,1,1,1,0,0,0]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>[4,1,1] [1,1,1,0,0,1,0,0,1,0,1,0]=>[6,5,3,1,2,4]=>[3,1,5,2,6,4]=>[6] [1,1,1,0,0,1,0,0,1,1,0,0]=>[5,6,3,1,2,4]=>[3,1,6,2,5,4]=>[5,1] [1,1,1,0,0,1,0,1,0,0,1,0]=>[6,4,3,1,2,5]=>[3,1,4,6,2,5]=>[6] [1,1,1,0,0,1,0,1,0,1,0,0]=>[5,4,3,1,2,6]=>[3,1,4,5,2,6]=>[5,1] [1,1,1,0,0,1,0,1,1,0,0,0]=>[4,5,3,1,2,6]=>[3,1,5,4,2,6]=>[4,1,1] [1,1,1,0,0,1,1,0,0,0,1,0]=>[6,3,4,1,2,5]=>[4,1,6,3,2,5]=>[6] [1,1,1,0,0,1,1,0,0,1,0,0]=>[5,3,4,1,2,6]=>[4,1,5,3,2,6]=>[5,1] [1,1,1,0,0,1,1,0,1,0,0,0]=>[4,3,5,1,2,6]=>[5,1,4,3,2,6]=>[3,2,1] [1,1,1,0,0,1,1,1,0,0,0,0]=>[3,4,5,1,2,6]=>[5,1,3,4,2,6]=>[3,1,1,1] [1,1,1,0,1,0,0,0,1,0,1,0]=>[6,5,2,1,3,4]=>[2,5,1,3,6,4]=>[6] [1,1,1,0,1,0,0,0,1,1,0,0]=>[5,6,2,1,3,4]=>[2,6,1,3,5,4]=>[5,1] [1,1,1,0,1,0,0,1,0,0,1,0]=>[6,4,2,1,3,5]=>[2,4,1,6,3,5]=>[6] [1,1,1,0,1,0,0,1,0,1,0,0]=>[5,4,2,1,3,6]=>[2,4,1,5,3,6]=>[5,1] [1,1,1,0,1,0,0,1,1,0,0,0]=>[4,5,2,1,3,6]=>[2,5,1,4,3,6]=>[4,1,1] [1,1,1,0,1,0,1,0,0,0,1,0]=>[6,3,2,1,4,5]=>[2,3,6,1,4,5]=>[6] [1,1,1,0,1,0,1,0,0,1,0,0]=>[5,3,2,1,4,6]=>[2,3,5,1,4,6]=>[5,1] [1,1,1,0,1,0,1,0,1,0,0,0]=>[4,3,2,1,5,6]=>[2,3,4,1,5,6]=>[4,1,1] [1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,2,1,5,6]=>[2,4,3,1,5,6]=>[3,1,1,1] [1,1,1,0,1,1,0,0,0,0,1,0]=>[6,2,3,1,4,5]=>[3,6,2,1,4,5]=>[6] [1,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,3,1,4,6]=>[3,5,2,1,4,6]=>[5,1] [1,1,1,0,1,1,0,0,1,0,0,0]=>[4,2,3,1,5,6]=>[3,4,2,1,5,6]=>[4,1,1] [1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,4,1,5,6]=>[4,3,2,1,5,6]=>[2,2,1,1] [1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,4,1,5,6]=>[4,2,3,1,5,6]=>[2,1,1,1,1] [1,1,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,2,3,4]=>[5,1,2,3,6,4]=>[6] [1,1,1,1,0,0,0,0,1,1,0,0]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>[5,1] [1,1,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,2,3,5]=>[4,1,2,6,3,5]=>[6] [1,1,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,2,3,6]=>[4,1,2,5,3,6]=>[5,1] [1,1,1,1,0,0,0,1,1,0,0,0]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>[4,1,1] [1,1,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,2,4,5]=>[3,1,6,2,4,5]=>[6] [1,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,2,4,6]=>[3,1,5,2,4,6]=>[5,1] [1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,2,5,6]=>[3,1,4,2,5,6]=>[4,1,1] [1,1,1,1,0,0,1,1,0,0,0,0]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>[3,1,1,1] [1,1,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,3,4,5]=>[2,6,1,3,4,5]=>[6] [1,1,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,3,4,6]=>[2,5,1,3,4,6]=>[5,1] [1,1,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,3,5,6]=>[2,4,1,3,5,6]=>[4,1,1] [1,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,4,5,6]=>[2,3,1,4,5,6]=>[3,1,1,1] [1,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,1,4,5,6]=>[3,2,1,4,5,6]=>[2,1,1,1,1] [1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>[6] [1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>[5,1] [1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>[4,1,1] [1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>[3,1,1,1] [1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[2,1,1,1,1] [1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[1,1,1,1,1,1] [1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7] [1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,3,2,1]=>[2,3,4,5,7,6,1]=>[6,1] [1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,3,2,1]=>[2,3,4,6,7,5,1]=>[7] [1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,3,2,1]=>[2,3,4,7,6,5,1]=>[5,2] [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,3,2,1]=>[2,3,4,7,5,6,1]=>[5,1,1] [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,3,2,1]=>[2,3,5,6,4,7,1]=>[7] [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,3,2,1]=>[2,3,5,7,4,6,1]=>[6,1] [1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,3,2,1]=>[2,3,6,5,7,4,1]=>[7] [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,3,2,1]=>[2,3,7,5,6,4,1]=>[4,3] [1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,3,2,1]=>[2,3,7,6,5,4,1]=>[4,2,1] [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,3,2,1]=>[2,3,6,7,4,5,1]=>[7] [1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,3,2,1]=>[2,3,7,6,4,5,1]=>[4,3] [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,3,2,1]=>[2,3,7,5,4,6,1]=>[4,2,1] [1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[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]=>[7,6,5,3,4,2,1]=>[2,4,5,3,6,7,1]=>[7] [1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,4,2,1]=>[2,4,5,3,7,6,1]=>[6,1] [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,4,2,1]=>[2,4,6,3,7,5,1]=>[7] [1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,4,2,1]=>[2,4,7,3,6,5,1]=>[5,2] [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,4,2,1]=>[2,4,7,3,5,6,1]=>[5,1,1] [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,5,2,1]=>[2,5,4,6,3,7,1]=>[7] [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,5,2,1]=>[2,5,4,7,3,6,1]=>[6,1] [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,6,2,1]=>[2,6,4,5,7,3,1]=>[7] [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,7,2,1]=>[2,7,4,5,6,3,1]=>[4,3] [1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,7,2,1]=>[2,7,4,6,5,3,1]=>[3,3,1] [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,6,2,1]=>[2,6,5,7,4,3,1]=>[7] [1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,7,2,1]=>[2,7,5,6,4,3,1]=>[4,3] [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,7,2,1]=>[2,7,6,5,4,3,1]=>[3,2,2] [1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,7,2,1]=>[2,7,6,4,5,3,1]=>[3,2,1,1] [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,5,2,1]=>[2,5,6,3,4,7,1]=>[7] [1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,5,2,1]=>[2,5,7,3,4,6,1]=>[6,1] [1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,6,2,1]=>[2,6,5,3,7,4,1]=>[7] [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,7,2,1]=>[2,7,5,3,6,4,1]=>[4,3] [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,7,2,1]=>[2,7,6,3,5,4,1]=>[3,3,1] [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,6,2,1]=>[2,6,4,7,3,5,1]=>[7] [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,7,2,1]=>[2,7,4,6,3,5,1]=>[4,3] [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,2,1]=>[2,7,4,5,3,6,1]=>[3,3,1] [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,7,2,1]=>[2,7,5,4,3,6,1]=>[3,2,1,1] [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,6,2,1]=>[2,6,7,3,4,5,1]=>[7] [1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,7,2,1]=>[2,7,6,3,4,5,1]=>[4,3] [1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,7,2,1]=>[2,7,5,3,4,6,1]=>[3,3,1] [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,7,2,1]=>[2,7,4,3,5,6,1]=>[3,2,1,1] [1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,2,1]=>[2,7,3,4,5,6,1]=>[3,1,1,1,1] [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,3,1]=>[3,4,2,5,6,7,1]=>[7] [1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,2,3,1]=>[3,4,2,5,7,6,1]=>[6,1] [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,2,3,1]=>[3,4,2,6,7,5,1]=>[7] [1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,2,3,1]=>[3,4,2,7,6,5,1]=>[5,2] [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,2,3,1]=>[3,4,2,7,5,6,1]=>[5,1,1] [1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,2,3,1]=>[3,5,2,6,4,7,1]=>[7] [1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,2,3,1]=>[3,5,2,7,4,6,1]=>[6,1] [1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,2,3,1]=>[3,6,2,5,7,4,1]=>[7] [1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,2,3,1]=>[3,7,2,5,6,4,1]=>[4,3] [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,2,3,1]=>[3,7,2,6,5,4,1]=>[4,2,1] [1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,2,3,1]=>[3,6,2,7,4,5,1]=>[7] [1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,2,3,1]=>[3,7,2,6,4,5,1]=>[4,3] [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,2,3,1]=>[3,7,2,5,4,6,1]=>[4,2,1] [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,2,3,1]=>[3,7,2,4,5,6,1]=>[4,1,1,1] [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,4,1]=>[4,3,5,2,6,7,1]=>[7] [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,2,4,1]=>[4,3,5,2,7,6,1]=>[6,1] [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,2,4,1]=>[4,3,6,2,7,5,1]=>[7] [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,2,4,1]=>[4,3,7,2,6,5,1]=>[5,2] [1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,2,4,1]=>[4,3,7,2,5,6,1]=>[5,1,1] [1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,5,1]=>[5,3,4,6,2,7,1]=>[7] [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,2,5,1]=>[5,3,4,7,2,6,1]=>[6,1] [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,6,1]=>[6,3,4,5,7,2,1]=>[7] [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,7,1]=>[7,3,4,5,6,2,1]=>[5,2] [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,2,7,1]=>[7,3,4,6,5,2,1]=>[4,2,1] [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,2,6,1]=>[6,3,5,7,4,2,1]=>[7] [1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,2,7,1]=>[7,3,5,6,4,2,1]=>[5,2] [1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,2,7,1]=>[7,3,6,5,4,2,1]=>[3,2,2] [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,2,7,1]=>[7,3,6,4,5,2,1]=>[3,2,1,1] [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,2,5,1]=>[5,4,6,3,2,7,1]=>[7] [1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,2,5,1]=>[5,4,7,3,2,6,1]=>[6,1] [1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,2,6,1]=>[6,4,5,3,7,2,1]=>[7] [1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,2,7,1]=>[7,4,5,3,6,2,1]=>[5,2] [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,2,7,1]=>[7,4,6,3,5,2,1]=>[4,2,1] [1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,2,6,1]=>[6,5,4,7,3,2,1]=>[7] [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,2,7,1]=>[7,5,4,6,3,2,1]=>[5,2] [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,2,7,1]=>[7,6,4,5,3,2,1]=>[3,2,2] [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,2,7,1]=>[7,6,5,4,3,2,1]=>[2,2,2,1] [1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,2,6,1]=>[6,5,7,3,4,2,1]=>[7] [1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,2,7,1]=>[7,5,6,3,4,2,1]=>[5,2] [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,2,7,1]=>[7,6,5,3,4,2,1]=>[3,2,2] [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,2,7,1]=>[7,6,4,3,5,2,1]=>[2,2,2,1] [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,2,7,1]=>[7,6,3,4,5,2,1]=>[2,2,1,1,1] [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,3,4,1]=>[4,5,2,3,6,7,1]=>[7] [1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,3,4,1]=>[4,5,2,3,7,6,1]=>[6,1] [1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,3,4,1]=>[4,6,2,3,7,5,1]=>[7] [1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,3,4,1]=>[4,7,2,3,6,5,1]=>[5,2] [1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,3,4,1]=>[4,7,2,3,5,6,1]=>[5,1,1] [1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,3,5,1]=>[5,4,2,6,3,7,1]=>[7] [1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,3,5,1]=>[5,4,2,7,3,6,1]=>[6,1] [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,3,6,1]=>[6,4,2,5,7,3,1]=>[7] [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,3,7,1]=>[7,4,2,5,6,3,1]=>[5,2] [1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,3,7,1]=>[7,4,2,6,5,3,1]=>[4,2,1] [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,3,6,1]=>[6,5,2,7,4,3,1]=>[7] [1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,3,7,1]=>[7,5,2,6,4,3,1]=>[5,2] [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,3,7,1]=>[7,6,2,5,4,3,1]=>[3,2,2] [1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,3,7,1]=>[7,6,2,4,5,3,1]=>[3,2,1,1] [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,4,5,1]=>[5,3,6,2,4,7,1]=>[7] [1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,4,5,1]=>[5,3,7,2,4,6,1]=>[6,1] [1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,4,6,1]=>[6,3,5,2,7,4,1]=>[7] [1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,4,7,1]=>[7,3,5,2,6,4,1]=>[5,2] [1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,4,7,1]=>[7,3,6,2,5,4,1]=>[4,2,1] [1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,5,6,1]=>[6,3,4,7,2,5,1]=>[7] [1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,5,7,1]=>[7,3,4,6,2,5,1]=>[5,2] [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,6,7,1]=>[7,3,4,5,2,6,1]=>[4,2,1] [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,6,7,1]=>[7,3,5,4,2,6,1]=>[3,2,1,1] [1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,5,6,1]=>[6,4,7,3,2,5,1]=>[7] [1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,5,7,1]=>[7,4,6,3,2,5,1]=>[5,2] [1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,6,7,1]=>[7,4,5,3,2,6,1]=>[4,2,1] [1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,6,7,1]=>[7,5,4,3,2,6,1]=>[2,2,2,1] [1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,6,7,1]=>[7,5,3,4,2,6,1]=>[2,2,1,1,1] [1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,4,5,1]=>[5,6,2,3,4,7,1]=>[7] [1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,4,5,1]=>[5,7,2,3,4,6,1]=>[6,1] [1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,4,6,1]=>[6,5,2,3,7,4,1]=>[7] [1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,4,7,1]=>[7,5,2,3,6,4,1]=>[5,2] [1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,4,7,1]=>[7,6,2,3,5,4,1]=>[4,2,1] [1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,5,6,1]=>[6,4,2,7,3,5,1]=>[7] [1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,5,7,1]=>[7,4,2,6,3,5,1]=>[5,2] [1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,6,7,1]=>[7,4,2,5,3,6,1]=>[4,2,1] [1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,6,7,1]=>[7,5,2,4,3,6,1]=>[3,2,1,1] [1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,5,6,1]=>[6,3,7,2,4,5,1]=>[7] [1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,5,7,1]=>[7,3,6,2,4,5,1]=>[5,2] [1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,6,7,1]=>[7,3,5,2,4,6,1]=>[4,2,1] [1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,6,7,1]=>[7,3,4,2,5,6,1]=>[3,2,1,1] [1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,6,7,1]=>[7,4,3,2,5,6,1]=>[2,2,1,1,1] [1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,5,6,1]=>[6,7,2,3,4,5,1]=>[7] [1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,5,7,1]=>[7,6,2,3,4,5,1]=>[5,2] [1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,6,7,1]=>[7,5,2,3,4,6,1]=>[4,2,1] [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,6,7,1]=>[7,4,2,3,5,6,1]=>[3,2,1,1] [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,6,7,1]=>[7,3,2,4,5,6,1]=>[2,2,1,1,1] [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1]=>[7,2,3,4,5,6,1]=>[2,1,1,1,1,1] [1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,1,2]=>[3,1,4,5,6,7,2]=>[7] [1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,3,1,2]=>[3,1,4,5,7,6,2]=>[6,1] [1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,3,1,2]=>[3,1,4,6,7,5,2]=>[7] [1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,3,1,2]=>[3,1,4,7,6,5,2]=>[5,2] [1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,3,1,2]=>[3,1,4,7,5,6,2]=>[5,1,1] [1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,3,1,2]=>[3,1,5,6,4,7,2]=>[7] [1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,3,1,2]=>[3,1,5,7,4,6,2]=>[6,1] [1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,3,1,2]=>[3,1,6,5,7,4,2]=>[7] [1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,3,1,2]=>[3,1,7,5,6,4,2]=>[4,3] [1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,3,1,2]=>[3,1,7,6,5,4,2]=>[4,2,1] [1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,3,1,2]=>[3,1,6,7,4,5,2]=>[7] [1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,3,1,2]=>[3,1,7,6,4,5,2]=>[4,3] [1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,3,1,2]=>[3,1,7,5,4,6,2]=>[4,2,1] [1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,3,1,2]=>[3,1,7,4,5,6,2]=>[4,1,1,1] [1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,4,1,2]=>[4,1,5,3,6,7,2]=>[7] [1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,4,1,2]=>[4,1,5,3,7,6,2]=>[6,1] [1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,4,1,2]=>[4,1,6,3,7,5,2]=>[7] [1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,4,1,2]=>[4,1,7,3,6,5,2]=>[5,2] [1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,4,1,2]=>[4,1,7,3,5,6,2]=>[5,1,1] [1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,5,1,2]=>[5,1,4,6,3,7,2]=>[7] [1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,5,1,2]=>[5,1,4,7,3,6,2]=>[6,1] [1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,6,1,2]=>[6,1,4,5,7,3,2]=>[7] [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,7,1,2]=>[7,1,4,5,6,3,2]=>[4,3] [1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,7,1,2]=>[7,1,4,6,5,3,2]=>[3,3,1] [1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,6,1,2]=>[6,1,5,7,4,3,2]=>[7] [1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,7,1,2]=>[7,1,5,6,4,3,2]=>[4,3] [1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,7,1,2]=>[7,1,6,5,4,3,2]=>[3,2,2] [1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,7,1,2]=>[7,1,6,4,5,3,2]=>[3,2,1,1] [1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,5,1,2]=>[5,1,6,3,4,7,2]=>[7] [1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,5,1,2]=>[5,1,7,3,4,6,2]=>[6,1] [1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,6,1,2]=>[6,1,5,3,7,4,2]=>[7] [1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,7,1,2]=>[7,1,5,3,6,4,2]=>[4,3] [1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,7,1,2]=>[7,1,6,3,5,4,2]=>[3,3,1] [1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,6,1,2]=>[6,1,4,7,3,5,2]=>[7] [1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,7,1,2]=>[7,1,4,6,3,5,2]=>[4,3] [1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,1,2]=>[7,1,4,5,3,6,2]=>[3,3,1] [1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,7,1,2]=>[7,1,5,4,3,6,2]=>[3,2,1,1] [1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,6,1,2]=>[6,1,7,3,4,5,2]=>[7] [1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,7,1,2]=>[7,1,6,3,4,5,2]=>[4,3] [1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,7,1,2]=>[7,1,5,3,4,6,2]=>[3,3,1] [1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,7,1,2]=>[7,1,4,3,5,6,2]=>[3,2,1,1] [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,1,2]=>[7,1,3,4,5,6,2]=>[3,1,1,1,1] [1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,1,3]=>[2,4,1,5,6,7,3]=>[7] [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,2,1,3]=>[2,4,1,5,7,6,3]=>[6,1] [1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,2,1,3]=>[2,4,1,6,7,5,3]=>[7] [1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,2,1,3]=>[2,4,1,7,6,5,3]=>[5,2] [1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,2,1,3]=>[2,4,1,7,5,6,3]=>[5,1,1] [1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,2,1,3]=>[2,5,1,6,4,7,3]=>[7] [1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,2,1,3]=>[2,5,1,7,4,6,3]=>[6,1] [1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,2,1,3]=>[2,6,1,5,7,4,3]=>[7] [1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,2,1,3]=>[2,7,1,5,6,4,3]=>[4,3] [1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,2,1,3]=>[2,7,1,6,5,4,3]=>[4,2,1] [1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,2,1,3]=>[2,6,1,7,4,5,3]=>[7] [1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,2,1,3]=>[2,7,1,6,4,5,3]=>[4,3] [1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,2,1,3]=>[2,7,1,5,4,6,3]=>[4,2,1] [1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,2,1,3]=>[2,7,1,4,5,6,3]=>[4,1,1,1] [1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,1,4]=>[2,3,5,1,6,7,4]=>[7] [1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,2,1,4]=>[2,3,5,1,7,6,4]=>[6,1] [1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,2,1,4]=>[2,3,6,1,7,5,4]=>[7] [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,2,1,4]=>[2,3,7,1,6,5,4]=>[5,2] [1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,2,1,4]=>[2,3,7,1,5,6,4]=>[5,1,1] [1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,1,5]=>[2,3,4,6,1,7,5]=>[7] [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,2,1,5]=>[2,3,4,7,1,6,5]=>[6,1] [1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,1,6]=>[2,3,4,5,7,1,6]=>[7] [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,1] [1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,2,1,7]=>[2,3,4,6,5,1,7]=>[5,1,1] [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,2,1,6]=>[2,3,5,7,4,1,6]=>[7] [1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,2,1,7]=>[2,3,5,6,4,1,7]=>[6,1] [1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,2,1,7]=>[2,3,6,5,4,1,7]=>[4,2,1] [1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,2,1,7]=>[2,3,6,4,5,1,7]=>[4,1,1,1] [1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,2,1,5]=>[2,4,6,3,1,7,5]=>[7] [1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,2,1,5]=>[2,4,7,3,1,6,5]=>[6,1] [1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,2,1,6]=>[2,4,5,3,7,1,6]=>[7] [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,2,1,7]=>[2,4,5,3,6,1,7]=>[6,1] [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,2,1,7]=>[2,4,6,3,5,1,7]=>[5,1,1] [1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,2,1,6]=>[2,5,4,7,3,1,6]=>[7] [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,2,1,7]=>[2,5,4,6,3,1,7]=>[6,1] [1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,2,1,7]=>[2,6,4,5,3,1,7]=>[3,3,1] [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,2,1,7]=>[2,6,5,4,3,1,7]=>[3,2,1,1] [1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,2,1,6]=>[2,5,7,3,4,1,6]=>[7] [1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,2,1,7]=>[2,5,6,3,4,1,7]=>[6,1] [1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,2,1,7]=>[2,6,5,3,4,1,7]=>[3,3,1] [1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,2,1,7]=>[2,6,4,3,5,1,7]=>[3,2,1,1] [1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,2,1,7]=>[2,6,3,4,5,1,7]=>[3,1,1,1,1] [1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,3,1,4]=>[3,5,2,1,6,7,4]=>[7] [1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,3,1,4]=>[3,5,2,1,7,6,4]=>[6,1] [1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,3,1,4]=>[3,6,2,1,7,5,4]=>[7] [1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,3,1,4]=>[3,7,2,1,6,5,4]=>[5,2] [1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,3,1,4]=>[3,7,2,1,5,6,4]=>[5,1,1] [1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,3,1,5]=>[3,4,2,6,1,7,5]=>[7] [1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,3,1,5]=>[3,4,2,7,1,6,5]=>[6,1] [1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,3,1,6]=>[3,4,2,5,7,1,6]=>[7] [1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,3,1,7]=>[3,4,2,5,6,1,7]=>[6,1] [1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,3,1,7]=>[3,4,2,6,5,1,7]=>[5,1,1] [1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,3,1,6]=>[3,5,2,7,4,1,6]=>[7] [1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,3,1,7]=>[3,5,2,6,4,1,7]=>[6,1] [1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,3,1,7]=>[3,6,2,5,4,1,7]=>[4,2,1] [1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,3,1,7]=>[3,6,2,4,5,1,7]=>[4,1,1,1] [1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,4,1,5]=>[4,3,6,2,1,7,5]=>[7] [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,4,1,5]=>[4,3,7,2,1,6,5]=>[6,1] [1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,4,1,6]=>[4,3,5,2,7,1,6]=>[7] [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,4,1,7]=>[4,3,5,2,6,1,7]=>[6,1] [1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,4,1,7]=>[4,3,6,2,5,1,7]=>[5,1,1] [1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,5,1,6]=>[5,3,4,7,2,1,6]=>[7] [1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,5,1,7]=>[5,3,4,6,2,1,7]=>[6,1] [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,6,1,7]=>[6,3,4,5,2,1,7]=>[4,2,1] [1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,6,1,7]=>[6,3,5,4,2,1,7]=>[3,2,1,1] [1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,5,1,6]=>[5,4,7,3,2,1,6]=>[7] [1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,5,1,7]=>[5,4,6,3,2,1,7]=>[6,1] [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,6,1,7]=>[6,4,5,3,2,1,7]=>[4,2,1] [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,6,1,7]=>[6,5,4,3,2,1,7]=>[2,2,2,1] [1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,6,1,7]=>[6,5,3,4,2,1,7]=>[2,2,1,1,1] [1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,4,1,5]=>[4,6,2,3,1,7,5]=>[7] [1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,4,1,5]=>[4,7,2,3,1,6,5]=>[6,1] [1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,4,1,6]=>[4,5,2,3,7,1,6]=>[7] [1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,4,1,7]=>[4,5,2,3,6,1,7]=>[6,1] [1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,4,1,7]=>[4,6,2,3,5,1,7]=>[5,1,1] [1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,5,1,6]=>[5,4,2,7,3,1,6]=>[7] [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,5,1,7]=>[5,4,2,6,3,1,7]=>[6,1] [1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,6,1,7]=>[6,4,2,5,3,1,7]=>[4,2,1] [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,6,1,7]=>[6,5,2,4,3,1,7]=>[3,2,1,1] [1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,5,1,6]=>[5,3,7,2,4,1,6]=>[7] [1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,5,1,7]=>[5,3,6,2,4,1,7]=>[6,1] [1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,6,1,7]=>[6,3,5,2,4,1,7]=>[4,2,1] [1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,6,1,7]=>[6,3,4,2,5,1,7]=>[3,2,1,1] [1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,6,1,7]=>[6,4,3,2,5,1,7]=>[2,2,1,1,1] [1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,5,1,6]=>[5,7,2,3,4,1,6]=>[7] [1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,5,1,7]=>[5,6,2,3,4,1,7]=>[6,1] [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,6,1,7]=>[6,5,2,3,4,1,7]=>[4,2,1] [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,6,1,7]=>[6,4,2,3,5,1,7]=>[3,2,1,1] [1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,6,1,7]=>[6,3,2,4,5,1,7]=>[2,2,1,1,1] [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,1,7]=>[6,2,3,4,5,1,7]=>[2,1,1,1,1,1] [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,1,2,3]=>[4,1,2,5,6,7,3]=>[7] [1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,1,2,3]=>[4,1,2,5,7,6,3]=>[6,1] [1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,1,2,3]=>[4,1,2,6,7,5,3]=>[7] [1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,1,2,3]=>[4,1,2,7,6,5,3]=>[5,2] [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,1,2,3]=>[4,1,2,7,5,6,3]=>[5,1,1] [1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,1,2,3]=>[5,1,2,6,4,7,3]=>[7] [1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,1,2,3]=>[5,1,2,7,4,6,3]=>[6,1] [1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,1,2,3]=>[6,1,2,5,7,4,3]=>[7] [1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,1,2,3]=>[7,1,2,5,6,4,3]=>[4,3] [1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,1,2,3]=>[7,1,2,6,5,4,3]=>[4,2,1] [1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,1,2,3]=>[6,1,2,7,4,5,3]=>[7] [1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,1,2,3]=>[7,1,2,6,4,5,3]=>[4,3] [1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,1,2,3]=>[7,1,2,5,4,6,3]=>[4,2,1] [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,1,2,3]=>[7,1,2,4,5,6,3]=>[4,1,1,1] [1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,1,2,4]=>[3,1,5,2,6,7,4]=>[7] [1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,1,2,4]=>[3,1,5,2,7,6,4]=>[6,1] [1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,1,2,4]=>[3,1,6,2,7,5,4]=>[7] [1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,1,2,4]=>[3,1,7,2,6,5,4]=>[5,2] [1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,1,2,4]=>[3,1,7,2,5,6,4]=>[5,1,1] [1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,1,2,5]=>[3,1,4,6,2,7,5]=>[7] [1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,1,2,5]=>[3,1,4,7,2,6,5]=>[6,1] [1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,1,2,6]=>[3,1,4,5,7,2,6]=>[7] [1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,1,2,7]=>[3,1,4,5,6,2,7]=>[6,1] [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,1,2,7]=>[3,1,4,6,5,2,7]=>[5,1,1] [1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,1,2,6]=>[3,1,5,7,4,2,6]=>[7] [1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,1,2,7]=>[3,1,5,6,4,2,7]=>[6,1] [1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,1,2,7]=>[3,1,6,5,4,2,7]=>[4,2,1] [1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,1,2,7]=>[3,1,6,4,5,2,7]=>[4,1,1,1] [1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,1,2,5]=>[4,1,6,3,2,7,5]=>[7] [1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,1,2,5]=>[4,1,7,3,2,6,5]=>[6,1] [1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,1,2,6]=>[4,1,5,3,7,2,6]=>[7] [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,1,2,7]=>[4,1,5,3,6,2,7]=>[6,1] [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,1,2,7]=>[4,1,6,3,5,2,7]=>[5,1,1] [1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,1,2,6]=>[5,1,4,7,3,2,6]=>[7] [1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,1,2,7]=>[5,1,4,6,3,2,7]=>[6,1] [1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,1,2,7]=>[6,1,4,5,3,2,7]=>[3,3,1] [1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,1,2,7]=>[6,1,5,4,3,2,7]=>[3,2,1,1] [1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,1,2,6]=>[5,1,7,3,4,2,6]=>[7] [1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,1,2,7]=>[5,1,6,3,4,2,7]=>[6,1] [1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,1,2,7]=>[6,1,5,3,4,2,7]=>[3,3,1] [1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,1,2,7]=>[6,1,4,3,5,2,7]=>[3,2,1,1] [1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,1,2,7]=>[6,1,3,4,5,2,7]=>[3,1,1,1,1] [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,1,3,4]=>[2,5,1,3,6,7,4]=>[7] [1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,1,3,4]=>[2,5,1,3,7,6,4]=>[6,1] [1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,1,3,4]=>[2,6,1,3,7,5,4]=>[7] [1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,1,3,4]=>[2,7,1,3,6,5,4]=>[5,2] [1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,1,3,4]=>[2,7,1,3,5,6,4]=>[5,1,1] [1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,1,3,5]=>[2,4,1,6,3,7,5]=>[7] [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,1,3,5]=>[2,4,1,7,3,6,5]=>[6,1] [1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,1,3,6]=>[2,4,1,5,7,3,6]=>[7] [1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,1,3,7]=>[2,4,1,5,6,3,7]=>[6,1] [1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,1,3,7]=>[2,4,1,6,5,3,7]=>[5,1,1] [1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,1,3,6]=>[2,5,1,7,4,3,6]=>[7] [1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,1,3,7]=>[2,5,1,6,4,3,7]=>[6,1] [1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,1,3,7]=>[2,6,1,5,4,3,7]=>[4,2,1] [1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,1,3,7]=>[2,6,1,4,5,3,7]=>[4,1,1,1] [1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,1,4,5]=>[2,3,6,1,4,7,5]=>[7] [1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,1,4,5]=>[2,3,7,1,4,6,5]=>[6,1] [1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,1,4,6]=>[2,3,5,1,7,4,6]=>[7] [1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,1,4,7]=>[2,3,5,1,6,4,7]=>[6,1] [1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,1,4,7]=>[2,3,6,1,5,4,7]=>[5,1,1] [1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,1,5,6]=>[2,3,4,7,1,5,6]=>[7] [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,1,5,7]=>[2,3,4,6,1,5,7]=>[6,1] [1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,1,6,7]=>[2,3,4,5,1,6,7]=>[5,1,1] [1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,1,6,7]=>[2,3,5,4,1,6,7]=>[4,1,1,1] [1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,1,5,6]=>[2,4,7,3,1,5,6]=>[7] [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,1,5,7]=>[2,4,6,3,1,5,7]=>[6,1] [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,1,6,7]=>[2,4,5,3,1,6,7]=>[5,1,1] [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,1,6,7]=>[2,5,4,3,1,6,7]=>[3,2,1,1] [1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,1,6,7]=>[2,5,3,4,1,6,7]=>[3,1,1,1,1] [1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,1,4,5]=>[3,6,2,1,4,7,5]=>[7] [1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,1,4,5]=>[3,7,2,1,4,6,5]=>[6,1] [1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,1,4,6]=>[3,5,2,1,7,4,6]=>[7] [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,1,4,7]=>[3,5,2,1,6,4,7]=>[6,1] [1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,1,4,7]=>[3,6,2,1,5,4,7]=>[5,1,1] [1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,1,5,6]=>[3,4,2,7,1,5,6]=>[7] [1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,1,5,7]=>[3,4,2,6,1,5,7]=>[6,1] [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,1,6,7]=>[3,4,2,5,1,6,7]=>[5,1,1] [1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,1,6,7]=>[3,5,2,4,1,6,7]=>[4,1,1,1] [1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,1,5,6]=>[4,3,7,2,1,5,6]=>[7] [1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,1,5,7]=>[4,3,6,2,1,5,7]=>[6,1] [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,1,6,7]=>[4,3,5,2,1,6,7]=>[5,1,1] [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,1,6,7]=>[5,3,4,2,1,6,7]=>[3,2,1,1] [1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,1,6,7]=>[5,4,3,2,1,6,7]=>[2,2,1,1,1] [1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,1,5,6]=>[4,7,2,3,1,5,6]=>[7] [1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,1,5,7]=>[4,6,2,3,1,5,7]=>[6,1] [1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,1,6,7]=>[4,5,2,3,1,6,7]=>[5,1,1] [1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,1,6,7]=>[5,4,2,3,1,6,7]=>[3,2,1,1] [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,1,6,7]=>[5,3,2,4,1,6,7]=>[2,2,1,1,1] [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,1,6,7]=>[5,2,3,4,1,6,7]=>[2,1,1,1,1,1] [1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[7,6,5,1,2,3,4]=>[5,1,2,3,6,7,4]=>[7] [1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[6,7,5,1,2,3,4]=>[5,1,2,3,7,6,4]=>[6,1] [1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[7,5,6,1,2,3,4]=>[6,1,2,3,7,5,4]=>[7] [1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[6,5,7,1,2,3,4]=>[7,1,2,3,6,5,4]=>[5,2] [1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,6,7,1,2,3,4]=>[7,1,2,3,5,6,4]=>[5,1,1] [1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[7,6,4,1,2,3,5]=>[4,1,2,6,3,7,5]=>[7] [1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[6,7,4,1,2,3,5]=>[4,1,2,7,3,6,5]=>[6,1] [1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[7,5,4,1,2,3,6]=>[4,1,2,5,7,3,6]=>[7] [1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1,2,3,7]=>[4,1,2,5,6,3,7]=>[6,1] [1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[5,6,4,1,2,3,7]=>[4,1,2,6,5,3,7]=>[5,1,1] [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,5,1,2,3,6]=>[5,1,2,7,4,3,6]=>[7] [1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,5,1,2,3,7]=>[5,1,2,6,4,3,7]=>[6,1] [1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,6,1,2,3,7]=>[6,1,2,5,4,3,7]=>[4,2,1] [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,5,6,1,2,3,7]=>[6,1,2,4,5,3,7]=>[4,1,1,1] [1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[7,6,3,1,2,4,5]=>[3,1,6,2,4,7,5]=>[7] [1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[6,7,3,1,2,4,5]=>[3,1,7,2,4,6,5]=>[6,1] [1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[7,5,3,1,2,4,6]=>[3,1,5,2,7,4,6]=>[7] [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[6,5,3,1,2,4,7]=>[3,1,5,2,6,4,7]=>[6,1] [1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,6,3,1,2,4,7]=>[3,1,6,2,5,4,7]=>[5,1,1] [1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[7,4,3,1,2,5,6]=>[3,1,4,7,2,5,6]=>[7] [1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1,2,5,7]=>[3,1,4,6,2,5,7]=>[6,1] [1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1,2,6,7]=>[3,1,4,5,2,6,7]=>[5,1,1] [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,5,3,1,2,6,7]=>[3,1,5,4,2,6,7]=>[4,1,1,1] [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,4,1,2,5,6]=>[4,1,7,3,2,5,6]=>[7] [1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,4,1,2,5,7]=>[4,1,6,3,2,5,7]=>[6,1] [1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,4,1,2,6,7]=>[4,1,5,3,2,6,7]=>[5,1,1] [1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,5,1,2,6,7]=>[5,1,4,3,2,6,7]=>[3,2,1,1] [1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,4,5,1,2,6,7]=>[5,1,3,4,2,6,7]=>[3,1,1,1,1] [1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[7,6,2,1,3,4,5]=>[2,6,1,3,4,7,5]=>[7] [1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[6,7,2,1,3,4,5]=>[2,7,1,3,4,6,5]=>[6,1] [1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[7,5,2,1,3,4,6]=>[2,5,1,3,7,4,6]=>[7] [1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,3,4,7]=>[2,5,1,3,6,4,7]=>[6,1] [1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,6,2,1,3,4,7]=>[2,6,1,3,5,4,7]=>[5,1,1] [1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1,3,5,6]=>[2,4,1,7,3,5,6]=>[7] [1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1,3,5,7]=>[2,4,1,6,3,5,7]=>[6,1] [1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1,3,6,7]=>[2,4,1,5,3,6,7]=>[5,1,1] [1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,2,1,3,6,7]=>[2,5,1,4,3,6,7]=>[4,1,1,1] [1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1,4,5,6]=>[2,3,7,1,4,5,6]=>[7] [1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1,4,5,7]=>[2,3,6,1,4,5,7]=>[6,1] [1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1,4,6,7]=>[2,3,5,1,4,6,7]=>[5,1,1] [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,5,6,7]=>[2,3,4,1,5,6,7]=>[4,1,1,1] [1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,4,2,1,5,6,7]=>[2,4,3,1,5,6,7]=>[3,1,1,1,1] [1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,3,1,4,5,6]=>[3,7,2,1,4,5,6]=>[7] [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,3,1,4,5,7]=>[3,6,2,1,4,5,7]=>[6,1] [1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,3,1,4,6,7]=>[3,5,2,1,4,6,7]=>[5,1,1] [1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,3,1,5,6,7]=>[3,4,2,1,5,6,7]=>[4,1,1,1] [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,4,1,5,6,7]=>[4,3,2,1,5,6,7]=>[2,2,1,1,1] [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,3,4,1,5,6,7]=>[4,2,3,1,5,6,7]=>[2,1,1,1,1,1] [1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,2,3,4,5]=>[6,1,2,3,4,7,5]=>[7] [1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,7,1,2,3,4,5]=>[7,1,2,3,4,6,5]=>[6,1] [1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,2,3,4,6]=>[5,1,2,3,7,4,6]=>[7] [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,2,3,4,7]=>[5,1,2,3,6,4,7]=>[6,1] [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,6,1,2,3,4,7]=>[6,1,2,3,5,4,7]=>[5,1,1] [1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,2,3,5,6]=>[4,1,2,7,3,5,6]=>[7] [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,2,3,5,7]=>[4,1,2,6,3,5,7]=>[6,1] [1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,2,3,6,7]=>[4,1,2,5,3,6,7]=>[5,1,1] [1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,5,1,2,3,6,7]=>[5,1,2,4,3,6,7]=>[4,1,1,1] [1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,2,4,5,6]=>[3,1,7,2,4,5,6]=>[7] [1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,2,4,5,7]=>[3,1,6,2,4,5,7]=>[6,1] [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,2,4,6,7]=>[3,1,5,2,4,6,7]=>[5,1,1] [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,2,5,6,7]=>[3,1,4,2,5,6,7]=>[4,1,1,1] [1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,4,1,2,5,6,7]=>[4,1,3,2,5,6,7]=>[3,1,1,1,1] [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,3,4,5,6]=>[2,7,1,3,4,5,6]=>[7] [1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,3,4,5,7]=>[2,6,1,3,4,5,7]=>[6,1] [1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,3,4,6,7]=>[2,5,1,3,4,6,7]=>[5,1,1] [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,3,5,6,7]=>[2,4,1,3,5,6,7]=>[4,1,1,1] [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,4,5,6,7]=>[2,3,1,4,5,6,7]=>[3,1,1,1,1] [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,3,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[2,1,1,1,1,1] [1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6]=>[7,1,2,3,4,5,6]=>[7] [1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,2,3,4,5,7]=>[6,1,2,3,4,5,7]=>[6,1] [1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,2,3,4,6,7]=>[5,1,2,3,4,6,7]=>[5,1,1] [1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,2,3,5,6,7]=>[4,1,2,3,5,6,7]=>[4,1,1,1] [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,2,4,5,6,7]=>[3,1,2,4,5,6,7]=>[3,1,1,1,1] [1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[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]=>[1,2,3,4,5,6,7]=>[1,1,1,1,1,1,1] [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8] [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,3,2,1]=>[2,3,4,5,6,8,7,1]=>[7,1] [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,3,2,1]=>[2,3,4,5,8,7,6,1]=>[6,2] [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,3,2,1]=>[2,3,4,5,8,6,7,1]=>[6,1,1] [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,3,2,1]=>[2,3,4,6,8,5,7,1]=>[7,1] [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,3,2,1]=>[2,3,4,8,6,7,5,1]=>[5,3] [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,3,2,1]=>[2,3,4,8,7,6,5,1]=>[5,2,1] [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,4,3,2,1]=>[2,3,4,8,7,5,6,1]=>[5,3] [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,4,3,2,1]=>[2,3,4,8,6,5,7,1]=>[5,2,1] [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,3,2,1]=>[2,3,4,8,5,6,7,1]=>[5,1,1,1] [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8] [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,5,3,2,1]=>[2,3,5,8,4,6,7,1]=>[6,1,1] [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,8,3,2,1]=>[2,3,8,5,7,6,4,1]=>[4,3,1] [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,8,3,2,1]=>[2,3,8,6,7,5,4,1]=>[4,4] [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,3,2,1]=>[2,3,8,7,6,5,4,1]=>[4,2,2] [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,6,3,2,1]=>[2,3,6,8,4,5,7,1]=>[7,1] [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,7,3,2,1]=>[2,3,7,5,8,4,6,1]=>[8] [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,8,3,2,1]=>[2,3,8,7,4,5,6,1]=>[4,4] [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,3,2,1]=>[2,3,8,4,5,6,7,1]=>[4,1,1,1,1] [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,4,2,1]=>[2,4,5,3,6,7,8,1]=>[8] [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,3,4,2,1]=>[2,4,5,3,8,7,6,1]=>[6,2] [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,3,4,2,1]=>[2,4,5,3,8,6,7,1]=>[6,1,1] [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,4,2,1]=>[2,4,6,3,7,5,8,1]=>[8] [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,4,2,1]=>[2,4,6,3,8,5,7,1]=>[7,1] [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,3,4,2,1]=>[2,4,8,3,7,5,6,1]=>[5,3] [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,4,2,1]=>[2,4,8,3,5,6,7,1]=>[5,1,1,1] [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,3,5,2,1]=>[2,5,4,8,3,7,6,1]=>[6,2] [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,3,5,2,1]=>[2,5,4,8,3,6,7,1]=>[6,1,1] [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,3,6,2,1]=>[2,6,4,5,8,3,7,1]=>[7,1] [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,7,2,1]=>[2,7,4,5,6,8,3,1]=>[8] [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,3,8,2,1]=>[2,8,7,5,6,4,3,1]=>[3,3,2] [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,3,8,2,1]=>[2,8,7,6,5,4,3,1]=>[3,2,2,1] [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,3,8,2,1]=>[2,8,7,5,4,6,3,1]=>[3,2,2,1] [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,4,5,2,1]=>[2,5,7,3,4,8,6,1]=>[8] [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,4,5,2,1]=>[2,5,8,3,4,6,7,1]=>[6,1,1] [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,4,6,2,1]=>[2,6,5,3,8,4,7,1]=>[7,1] [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,5,6,2,1]=>[2,6,4,7,3,5,8,1]=>[8] [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[4,5,3,6,7,8,2,1]=>[2,8,5,4,3,6,7,1]=>[3,2,1,1,1] [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[5,3,4,6,7,8,2,1]=>[2,8,5,3,4,6,7,1]=>[3,3,1,1] [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[4,3,5,6,7,8,2,1]=>[2,8,4,3,5,6,7,1]=>[3,2,1,1,1] [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,2,3,1]=>[3,4,2,5,6,7,8,1]=>[8] [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,2,3,1]=>[3,4,2,6,8,5,7,1]=>[7,1] [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,2,3,1]=>[3,4,2,8,6,7,5,1]=>[5,3] [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,2,3,1]=>[3,4,2,8,5,6,7,1]=>[5,1,1,1] [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,5,2,3,1]=>[3,5,2,6,4,7,8,1]=>[8] [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,5,2,3,1]=>[3,5,2,7,4,8,6,1]=>[8] [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,5,2,3,1]=>[3,5,2,8,4,7,6,1]=>[6,2] [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,5,2,3,1]=>[3,5,2,8,4,6,7,1]=>[6,1,1] [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,7,2,3,1]=>[3,7,2,6,8,5,4,1]=>[8] [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,8,2,3,1]=>[3,8,2,6,7,5,4,1]=>[4,4] [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,2,3,1]=>[3,8,2,7,6,5,4,1]=>[4,2,2] [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,6,2,3,1]=>[3,6,2,8,4,5,7,1]=>[7,1] [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,8,2,3,1]=>[3,8,2,5,4,6,7,1]=>[4,2,1,1] [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,2,3,1]=>[3,8,2,4,5,6,7,1]=>[4,1,1,1,1] [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,2,4,1]=>[4,3,5,2,6,7,8,1]=>[8] [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,3,2,4,1]=>[4,3,5,2,8,6,7,1]=>[6,1,1] [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,3,2,4,1]=>[4,3,7,2,6,8,5,1]=>[8] [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,2,4,1]=>[4,3,8,2,7,6,5,1]=>[5,2,1] [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,3,2,4,1]=>[4,3,7,2,8,5,6,1]=>[8] [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,3,2,4,1]=>[4,3,8,2,7,5,6,1]=>[5,3] [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,3,2,4,1]=>[4,3,8,2,6,5,7,1]=>[5,2,1] [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,2,4,1]=>[4,3,8,2,5,6,7,1]=>[5,1,1,1] [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,3,2,5,1]=>[5,3,4,8,2,7,6,1]=>[6,2] [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,3,2,5,1]=>[5,3,4,8,2,6,7,1]=>[6,1,1] [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,3,2,6,1]=>[6,3,4,5,8,2,7,1]=>[7,1] [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,3,2,8,1]=>[8,3,7,4,5,6,2,1]=>[3,2,1,1,1] [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,2,5,1]=>[5,4,6,3,2,7,8,1]=>[8] [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,4,2,5,1]=>[5,4,7,3,2,8,6,1]=>[8] [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,4,2,5,1]=>[5,4,8,3,2,7,6,1]=>[6,2] [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,4,2,6,1]=>[6,4,5,3,7,2,8,1]=>[8] [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,4,2,6,1]=>[6,4,5,3,8,2,7,1]=>[7,1] [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,4,2,7,1]=>[7,4,6,3,8,5,2,1]=>[8] [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,4,2,8,1]=>[8,4,6,3,7,5,2,1]=>[6,2] [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,4,2,8,1]=>[8,4,7,3,6,5,2,1]=>[4,2,2] [1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,6,2,7,1]=>[7,6,4,5,8,3,2,1]=>[8] [1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,6,2,8,1]=>[8,6,4,5,7,3,2,1]=>[6,2] [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,6,2,7,1]=>[7,6,5,8,4,3,2,1]=>[8] [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[7,4,5,3,6,2,8,1]=>[8,6,5,7,4,3,2,1]=>[6,2] [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[6,4,5,3,7,2,8,1]=>[8,7,5,6,4,3,2,1]=>[4,2,2] [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,7,2,8,1]=>[8,7,6,5,4,3,2,1]=>[2,2,2,2] [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,7,2,8,1]=>[8,7,6,4,5,3,2,1]=>[2,2,2,1,1] [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[6,5,3,4,7,2,8,1]=>[8,7,5,3,6,4,2,1]=>[4,2,2] [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[6,4,3,5,7,2,8,1]=>[8,7,4,6,3,5,2,1]=>[4,2,2] [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,2,3,4,1]=>[4,5,2,3,6,7,8,1]=>[8] [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,2,3,4,1]=>[4,5,2,3,8,6,7,1]=>[6,1,1] [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,2,3,4,1]=>[4,6,2,3,7,5,8,1]=>[8] [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,2,3,4,1]=>[4,8,2,3,5,6,7,1]=>[5,1,1,1] [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,2,3,5,1]=>[5,4,2,6,3,7,8,1]=>[8] [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,2,3,5,1]=>[5,4,2,6,3,8,7,1]=>[7,1] [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,2,3,5,1]=>[5,4,2,8,3,6,7,1]=>[6,1,1] [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,2,3,8,1]=>[8,4,2,5,7,6,3,1]=>[5,2,1] [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,2,3,8,1]=>[8,5,2,7,4,6,3,1]=>[5,2,1] [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,2,3,8,1]=>[8,6,2,5,7,4,3,1]=>[6,2] [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,2,3,8,1]=>[8,6,2,7,4,5,3,1]=>[6,2] [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,2,3,8,1]=>[8,7,2,6,4,5,3,1]=>[3,3,2] [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,2,3,8,1]=>[8,7,2,4,5,6,3,1]=>[3,2,1,1,1] [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,2,4,5,1]=>[5,3,8,2,4,6,7,1]=>[6,1,1] [1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,2,5,6,1]=>[6,3,4,8,2,5,7,1]=>[7,1] [1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[6,7,4,3,2,5,8,1]=>[8,3,4,7,2,6,5,1]=>[5,2,1] [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,2,6,7,1]=>[7,3,4,5,8,2,6,1]=>[8] [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[8,5,3,4,2,6,7,1]=>[7,4,5,3,8,2,6,1]=>[8] [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,2,6,7,1]=>[7,5,8,3,4,2,6,1]=>[8] [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[7,3,4,5,2,6,8,1]=>[8,5,7,3,4,2,6,1]=>[6,2] [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,2,7,8,1]=>[8,5,6,3,4,2,7,1]=>[5,2,1] [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[7,6,8,2,3,4,5,1]=>[5,8,2,3,4,7,6,1]=>[6,2] [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,2,3,4,5,1]=>[5,8,2,3,4,6,7,1]=>[6,1,1] [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[7,8,5,2,3,4,6,1]=>[6,5,2,3,8,4,7,1]=>[7,1] [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,2,3,4,8,1]=>[8,5,2,3,6,7,4,1]=>[6,2] [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[7,6,4,2,3,5,8,1]=>[8,4,2,6,3,7,5,1]=>[6,2] [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[8,5,4,2,3,6,7,1]=>[7,4,2,5,8,3,6,1]=>[8] [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,5,6,2,3,7,8,1]=>[8,6,2,4,5,3,7,1]=>[3,2,1,1,1] [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,2,4,6,8,1]=>[8,3,5,2,7,4,6,1]=>[6,2] [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,3,2,6,7,8,1]=>[8,3,5,4,2,6,7,1]=>[3,2,1,1,1] [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[8,3,4,2,5,6,7,1]=>[7,4,8,3,2,5,6,1]=>[8] [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,4,5,2,6,7,8,1]=>[8,5,3,4,2,6,7,1]=>[2,2,1,1,1,1] [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[8,5,2,3,4,6,7,1]=>[7,5,2,3,8,4,6,1]=>[8] [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[7,5,2,3,4,6,8,1]=>[8,5,2,3,7,4,6,1]=>[6,2] [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,3,1,2]=>[3,1,4,5,6,7,8,2]=>[8] [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,3,1,2]=>[3,1,4,5,6,8,7,2]=>[7,1] [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,3,1,2]=>[3,1,4,5,8,6,7,2]=>[6,1,1] [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,3,1,2]=>[3,1,4,8,7,6,5,2]=>[5,2,1] [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,4,3,1,2]=>[3,1,4,8,6,5,7,2]=>[5,2,1] [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,3,1,2]=>[3,1,4,8,5,6,7,2]=>[5,1,1,1] [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,5,3,1,2]=>[3,1,5,6,4,8,7,2]=>[7,1] [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,6,3,1,2]=>[3,1,6,5,7,4,8,2]=>[8] [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,3,1,2]=>[3,1,8,7,6,5,4,2]=>[4,2,2] [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,6,3,1,2]=>[3,1,6,8,4,5,7,2]=>[7,1] [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,7,3,1,2]=>[3,1,7,6,4,8,5,2]=>[8] [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,8,3,1,2]=>[3,1,8,6,4,7,5,2]=>[4,4] [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,8,3,1,2]=>[3,1,8,5,7,4,6,2]=>[4,4] [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,8,3,1,2]=>[3,1,8,5,4,6,7,2]=>[4,2,1,1] [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,3,1,2]=>[3,1,8,4,5,6,7,2]=>[4,1,1,1,1] [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,4,1,2]=>[4,1,5,3,6,7,8,2]=>[8] [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,4,1,2]=>[4,1,6,3,7,5,8,2]=>[8] [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,4,1,2]=>[4,1,6,3,8,5,7,2]=>[7,1] [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,3,4,1,2]=>[4,1,7,3,8,5,6,2]=>[8] [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,3,4,1,2]=>[4,1,8,3,7,5,6,2]=>[5,3] [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,3,4,1,2]=>[4,1,8,3,6,5,7,2]=>[5,2,1] [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,4,1,2]=>[4,1,8,3,5,6,7,2]=>[5,1,1,1] [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,3,5,1,2]=>[5,1,4,8,3,7,6,2]=>[6,2] [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,8,1,2]=>[8,1,4,5,6,7,3,2]=>[5,3] [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,3,7,1,2]=>[7,1,6,5,8,4,3,2]=>[8] [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,3,8,1,2]=>[8,1,7,5,6,4,3,2]=>[3,3,2] [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,3,8,1,2]=>[8,1,7,6,5,4,3,2]=>[3,2,2,1] [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,3,8,1,2]=>[8,1,6,7,4,5,3,2]=>[5,3] [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,3,8,1,2]=>[8,1,7,6,4,5,3,2]=>[3,3,2] [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,5,1,2]=>[5,1,6,3,4,7,8,2]=>[8] [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,4,5,1,2]=>[5,1,7,3,4,8,6,2]=>[8] [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,4,6,1,2]=>[6,1,5,3,8,4,7,2]=>[7,1] [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,4,8,1,2]=>[8,1,6,3,7,5,4,2]=>[5,3] [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,5,6,1,2]=>[6,1,4,8,3,5,7,2]=>[7,1] [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[6,7,4,3,5,8,1,2]=>[8,1,4,7,3,6,5,2]=>[4,3,1] [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,5,6,1,2]=>[6,1,8,3,4,5,7,2]=>[7,1] [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[8,5,3,4,6,7,1,2]=>[7,1,5,3,8,4,6,2]=>[8] [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,4,6,8,1,2]=>[8,1,5,3,7,4,6,2]=>[5,3] [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,7,8,1,2]=>[8,1,6,3,5,4,7,2]=>[3,3,1,1] [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,6,7,1,2]=>[7,1,4,8,3,5,6,2]=>[8] [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[6,4,3,5,7,8,1,2]=>[8,1,4,6,3,5,7,2]=>[4,3,1] [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,7,8,1,2]=>[8,1,4,5,3,6,7,2]=>[3,3,1,1] [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[4,5,3,6,7,8,1,2]=>[8,1,5,4,3,6,7,2]=>[3,2,1,1,1] [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,7,1,2]=>[7,1,8,3,4,5,6,2]=>[8] [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[7,3,4,5,6,8,1,2]=>[8,1,7,3,4,5,6,2]=>[5,3] [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,2,1,3]=>[2,4,1,5,6,7,8,3]=>[8] [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,2,1,3]=>[2,4,1,6,8,5,7,3]=>[7,1] [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,2,1,3]=>[2,4,1,8,5,6,7,3]=>[5,1,1,1] [1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,6,2,1,3]=>[2,6,1,5,7,4,8,3]=>[8] [1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,2,1,3]=>[2,8,1,7,6,5,4,3]=>[4,2,2] [1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,8,2,1,3]=>[2,8,1,7,5,6,4,3]=>[4,2,1,1] [1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,6,2,1,3]=>[2,6,1,8,4,5,7,3]=>[7,1] [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,2,1,4]=>[2,3,5,1,6,7,8,4]=>[8] [1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,2,1,4]=>[2,3,6,1,7,5,8,4]=>[8] [1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,2,1,4]=>[2,3,6,1,8,5,7,4]=>[7,1] [1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,3,2,1,4]=>[2,3,7,1,6,8,5,4]=>[8] [1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,3,2,1,4]=>[2,3,8,1,6,5,7,4]=>[5,2,1] [1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,2,1,4]=>[2,3,8,1,5,6,7,4]=>[5,1,1,1] [1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,3,2,1,5]=>[2,3,4,6,1,8,7,5]=>[7,1] [1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,3,2,1,5]=>[2,3,4,8,1,7,6,5]=>[6,2] [1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,3,2,1,5]=>[2,3,4,8,1,6,7,5]=>[6,1,1] [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,3,2,1,6]=>[2,3,4,5,8,1,7,6]=>[7,1] [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,3,2,1,8]=>[2,3,4,7,6,5,1,8]=>[5,2,1] [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,3,2,1,8]=>[2,3,4,7,5,6,1,8]=>[5,1,1,1] [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,3,2,1,8]=>[2,3,7,5,6,4,1,8]=>[4,3,1] [1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,3,2,1,8]=>[2,3,7,6,5,4,1,8]=>[4,2,1,1] [1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,3,2,1,7]=>[2,3,6,8,4,5,1,7]=>[8] [1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,3,2,1,8]=>[2,3,7,5,4,6,1,8]=>[4,2,1,1] [1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,4,2,1,6]=>[2,4,5,3,7,1,8,6]=>[8] [1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,4,2,1,8]=>[2,4,6,3,7,5,1,8]=>[7,1] [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,4,2,1,8]=>[2,4,7,3,5,6,1,8]=>[5,1,1,1] [1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,5,2,1,6]=>[2,5,4,8,3,1,7,6]=>[7,1] [1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,5,2,1,8]=>[2,5,4,6,3,7,1,8]=>[7,1] [1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,2,1,8]=>[2,7,4,5,6,3,1,8]=>[4,3,1] [1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,7,2,1,8]=>[2,7,6,3,5,4,1,8]=>[3,3,1,1] [1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[7,3,4,5,6,2,1,8]=>[2,6,7,3,4,5,1,8]=>[7,1] [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,2,3,1,4]=>[3,5,2,1,6,7,8,4]=>[8] [1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,2,3,1,4]=>[3,5,2,1,7,8,6,4]=>[8] [1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,2,3,1,4]=>[3,6,2,1,7,5,8,4]=>[8] [1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,2,3,1,4]=>[3,8,2,1,7,6,5,4]=>[5,2,1] [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,2,3,1,4]=>[3,8,2,1,5,6,7,4]=>[5,1,1,1] [1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,2,3,1,8]=>[3,4,2,7,5,6,1,8]=>[5,1,1,1] [1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,2,3,1,6]=>[3,5,2,7,4,1,8,6]=>[8] [1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,2,3,1,7]=>[3,5,2,6,4,8,1,7]=>[8] [1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,2,3,1,8]=>[3,5,2,6,4,7,1,8]=>[7,1] [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,2,3,1,8]=>[3,5,2,7,4,6,1,8]=>[6,1,1] [1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,2,3,1,8]=>[3,7,2,5,6,4,1,8]=>[4,3,1] [1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,2,3,1,7]=>[3,6,2,8,4,5,1,7]=>[8] [1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,2,4,1,5]=>[4,3,8,2,1,6,7,5]=>[6,1,1] [1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,2,4,1,6]=>[4,3,5,2,7,1,8,6]=>[8] [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,2,4,1,8]=>[4,3,7,2,5,6,1,8]=>[5,1,1,1] [1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[6,7,4,3,2,5,1,8]=>[5,3,4,7,2,6,1,8]=>[6,1,1] [1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,2,6,1,7]=>[6,3,4,5,8,2,1,7]=>[8] [1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,2,6,1,7]=>[6,3,5,8,4,2,1,7]=>[8] [1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,2,7,1,8]=>[7,3,6,5,4,2,1,8]=>[3,2,2,1] [1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,2,5,1,6]=>[5,4,8,3,2,1,7,6]=>[7,1] [1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[7,4,3,5,2,6,1,8]=>[6,5,4,7,3,2,1,8]=>[7,1] [1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,2,7,1,8]=>[7,6,4,5,3,2,1,8]=>[3,2,2,1] [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[4,5,3,6,2,7,1,8]=>[7,6,5,4,3,2,1,8]=>[2,2,2,1,1] [1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,2,6,1,7]=>[6,5,8,3,4,2,1,7]=>[8] [1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[7,3,4,5,2,6,1,8]=>[6,5,7,3,4,2,1,8]=>[7,1] [1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,2,7,1,8]=>[7,5,6,3,4,2,1,8]=>[5,2,1] [1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,2,7,1,8]=>[7,6,3,4,5,2,1,8]=>[2,2,1,1,1,1] [1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[8,7,5,2,3,4,1,6]=>[4,5,2,3,7,1,8,6]=>[8] [1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[7,8,5,2,3,4,1,6]=>[4,5,2,3,8,1,7,6]=>[7,1] [1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,2,3,4,1,8]=>[4,5,2,3,6,7,1,8]=>[7,1] [1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[6,7,5,2,3,4,1,8]=>[4,5,2,3,7,6,1,8]=>[6,1,1] [1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[7,5,6,2,3,4,1,8]=>[4,6,2,3,7,5,1,8]=>[7,1] [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[6,5,7,2,3,4,1,8]=>[4,7,2,3,6,5,1,8]=>[5,2,1] [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,2,3,4,1,8]=>[4,7,2,3,5,6,1,8]=>[5,1,1,1] [1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[8,7,4,2,3,5,1,6]=>[5,4,2,7,3,1,8,6]=>[8] [1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[7,6,4,2,3,5,1,8]=>[5,4,2,6,3,7,1,8]=>[7,1] [1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[5,4,6,2,3,7,1,8]=>[7,6,2,5,4,3,1,8]=>[3,2,2,1] [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,5,6,2,3,7,1,8]=>[7,6,2,4,5,3,1,8]=>[3,2,1,1,1] [1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[8,6,3,2,4,5,1,7]=>[5,3,6,2,4,8,1,7]=>[8] [1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[7,6,3,2,4,5,1,8]=>[5,3,6,2,4,7,1,8]=>[7,1] [1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,2,4,6,1,8]=>[6,3,5,2,7,4,1,8]=>[7,1] [1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[6,5,3,2,4,7,1,8]=>[7,3,5,2,6,4,1,8]=>[5,2,1] [1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[5,3,4,2,6,7,1,8]=>[7,4,5,3,2,6,1,8]=>[4,2,1,1] [1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,6,2,3,4,7,1,8]=>[7,6,2,3,5,4,1,8]=>[4,2,1,1] [1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[7,4,2,3,5,6,1,8]=>[6,4,2,7,3,5,1,8]=>[7,1] [1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[6,4,2,3,5,7,1,8]=>[7,4,2,6,3,5,1,8]=>[5,2,1] [1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,4,6,7,1,8]=>[7,3,5,2,4,6,1,8]=>[4,2,1,1] [1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,2,3,4,5,7,1,8]=>[7,6,2,3,4,5,1,8]=>[5,2,1] [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[4,2,3,5,6,7,1,8]=>[7,4,2,3,5,6,1,8]=>[3,2,1,1,1] [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,1,2,3]=>[4,1,2,5,6,7,8,3]=>[8] [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,1,2,3]=>[4,1,2,5,6,8,7,3]=>[7,1] [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,1,2,3]=>[4,1,2,5,8,6,7,3]=>[6,1,1] [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,1,2,3]=>[4,1,2,6,8,5,7,3]=>[7,1] [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,1,2,3]=>[4,1,2,8,7,6,5,3]=>[5,2,1] [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,1,2,3]=>[4,1,2,8,5,6,7,3]=>[5,1,1,1] [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,5,1,2,3]=>[5,1,2,6,4,8,7,3]=>[7,1] [1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,6,1,2,3]=>[6,1,2,5,8,4,7,3]=>[7,1] [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,8,1,2,3]=>[8,1,2,5,6,7,4,3]=>[4,4] [1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,7,1,2,3]=>[7,1,2,6,8,5,4,3]=>[8] [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,8,1,2,3]=>[8,1,2,6,7,5,4,3]=>[4,4] [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,1,2,3]=>[8,1,2,7,6,5,4,3]=>[4,2,2] [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,6,1,2,3]=>[6,1,2,7,4,5,8,3]=>[8] [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,6,1,2,3]=>[6,1,2,8,4,5,7,3]=>[7,1] [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,8,1,2,3]=>[8,1,2,7,4,6,5,3]=>[4,3,1] [1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,8,1,2,3]=>[8,1,2,7,4,5,6,3]=>[4,4] [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,8,1,2,3]=>[8,1,2,6,4,5,7,3]=>[4,3,1] [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,1,2,3]=>[8,1,2,4,5,6,7,3]=>[4,1,1,1,1] [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,1,2,4]=>[3,1,5,2,6,7,8,4]=>[8] [1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,1,2,4]=>[3,1,6,2,7,5,8,4]=>[8] [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,1,2,4]=>[3,1,6,2,8,5,7,4]=>[7,1] [1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,3,1,2,4]=>[3,1,7,2,8,5,6,4]=>[8] [1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,3,1,2,4]=>[3,1,8,2,7,5,6,4]=>[5,3] [1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,3,1,2,4]=>[3,1,8,2,6,5,7,4]=>[5,2,1] [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,1,2,4]=>[3,1,8,2,5,6,7,4]=>[5,1,1,1] [1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,3,1,2,5]=>[3,1,4,6,2,8,7,5]=>[7,1] [1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,3,1,2,5]=>[3,1,4,8,2,6,7,5]=>[6,1,1] [1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,3,1,2,8]=>[3,1,4,7,5,6,2,8]=>[5,1,1,1] [1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,4,1,2,6]=>[4,1,5,3,7,2,8,6]=>[8] [1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,4,1,2,6]=>[4,1,5,3,8,2,7,6]=>[7,1] [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,4,1,2,8]=>[4,1,7,3,6,5,2,8]=>[5,2,1] [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[5,6,4,3,7,1,2,8]=>[7,1,4,6,5,3,2,8]=>[3,3,1,1] [1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[6,5,3,4,7,1,2,8]=>[7,1,5,3,6,4,2,8]=>[4,3,1] [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,2,1,3,4]=>[2,5,1,3,6,7,8,4]=>[8] [1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,2,1,3,4]=>[2,5,1,3,6,8,7,4]=>[7,1] [1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,2,1,3,4]=>[2,5,1,3,8,6,7,4]=>[6,1,1] [1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,2,1,3,4]=>[2,6,1,3,8,5,7,4]=>[7,1] [1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,2,1,3,4]=>[2,8,1,3,6,5,7,4]=>[5,2,1] [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,2,1,3,4]=>[2,8,1,3,5,6,7,4]=>[5,1,1,1] [1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,2,1,3,5]=>[2,4,1,6,3,7,8,5]=>[8] [1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,2,1,3,5]=>[2,4,1,7,3,8,6,5]=>[8] [1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,2,1,3,6]=>[2,4,1,5,7,3,8,6]=>[8] [1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,2,1,3,6]=>[2,4,1,5,8,3,7,6]=>[7,1] [1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,2,1,3,8]=>[2,4,1,7,5,6,3,8]=>[5,1,1,1] [1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,2,1,3,7]=>[2,5,1,6,4,8,3,7]=>[8] [1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,2,1,3,8]=>[2,6,1,5,7,4,3,8]=>[7,1] [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,2,1,4,5]=>[2,3,6,1,4,7,8,5]=>[8] [1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,2,1,4,5]=>[2,3,6,1,4,8,7,5]=>[7,1] [1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,2,1,4,5]=>[2,3,7,1,4,8,6,5]=>[8] [1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,2,1,4,6]=>[2,3,5,1,8,4,7,6]=>[7,1] [1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,2,1,4,7]=>[2,3,6,1,8,5,4,7]=>[8] [1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,2,1,4,8]=>[2,3,7,1,5,6,4,8]=>[5,1,1,1] [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,2,1,5,6]=>[2,3,4,7,1,5,8,6]=>[8] [1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,2,1,5,6]=>[2,3,4,8,1,5,7,6]=>[7,1] [1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,2,1,5,7]=>[2,3,4,6,1,8,5,7]=>[8] [1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[6,7,4,3,2,1,5,8]=>[2,3,4,7,1,6,5,8]=>[6,1,1] [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,2,1,6,7]=>[2,3,4,5,8,1,6,7]=>[8] [1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,2,1,5,7]=>[2,4,6,3,1,8,5,7]=>[8] [1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,2,1,6,7]=>[2,5,4,8,3,1,6,7]=>[8] [1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,2,1,6,7]=>[2,5,8,3,4,1,6,7]=>[8] [1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[7,8,6,2,3,1,4,5]=>[3,6,2,1,4,8,7,5]=>[7,1] [1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,2,3,1,4,5]=>[3,8,2,1,4,6,7,5]=>[6,1,1] [1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[8,7,5,2,3,1,4,6]=>[3,5,2,1,7,4,8,6]=>[8] [1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[8,6,5,2,3,1,4,7]=>[3,5,2,1,6,8,4,7]=>[8] [1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[8,5,6,2,3,1,4,7]=>[3,6,2,1,8,5,4,7]=>[8] [1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[7,6,4,2,3,1,5,8]=>[3,4,2,6,1,7,5,8]=>[7,1] [1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[7,8,3,2,4,1,5,6]=>[4,3,8,2,1,5,7,6]=>[7,1] [1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[8,6,3,2,4,1,5,7]=>[4,3,6,2,1,8,5,7]=>[8] [1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[7,6,3,2,4,1,5,8]=>[4,3,6,2,1,7,5,8]=>[7,1] [1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[5,6,3,2,4,1,7,8]=>[4,3,6,2,5,1,7,8]=>[5,1,1,1] [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,3,4,1,5,6]=>[4,8,2,3,1,5,7,6]=>[7,1] [1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[7,6,2,3,4,1,5,8]=>[4,6,2,3,1,7,5,8]=>[7,1] [1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[8,5,2,3,4,1,6,7]=>[4,5,2,3,8,1,6,7]=>[8] [1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[7,5,2,3,4,1,6,8]=>[4,5,2,3,7,1,6,8]=>[7,1] [1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[8,4,2,3,5,1,6,7]=>[5,4,2,8,3,1,6,7]=>[8] [1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[6,3,2,4,5,1,7,8]=>[5,3,6,2,4,1,7,8]=>[6,1,1] [1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[7,2,3,4,5,1,6,8]=>[5,7,2,3,4,1,6,8]=>[7,1] [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,4,6,1,7,8]=>[6,5,2,3,4,1,7,8]=>[4,2,1,1] [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,1,2,3,4]=>[5,1,2,3,6,7,8,4]=>[8] [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,1,2,3,4]=>[5,1,2,3,6,8,7,4]=>[7,1] [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,1,2,3,4]=>[5,1,2,3,7,8,6,4]=>[8] [1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,1,2,3,4]=>[5,1,2,3,8,7,6,4]=>[6,2] [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,1,2,3,4]=>[5,1,2,3,8,6,7,4]=>[6,1,1] [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,1,2,3,4]=>[6,1,2,3,7,5,8,4]=>[8] [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,1,2,3,4]=>[6,1,2,3,8,5,7,4]=>[7,1] [1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,1,2,3,4]=>[7,1,2,3,6,8,5,4]=>[8] [1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,1,2,3,4]=>[8,1,2,3,6,7,5,4]=>[5,3] [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,1,2,3,4]=>[8,1,2,3,7,6,5,4]=>[5,2,1] [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,1,2,3,4]=>[7,1,2,3,8,5,6,4]=>[8] [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,1,2,3,4]=>[8,1,2,3,7,5,6,4]=>[5,3] [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,1,2,3,4]=>[8,1,2,3,6,5,7,4]=>[5,2,1] [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,1,2,3,4]=>[8,1,2,3,5,6,7,4]=>[5,1,1,1] [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,1,2,3,5]=>[4,1,2,6,3,7,8,5]=>[8] [1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,1,2,3,5]=>[4,1,2,6,3,8,7,5]=>[7,1] [1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,1,2,3,5]=>[4,1,2,7,3,8,6,5]=>[8] [1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,1,2,3,6]=>[4,1,2,5,7,3,8,6]=>[8] [1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,1,2,3,7]=>[4,1,2,5,6,8,3,7]=>[8] [1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,1,2,3,8]=>[4,1,2,5,7,6,3,8]=>[6,1,1] [1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,1,2,3,7]=>[4,1,2,6,8,5,3,7]=>[8] [1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,1,2,3,8]=>[4,1,2,6,7,5,3,8]=>[7,1] [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,1,2,3,8]=>[4,1,2,7,5,6,3,8]=>[5,1,1,1] [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,1,2,3,8]=>[7,1,2,6,5,4,3,8]=>[4,2,1,1] [1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,1,2,3,8]=>[7,1,2,6,4,5,3,8]=>[4,3,1] [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,1,2,3,8]=>[7,1,2,5,4,6,3,8]=>[4,2,1,1] [1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,1,2,4,5]=>[3,1,6,2,4,7,8,5]=>[8] [1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,1,2,4,5]=>[3,1,6,2,4,8,7,5]=>[7,1] [1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,1,2,4,6]=>[3,1,5,2,7,4,8,6]=>[8] [1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,1,2,4,6]=>[3,1,5,2,8,4,7,6]=>[7,1] [1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,1,2,4,8]=>[3,1,7,2,5,6,4,8]=>[5,1,1,1] [1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,1,2,5,7]=>[3,1,4,6,2,8,5,7]=>[8] [1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[5,6,4,3,1,2,7,8]=>[3,1,4,6,5,2,7,8]=>[5,1,1,1] [1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,1,2,7,8]=>[3,1,6,5,4,2,7,8]=>[4,2,1,1] [1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[7,6,3,4,1,2,5,8]=>[4,1,6,3,2,7,5,8]=>[7,1] [1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[8,5,3,4,1,2,6,7]=>[4,1,5,3,8,2,6,7]=>[8] [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,1,2,7,8]=>[4,1,6,3,5,2,7,8]=>[5,1,1,1] [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,1,2,7,8]=>[6,1,4,5,3,2,7,8]=>[3,3,1,1] [1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[8,6,7,2,1,3,4,5]=>[2,7,1,3,4,8,6,5]=>[8] [1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[8,7,5,2,1,3,4,6]=>[2,5,1,3,7,4,8,6]=>[8] [1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[7,8,5,2,1,3,4,6]=>[2,5,1,3,8,4,7,6]=>[7,1] [1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[8,6,5,2,1,3,4,7]=>[2,5,1,3,6,8,4,7]=>[8] [1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,2,1,3,4,8]=>[2,7,1,3,5,6,4,8]=>[5,1,1,1] [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,2,1,3,5,7]=>[2,4,1,6,3,8,5,7]=>[8] [1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[7,6,4,2,1,3,5,8]=>[2,4,1,6,3,7,5,8]=>[7,1] [1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[5,6,4,2,1,3,7,8]=>[2,4,1,6,5,3,7,8]=>[5,1,1,1] [1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[6,4,5,2,1,3,7,8]=>[2,5,1,6,4,3,7,8]=>[6,1,1] [1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[5,4,6,2,1,3,7,8]=>[2,6,1,5,4,3,7,8]=>[4,2,1,1] [1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[8,7,3,2,1,4,5,6]=>[2,3,7,1,4,5,8,6]=>[8] [1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[7,8,3,2,1,4,5,6]=>[2,3,8,1,4,5,7,6]=>[7,1] [1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[7,6,3,2,1,4,5,8]=>[2,3,6,1,4,7,5,8]=>[7,1] [1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[5,6,3,2,1,4,7,8]=>[2,3,6,1,5,4,7,8]=>[5,1,1,1] [1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[8,4,3,2,1,5,6,7]=>[2,3,4,8,1,5,6,7]=>[8] [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[7,4,3,2,1,5,6,8]=>[2,3,4,7,1,5,6,8]=>[7,1] [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,1,6,7,8]=>[2,3,4,5,1,6,7,8]=>[5,1,1,1] [1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,3,2,1,6,7,8]=>[2,3,5,4,1,6,7,8]=>[4,1,1,1,1] [1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[8,3,4,2,1,5,6,7]=>[2,4,8,3,1,5,6,7]=>[8] [1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[5,3,4,2,1,6,7,8]=>[2,4,5,3,1,6,7,8]=>[5,1,1,1] [1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[4,3,5,2,1,6,7,8]=>[2,5,4,3,1,6,7,8]=>[3,2,1,1,1] [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[3,4,5,2,1,6,7,8]=>[2,5,3,4,1,6,7,8]=>[3,1,1,1,1,1] [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,3,1,4,5,6]=>[3,8,2,1,4,5,7,6]=>[7,1] [1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[8,6,2,3,1,4,5,7]=>[3,6,2,1,4,8,5,7]=>[8] [1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[7,6,2,3,1,4,5,8]=>[3,6,2,1,4,7,5,8]=>[7,1] [1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[7,5,2,3,1,4,6,8]=>[3,5,2,1,7,4,6,8]=>[7,1] [1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[6,5,2,3,1,4,7,8]=>[3,5,2,1,6,4,7,8]=>[6,1,1] [1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[5,6,2,3,1,4,7,8]=>[3,6,2,1,5,4,7,8]=>[5,1,1,1] [1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[8,4,2,3,1,5,6,7]=>[3,4,2,8,1,5,6,7]=>[8] [1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[7,4,2,3,1,5,6,8]=>[3,4,2,7,1,5,6,8]=>[7,1] [1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,2,3,1,6,7,8]=>[3,4,2,5,1,6,7,8]=>[5,1,1,1] [1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[4,5,2,3,1,6,7,8]=>[3,5,2,4,1,6,7,8]=>[4,1,1,1,1] [1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[8,3,2,4,1,5,6,7]=>[4,3,8,2,1,5,6,7]=>[8] [1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[7,3,2,4,1,5,6,8]=>[4,3,7,2,1,5,6,8]=>[7,1] [1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,4,1,6,7,8]=>[4,3,5,2,1,6,7,8]=>[5,1,1,1] [1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,5,1,6,7,8]=>[5,3,4,2,1,6,7,8]=>[3,2,1,1,1] [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[3,4,2,5,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[2,2,1,1,1,1] [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[8,2,3,4,1,5,6,7]=>[4,8,2,3,1,5,6,7]=>[8] [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,4,1,6,7,8]=>[4,5,2,3,1,6,7,8]=>[5,1,1,1] [1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[4,2,3,5,1,6,7,8]=>[5,4,2,3,1,6,7,8]=>[3,2,1,1,1] [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,4,5,1,6,7,8]=>[5,3,2,4,1,6,7,8]=>[2,2,1,1,1,1] [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,1,6,7,8]=>[5,2,3,4,1,6,7,8]=>[2,1,1,1,1,1,1] [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,1,2,3,4,5]=>[6,1,2,3,4,7,8,5]=>[8] [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[7,8,6,1,2,3,4,5]=>[6,1,2,3,4,8,7,5]=>[7,1] [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[8,6,7,1,2,3,4,5]=>[7,1,2,3,4,8,6,5]=>[8] [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[7,6,8,1,2,3,4,5]=>[8,1,2,3,4,7,6,5]=>[6,2] [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,1,2,3,4,5]=>[8,1,2,3,4,6,7,5]=>[6,1,1] [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[8,7,5,1,2,3,4,6]=>[5,1,2,3,7,4,8,6]=>[8] [1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[7,8,5,1,2,3,4,6]=>[5,1,2,3,8,4,7,6]=>[7,1] [1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[8,6,5,1,2,3,4,7]=>[5,1,2,3,6,8,4,7]=>[8] [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,1,2,3,4,8]=>[5,1,2,3,6,7,4,8]=>[7,1] [1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[6,7,5,1,2,3,4,8]=>[5,1,2,3,7,6,4,8]=>[6,1,1] [1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[8,5,6,1,2,3,4,7]=>[6,1,2,3,8,5,4,7]=>[8] [1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[7,5,6,1,2,3,4,8]=>[6,1,2,3,7,5,4,8]=>[7,1] [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[6,5,7,1,2,3,4,8]=>[7,1,2,3,6,5,4,8]=>[5,2,1] [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,1,2,3,4,8]=>[7,1,2,3,5,6,4,8]=>[5,1,1,1] [1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[8,7,4,1,2,3,5,6]=>[4,1,2,7,3,5,8,6]=>[8] [1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,1,2,3,5,7]=>[4,1,2,6,3,8,5,7]=>[8] [1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[7,6,4,1,2,3,5,8]=>[4,1,2,6,3,7,5,8]=>[7,1] [1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[7,5,4,1,2,3,6,8]=>[4,1,2,5,7,3,6,8]=>[7,1] [1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[8,4,3,1,2,5,6,7]=>[3,1,4,8,2,5,6,7]=>[8] [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[8,3,4,1,2,5,6,7]=>[4,1,8,3,2,5,6,7]=>[8] [1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[7,3,4,1,2,5,6,8]=>[4,1,7,3,2,5,6,8]=>[7,1] [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[3,4,5,1,2,6,7,8]=>[5,1,3,4,2,6,7,8]=>[3,1,1,1,1,1] [1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[8,4,2,1,3,5,6,7]=>[2,4,1,8,3,5,6,7]=>[8] [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[8,3,2,1,4,5,6,7]=>[2,3,8,1,4,5,6,7]=>[8] [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,1,5,6,7,8]=>[2,3,4,1,5,6,7,8]=>[4,1,1,1,1] [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[3,4,2,1,5,6,7,8]=>[2,4,3,1,5,6,7,8]=>[3,1,1,1,1,1] [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[8,2,3,1,4,5,6,7]=>[3,8,2,1,4,5,6,7]=>[8] [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,1,4,6,7,8]=>[3,5,2,1,4,6,7,8]=>[5,1,1,1] [1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[4,2,3,1,5,6,7,8]=>[3,4,2,1,5,6,7,8]=>[4,1,1,1,1] [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[3,2,4,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>[2,2,1,1,1,1] [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,1,5,6,7,8]=>[4,2,3,1,5,6,7,8]=>[2,1,1,1,1,1,1] [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[8,4,1,2,3,5,6,7]=>[4,1,2,8,3,5,6,7]=>[8] [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[4,5,1,2,3,6,7,8]=>[5,1,2,4,3,6,7,8]=>[4,1,1,1,1] [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[8,3,1,2,4,5,6,7]=>[3,1,8,2,4,5,6,7]=>[8] [1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[6,3,1,2,4,5,7,8]=>[3,1,6,2,4,5,7,8]=>[6,1,1] [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[4,3,1,2,5,6,7,8]=>[3,1,4,2,5,6,7,8]=>[4,1,1,1,1] [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[3,4,1,2,5,6,7,8]=>[4,1,3,2,5,6,7,8]=>[3,1,1,1,1,1] [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[5,2,1,3,4,6,7,8]=>[2,5,1,3,4,6,7,8]=>[5,1,1,1] [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[4,2,1,3,5,6,7,8]=>[2,4,1,3,5,6,7,8]=>[4,1,1,1,1] [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1,4,5,6,7,8]=>[2,3,1,4,5,6,7,8]=>[3,1,1,1,1,1] [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>[2,1,1,1,1,1,1] [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[8,1,2,3,4,5,6,7]=>[8,1,2,3,4,5,6,7]=>[8] [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,1,2,3,4,5,6,8]=>[7,1,2,3,4,5,6,8]=>[7,1] [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[5,1,2,3,4,6,7,8]=>[5,1,2,3,4,6,7,8]=>[5,1,1,1] [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[4,1,2,3,5,6,7,8]=>[4,1,2,3,5,6,7,8]=>[4,1,1,1,1] [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8]=>[3,1,2,4,5,6,7,8]=>[3,1,1,1,1,1] [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>[2,1,1,1,1,1,1] [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[1,1,1,1,1,1,1,1] [1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[6,7,8,9,10,5,4,3,2,1]=>[2,3,4,5,10,6,7,8,9,1]=>[6,1,1,1,1]
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
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 maxima 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 weak deficiency positions of $\chi(\pi)$, and
  • the set of minimal elements in the decreasing runs of $\pi$ is the set of weak deficiency values of $\chi(\pi)$.
Map
cycle type
Description
The cycle type of a permutation as a partition.