Identifier
-
Mp00086:
Permutations
—first fundamental transformation⟶
Permutations
Mp00240: Permutations —weak exceedance partition⟶ Set partitions
Mp00080: Set partitions —to permutation⟶ Permutations
St000224: Permutations ⟶ ℤ
Values
=>
Cc0009;cc-rep-2
[1]=>[1]=>{{1}}=>[1]=>0
[1,2]=>[1,2]=>{{1},{2}}=>[1,2]=>0
[2,1]=>[2,1]=>{{1,2}}=>[2,1]=>1
[1,2,3]=>[1,2,3]=>{{1},{2},{3}}=>[1,2,3]=>0
[1,3,2]=>[1,3,2]=>{{1},{2,3}}=>[1,3,2]=>1
[2,1,3]=>[2,1,3]=>{{1,2},{3}}=>[2,1,3]=>1
[2,3,1]=>[3,2,1]=>{{1,3},{2}}=>[3,2,1]=>2
[3,1,2]=>[2,3,1]=>{{1,2,3}}=>[2,3,1]=>2
[3,2,1]=>[3,1,2]=>{{1,3},{2}}=>[3,2,1]=>2
[1,2,3,4]=>[1,2,3,4]=>{{1},{2},{3},{4}}=>[1,2,3,4]=>0
[1,2,4,3]=>[1,2,4,3]=>{{1},{2},{3,4}}=>[1,2,4,3]=>1
[1,3,2,4]=>[1,3,2,4]=>{{1},{2,3},{4}}=>[1,3,2,4]=>1
[1,3,4,2]=>[1,4,3,2]=>{{1},{2,4},{3}}=>[1,4,3,2]=>2
[1,4,2,3]=>[1,3,4,2]=>{{1},{2,3,4}}=>[1,3,4,2]=>2
[1,4,3,2]=>[1,4,2,3]=>{{1},{2,4},{3}}=>[1,4,3,2]=>2
[2,1,3,4]=>[2,1,3,4]=>{{1,2},{3},{4}}=>[2,1,3,4]=>1
[2,1,4,3]=>[2,1,4,3]=>{{1,2},{3,4}}=>[2,1,4,3]=>2
[2,3,1,4]=>[3,2,1,4]=>{{1,3},{2},{4}}=>[3,2,1,4]=>2
[2,3,4,1]=>[4,2,3,1]=>{{1,4},{2},{3}}=>[4,2,3,1]=>3
[2,4,1,3]=>[3,2,4,1]=>{{1,3,4},{2}}=>[3,2,4,1]=>3
[2,4,3,1]=>[4,2,1,3]=>{{1,4},{2},{3}}=>[4,2,3,1]=>3
[3,1,2,4]=>[2,3,1,4]=>{{1,2,3},{4}}=>[2,3,1,4]=>2
[3,1,4,2]=>[3,4,1,2]=>{{1,3},{2,4}}=>[3,4,1,2]=>4
[3,2,1,4]=>[3,1,2,4]=>{{1,3},{2},{4}}=>[3,2,1,4]=>2
[3,2,4,1]=>[4,3,2,1]=>{{1,4},{2,3}}=>[4,3,2,1]=>4
[3,4,1,2]=>[2,4,3,1]=>{{1,2,4},{3}}=>[2,4,3,1]=>3
[3,4,2,1]=>[4,1,3,2]=>{{1,4},{2},{3}}=>[4,2,3,1]=>3
[4,1,2,3]=>[2,3,4,1]=>{{1,2,3,4}}=>[2,3,4,1]=>3
[4,1,3,2]=>[3,4,2,1]=>{{1,3},{2,4}}=>[3,4,1,2]=>4
[4,2,1,3]=>[3,1,4,2]=>{{1,3,4},{2}}=>[3,2,4,1]=>3
[4,2,3,1]=>[4,3,1,2]=>{{1,4},{2,3}}=>[4,3,2,1]=>4
[4,3,1,2]=>[2,4,1,3]=>{{1,2,4},{3}}=>[2,4,3,1]=>3
[4,3,2,1]=>[4,1,2,3]=>{{1,4},{2},{3}}=>[4,2,3,1]=>3
[1,2,3,4,5]=>[1,2,3,4,5]=>{{1},{2},{3},{4},{5}}=>[1,2,3,4,5]=>0
[1,2,3,5,4]=>[1,2,3,5,4]=>{{1},{2},{3},{4,5}}=>[1,2,3,5,4]=>1
[1,2,4,3,5]=>[1,2,4,3,5]=>{{1},{2},{3,4},{5}}=>[1,2,4,3,5]=>1
[1,2,4,5,3]=>[1,2,5,4,3]=>{{1},{2},{3,5},{4}}=>[1,2,5,4,3]=>2
[1,2,5,3,4]=>[1,2,4,5,3]=>{{1},{2},{3,4,5}}=>[1,2,4,5,3]=>2
[1,2,5,4,3]=>[1,2,5,3,4]=>{{1},{2},{3,5},{4}}=>[1,2,5,4,3]=>2
[1,3,2,4,5]=>[1,3,2,4,5]=>{{1},{2,3},{4},{5}}=>[1,3,2,4,5]=>1
[1,3,2,5,4]=>[1,3,2,5,4]=>{{1},{2,3},{4,5}}=>[1,3,2,5,4]=>2
[1,3,4,2,5]=>[1,4,3,2,5]=>{{1},{2,4},{3},{5}}=>[1,4,3,2,5]=>2
[1,3,4,5,2]=>[1,5,3,4,2]=>{{1},{2,5},{3},{4}}=>[1,5,3,4,2]=>3
[1,3,5,2,4]=>[1,4,3,5,2]=>{{1},{2,4,5},{3}}=>[1,4,3,5,2]=>3
[1,3,5,4,2]=>[1,5,3,2,4]=>{{1},{2,5},{3},{4}}=>[1,5,3,4,2]=>3
[1,4,2,3,5]=>[1,3,4,2,5]=>{{1},{2,3,4},{5}}=>[1,3,4,2,5]=>2
[1,4,2,5,3]=>[1,4,5,2,3]=>{{1},{2,4},{3,5}}=>[1,4,5,2,3]=>4
[1,4,3,2,5]=>[1,4,2,3,5]=>{{1},{2,4},{3},{5}}=>[1,4,3,2,5]=>2
[1,4,3,5,2]=>[1,5,4,3,2]=>{{1},{2,5},{3,4}}=>[1,5,4,3,2]=>4
[1,4,5,2,3]=>[1,3,5,4,2]=>{{1},{2,3,5},{4}}=>[1,3,5,4,2]=>3
[1,4,5,3,2]=>[1,5,2,4,3]=>{{1},{2,5},{3},{4}}=>[1,5,3,4,2]=>3
[1,5,2,3,4]=>[1,3,4,5,2]=>{{1},{2,3,4,5}}=>[1,3,4,5,2]=>3
[1,5,2,4,3]=>[1,4,5,3,2]=>{{1},{2,4},{3,5}}=>[1,4,5,2,3]=>4
[1,5,3,2,4]=>[1,4,2,5,3]=>{{1},{2,4,5},{3}}=>[1,4,3,5,2]=>3
[1,5,3,4,2]=>[1,5,4,2,3]=>{{1},{2,5},{3,4}}=>[1,5,4,3,2]=>4
[1,5,4,2,3]=>[1,3,5,2,4]=>{{1},{2,3,5},{4}}=>[1,3,5,4,2]=>3
[1,5,4,3,2]=>[1,5,2,3,4]=>{{1},{2,5},{3},{4}}=>[1,5,3,4,2]=>3
[2,1,3,4,5]=>[2,1,3,4,5]=>{{1,2},{3},{4},{5}}=>[2,1,3,4,5]=>1
[2,1,3,5,4]=>[2,1,3,5,4]=>{{1,2},{3},{4,5}}=>[2,1,3,5,4]=>2
[2,1,4,3,5]=>[2,1,4,3,5]=>{{1,2},{3,4},{5}}=>[2,1,4,3,5]=>2
[2,1,4,5,3]=>[2,1,5,4,3]=>{{1,2},{3,5},{4}}=>[2,1,5,4,3]=>3
[2,1,5,3,4]=>[2,1,4,5,3]=>{{1,2},{3,4,5}}=>[2,1,4,5,3]=>3
[2,1,5,4,3]=>[2,1,5,3,4]=>{{1,2},{3,5},{4}}=>[2,1,5,4,3]=>3
[2,3,1,4,5]=>[3,2,1,4,5]=>{{1,3},{2},{4},{5}}=>[3,2,1,4,5]=>2
[2,3,1,5,4]=>[3,2,1,5,4]=>{{1,3},{2},{4,5}}=>[3,2,1,5,4]=>3
[2,3,4,1,5]=>[4,2,3,1,5]=>{{1,4},{2},{3},{5}}=>[4,2,3,1,5]=>3
[2,3,4,5,1]=>[5,2,3,4,1]=>{{1,5},{2},{3},{4}}=>[5,2,3,4,1]=>4
[2,3,5,1,4]=>[4,2,3,5,1]=>{{1,4,5},{2},{3}}=>[4,2,3,5,1]=>4
[2,3,5,4,1]=>[5,2,3,1,4]=>{{1,5},{2},{3},{4}}=>[5,2,3,4,1]=>4
[2,4,1,3,5]=>[3,2,4,1,5]=>{{1,3,4},{2},{5}}=>[3,2,4,1,5]=>3
[2,4,1,5,3]=>[4,2,5,1,3]=>{{1,4},{2},{3,5}}=>[4,2,5,1,3]=>5
[2,4,3,1,5]=>[4,2,1,3,5]=>{{1,4},{2},{3},{5}}=>[4,2,3,1,5]=>3
[2,4,3,5,1]=>[5,2,4,3,1]=>{{1,5},{2},{3,4}}=>[5,2,4,3,1]=>5
[2,4,5,1,3]=>[3,2,5,4,1]=>{{1,3,5},{2},{4}}=>[3,2,5,4,1]=>4
[2,4,5,3,1]=>[5,2,1,4,3]=>{{1,5},{2},{3},{4}}=>[5,2,3,4,1]=>4
[2,5,1,3,4]=>[3,2,4,5,1]=>{{1,3,4,5},{2}}=>[3,2,4,5,1]=>4
[2,5,1,4,3]=>[4,2,5,3,1]=>{{1,4},{2},{3,5}}=>[4,2,5,1,3]=>5
[2,5,3,1,4]=>[4,2,1,5,3]=>{{1,4,5},{2},{3}}=>[4,2,3,5,1]=>4
[2,5,3,4,1]=>[5,2,4,1,3]=>{{1,5},{2},{3,4}}=>[5,2,4,3,1]=>5
[2,5,4,1,3]=>[3,2,5,1,4]=>{{1,3,5},{2},{4}}=>[3,2,5,4,1]=>4
[2,5,4,3,1]=>[5,2,1,3,4]=>{{1,5},{2},{3},{4}}=>[5,2,3,4,1]=>4
[3,1,2,4,5]=>[2,3,1,4,5]=>{{1,2,3},{4},{5}}=>[2,3,1,4,5]=>2
[3,1,2,5,4]=>[2,3,1,5,4]=>{{1,2,3},{4,5}}=>[2,3,1,5,4]=>3
[3,1,4,2,5]=>[3,4,1,2,5]=>{{1,3},{2,4},{5}}=>[3,4,1,2,5]=>4
[3,1,4,5,2]=>[3,5,1,4,2]=>{{1,3},{2,5},{4}}=>[3,5,1,4,2]=>5
[3,1,5,2,4]=>[3,4,1,5,2]=>{{1,3},{2,4,5}}=>[3,4,1,5,2]=>5
[3,1,5,4,2]=>[3,5,1,2,4]=>{{1,3},{2,5},{4}}=>[3,5,1,4,2]=>5
[3,2,1,4,5]=>[3,1,2,4,5]=>{{1,3},{2},{4},{5}}=>[3,2,1,4,5]=>2
[3,2,1,5,4]=>[3,1,2,5,4]=>{{1,3},{2},{4,5}}=>[3,2,1,5,4]=>3
[3,2,4,1,5]=>[4,3,2,1,5]=>{{1,4},{2,3},{5}}=>[4,3,2,1,5]=>4
[3,2,4,5,1]=>[5,3,2,4,1]=>{{1,5},{2,3},{4}}=>[5,3,2,4,1]=>5
[3,2,5,1,4]=>[4,3,2,5,1]=>{{1,4,5},{2,3}}=>[4,3,2,5,1]=>5
[3,2,5,4,1]=>[5,3,2,1,4]=>{{1,5},{2,3},{4}}=>[5,3,2,4,1]=>5
[3,4,1,2,5]=>[2,4,3,1,5]=>{{1,2,4},{3},{5}}=>[2,4,3,1,5]=>3
[3,4,1,5,2]=>[4,5,3,1,2]=>{{1,4},{2,5},{3}}=>[4,5,3,1,2]=>6
[3,4,2,1,5]=>[4,1,3,2,5]=>{{1,4},{2},{3},{5}}=>[4,2,3,1,5]=>3
[3,4,2,5,1]=>[5,4,3,2,1]=>{{1,5},{2,4},{3}}=>[5,4,3,2,1]=>6
[3,4,5,1,2]=>[2,5,3,4,1]=>{{1,2,5},{3},{4}}=>[2,5,3,4,1]=>4
[3,4,5,2,1]=>[5,1,3,4,2]=>{{1,5},{2},{3},{4}}=>[5,2,3,4,1]=>4
[3,5,1,2,4]=>[2,4,3,5,1]=>{{1,2,4,5},{3}}=>[2,4,3,5,1]=>4
[3,5,1,4,2]=>[4,5,3,2,1]=>{{1,4},{2,5},{3}}=>[4,5,3,1,2]=>6
[3,5,2,1,4]=>[4,1,3,5,2]=>{{1,4,5},{2},{3}}=>[4,2,3,5,1]=>4
[3,5,2,4,1]=>[5,4,3,1,2]=>{{1,5},{2,4},{3}}=>[5,4,3,2,1]=>6
[3,5,4,1,2]=>[2,5,3,1,4]=>{{1,2,5},{3},{4}}=>[2,5,3,4,1]=>4
[3,5,4,2,1]=>[5,1,3,2,4]=>{{1,5},{2},{3},{4}}=>[5,2,3,4,1]=>4
[4,1,2,3,5]=>[2,3,4,1,5]=>{{1,2,3,4},{5}}=>[2,3,4,1,5]=>3
[4,1,2,5,3]=>[2,4,5,1,3]=>{{1,2,4},{3,5}}=>[2,4,5,1,3]=>5
[4,1,3,2,5]=>[3,4,2,1,5]=>{{1,3},{2,4},{5}}=>[3,4,1,2,5]=>4
[4,1,3,5,2]=>[3,5,4,1,2]=>{{1,3,4},{2,5}}=>[3,5,4,1,2]=>6
[4,1,5,2,3]=>[4,3,5,1,2]=>{{1,4},{2,3,5}}=>[4,3,5,1,2]=>6
[4,1,5,3,2]=>[4,5,2,1,3]=>{{1,4},{2,5},{3}}=>[4,5,3,1,2]=>6
[4,2,1,3,5]=>[3,1,4,2,5]=>{{1,3,4},{2},{5}}=>[3,2,4,1,5]=>3
[4,2,1,5,3]=>[4,1,5,2,3]=>{{1,4},{2},{3,5}}=>[4,2,5,1,3]=>5
[4,2,3,1,5]=>[4,3,1,2,5]=>{{1,4},{2,3},{5}}=>[4,3,2,1,5]=>4
[4,2,3,5,1]=>[5,3,4,2,1]=>{{1,5},{2,3,4}}=>[5,3,4,2,1]=>6
[4,2,5,1,3]=>[3,4,5,2,1]=>{{1,3,5},{2,4}}=>[3,4,5,2,1]=>6
[4,2,5,3,1]=>[5,4,1,2,3]=>{{1,5},{2,4},{3}}=>[5,4,3,2,1]=>6
[4,3,1,2,5]=>[2,4,1,3,5]=>{{1,2,4},{3},{5}}=>[2,4,3,1,5]=>3
[4,3,1,5,2]=>[4,5,1,3,2]=>{{1,4},{2,5},{3}}=>[4,5,3,1,2]=>6
[4,3,2,1,5]=>[4,1,2,3,5]=>{{1,4},{2},{3},{5}}=>[4,2,3,1,5]=>3
[4,3,2,5,1]=>[5,4,2,3,1]=>{{1,5},{2,4},{3}}=>[5,4,3,2,1]=>6
[4,3,5,1,2]=>[2,5,4,3,1]=>{{1,2,5},{3,4}}=>[2,5,4,3,1]=>5
[4,3,5,2,1]=>[5,1,4,3,2]=>{{1,5},{2},{3,4}}=>[5,2,4,3,1]=>5
[4,5,1,2,3]=>[2,3,5,4,1]=>{{1,2,3,5},{4}}=>[2,3,5,4,1]=>4
[4,5,1,3,2]=>[3,5,2,4,1]=>{{1,3},{2,5},{4}}=>[3,5,1,4,2]=>5
[4,5,2,1,3]=>[3,1,5,4,2]=>{{1,3,5},{2},{4}}=>[3,2,5,4,1]=>4
[4,5,2,3,1]=>[5,3,1,4,2]=>{{1,5},{2,3},{4}}=>[5,3,2,4,1]=>5
[4,5,3,1,2]=>[2,5,1,4,3]=>{{1,2,5},{3},{4}}=>[2,5,3,4,1]=>4
[4,5,3,2,1]=>[5,1,2,4,3]=>{{1,5},{2},{3},{4}}=>[5,2,3,4,1]=>4
[5,1,2,3,4]=>[2,3,4,5,1]=>{{1,2,3,4,5}}=>[2,3,4,5,1]=>4
[5,1,2,4,3]=>[2,4,5,3,1]=>{{1,2,4},{3,5}}=>[2,4,5,1,3]=>5
[5,1,3,2,4]=>[3,4,2,5,1]=>{{1,3},{2,4,5}}=>[3,4,1,5,2]=>5
[5,1,3,4,2]=>[3,5,4,2,1]=>{{1,3,4},{2,5}}=>[3,5,4,1,2]=>6
[5,1,4,2,3]=>[4,3,5,2,1]=>{{1,4},{2,3,5}}=>[4,3,5,1,2]=>6
[5,1,4,3,2]=>[4,5,2,3,1]=>{{1,4},{2,5},{3}}=>[4,5,3,1,2]=>6
[5,2,1,3,4]=>[3,1,4,5,2]=>{{1,3,4,5},{2}}=>[3,2,4,5,1]=>4
[5,2,1,4,3]=>[4,1,5,3,2]=>{{1,4},{2},{3,5}}=>[4,2,5,1,3]=>5
[5,2,3,1,4]=>[4,3,1,5,2]=>{{1,4,5},{2,3}}=>[4,3,2,5,1]=>5
[5,2,3,4,1]=>[5,3,4,1,2]=>{{1,5},{2,3,4}}=>[5,3,4,2,1]=>6
[5,2,4,1,3]=>[3,4,5,1,2]=>{{1,3,5},{2,4}}=>[3,4,5,2,1]=>6
[5,2,4,3,1]=>[5,4,1,3,2]=>{{1,5},{2,4},{3}}=>[5,4,3,2,1]=>6
[5,3,1,2,4]=>[2,4,1,5,3]=>{{1,2,4,5},{3}}=>[2,4,3,5,1]=>4
[5,3,1,4,2]=>[4,5,1,2,3]=>{{1,4},{2,5},{3}}=>[4,5,3,1,2]=>6
[5,3,2,1,4]=>[4,1,2,5,3]=>{{1,4,5},{2},{3}}=>[4,2,3,5,1]=>4
[5,3,2,4,1]=>[5,4,2,1,3]=>{{1,5},{2,4},{3}}=>[5,4,3,2,1]=>6
[5,3,4,1,2]=>[2,5,4,1,3]=>{{1,2,5},{3,4}}=>[2,5,4,3,1]=>5
[5,3,4,2,1]=>[5,1,4,2,3]=>{{1,5},{2},{3,4}}=>[5,2,4,3,1]=>5
[5,4,1,2,3]=>[2,3,5,1,4]=>{{1,2,3,5},{4}}=>[2,3,5,4,1]=>4
[5,4,1,3,2]=>[3,5,2,1,4]=>{{1,3},{2,5},{4}}=>[3,5,1,4,2]=>5
[5,4,2,1,3]=>[3,1,5,2,4]=>{{1,3,5},{2},{4}}=>[3,2,5,4,1]=>4
[5,4,2,3,1]=>[5,3,1,2,4]=>{{1,5},{2,3},{4}}=>[5,3,2,4,1]=>5
[5,4,3,1,2]=>[2,5,1,3,4]=>{{1,2,5},{3},{4}}=>[2,5,3,4,1]=>4
[5,4,3,2,1]=>[5,1,2,3,4]=>{{1,5},{2},{3},{4}}=>[5,2,3,4,1]=>4
[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>{{1},{2},{3},{4},{5},{6}}=>[1,2,3,4,5,6]=>0
[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>{{1},{2},{3},{4},{5,6}}=>[1,2,3,4,6,5]=>1
[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>{{1},{2},{3},{4,5},{6}}=>[1,2,3,5,4,6]=>1
[1,2,3,5,6,4]=>[1,2,3,6,5,4]=>{{1},{2},{3},{4,6},{5}}=>[1,2,3,6,5,4]=>2
[1,2,3,6,4,5]=>[1,2,3,5,6,4]=>{{1},{2},{3},{4,5,6}}=>[1,2,3,5,6,4]=>2
[1,2,3,6,5,4]=>[1,2,3,6,4,5]=>{{1},{2},{3},{4,6},{5}}=>[1,2,3,6,5,4]=>2
[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>{{1},{2},{3,4},{5},{6}}=>[1,2,4,3,5,6]=>1
[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>{{1},{2},{3,4},{5,6}}=>[1,2,4,3,6,5]=>2
[1,2,4,5,3,6]=>[1,2,5,4,3,6]=>{{1},{2},{3,5},{4},{6}}=>[1,2,5,4,3,6]=>2
[1,2,4,5,6,3]=>[1,2,6,4,5,3]=>{{1},{2},{3,6},{4},{5}}=>[1,2,6,4,5,3]=>3
[1,2,4,6,3,5]=>[1,2,5,4,6,3]=>{{1},{2},{3,5,6},{4}}=>[1,2,5,4,6,3]=>3
[1,2,4,6,5,3]=>[1,2,6,4,3,5]=>{{1},{2},{3,6},{4},{5}}=>[1,2,6,4,5,3]=>3
[1,2,5,3,4,6]=>[1,2,4,5,3,6]=>{{1},{2},{3,4,5},{6}}=>[1,2,4,5,3,6]=>2
[1,2,5,3,6,4]=>[1,2,5,6,3,4]=>{{1},{2},{3,5},{4,6}}=>[1,2,5,6,3,4]=>4
[1,2,5,4,3,6]=>[1,2,5,3,4,6]=>{{1},{2},{3,5},{4},{6}}=>[1,2,5,4,3,6]=>2
[1,2,5,4,6,3]=>[1,2,6,5,4,3]=>{{1},{2},{3,6},{4,5}}=>[1,2,6,5,4,3]=>4
[1,2,5,6,3,4]=>[1,2,4,6,5,3]=>{{1},{2},{3,4,6},{5}}=>[1,2,4,6,5,3]=>3
[1,2,5,6,4,3]=>[1,2,6,3,5,4]=>{{1},{2},{3,6},{4},{5}}=>[1,2,6,4,5,3]=>3
[1,2,6,3,4,5]=>[1,2,4,5,6,3]=>{{1},{2},{3,4,5,6}}=>[1,2,4,5,6,3]=>3
[1,2,6,3,5,4]=>[1,2,5,6,4,3]=>{{1},{2},{3,5},{4,6}}=>[1,2,5,6,3,4]=>4
[1,2,6,4,3,5]=>[1,2,5,3,6,4]=>{{1},{2},{3,5,6},{4}}=>[1,2,5,4,6,3]=>3
[1,2,6,4,5,3]=>[1,2,6,5,3,4]=>{{1},{2},{3,6},{4,5}}=>[1,2,6,5,4,3]=>4
[1,2,6,5,3,4]=>[1,2,4,6,3,5]=>{{1},{2},{3,4,6},{5}}=>[1,2,4,6,5,3]=>3
[1,2,6,5,4,3]=>[1,2,6,3,4,5]=>{{1},{2},{3,6},{4},{5}}=>[1,2,6,4,5,3]=>3
[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>{{1},{2,3},{4},{5},{6}}=>[1,3,2,4,5,6]=>1
[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>{{1},{2,3},{4},{5,6}}=>[1,3,2,4,6,5]=>2
[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>{{1},{2,3},{4,5},{6}}=>[1,3,2,5,4,6]=>2
[1,3,2,5,6,4]=>[1,3,2,6,5,4]=>{{1},{2,3},{4,6},{5}}=>[1,3,2,6,5,4]=>3
[1,3,2,6,4,5]=>[1,3,2,5,6,4]=>{{1},{2,3},{4,5,6}}=>[1,3,2,5,6,4]=>3
[1,3,2,6,5,4]=>[1,3,2,6,4,5]=>{{1},{2,3},{4,6},{5}}=>[1,3,2,6,5,4]=>3
[1,3,4,2,5,6]=>[1,4,3,2,5,6]=>{{1},{2,4},{3},{5},{6}}=>[1,4,3,2,5,6]=>2
[1,3,4,2,6,5]=>[1,4,3,2,6,5]=>{{1},{2,4},{3},{5,6}}=>[1,4,3,2,6,5]=>3
[1,3,4,5,2,6]=>[1,5,3,4,2,6]=>{{1},{2,5},{3},{4},{6}}=>[1,5,3,4,2,6]=>3
[1,3,4,5,6,2]=>[1,6,3,4,5,2]=>{{1},{2,6},{3},{4},{5}}=>[1,6,3,4,5,2]=>4
[1,3,4,6,2,5]=>[1,5,3,4,6,2]=>{{1},{2,5,6},{3},{4}}=>[1,5,3,4,6,2]=>4
[1,3,4,6,5,2]=>[1,6,3,4,2,5]=>{{1},{2,6},{3},{4},{5}}=>[1,6,3,4,5,2]=>4
[1,3,5,2,4,6]=>[1,4,3,5,2,6]=>{{1},{2,4,5},{3},{6}}=>[1,4,3,5,2,6]=>3
[1,3,5,2,6,4]=>[1,5,3,6,2,4]=>{{1},{2,5},{3},{4,6}}=>[1,5,3,6,2,4]=>5
[1,3,5,4,2,6]=>[1,5,3,2,4,6]=>{{1},{2,5},{3},{4},{6}}=>[1,5,3,4,2,6]=>3
[1,3,5,4,6,2]=>[1,6,3,5,4,2]=>{{1},{2,6},{3},{4,5}}=>[1,6,3,5,4,2]=>5
[1,3,5,6,2,4]=>[1,4,3,6,5,2]=>{{1},{2,4,6},{3},{5}}=>[1,4,3,6,5,2]=>4
[1,3,5,6,4,2]=>[1,6,3,2,5,4]=>{{1},{2,6},{3},{4},{5}}=>[1,6,3,4,5,2]=>4
[1,3,6,2,4,5]=>[1,4,3,5,6,2]=>{{1},{2,4,5,6},{3}}=>[1,4,3,5,6,2]=>4
[1,3,6,2,5,4]=>[1,5,3,6,4,2]=>{{1},{2,5},{3},{4,6}}=>[1,5,3,6,2,4]=>5
[1,3,6,4,2,5]=>[1,5,3,2,6,4]=>{{1},{2,5,6},{3},{4}}=>[1,5,3,4,6,2]=>4
[1,3,6,4,5,2]=>[1,6,3,5,2,4]=>{{1},{2,6},{3},{4,5}}=>[1,6,3,5,4,2]=>5
[1,3,6,5,2,4]=>[1,4,3,6,2,5]=>{{1},{2,4,6},{3},{5}}=>[1,4,3,6,5,2]=>4
[1,3,6,5,4,2]=>[1,6,3,2,4,5]=>{{1},{2,6},{3},{4},{5}}=>[1,6,3,4,5,2]=>4
[1,4,2,3,5,6]=>[1,3,4,2,5,6]=>{{1},{2,3,4},{5},{6}}=>[1,3,4,2,5,6]=>2
[1,4,2,3,6,5]=>[1,3,4,2,6,5]=>{{1},{2,3,4},{5,6}}=>[1,3,4,2,6,5]=>3
[1,4,2,5,3,6]=>[1,4,5,2,3,6]=>{{1},{2,4},{3,5},{6}}=>[1,4,5,2,3,6]=>4
[1,4,2,5,6,3]=>[1,4,6,2,5,3]=>{{1},{2,4},{3,6},{5}}=>[1,4,6,2,5,3]=>5
[1,4,2,6,3,5]=>[1,4,5,2,6,3]=>{{1},{2,4},{3,5,6}}=>[1,4,5,2,6,3]=>5
[1,4,2,6,5,3]=>[1,4,6,2,3,5]=>{{1},{2,4},{3,6},{5}}=>[1,4,6,2,5,3]=>5
[1,4,3,2,5,6]=>[1,4,2,3,5,6]=>{{1},{2,4},{3},{5},{6}}=>[1,4,3,2,5,6]=>2
[1,4,3,2,6,5]=>[1,4,2,3,6,5]=>{{1},{2,4},{3},{5,6}}=>[1,4,3,2,6,5]=>3
[1,4,3,5,2,6]=>[1,5,4,3,2,6]=>{{1},{2,5},{3,4},{6}}=>[1,5,4,3,2,6]=>4
[1,4,3,5,6,2]=>[1,6,4,3,5,2]=>{{1},{2,6},{3,4},{5}}=>[1,6,4,3,5,2]=>5
[1,4,3,6,2,5]=>[1,5,4,3,6,2]=>{{1},{2,5,6},{3,4}}=>[1,5,4,3,6,2]=>5
[1,4,3,6,5,2]=>[1,6,4,3,2,5]=>{{1},{2,6},{3,4},{5}}=>[1,6,4,3,5,2]=>5
[1,4,5,2,3,6]=>[1,3,5,4,2,6]=>{{1},{2,3,5},{4},{6}}=>[1,3,5,4,2,6]=>3
[1,4,5,2,6,3]=>[1,5,6,4,2,3]=>{{1},{2,5},{3,6},{4}}=>[1,5,6,4,2,3]=>6
[1,4,5,3,2,6]=>[1,5,2,4,3,6]=>{{1},{2,5},{3},{4},{6}}=>[1,5,3,4,2,6]=>3
[1,4,5,3,6,2]=>[1,6,5,4,3,2]=>{{1},{2,6},{3,5},{4}}=>[1,6,5,4,3,2]=>6
[1,4,5,6,2,3]=>[1,3,6,4,5,2]=>{{1},{2,3,6},{4},{5}}=>[1,3,6,4,5,2]=>4
[1,4,5,6,3,2]=>[1,6,2,4,5,3]=>{{1},{2,6},{3},{4},{5}}=>[1,6,3,4,5,2]=>4
[1,4,6,2,3,5]=>[1,3,5,4,6,2]=>{{1},{2,3,5,6},{4}}=>[1,3,5,4,6,2]=>4
[1,4,6,2,5,3]=>[1,5,6,4,3,2]=>{{1},{2,5},{3,6},{4}}=>[1,5,6,4,2,3]=>6
[1,4,6,3,2,5]=>[1,5,2,4,6,3]=>{{1},{2,5,6},{3},{4}}=>[1,5,3,4,6,2]=>4
[1,4,6,3,5,2]=>[1,6,5,4,2,3]=>{{1},{2,6},{3,5},{4}}=>[1,6,5,4,3,2]=>6
[1,4,6,5,2,3]=>[1,3,6,4,2,5]=>{{1},{2,3,6},{4},{5}}=>[1,3,6,4,5,2]=>4
[1,4,6,5,3,2]=>[1,6,2,4,3,5]=>{{1},{2,6},{3},{4},{5}}=>[1,6,3,4,5,2]=>4
[1,5,2,3,4,6]=>[1,3,4,5,2,6]=>{{1},{2,3,4,5},{6}}=>[1,3,4,5,2,6]=>3
[1,5,2,3,6,4]=>[1,3,5,6,2,4]=>{{1},{2,3,5},{4,6}}=>[1,3,5,6,2,4]=>5
[1,5,2,4,3,6]=>[1,4,5,3,2,6]=>{{1},{2,4},{3,5},{6}}=>[1,4,5,2,3,6]=>4
[1,5,2,4,6,3]=>[1,4,6,5,2,3]=>{{1},{2,4,5},{3,6}}=>[1,4,6,5,2,3]=>6
[1,5,2,6,3,4]=>[1,5,4,6,2,3]=>{{1},{2,5},{3,4,6}}=>[1,5,4,6,2,3]=>6
[1,5,2,6,4,3]=>[1,5,6,3,2,4]=>{{1},{2,5},{3,6},{4}}=>[1,5,6,4,2,3]=>6
[1,5,3,2,4,6]=>[1,4,2,5,3,6]=>{{1},{2,4,5},{3},{6}}=>[1,4,3,5,2,6]=>3
[1,5,3,2,6,4]=>[1,5,2,6,3,4]=>{{1},{2,5},{3},{4,6}}=>[1,5,3,6,2,4]=>5
[1,5,3,4,2,6]=>[1,5,4,2,3,6]=>{{1},{2,5},{3,4},{6}}=>[1,5,4,3,2,6]=>4
[1,5,3,4,6,2]=>[1,6,4,5,3,2]=>{{1},{2,6},{3,4,5}}=>[1,6,4,5,3,2]=>6
[1,5,3,6,2,4]=>[1,4,5,6,3,2]=>{{1},{2,4,6},{3,5}}=>[1,4,5,6,3,2]=>6
[1,5,3,6,4,2]=>[1,6,5,2,3,4]=>{{1},{2,6},{3,5},{4}}=>[1,6,5,4,3,2]=>6
[1,5,4,2,3,6]=>[1,3,5,2,4,6]=>{{1},{2,3,5},{4},{6}}=>[1,3,5,4,2,6]=>3
[1,5,4,2,6,3]=>[1,5,6,2,4,3]=>{{1},{2,5},{3,6},{4}}=>[1,5,6,4,2,3]=>6
[1,5,4,3,2,6]=>[1,5,2,3,4,6]=>{{1},{2,5},{3},{4},{6}}=>[1,5,3,4,2,6]=>3
[1,5,4,3,6,2]=>[1,6,5,3,4,2]=>{{1},{2,6},{3,5},{4}}=>[1,6,5,4,3,2]=>6
[1,5,4,6,2,3]=>[1,3,6,5,4,2]=>{{1},{2,3,6},{4,5}}=>[1,3,6,5,4,2]=>5
[1,5,4,6,3,2]=>[1,6,2,5,4,3]=>{{1},{2,6},{3},{4,5}}=>[1,6,3,5,4,2]=>5
[1,5,6,2,3,4]=>[1,3,4,6,5,2]=>{{1},{2,3,4,6},{5}}=>[1,3,4,6,5,2]=>4
[1,5,6,2,4,3]=>[1,4,6,3,5,2]=>{{1},{2,4},{3,6},{5}}=>[1,4,6,2,5,3]=>5
[1,5,6,3,2,4]=>[1,4,2,6,5,3]=>{{1},{2,4,6},{3},{5}}=>[1,4,3,6,5,2]=>4
[1,5,6,3,4,2]=>[1,6,4,2,5,3]=>{{1},{2,6},{3,4},{5}}=>[1,6,4,3,5,2]=>5
[1,5,6,4,2,3]=>[1,3,6,2,5,4]=>{{1},{2,3,6},{4},{5}}=>[1,3,6,4,5,2]=>4
[1,5,6,4,3,2]=>[1,6,2,3,5,4]=>{{1},{2,6},{3},{4},{5}}=>[1,6,3,4,5,2]=>4
[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}=>[1,3,4,5,6,2]=>4
[1,6,2,3,5,4]=>[1,3,5,6,4,2]=>{{1},{2,3,5},{4,6}}=>[1,3,5,6,2,4]=>5
[1,6,2,4,3,5]=>[1,4,5,3,6,2]=>{{1},{2,4},{3,5,6}}=>[1,4,5,2,6,3]=>5
[1,6,2,4,5,3]=>[1,4,6,5,3,2]=>{{1},{2,4,5},{3,6}}=>[1,4,6,5,2,3]=>6
[1,6,2,5,3,4]=>[1,5,4,6,3,2]=>{{1},{2,5},{3,4,6}}=>[1,5,4,6,2,3]=>6
[1,6,2,5,4,3]=>[1,5,6,3,4,2]=>{{1},{2,5},{3,6},{4}}=>[1,5,6,4,2,3]=>6
[1,6,3,2,4,5]=>[1,4,2,5,6,3]=>{{1},{2,4,5,6},{3}}=>[1,4,3,5,6,2]=>4
[1,6,3,2,5,4]=>[1,5,2,6,4,3]=>{{1},{2,5},{3},{4,6}}=>[1,5,3,6,2,4]=>5
[1,6,3,4,2,5]=>[1,5,4,2,6,3]=>{{1},{2,5,6},{3,4}}=>[1,5,4,3,6,2]=>5
[1,6,3,4,5,2]=>[1,6,4,5,2,3]=>{{1},{2,6},{3,4,5}}=>[1,6,4,5,3,2]=>6
[1,6,3,5,2,4]=>[1,4,5,6,2,3]=>{{1},{2,4,6},{3,5}}=>[1,4,5,6,3,2]=>6
[1,6,3,5,4,2]=>[1,6,5,2,4,3]=>{{1},{2,6},{3,5},{4}}=>[1,6,5,4,3,2]=>6
[1,6,4,2,3,5]=>[1,3,5,2,6,4]=>{{1},{2,3,5,6},{4}}=>[1,3,5,4,6,2]=>4
[1,6,4,2,5,3]=>[1,5,6,2,3,4]=>{{1},{2,5},{3,6},{4}}=>[1,5,6,4,2,3]=>6
[1,6,4,3,2,5]=>[1,5,2,3,6,4]=>{{1},{2,5,6},{3},{4}}=>[1,5,3,4,6,2]=>4
[1,6,4,3,5,2]=>[1,6,5,3,2,4]=>{{1},{2,6},{3,5},{4}}=>[1,6,5,4,3,2]=>6
[1,6,4,5,2,3]=>[1,3,6,5,2,4]=>{{1},{2,3,6},{4,5}}=>[1,3,6,5,4,2]=>5
[1,6,4,5,3,2]=>[1,6,2,5,3,4]=>{{1},{2,6},{3},{4,5}}=>[1,6,3,5,4,2]=>5
[1,6,5,2,3,4]=>[1,3,4,6,2,5]=>{{1},{2,3,4,6},{5}}=>[1,3,4,6,5,2]=>4
[1,6,5,2,4,3]=>[1,4,6,3,2,5]=>{{1},{2,4},{3,6},{5}}=>[1,4,6,2,5,3]=>5
[1,6,5,3,2,4]=>[1,4,2,6,3,5]=>{{1},{2,4,6},{3},{5}}=>[1,4,3,6,5,2]=>4
[1,6,5,3,4,2]=>[1,6,4,2,3,5]=>{{1},{2,6},{3,4},{5}}=>[1,6,4,3,5,2]=>5
[1,6,5,4,2,3]=>[1,3,6,2,4,5]=>{{1},{2,3,6},{4},{5}}=>[1,3,6,4,5,2]=>4
[1,6,5,4,3,2]=>[1,6,2,3,4,5]=>{{1},{2,6},{3},{4},{5}}=>[1,6,3,4,5,2]=>4
[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>{{1,2},{3},{4},{5},{6}}=>[2,1,3,4,5,6]=>1
[2,1,3,4,6,5]=>[2,1,3,4,6,5]=>{{1,2},{3},{4},{5,6}}=>[2,1,3,4,6,5]=>2
[2,1,3,5,4,6]=>[2,1,3,5,4,6]=>{{1,2},{3},{4,5},{6}}=>[2,1,3,5,4,6]=>2
[2,1,3,5,6,4]=>[2,1,3,6,5,4]=>{{1,2},{3},{4,6},{5}}=>[2,1,3,6,5,4]=>3
[2,1,3,6,4,5]=>[2,1,3,5,6,4]=>{{1,2},{3},{4,5,6}}=>[2,1,3,5,6,4]=>3
[2,1,3,6,5,4]=>[2,1,3,6,4,5]=>{{1,2},{3},{4,6},{5}}=>[2,1,3,6,5,4]=>3
[2,1,4,3,5,6]=>[2,1,4,3,5,6]=>{{1,2},{3,4},{5},{6}}=>[2,1,4,3,5,6]=>2
[2,1,4,3,6,5]=>[2,1,4,3,6,5]=>{{1,2},{3,4},{5,6}}=>[2,1,4,3,6,5]=>3
[2,1,4,5,3,6]=>[2,1,5,4,3,6]=>{{1,2},{3,5},{4},{6}}=>[2,1,5,4,3,6]=>3
[2,1,4,5,6,3]=>[2,1,6,4,5,3]=>{{1,2},{3,6},{4},{5}}=>[2,1,6,4,5,3]=>4
[2,1,4,6,3,5]=>[2,1,5,4,6,3]=>{{1,2},{3,5,6},{4}}=>[2,1,5,4,6,3]=>4
[2,1,4,6,5,3]=>[2,1,6,4,3,5]=>{{1,2},{3,6},{4},{5}}=>[2,1,6,4,5,3]=>4
[2,1,5,3,4,6]=>[2,1,4,5,3,6]=>{{1,2},{3,4,5},{6}}=>[2,1,4,5,3,6]=>3
[2,1,5,3,6,4]=>[2,1,5,6,3,4]=>{{1,2},{3,5},{4,6}}=>[2,1,5,6,3,4]=>5
[2,1,5,4,3,6]=>[2,1,5,3,4,6]=>{{1,2},{3,5},{4},{6}}=>[2,1,5,4,3,6]=>3
[2,1,5,4,6,3]=>[2,1,6,5,4,3]=>{{1,2},{3,6},{4,5}}=>[2,1,6,5,4,3]=>5
[2,1,5,6,3,4]=>[2,1,4,6,5,3]=>{{1,2},{3,4,6},{5}}=>[2,1,4,6,5,3]=>4
[2,1,5,6,4,3]=>[2,1,6,3,5,4]=>{{1,2},{3,6},{4},{5}}=>[2,1,6,4,5,3]=>4
[2,1,6,3,4,5]=>[2,1,4,5,6,3]=>{{1,2},{3,4,5,6}}=>[2,1,4,5,6,3]=>4
[2,1,6,3,5,4]=>[2,1,5,6,4,3]=>{{1,2},{3,5},{4,6}}=>[2,1,5,6,3,4]=>5
[2,1,6,4,3,5]=>[2,1,5,3,6,4]=>{{1,2},{3,5,6},{4}}=>[2,1,5,4,6,3]=>4
[2,1,6,4,5,3]=>[2,1,6,5,3,4]=>{{1,2},{3,6},{4,5}}=>[2,1,6,5,4,3]=>5
[2,1,6,5,3,4]=>[2,1,4,6,3,5]=>{{1,2},{3,4,6},{5}}=>[2,1,4,6,5,3]=>4
[2,1,6,5,4,3]=>[2,1,6,3,4,5]=>{{1,2},{3,6},{4},{5}}=>[2,1,6,4,5,3]=>4
[2,3,1,4,5,6]=>[3,2,1,4,5,6]=>{{1,3},{2},{4},{5},{6}}=>[3,2,1,4,5,6]=>2
[2,3,1,4,6,5]=>[3,2,1,4,6,5]=>{{1,3},{2},{4},{5,6}}=>[3,2,1,4,6,5]=>3
[2,3,1,5,4,6]=>[3,2,1,5,4,6]=>{{1,3},{2},{4,5},{6}}=>[3,2,1,5,4,6]=>3
[2,3,1,5,6,4]=>[3,2,1,6,5,4]=>{{1,3},{2},{4,6},{5}}=>[3,2,1,6,5,4]=>4
[2,3,1,6,4,5]=>[3,2,1,5,6,4]=>{{1,3},{2},{4,5,6}}=>[3,2,1,5,6,4]=>4
[2,3,1,6,5,4]=>[3,2,1,6,4,5]=>{{1,3},{2},{4,6},{5}}=>[3,2,1,6,5,4]=>4
[2,3,4,1,5,6]=>[4,2,3,1,5,6]=>{{1,4},{2},{3},{5},{6}}=>[4,2,3,1,5,6]=>3
[2,3,4,1,6,5]=>[4,2,3,1,6,5]=>{{1,4},{2},{3},{5,6}}=>[4,2,3,1,6,5]=>4
[2,3,4,5,1,6]=>[5,2,3,4,1,6]=>{{1,5},{2},{3},{4},{6}}=>[5,2,3,4,1,6]=>4
[2,3,4,5,6,1]=>[6,2,3,4,5,1]=>{{1,6},{2},{3},{4},{5}}=>[6,2,3,4,5,1]=>5
[2,3,4,6,1,5]=>[5,2,3,4,6,1]=>{{1,5,6},{2},{3},{4}}=>[5,2,3,4,6,1]=>5
[2,3,4,6,5,1]=>[6,2,3,4,1,5]=>{{1,6},{2},{3},{4},{5}}=>[6,2,3,4,5,1]=>5
[2,3,5,1,4,6]=>[4,2,3,5,1,6]=>{{1,4,5},{2},{3},{6}}=>[4,2,3,5,1,6]=>4
[2,3,5,1,6,4]=>[5,2,3,6,1,4]=>{{1,5},{2},{3},{4,6}}=>[5,2,3,6,1,4]=>6
[2,3,5,4,1,6]=>[5,2,3,1,4,6]=>{{1,5},{2},{3},{4},{6}}=>[5,2,3,4,1,6]=>4
[2,3,5,4,6,1]=>[6,2,3,5,4,1]=>{{1,6},{2},{3},{4,5}}=>[6,2,3,5,4,1]=>6
[2,3,5,6,1,4]=>[4,2,3,6,5,1]=>{{1,4,6},{2},{3},{5}}=>[4,2,3,6,5,1]=>5
[2,3,5,6,4,1]=>[6,2,3,1,5,4]=>{{1,6},{2},{3},{4},{5}}=>[6,2,3,4,5,1]=>5
[2,3,6,1,4,5]=>[4,2,3,5,6,1]=>{{1,4,5,6},{2},{3}}=>[4,2,3,5,6,1]=>5
[2,3,6,1,5,4]=>[5,2,3,6,4,1]=>{{1,5},{2},{3},{4,6}}=>[5,2,3,6,1,4]=>6
[2,3,6,4,1,5]=>[5,2,3,1,6,4]=>{{1,5,6},{2},{3},{4}}=>[5,2,3,4,6,1]=>5
[2,3,6,4,5,1]=>[6,2,3,5,1,4]=>{{1,6},{2},{3},{4,5}}=>[6,2,3,5,4,1]=>6
[2,3,6,5,1,4]=>[4,2,3,6,1,5]=>{{1,4,6},{2},{3},{5}}=>[4,2,3,6,5,1]=>5
[2,3,6,5,4,1]=>[6,2,3,1,4,5]=>{{1,6},{2},{3},{4},{5}}=>[6,2,3,4,5,1]=>5
[2,4,1,3,5,6]=>[3,2,4,1,5,6]=>{{1,3,4},{2},{5},{6}}=>[3,2,4,1,5,6]=>3
[2,4,1,3,6,5]=>[3,2,4,1,6,5]=>{{1,3,4},{2},{5,6}}=>[3,2,4,1,6,5]=>4
[2,4,1,5,3,6]=>[4,2,5,1,3,6]=>{{1,4},{2},{3,5},{6}}=>[4,2,5,1,3,6]=>5
[2,4,1,5,6,3]=>[4,2,6,1,5,3]=>{{1,4},{2},{3,6},{5}}=>[4,2,6,1,5,3]=>6
[2,4,1,6,3,5]=>[4,2,5,1,6,3]=>{{1,4},{2},{3,5,6}}=>[4,2,5,1,6,3]=>6
[2,4,1,6,5,3]=>[4,2,6,1,3,5]=>{{1,4},{2},{3,6},{5}}=>[4,2,6,1,5,3]=>6
[2,4,3,1,5,6]=>[4,2,1,3,5,6]=>{{1,4},{2},{3},{5},{6}}=>[4,2,3,1,5,6]=>3
[2,4,3,1,6,5]=>[4,2,1,3,6,5]=>{{1,4},{2},{3},{5,6}}=>[4,2,3,1,6,5]=>4
[2,4,3,5,1,6]=>[5,2,4,3,1,6]=>{{1,5},{2},{3,4},{6}}=>[5,2,4,3,1,6]=>5
[2,4,3,5,6,1]=>[6,2,4,3,5,1]=>{{1,6},{2},{3,4},{5}}=>[6,2,4,3,5,1]=>6
[2,4,3,6,1,5]=>[5,2,4,3,6,1]=>{{1,5,6},{2},{3,4}}=>[5,2,4,3,6,1]=>6
[2,4,3,6,5,1]=>[6,2,4,3,1,5]=>{{1,6},{2},{3,4},{5}}=>[6,2,4,3,5,1]=>6
[2,4,5,1,3,6]=>[3,2,5,4,1,6]=>{{1,3,5},{2},{4},{6}}=>[3,2,5,4,1,6]=>4
[2,4,5,1,6,3]=>[5,2,6,4,1,3]=>{{1,5},{2},{3,6},{4}}=>[5,2,6,4,1,3]=>7
[2,4,5,3,1,6]=>[5,2,1,4,3,6]=>{{1,5},{2},{3},{4},{6}}=>[5,2,3,4,1,6]=>4
[2,4,5,3,6,1]=>[6,2,5,4,3,1]=>{{1,6},{2},{3,5},{4}}=>[6,2,5,4,3,1]=>7
[2,4,5,6,1,3]=>[3,2,6,4,5,1]=>{{1,3,6},{2},{4},{5}}=>[3,2,6,4,5,1]=>5
[2,4,5,6,3,1]=>[6,2,1,4,5,3]=>{{1,6},{2},{3},{4},{5}}=>[6,2,3,4,5,1]=>5
[2,4,6,1,3,5]=>[3,2,5,4,6,1]=>{{1,3,5,6},{2},{4}}=>[3,2,5,4,6,1]=>5
[2,4,6,1,5,3]=>[5,2,6,4,3,1]=>{{1,5},{2},{3,6},{4}}=>[5,2,6,4,1,3]=>7
[2,4,6,3,1,5]=>[5,2,1,4,6,3]=>{{1,5,6},{2},{3},{4}}=>[5,2,3,4,6,1]=>5
[2,4,6,3,5,1]=>[6,2,5,4,1,3]=>{{1,6},{2},{3,5},{4}}=>[6,2,5,4,3,1]=>7
[2,4,6,5,1,3]=>[3,2,6,4,1,5]=>{{1,3,6},{2},{4},{5}}=>[3,2,6,4,5,1]=>5
[2,4,6,5,3,1]=>[6,2,1,4,3,5]=>{{1,6},{2},{3},{4},{5}}=>[6,2,3,4,5,1]=>5
[2,5,1,3,4,6]=>[3,2,4,5,1,6]=>{{1,3,4,5},{2},{6}}=>[3,2,4,5,1,6]=>4
[2,5,1,3,6,4]=>[3,2,5,6,1,4]=>{{1,3,5},{2},{4,6}}=>[3,2,5,6,1,4]=>6
[2,5,1,4,3,6]=>[4,2,5,3,1,6]=>{{1,4},{2},{3,5},{6}}=>[4,2,5,1,3,6]=>5
[2,5,1,4,6,3]=>[4,2,6,5,1,3]=>{{1,4,5},{2},{3,6}}=>[4,2,6,5,1,3]=>7
[2,5,1,6,3,4]=>[5,2,4,6,1,3]=>{{1,5},{2},{3,4,6}}=>[5,2,4,6,1,3]=>7
[2,5,1,6,4,3]=>[5,2,6,3,1,4]=>{{1,5},{2},{3,6},{4}}=>[5,2,6,4,1,3]=>7
[2,5,3,1,4,6]=>[4,2,1,5,3,6]=>{{1,4,5},{2},{3},{6}}=>[4,2,3,5,1,6]=>4
[2,5,3,1,6,4]=>[5,2,1,6,3,4]=>{{1,5},{2},{3},{4,6}}=>[5,2,3,6,1,4]=>6
[2,5,3,4,1,6]=>[5,2,4,1,3,6]=>{{1,5},{2},{3,4},{6}}=>[5,2,4,3,1,6]=>5
[2,5,3,4,6,1]=>[6,2,4,5,3,1]=>{{1,6},{2},{3,4,5}}=>[6,2,4,5,3,1]=>7
[2,5,3,6,1,4]=>[4,2,5,6,3,1]=>{{1,4,6},{2},{3,5}}=>[4,2,5,6,3,1]=>7
[2,5,3,6,4,1]=>[6,2,5,1,3,4]=>{{1,6},{2},{3,5},{4}}=>[6,2,5,4,3,1]=>7
[2,5,4,1,3,6]=>[3,2,5,1,4,6]=>{{1,3,5},{2},{4},{6}}=>[3,2,5,4,1,6]=>4
[2,5,4,1,6,3]=>[5,2,6,1,4,3]=>{{1,5},{2},{3,6},{4}}=>[5,2,6,4,1,3]=>7
[2,5,4,3,1,6]=>[5,2,1,3,4,6]=>{{1,5},{2},{3},{4},{6}}=>[5,2,3,4,1,6]=>4
[2,5,4,3,6,1]=>[6,2,5,3,4,1]=>{{1,6},{2},{3,5},{4}}=>[6,2,5,4,3,1]=>7
[2,5,4,6,1,3]=>[3,2,6,5,4,1]=>{{1,3,6},{2},{4,5}}=>[3,2,6,5,4,1]=>6
[2,5,4,6,3,1]=>[6,2,1,5,4,3]=>{{1,6},{2},{3},{4,5}}=>[6,2,3,5,4,1]=>6
[2,5,6,1,3,4]=>[3,2,4,6,5,1]=>{{1,3,4,6},{2},{5}}=>[3,2,4,6,5,1]=>5
[2,5,6,1,4,3]=>[4,2,6,3,5,1]=>{{1,4},{2},{3,6},{5}}=>[4,2,6,1,5,3]=>6
[2,5,6,3,1,4]=>[4,2,1,6,5,3]=>{{1,4,6},{2},{3},{5}}=>[4,2,3,6,5,1]=>5
[2,5,6,3,4,1]=>[6,2,4,1,5,3]=>{{1,6},{2},{3,4},{5}}=>[6,2,4,3,5,1]=>6
[2,5,6,4,1,3]=>[3,2,6,1,5,4]=>{{1,3,6},{2},{4},{5}}=>[3,2,6,4,5,1]=>5
[2,5,6,4,3,1]=>[6,2,1,3,5,4]=>{{1,6},{2},{3},{4},{5}}=>[6,2,3,4,5,1]=>5
[2,6,1,3,4,5]=>[3,2,4,5,6,1]=>{{1,3,4,5,6},{2}}=>[3,2,4,5,6,1]=>5
[2,6,1,3,5,4]=>[3,2,5,6,4,1]=>{{1,3,5},{2},{4,6}}=>[3,2,5,6,1,4]=>6
[2,6,1,4,3,5]=>[4,2,5,3,6,1]=>{{1,4},{2},{3,5,6}}=>[4,2,5,1,6,3]=>6
[2,6,1,4,5,3]=>[4,2,6,5,3,1]=>{{1,4,5},{2},{3,6}}=>[4,2,6,5,1,3]=>7
[2,6,1,5,3,4]=>[5,2,4,6,3,1]=>{{1,5},{2},{3,4,6}}=>[5,2,4,6,1,3]=>7
[2,6,1,5,4,3]=>[5,2,6,3,4,1]=>{{1,5},{2},{3,6},{4}}=>[5,2,6,4,1,3]=>7
[2,6,3,1,4,5]=>[4,2,1,5,6,3]=>{{1,4,5,6},{2},{3}}=>[4,2,3,5,6,1]=>5
[2,6,3,1,5,4]=>[5,2,1,6,4,3]=>{{1,5},{2},{3},{4,6}}=>[5,2,3,6,1,4]=>6
[2,6,3,4,1,5]=>[5,2,4,1,6,3]=>{{1,5,6},{2},{3,4}}=>[5,2,4,3,6,1]=>6
[2,6,3,4,5,1]=>[6,2,4,5,1,3]=>{{1,6},{2},{3,4,5}}=>[6,2,4,5,3,1]=>7
[2,6,3,5,1,4]=>[4,2,5,6,1,3]=>{{1,4,6},{2},{3,5}}=>[4,2,5,6,3,1]=>7
[2,6,3,5,4,1]=>[6,2,5,1,4,3]=>{{1,6},{2},{3,5},{4}}=>[6,2,5,4,3,1]=>7
[2,6,4,1,3,5]=>[3,2,5,1,6,4]=>{{1,3,5,6},{2},{4}}=>[3,2,5,4,6,1]=>5
[2,6,4,1,5,3]=>[5,2,6,1,3,4]=>{{1,5},{2},{3,6},{4}}=>[5,2,6,4,1,3]=>7
[2,6,4,3,1,5]=>[5,2,1,3,6,4]=>{{1,5,6},{2},{3},{4}}=>[5,2,3,4,6,1]=>5
[2,6,4,3,5,1]=>[6,2,5,3,1,4]=>{{1,6},{2},{3,5},{4}}=>[6,2,5,4,3,1]=>7
[2,6,4,5,1,3]=>[3,2,6,5,1,4]=>{{1,3,6},{2},{4,5}}=>[3,2,6,5,4,1]=>6
[2,6,4,5,3,1]=>[6,2,1,5,3,4]=>{{1,6},{2},{3},{4,5}}=>[6,2,3,5,4,1]=>6
[2,6,5,1,3,4]=>[3,2,4,6,1,5]=>{{1,3,4,6},{2},{5}}=>[3,2,4,6,5,1]=>5
[2,6,5,1,4,3]=>[4,2,6,3,1,5]=>{{1,4},{2},{3,6},{5}}=>[4,2,6,1,5,3]=>6
[2,6,5,3,1,4]=>[4,2,1,6,3,5]=>{{1,4,6},{2},{3},{5}}=>[4,2,3,6,5,1]=>5
[2,6,5,3,4,1]=>[6,2,4,1,3,5]=>{{1,6},{2},{3,4},{5}}=>[6,2,4,3,5,1]=>6
[2,6,5,4,1,3]=>[3,2,6,1,4,5]=>{{1,3,6},{2},{4},{5}}=>[3,2,6,4,5,1]=>5
[2,6,5,4,3,1]=>[6,2,1,3,4,5]=>{{1,6},{2},{3},{4},{5}}=>[6,2,3,4,5,1]=>5
[3,1,2,4,5,6]=>[2,3,1,4,5,6]=>{{1,2,3},{4},{5},{6}}=>[2,3,1,4,5,6]=>2
[3,1,2,4,6,5]=>[2,3,1,4,6,5]=>{{1,2,3},{4},{5,6}}=>[2,3,1,4,6,5]=>3
[3,1,2,5,4,6]=>[2,3,1,5,4,6]=>{{1,2,3},{4,5},{6}}=>[2,3,1,5,4,6]=>3
[3,1,2,5,6,4]=>[2,3,1,6,5,4]=>{{1,2,3},{4,6},{5}}=>[2,3,1,6,5,4]=>4
[3,1,2,6,4,5]=>[2,3,1,5,6,4]=>{{1,2,3},{4,5,6}}=>[2,3,1,5,6,4]=>4
[3,1,2,6,5,4]=>[2,3,1,6,4,5]=>{{1,2,3},{4,6},{5}}=>[2,3,1,6,5,4]=>4
[3,1,4,2,5,6]=>[3,4,1,2,5,6]=>{{1,3},{2,4},{5},{6}}=>[3,4,1,2,5,6]=>4
[3,1,4,2,6,5]=>[3,4,1,2,6,5]=>{{1,3},{2,4},{5,6}}=>[3,4,1,2,6,5]=>5
[3,1,4,5,2,6]=>[3,5,1,4,2,6]=>{{1,3},{2,5},{4},{6}}=>[3,5,1,4,2,6]=>5
[3,1,4,5,6,2]=>[3,6,1,4,5,2]=>{{1,3},{2,6},{4},{5}}=>[3,6,1,4,5,2]=>6
[3,1,4,6,2,5]=>[3,5,1,4,6,2]=>{{1,3},{2,5,6},{4}}=>[3,5,1,4,6,2]=>6
[3,1,4,6,5,2]=>[3,6,1,4,2,5]=>{{1,3},{2,6},{4},{5}}=>[3,6,1,4,5,2]=>6
[3,1,5,2,4,6]=>[3,4,1,5,2,6]=>{{1,3},{2,4,5},{6}}=>[3,4,1,5,2,6]=>5
[3,1,5,2,6,4]=>[3,5,1,6,2,4]=>{{1,3},{2,5},{4,6}}=>[3,5,1,6,2,4]=>7
[3,1,5,4,2,6]=>[3,5,1,2,4,6]=>{{1,3},{2,5},{4},{6}}=>[3,5,1,4,2,6]=>5
[3,1,5,4,6,2]=>[3,6,1,5,4,2]=>{{1,3},{2,6},{4,5}}=>[3,6,1,5,4,2]=>7
[3,1,5,6,2,4]=>[3,4,1,6,5,2]=>{{1,3},{2,4,6},{5}}=>[3,4,1,6,5,2]=>6
[3,1,5,6,4,2]=>[3,6,1,2,5,4]=>{{1,3},{2,6},{4},{5}}=>[3,6,1,4,5,2]=>6
[3,1,6,2,4,5]=>[3,4,1,5,6,2]=>{{1,3},{2,4,5,6}}=>[3,4,1,5,6,2]=>6
[3,1,6,2,5,4]=>[3,5,1,6,4,2]=>{{1,3},{2,5},{4,6}}=>[3,5,1,6,2,4]=>7
[3,1,6,4,2,5]=>[3,5,1,2,6,4]=>{{1,3},{2,5,6},{4}}=>[3,5,1,4,6,2]=>6
[3,1,6,4,5,2]=>[3,6,1,5,2,4]=>{{1,3},{2,6},{4,5}}=>[3,6,1,5,4,2]=>7
[3,1,6,5,2,4]=>[3,4,1,6,2,5]=>{{1,3},{2,4,6},{5}}=>[3,4,1,6,5,2]=>6
[3,1,6,5,4,2]=>[3,6,1,2,4,5]=>{{1,3},{2,6},{4},{5}}=>[3,6,1,4,5,2]=>6
[3,2,1,4,5,6]=>[3,1,2,4,5,6]=>{{1,3},{2},{4},{5},{6}}=>[3,2,1,4,5,6]=>2
[3,2,1,4,6,5]=>[3,1,2,4,6,5]=>{{1,3},{2},{4},{5,6}}=>[3,2,1,4,6,5]=>3
[3,2,1,5,4,6]=>[3,1,2,5,4,6]=>{{1,3},{2},{4,5},{6}}=>[3,2,1,5,4,6]=>3
[3,2,1,5,6,4]=>[3,1,2,6,5,4]=>{{1,3},{2},{4,6},{5}}=>[3,2,1,6,5,4]=>4
[3,2,1,6,4,5]=>[3,1,2,5,6,4]=>{{1,3},{2},{4,5,6}}=>[3,2,1,5,6,4]=>4
[3,2,1,6,5,4]=>[3,1,2,6,4,5]=>{{1,3},{2},{4,6},{5}}=>[3,2,1,6,5,4]=>4
[3,2,4,1,5,6]=>[4,3,2,1,5,6]=>{{1,4},{2,3},{5},{6}}=>[4,3,2,1,5,6]=>4
[3,2,4,1,6,5]=>[4,3,2,1,6,5]=>{{1,4},{2,3},{5,6}}=>[4,3,2,1,6,5]=>5
[3,2,4,5,1,6]=>[5,3,2,4,1,6]=>{{1,5},{2,3},{4},{6}}=>[5,3,2,4,1,6]=>5
[3,2,4,5,6,1]=>[6,3,2,4,5,1]=>{{1,6},{2,3},{4},{5}}=>[6,3,2,4,5,1]=>6
[3,2,4,6,1,5]=>[5,3,2,4,6,1]=>{{1,5,6},{2,3},{4}}=>[5,3,2,4,6,1]=>6
[3,2,4,6,5,1]=>[6,3,2,4,1,5]=>{{1,6},{2,3},{4},{5}}=>[6,3,2,4,5,1]=>6
[3,2,5,1,4,6]=>[4,3,2,5,1,6]=>{{1,4,5},{2,3},{6}}=>[4,3,2,5,1,6]=>5
[3,2,5,1,6,4]=>[5,3,2,6,1,4]=>{{1,5},{2,3},{4,6}}=>[5,3,2,6,1,4]=>7
[3,2,5,4,1,6]=>[5,3,2,1,4,6]=>{{1,5},{2,3},{4},{6}}=>[5,3,2,4,1,6]=>5
[3,2,5,4,6,1]=>[6,3,2,5,4,1]=>{{1,6},{2,3},{4,5}}=>[6,3,2,5,4,1]=>7
[3,2,5,6,1,4]=>[4,3,2,6,5,1]=>{{1,4,6},{2,3},{5}}=>[4,3,2,6,5,1]=>6
[3,2,5,6,4,1]=>[6,3,2,1,5,4]=>{{1,6},{2,3},{4},{5}}=>[6,3,2,4,5,1]=>6
[3,2,6,1,4,5]=>[4,3,2,5,6,1]=>{{1,4,5,6},{2,3}}=>[4,3,2,5,6,1]=>6
[3,2,6,1,5,4]=>[5,3,2,6,4,1]=>{{1,5},{2,3},{4,6}}=>[5,3,2,6,1,4]=>7
[3,2,6,4,1,5]=>[5,3,2,1,6,4]=>{{1,5,6},{2,3},{4}}=>[5,3,2,4,6,1]=>6
[3,2,6,4,5,1]=>[6,3,2,5,1,4]=>{{1,6},{2,3},{4,5}}=>[6,3,2,5,4,1]=>7
[3,2,6,5,1,4]=>[4,3,2,6,1,5]=>{{1,4,6},{2,3},{5}}=>[4,3,2,6,5,1]=>6
[3,2,6,5,4,1]=>[6,3,2,1,4,5]=>{{1,6},{2,3},{4},{5}}=>[6,3,2,4,5,1]=>6
[3,4,1,2,5,6]=>[2,4,3,1,5,6]=>{{1,2,4},{3},{5},{6}}=>[2,4,3,1,5,6]=>3
[3,4,1,2,6,5]=>[2,4,3,1,6,5]=>{{1,2,4},{3},{5,6}}=>[2,4,3,1,6,5]=>4
[3,4,1,5,2,6]=>[4,5,3,1,2,6]=>{{1,4},{2,5},{3},{6}}=>[4,5,3,1,2,6]=>6
[3,4,1,5,6,2]=>[4,6,3,1,5,2]=>{{1,4},{2,6},{3},{5}}=>[4,6,3,1,5,2]=>7
[3,4,1,6,2,5]=>[4,5,3,1,6,2]=>{{1,4},{2,5,6},{3}}=>[4,5,3,1,6,2]=>7
[3,4,1,6,5,2]=>[4,6,3,1,2,5]=>{{1,4},{2,6},{3},{5}}=>[4,6,3,1,5,2]=>7
[3,4,2,1,5,6]=>[4,1,3,2,5,6]=>{{1,4},{2},{3},{5},{6}}=>[4,2,3,1,5,6]=>3
[3,4,2,1,6,5]=>[4,1,3,2,6,5]=>{{1,4},{2},{3},{5,6}}=>[4,2,3,1,6,5]=>4
[3,4,2,5,1,6]=>[5,4,3,2,1,6]=>{{1,5},{2,4},{3},{6}}=>[5,4,3,2,1,6]=>6
[3,4,2,5,6,1]=>[6,4,3,2,5,1]=>{{1,6},{2,4},{3},{5}}=>[6,4,3,2,5,1]=>7
[3,4,2,6,1,5]=>[5,4,3,2,6,1]=>{{1,5,6},{2,4},{3}}=>[5,4,3,2,6,1]=>7
[3,4,2,6,5,1]=>[6,4,3,2,1,5]=>{{1,6},{2,4},{3},{5}}=>[6,4,3,2,5,1]=>7
[3,4,5,1,2,6]=>[2,5,3,4,1,6]=>{{1,2,5},{3},{4},{6}}=>[2,5,3,4,1,6]=>4
[3,4,5,1,6,2]=>[5,6,3,4,1,2]=>{{1,5},{2,6},{3},{4}}=>[5,6,3,4,1,2]=>8
[3,4,5,2,1,6]=>[5,1,3,4,2,6]=>{{1,5},{2},{3},{4},{6}}=>[5,2,3,4,1,6]=>4
[3,4,5,2,6,1]=>[6,5,3,4,2,1]=>{{1,6},{2,5},{3},{4}}=>[6,5,3,4,2,1]=>8
[3,4,5,6,1,2]=>[2,6,3,4,5,1]=>{{1,2,6},{3},{4},{5}}=>[2,6,3,4,5,1]=>5
[3,4,5,6,2,1]=>[6,1,3,4,5,2]=>{{1,6},{2},{3},{4},{5}}=>[6,2,3,4,5,1]=>5
[3,4,6,1,2,5]=>[2,5,3,4,6,1]=>{{1,2,5,6},{3},{4}}=>[2,5,3,4,6,1]=>5
[3,4,6,1,5,2]=>[5,6,3,4,2,1]=>{{1,5},{2,6},{3},{4}}=>[5,6,3,4,1,2]=>8
[3,4,6,2,1,5]=>[5,1,3,4,6,2]=>{{1,5,6},{2},{3},{4}}=>[5,2,3,4,6,1]=>5
[3,4,6,2,5,1]=>[6,5,3,4,1,2]=>{{1,6},{2,5},{3},{4}}=>[6,5,3,4,2,1]=>8
[3,4,6,5,1,2]=>[2,6,3,4,1,5]=>{{1,2,6},{3},{4},{5}}=>[2,6,3,4,5,1]=>5
[3,4,6,5,2,1]=>[6,1,3,4,2,5]=>{{1,6},{2},{3},{4},{5}}=>[6,2,3,4,5,1]=>5
[3,5,1,2,4,6]=>[2,4,3,5,1,6]=>{{1,2,4,5},{3},{6}}=>[2,4,3,5,1,6]=>4
[3,5,1,2,6,4]=>[2,5,3,6,1,4]=>{{1,2,5},{3},{4,6}}=>[2,5,3,6,1,4]=>6
[3,5,1,4,2,6]=>[4,5,3,2,1,6]=>{{1,4},{2,5},{3},{6}}=>[4,5,3,1,2,6]=>6
[3,5,1,4,6,2]=>[4,6,3,5,1,2]=>{{1,4,5},{2,6},{3}}=>[4,6,3,5,1,2]=>8
[3,5,1,6,2,4]=>[5,4,3,6,1,2]=>{{1,5},{2,4,6},{3}}=>[5,4,3,6,1,2]=>8
[3,5,1,6,4,2]=>[5,6,3,2,1,4]=>{{1,5},{2,6},{3},{4}}=>[5,6,3,4,1,2]=>8
[3,5,2,1,4,6]=>[4,1,3,5,2,6]=>{{1,4,5},{2},{3},{6}}=>[4,2,3,5,1,6]=>4
[3,5,2,1,6,4]=>[5,1,3,6,2,4]=>{{1,5},{2},{3},{4,6}}=>[5,2,3,6,1,4]=>6
[3,5,2,4,1,6]=>[5,4,3,1,2,6]=>{{1,5},{2,4},{3},{6}}=>[5,4,3,2,1,6]=>6
[3,5,2,4,6,1]=>[6,4,3,5,2,1]=>{{1,6},{2,4,5},{3}}=>[6,4,3,5,2,1]=>8
[3,5,2,6,1,4]=>[4,5,3,6,2,1]=>{{1,4,6},{2,5},{3}}=>[4,5,3,6,2,1]=>8
[3,5,2,6,4,1]=>[6,5,3,1,2,4]=>{{1,6},{2,5},{3},{4}}=>[6,5,3,4,2,1]=>8
[3,5,4,1,2,6]=>[2,5,3,1,4,6]=>{{1,2,5},{3},{4},{6}}=>[2,5,3,4,1,6]=>4
[3,5,4,1,6,2]=>[5,6,3,1,4,2]=>{{1,5},{2,6},{3},{4}}=>[5,6,3,4,1,2]=>8
[3,5,4,2,1,6]=>[5,1,3,2,4,6]=>{{1,5},{2},{3},{4},{6}}=>[5,2,3,4,1,6]=>4
[3,5,4,2,6,1]=>[6,5,3,2,4,1]=>{{1,6},{2,5},{3},{4}}=>[6,5,3,4,2,1]=>8
[3,5,4,6,1,2]=>[2,6,3,5,4,1]=>{{1,2,6},{3},{4,5}}=>[2,6,3,5,4,1]=>6
[3,5,4,6,2,1]=>[6,1,3,5,4,2]=>{{1,6},{2},{3},{4,5}}=>[6,2,3,5,4,1]=>6
[3,5,6,1,2,4]=>[2,4,3,6,5,1]=>{{1,2,4,6},{3},{5}}=>[2,4,3,6,5,1]=>5
[3,5,6,1,4,2]=>[4,6,3,2,5,1]=>{{1,4},{2,6},{3},{5}}=>[4,6,3,1,5,2]=>7
[3,5,6,2,1,4]=>[4,1,3,6,5,2]=>{{1,4,6},{2},{3},{5}}=>[4,2,3,6,5,1]=>5
[3,5,6,2,4,1]=>[6,4,3,1,5,2]=>{{1,6},{2,4},{3},{5}}=>[6,4,3,2,5,1]=>7
[3,5,6,4,1,2]=>[2,6,3,1,5,4]=>{{1,2,6},{3},{4},{5}}=>[2,6,3,4,5,1]=>5
[3,5,6,4,2,1]=>[6,1,3,2,5,4]=>{{1,6},{2},{3},{4},{5}}=>[6,2,3,4,5,1]=>5
[3,6,1,2,4,5]=>[2,4,3,5,6,1]=>{{1,2,4,5,6},{3}}=>[2,4,3,5,6,1]=>5
[3,6,1,2,5,4]=>[2,5,3,6,4,1]=>{{1,2,5},{3},{4,6}}=>[2,5,3,6,1,4]=>6
[3,6,1,4,2,5]=>[4,5,3,2,6,1]=>{{1,4},{2,5,6},{3}}=>[4,5,3,1,6,2]=>7
[3,6,1,4,5,2]=>[4,6,3,5,2,1]=>{{1,4,5},{2,6},{3}}=>[4,6,3,5,1,2]=>8
[3,6,1,5,2,4]=>[5,4,3,6,2,1]=>{{1,5},{2,4,6},{3}}=>[5,4,3,6,1,2]=>8
[3,6,1,5,4,2]=>[5,6,3,2,4,1]=>{{1,5},{2,6},{3},{4}}=>[5,6,3,4,1,2]=>8
[3,6,2,1,4,5]=>[4,1,3,5,6,2]=>{{1,4,5,6},{2},{3}}=>[4,2,3,5,6,1]=>5
[3,6,2,1,5,4]=>[5,1,3,6,4,2]=>{{1,5},{2},{3},{4,6}}=>[5,2,3,6,1,4]=>6
[3,6,2,4,1,5]=>[5,4,3,1,6,2]=>{{1,5,6},{2,4},{3}}=>[5,4,3,2,6,1]=>7
[3,6,2,4,5,1]=>[6,4,3,5,1,2]=>{{1,6},{2,4,5},{3}}=>[6,4,3,5,2,1]=>8
[3,6,2,5,1,4]=>[4,5,3,6,1,2]=>{{1,4,6},{2,5},{3}}=>[4,5,3,6,2,1]=>8
[3,6,2,5,4,1]=>[6,5,3,1,4,2]=>{{1,6},{2,5},{3},{4}}=>[6,5,3,4,2,1]=>8
[3,6,4,1,2,5]=>[2,5,3,1,6,4]=>{{1,2,5,6},{3},{4}}=>[2,5,3,4,6,1]=>5
[3,6,4,1,5,2]=>[5,6,3,1,2,4]=>{{1,5},{2,6},{3},{4}}=>[5,6,3,4,1,2]=>8
[3,6,4,2,1,5]=>[5,1,3,2,6,4]=>{{1,5,6},{2},{3},{4}}=>[5,2,3,4,6,1]=>5
[3,6,4,2,5,1]=>[6,5,3,2,1,4]=>{{1,6},{2,5},{3},{4}}=>[6,5,3,4,2,1]=>8
[3,6,4,5,1,2]=>[2,6,3,5,1,4]=>{{1,2,6},{3},{4,5}}=>[2,6,3,5,4,1]=>6
[3,6,4,5,2,1]=>[6,1,3,5,2,4]=>{{1,6},{2},{3},{4,5}}=>[6,2,3,5,4,1]=>6
[3,6,5,1,2,4]=>[2,4,3,6,1,5]=>{{1,2,4,6},{3},{5}}=>[2,4,3,6,5,1]=>5
[3,6,5,1,4,2]=>[4,6,3,2,1,5]=>{{1,4},{2,6},{3},{5}}=>[4,6,3,1,5,2]=>7
[3,6,5,2,1,4]=>[4,1,3,6,2,5]=>{{1,4,6},{2},{3},{5}}=>[4,2,3,6,5,1]=>5
[3,6,5,2,4,1]=>[6,4,3,1,2,5]=>{{1,6},{2,4},{3},{5}}=>[6,4,3,2,5,1]=>7
[3,6,5,4,1,2]=>[2,6,3,1,4,5]=>{{1,2,6},{3},{4},{5}}=>[2,6,3,4,5,1]=>5
[3,6,5,4,2,1]=>[6,1,3,2,4,5]=>{{1,6},{2},{3},{4},{5}}=>[6,2,3,4,5,1]=>5
[4,1,2,3,5,6]=>[2,3,4,1,5,6]=>{{1,2,3,4},{5},{6}}=>[2,3,4,1,5,6]=>3
[4,1,2,3,6,5]=>[2,3,4,1,6,5]=>{{1,2,3,4},{5,6}}=>[2,3,4,1,6,5]=>4
[4,1,2,5,3,6]=>[2,4,5,1,3,6]=>{{1,2,4},{3,5},{6}}=>[2,4,5,1,3,6]=>5
[4,1,2,5,6,3]=>[2,4,6,1,5,3]=>{{1,2,4},{3,6},{5}}=>[2,4,6,1,5,3]=>6
[4,1,2,6,3,5]=>[2,4,5,1,6,3]=>{{1,2,4},{3,5,6}}=>[2,4,5,1,6,3]=>6
[4,1,2,6,5,3]=>[2,4,6,1,3,5]=>{{1,2,4},{3,6},{5}}=>[2,4,6,1,5,3]=>6
[4,1,3,2,5,6]=>[3,4,2,1,5,6]=>{{1,3},{2,4},{5},{6}}=>[3,4,1,2,5,6]=>4
[4,1,3,2,6,5]=>[3,4,2,1,6,5]=>{{1,3},{2,4},{5,6}}=>[3,4,1,2,6,5]=>5
[4,1,3,5,2,6]=>[3,5,4,1,2,6]=>{{1,3,4},{2,5},{6}}=>[3,5,4,1,2,6]=>6
[4,1,3,5,6,2]=>[3,6,4,1,5,2]=>{{1,3,4},{2,6},{5}}=>[3,6,4,1,5,2]=>7
[4,1,3,6,2,5]=>[3,5,4,1,6,2]=>{{1,3,4},{2,5,6}}=>[3,5,4,1,6,2]=>7
[4,1,3,6,5,2]=>[3,6,4,1,2,5]=>{{1,3,4},{2,6},{5}}=>[3,6,4,1,5,2]=>7
[4,1,5,2,3,6]=>[4,3,5,1,2,6]=>{{1,4},{2,3,5},{6}}=>[4,3,5,1,2,6]=>6
[4,1,5,2,6,3]=>[4,5,6,1,2,3]=>{{1,4},{2,5},{3,6}}=>[4,5,6,1,2,3]=>9
[4,1,5,3,2,6]=>[4,5,2,1,3,6]=>{{1,4},{2,5},{3},{6}}=>[4,5,3,1,2,6]=>6
[4,1,5,3,6,2]=>[4,6,5,1,3,2]=>{{1,4},{2,6},{3,5}}=>[4,6,5,1,3,2]=>9
[4,1,5,6,2,3]=>[4,3,6,1,5,2]=>{{1,4},{2,3,6},{5}}=>[4,3,6,1,5,2]=>7
[4,1,5,6,3,2]=>[4,6,2,1,5,3]=>{{1,4},{2,6},{3},{5}}=>[4,6,3,1,5,2]=>7
[4,1,6,2,3,5]=>[4,3,5,1,6,2]=>{{1,4},{2,3,5,6}}=>[4,3,5,1,6,2]=>7
[4,1,6,2,5,3]=>[4,5,6,1,3,2]=>{{1,4},{2,5},{3,6}}=>[4,5,6,1,2,3]=>9
[4,1,6,3,2,5]=>[4,5,2,1,6,3]=>{{1,4},{2,5,6},{3}}=>[4,5,3,1,6,2]=>7
[4,1,6,3,5,2]=>[4,6,5,1,2,3]=>{{1,4},{2,6},{3,5}}=>[4,6,5,1,3,2]=>9
[4,1,6,5,2,3]=>[4,3,6,1,2,5]=>{{1,4},{2,3,6},{5}}=>[4,3,6,1,5,2]=>7
[4,1,6,5,3,2]=>[4,6,2,1,3,5]=>{{1,4},{2,6},{3},{5}}=>[4,6,3,1,5,2]=>7
[4,2,1,3,5,6]=>[3,1,4,2,5,6]=>{{1,3,4},{2},{5},{6}}=>[3,2,4,1,5,6]=>3
[4,2,1,3,6,5]=>[3,1,4,2,6,5]=>{{1,3,4},{2},{5,6}}=>[3,2,4,1,6,5]=>4
[4,2,1,5,3,6]=>[4,1,5,2,3,6]=>{{1,4},{2},{3,5},{6}}=>[4,2,5,1,3,6]=>5
[4,2,1,5,6,3]=>[4,1,6,2,5,3]=>{{1,4},{2},{3,6},{5}}=>[4,2,6,1,5,3]=>6
[4,2,1,6,3,5]=>[4,1,5,2,6,3]=>{{1,4},{2},{3,5,6}}=>[4,2,5,1,6,3]=>6
[4,2,1,6,5,3]=>[4,1,6,2,3,5]=>{{1,4},{2},{3,6},{5}}=>[4,2,6,1,5,3]=>6
[4,2,3,1,5,6]=>[4,3,1,2,5,6]=>{{1,4},{2,3},{5},{6}}=>[4,3,2,1,5,6]=>4
[4,2,3,1,6,5]=>[4,3,1,2,6,5]=>{{1,4},{2,3},{5,6}}=>[4,3,2,1,6,5]=>5
[4,2,3,5,1,6]=>[5,3,4,2,1,6]=>{{1,5},{2,3,4},{6}}=>[5,3,4,2,1,6]=>6
[4,2,3,5,6,1]=>[6,3,4,2,5,1]=>{{1,6},{2,3,4},{5}}=>[6,3,4,2,5,1]=>7
[4,2,3,6,1,5]=>[5,3,4,2,6,1]=>{{1,5,6},{2,3,4}}=>[5,3,4,2,6,1]=>7
[4,2,3,6,5,1]=>[6,3,4,2,1,5]=>{{1,6},{2,3,4},{5}}=>[6,3,4,2,5,1]=>7
[4,2,5,1,3,6]=>[3,4,5,2,1,6]=>{{1,3,5},{2,4},{6}}=>[3,4,5,2,1,6]=>6
[4,2,5,1,6,3]=>[5,4,6,2,1,3]=>{{1,5},{2,4},{3,6}}=>[5,4,6,2,1,3]=>9
[4,2,5,3,1,6]=>[5,4,1,2,3,6]=>{{1,5},{2,4},{3},{6}}=>[5,4,3,2,1,6]=>6
[4,2,5,3,6,1]=>[6,4,5,2,3,1]=>{{1,6},{2,4},{3,5}}=>[6,4,5,2,3,1]=>9
[4,2,5,6,1,3]=>[3,4,6,2,5,1]=>{{1,3,6},{2,4},{5}}=>[3,4,6,2,5,1]=>7
[4,2,5,6,3,1]=>[6,4,1,2,5,3]=>{{1,6},{2,4},{3},{5}}=>[6,4,3,2,5,1]=>7
[4,2,6,1,3,5]=>[3,4,5,2,6,1]=>{{1,3,5,6},{2,4}}=>[3,4,5,2,6,1]=>7
[4,2,6,1,5,3]=>[5,4,6,2,3,1]=>{{1,5},{2,4},{3,6}}=>[5,4,6,2,1,3]=>9
[4,2,6,3,1,5]=>[5,4,1,2,6,3]=>{{1,5,6},{2,4},{3}}=>[5,4,3,2,6,1]=>7
[4,2,6,3,5,1]=>[6,4,5,2,1,3]=>{{1,6},{2,4},{3,5}}=>[6,4,5,2,3,1]=>9
[4,2,6,5,1,3]=>[3,4,6,2,1,5]=>{{1,3,6},{2,4},{5}}=>[3,4,6,2,5,1]=>7
[4,2,6,5,3,1]=>[6,4,1,2,3,5]=>{{1,6},{2,4},{3},{5}}=>[6,4,3,2,5,1]=>7
[4,3,1,2,5,6]=>[2,4,1,3,5,6]=>{{1,2,4},{3},{5},{6}}=>[2,4,3,1,5,6]=>3
[4,3,1,2,6,5]=>[2,4,1,3,6,5]=>{{1,2,4},{3},{5,6}}=>[2,4,3,1,6,5]=>4
[4,3,1,5,2,6]=>[4,5,1,3,2,6]=>{{1,4},{2,5},{3},{6}}=>[4,5,3,1,2,6]=>6
[4,3,1,5,6,2]=>[4,6,1,3,5,2]=>{{1,4},{2,6},{3},{5}}=>[4,6,3,1,5,2]=>7
[4,3,1,6,2,5]=>[4,5,1,3,6,2]=>{{1,4},{2,5,6},{3}}=>[4,5,3,1,6,2]=>7
[4,3,1,6,5,2]=>[4,6,1,3,2,5]=>{{1,4},{2,6},{3},{5}}=>[4,6,3,1,5,2]=>7
[4,3,2,1,5,6]=>[4,1,2,3,5,6]=>{{1,4},{2},{3},{5},{6}}=>[4,2,3,1,5,6]=>3
[4,3,2,1,6,5]=>[4,1,2,3,6,5]=>{{1,4},{2},{3},{5,6}}=>[4,2,3,1,6,5]=>4
[4,3,2,5,1,6]=>[5,4,2,3,1,6]=>{{1,5},{2,4},{3},{6}}=>[5,4,3,2,1,6]=>6
[4,3,2,5,6,1]=>[6,4,2,3,5,1]=>{{1,6},{2,4},{3},{5}}=>[6,4,3,2,5,1]=>7
[4,3,2,6,1,5]=>[5,4,2,3,6,1]=>{{1,5,6},{2,4},{3}}=>[5,4,3,2,6,1]=>7
[4,3,2,6,5,1]=>[6,4,2,3,1,5]=>{{1,6},{2,4},{3},{5}}=>[6,4,3,2,5,1]=>7
[4,3,5,1,2,6]=>[2,5,4,3,1,6]=>{{1,2,5},{3,4},{6}}=>[2,5,4,3,1,6]=>5
[4,3,5,1,6,2]=>[5,6,4,3,1,2]=>{{1,5},{2,6},{3,4}}=>[5,6,4,3,1,2]=>9
[4,3,5,2,1,6]=>[5,1,4,3,2,6]=>{{1,5},{2},{3,4},{6}}=>[5,2,4,3,1,6]=>5
[4,3,5,2,6,1]=>[6,5,4,3,2,1]=>{{1,6},{2,5},{3,4}}=>[6,5,4,3,2,1]=>9
[4,3,5,6,1,2]=>[2,6,4,3,5,1]=>{{1,2,6},{3,4},{5}}=>[2,6,4,3,5,1]=>6
[4,3,5,6,2,1]=>[6,1,4,3,5,2]=>{{1,6},{2},{3,4},{5}}=>[6,2,4,3,5,1]=>6
[4,3,6,1,2,5]=>[2,5,4,3,6,1]=>{{1,2,5,6},{3,4}}=>[2,5,4,3,6,1]=>6
[4,3,6,1,5,2]=>[5,6,4,3,2,1]=>{{1,5},{2,6},{3,4}}=>[5,6,4,3,1,2]=>9
[4,3,6,2,1,5]=>[5,1,4,3,6,2]=>{{1,5,6},{2},{3,4}}=>[5,2,4,3,6,1]=>6
[4,3,6,2,5,1]=>[6,5,4,3,1,2]=>{{1,6},{2,5},{3,4}}=>[6,5,4,3,2,1]=>9
[4,3,6,5,1,2]=>[2,6,4,3,1,5]=>{{1,2,6},{3,4},{5}}=>[2,6,4,3,5,1]=>6
[4,3,6,5,2,1]=>[6,1,4,3,2,5]=>{{1,6},{2},{3,4},{5}}=>[6,2,4,3,5,1]=>6
[4,5,1,2,3,6]=>[2,3,5,4,1,6]=>{{1,2,3,5},{4},{6}}=>[2,3,5,4,1,6]=>4
[4,5,1,2,6,3]=>[2,5,6,4,1,3]=>{{1,2,5},{3,6},{4}}=>[2,5,6,4,1,3]=>7
[4,5,1,3,2,6]=>[3,5,2,4,1,6]=>{{1,3},{2,5},{4},{6}}=>[3,5,1,4,2,6]=>5
[4,5,1,3,6,2]=>[3,6,5,4,1,2]=>{{1,3,5},{2,6},{4}}=>[3,6,5,4,1,2]=>8
[4,5,1,6,2,3]=>[5,3,6,4,1,2]=>{{1,5},{2,3,6},{4}}=>[5,3,6,4,1,2]=>8
[4,5,1,6,3,2]=>[5,6,2,4,1,3]=>{{1,5},{2,6},{3},{4}}=>[5,6,3,4,1,2]=>8
[4,5,2,1,3,6]=>[3,1,5,4,2,6]=>{{1,3,5},{2},{4},{6}}=>[3,2,5,4,1,6]=>4
[4,5,2,1,6,3]=>[5,1,6,4,2,3]=>{{1,5},{2},{3,6},{4}}=>[5,2,6,4,1,3]=>7
[4,5,2,3,1,6]=>[5,3,1,4,2,6]=>{{1,5},{2,3},{4},{6}}=>[5,3,2,4,1,6]=>5
[4,5,2,3,6,1]=>[6,3,5,4,2,1]=>{{1,6},{2,3,5},{4}}=>[6,3,5,4,2,1]=>8
[4,5,2,6,1,3]=>[3,5,6,4,2,1]=>{{1,3,6},{2,5},{4}}=>[3,5,6,4,2,1]=>8
[4,5,2,6,3,1]=>[6,5,1,4,2,3]=>{{1,6},{2,5},{3},{4}}=>[6,5,3,4,2,1]=>8
[4,5,3,1,2,6]=>[2,5,1,4,3,6]=>{{1,2,5},{3},{4},{6}}=>[2,5,3,4,1,6]=>4
[4,5,3,1,6,2]=>[5,6,1,4,3,2]=>{{1,5},{2,6},{3},{4}}=>[5,6,3,4,1,2]=>8
[4,5,3,2,1,6]=>[5,1,2,4,3,6]=>{{1,5},{2},{3},{4},{6}}=>[5,2,3,4,1,6]=>4
[4,5,3,2,6,1]=>[6,5,2,4,3,1]=>{{1,6},{2,5},{3},{4}}=>[6,5,3,4,2,1]=>8
[4,5,3,6,1,2]=>[2,6,5,4,3,1]=>{{1,2,6},{3,5},{4}}=>[2,6,5,4,3,1]=>7
[4,5,3,6,2,1]=>[6,1,5,4,3,2]=>{{1,6},{2},{3,5},{4}}=>[6,2,5,4,3,1]=>7
[4,5,6,1,2,3]=>[2,3,6,4,5,1]=>{{1,2,3,6},{4},{5}}=>[2,3,6,4,5,1]=>5
[4,5,6,1,3,2]=>[3,6,2,4,5,1]=>{{1,3},{2,6},{4},{5}}=>[3,6,1,4,5,2]=>6
[4,5,6,2,1,3]=>[3,1,6,4,5,2]=>{{1,3,6},{2},{4},{5}}=>[3,2,6,4,5,1]=>5
[4,5,6,2,3,1]=>[6,3,1,4,5,2]=>{{1,6},{2,3},{4},{5}}=>[6,3,2,4,5,1]=>6
[4,5,6,3,1,2]=>[2,6,1,4,5,3]=>{{1,2,6},{3},{4},{5}}=>[2,6,3,4,5,1]=>5
[4,5,6,3,2,1]=>[6,1,2,4,5,3]=>{{1,6},{2},{3},{4},{5}}=>[6,2,3,4,5,1]=>5
[4,6,1,2,3,5]=>[2,3,5,4,6,1]=>{{1,2,3,5,6},{4}}=>[2,3,5,4,6,1]=>5
[4,6,1,2,5,3]=>[2,5,6,4,3,1]=>{{1,2,5},{3,6},{4}}=>[2,5,6,4,1,3]=>7
[4,6,1,3,2,5]=>[3,5,2,4,6,1]=>{{1,3},{2,5,6},{4}}=>[3,5,1,4,6,2]=>6
[4,6,1,3,5,2]=>[3,6,5,4,2,1]=>{{1,3,5},{2,6},{4}}=>[3,6,5,4,1,2]=>8
[4,6,1,5,2,3]=>[5,3,6,4,2,1]=>{{1,5},{2,3,6},{4}}=>[5,3,6,4,1,2]=>8
[4,6,1,5,3,2]=>[5,6,2,4,3,1]=>{{1,5},{2,6},{3},{4}}=>[5,6,3,4,1,2]=>8
[4,6,2,1,3,5]=>[3,1,5,4,6,2]=>{{1,3,5,6},{2},{4}}=>[3,2,5,4,6,1]=>5
[4,6,2,1,5,3]=>[5,1,6,4,3,2]=>{{1,5},{2},{3,6},{4}}=>[5,2,6,4,1,3]=>7
[4,6,2,3,1,5]=>[5,3,1,4,6,2]=>{{1,5,6},{2,3},{4}}=>[5,3,2,4,6,1]=>6
[4,6,2,3,5,1]=>[6,3,5,4,1,2]=>{{1,6},{2,3,5},{4}}=>[6,3,5,4,2,1]=>8
[4,6,2,5,1,3]=>[3,5,6,4,1,2]=>{{1,3,6},{2,5},{4}}=>[3,5,6,4,2,1]=>8
[4,6,2,5,3,1]=>[6,5,1,4,3,2]=>{{1,6},{2,5},{3},{4}}=>[6,5,3,4,2,1]=>8
[4,6,3,1,2,5]=>[2,5,1,4,6,3]=>{{1,2,5,6},{3},{4}}=>[2,5,3,4,6,1]=>5
[4,6,3,1,5,2]=>[5,6,1,4,2,3]=>{{1,5},{2,6},{3},{4}}=>[5,6,3,4,1,2]=>8
[4,6,3,2,1,5]=>[5,1,2,4,6,3]=>{{1,5,6},{2},{3},{4}}=>[5,2,3,4,6,1]=>5
[4,6,3,2,5,1]=>[6,5,2,4,1,3]=>{{1,6},{2,5},{3},{4}}=>[6,5,3,4,2,1]=>8
[4,6,3,5,1,2]=>[2,6,5,4,1,3]=>{{1,2,6},{3,5},{4}}=>[2,6,5,4,3,1]=>7
[4,6,3,5,2,1]=>[6,1,5,4,2,3]=>{{1,6},{2},{3,5},{4}}=>[6,2,5,4,3,1]=>7
[4,6,5,1,2,3]=>[2,3,6,4,1,5]=>{{1,2,3,6},{4},{5}}=>[2,3,6,4,5,1]=>5
[4,6,5,1,3,2]=>[3,6,2,4,1,5]=>{{1,3},{2,6},{4},{5}}=>[3,6,1,4,5,2]=>6
[4,6,5,2,1,3]=>[3,1,6,4,2,5]=>{{1,3,6},{2},{4},{5}}=>[3,2,6,4,5,1]=>5
[4,6,5,2,3,1]=>[6,3,1,4,2,5]=>{{1,6},{2,3},{4},{5}}=>[6,3,2,4,5,1]=>6
[4,6,5,3,1,2]=>[2,6,1,4,3,5]=>{{1,2,6},{3},{4},{5}}=>[2,6,3,4,5,1]=>5
[4,6,5,3,2,1]=>[6,1,2,4,3,5]=>{{1,6},{2},{3},{4},{5}}=>[6,2,3,4,5,1]=>5
[5,1,2,3,4,6]=>[2,3,4,5,1,6]=>{{1,2,3,4,5},{6}}=>[2,3,4,5,1,6]=>4
[5,1,2,3,6,4]=>[2,3,5,6,1,4]=>{{1,2,3,5},{4,6}}=>[2,3,5,6,1,4]=>6
[5,1,2,4,3,6]=>[2,4,5,3,1,6]=>{{1,2,4},{3,5},{6}}=>[2,4,5,1,3,6]=>5
[5,1,2,4,6,3]=>[2,4,6,5,1,3]=>{{1,2,4,5},{3,6}}=>[2,4,6,5,1,3]=>7
[5,1,2,6,3,4]=>[2,5,4,6,1,3]=>{{1,2,5},{3,4,6}}=>[2,5,4,6,1,3]=>7
[5,1,2,6,4,3]=>[2,5,6,3,1,4]=>{{1,2,5},{3,6},{4}}=>[2,5,6,4,1,3]=>7
[5,1,3,2,4,6]=>[3,4,2,5,1,6]=>{{1,3},{2,4,5},{6}}=>[3,4,1,5,2,6]=>5
[5,1,3,2,6,4]=>[3,5,2,6,1,4]=>{{1,3},{2,5},{4,6}}=>[3,5,1,6,2,4]=>7
[5,1,3,4,2,6]=>[3,5,4,2,1,6]=>{{1,3,4},{2,5},{6}}=>[3,5,4,1,2,6]=>6
[5,1,3,4,6,2]=>[3,6,4,5,1,2]=>{{1,3,4,5},{2,6}}=>[3,6,4,5,1,2]=>8
[5,1,3,6,2,4]=>[3,4,5,6,1,2]=>{{1,3,5},{2,4,6}}=>[3,4,5,6,1,2]=>8
[5,1,3,6,4,2]=>[3,6,5,2,1,4]=>{{1,3,5},{2,6},{4}}=>[3,6,5,4,1,2]=>8
[5,1,4,2,3,6]=>[4,3,5,2,1,6]=>{{1,4},{2,3,5},{6}}=>[4,3,5,1,2,6]=>6
[5,1,4,2,6,3]=>[4,5,6,2,1,3]=>{{1,4},{2,5},{3,6}}=>[4,5,6,1,2,3]=>9
[5,1,4,3,2,6]=>[4,5,2,3,1,6]=>{{1,4},{2,5},{3},{6}}=>[4,5,3,1,2,6]=>6
[5,1,4,3,6,2]=>[4,6,5,3,1,2]=>{{1,4},{2,6},{3,5}}=>[4,6,5,1,3,2]=>9
[5,1,4,6,2,3]=>[4,3,6,5,1,2]=>{{1,4,5},{2,3,6}}=>[4,3,6,5,1,2]=>8
[5,1,4,6,3,2]=>[4,6,2,5,1,3]=>{{1,4,5},{2,6},{3}}=>[4,6,3,5,1,2]=>8
[5,1,6,2,3,4]=>[5,3,4,6,1,2]=>{{1,5},{2,3,4,6}}=>[5,3,4,6,1,2]=>8
[5,1,6,2,4,3]=>[5,4,6,3,1,2]=>{{1,5},{2,4},{3,6}}=>[5,4,6,2,1,3]=>9
[5,1,6,3,2,4]=>[5,4,2,6,1,3]=>{{1,5},{2,4,6},{3}}=>[5,4,3,6,1,2]=>8
[5,1,6,3,4,2]=>[5,6,4,2,1,3]=>{{1,5},{2,6},{3,4}}=>[5,6,4,3,1,2]=>9
[5,1,6,4,2,3]=>[5,3,6,2,1,4]=>{{1,5},{2,3,6},{4}}=>[5,3,6,4,1,2]=>8
[5,1,6,4,3,2]=>[5,6,2,3,1,4]=>{{1,5},{2,6},{3},{4}}=>[5,6,3,4,1,2]=>8
[5,2,1,3,4,6]=>[3,1,4,5,2,6]=>{{1,3,4,5},{2},{6}}=>[3,2,4,5,1,6]=>4
[5,2,1,3,6,4]=>[3,1,5,6,2,4]=>{{1,3,5},{2},{4,6}}=>[3,2,5,6,1,4]=>6
[5,2,1,4,3,6]=>[4,1,5,3,2,6]=>{{1,4},{2},{3,5},{6}}=>[4,2,5,1,3,6]=>5
[5,2,1,4,6,3]=>[4,1,6,5,2,3]=>{{1,4,5},{2},{3,6}}=>[4,2,6,5,1,3]=>7
[5,2,1,6,3,4]=>[5,1,4,6,2,3]=>{{1,5},{2},{3,4,6}}=>[5,2,4,6,1,3]=>7
[5,2,1,6,4,3]=>[5,1,6,3,2,4]=>{{1,5},{2},{3,6},{4}}=>[5,2,6,4,1,3]=>7
[5,2,3,1,4,6]=>[4,3,1,5,2,6]=>{{1,4,5},{2,3},{6}}=>[4,3,2,5,1,6]=>5
[5,2,3,1,6,4]=>[5,3,1,6,2,4]=>{{1,5},{2,3},{4,6}}=>[5,3,2,6,1,4]=>7
[5,2,3,4,1,6]=>[5,3,4,1,2,6]=>{{1,5},{2,3,4},{6}}=>[5,3,4,2,1,6]=>6
[5,2,3,4,6,1]=>[6,3,4,5,2,1]=>{{1,6},{2,3,4,5}}=>[6,3,4,5,2,1]=>8
[5,2,3,6,1,4]=>[4,3,5,6,2,1]=>{{1,4,6},{2,3,5}}=>[4,3,5,6,2,1]=>8
[5,2,3,6,4,1]=>[6,3,5,1,2,4]=>{{1,6},{2,3,5},{4}}=>[6,3,5,4,2,1]=>8
[5,2,4,1,3,6]=>[3,4,5,1,2,6]=>{{1,3,5},{2,4},{6}}=>[3,4,5,2,1,6]=>6
[5,2,4,1,6,3]=>[5,4,6,1,2,3]=>{{1,5},{2,4},{3,6}}=>[5,4,6,2,1,3]=>9
[5,2,4,3,1,6]=>[5,4,1,3,2,6]=>{{1,5},{2,4},{3},{6}}=>[5,4,3,2,1,6]=>6
[5,2,4,3,6,1]=>[6,4,5,3,2,1]=>{{1,6},{2,4},{3,5}}=>[6,4,5,2,3,1]=>9
[5,2,4,6,1,3]=>[3,4,6,5,2,1]=>{{1,3,6},{2,4,5}}=>[3,4,6,5,2,1]=>8
[5,2,4,6,3,1]=>[6,4,1,5,2,3]=>{{1,6},{2,4,5},{3}}=>[6,4,3,5,2,1]=>8
[5,2,6,1,3,4]=>[3,5,4,6,2,1]=>{{1,3,4,6},{2,5}}=>[3,5,4,6,2,1]=>8
[5,2,6,1,4,3]=>[4,5,6,3,2,1]=>{{1,4},{2,5},{3,6}}=>[4,5,6,1,2,3]=>9
[5,2,6,3,1,4]=>[4,5,1,6,2,3]=>{{1,4,6},{2,5},{3}}=>[4,5,3,6,2,1]=>8
[5,2,6,3,4,1]=>[6,5,4,1,2,3]=>{{1,6},{2,5},{3,4}}=>[6,5,4,3,2,1]=>9
[5,2,6,4,1,3]=>[3,5,6,1,2,4]=>{{1,3,6},{2,5},{4}}=>[3,5,6,4,2,1]=>8
[5,2,6,4,3,1]=>[6,5,1,3,2,4]=>{{1,6},{2,5},{3},{4}}=>[6,5,3,4,2,1]=>8
[5,3,1,2,4,6]=>[2,4,1,5,3,6]=>{{1,2,4,5},{3},{6}}=>[2,4,3,5,1,6]=>4
[5,3,1,2,6,4]=>[2,5,1,6,3,4]=>{{1,2,5},{3},{4,6}}=>[2,5,3,6,1,4]=>6
[5,3,1,4,2,6]=>[4,5,1,2,3,6]=>{{1,4},{2,5},{3},{6}}=>[4,5,3,1,2,6]=>6
[5,3,1,4,6,2]=>[4,6,1,5,3,2]=>{{1,4,5},{2,6},{3}}=>[4,6,3,5,1,2]=>8
[5,3,1,6,2,4]=>[5,4,1,6,3,2]=>{{1,5},{2,4,6},{3}}=>[5,4,3,6,1,2]=>8
[5,3,1,6,4,2]=>[5,6,1,2,3,4]=>{{1,5},{2,6},{3},{4}}=>[5,6,3,4,1,2]=>8
[5,3,2,1,4,6]=>[4,1,2,5,3,6]=>{{1,4,5},{2},{3},{6}}=>[4,2,3,5,1,6]=>4
[5,3,2,1,6,4]=>[5,1,2,6,3,4]=>{{1,5},{2},{3},{4,6}}=>[5,2,3,6,1,4]=>6
[5,3,2,4,1,6]=>[5,4,2,1,3,6]=>{{1,5},{2,4},{3},{6}}=>[5,4,3,2,1,6]=>6
[5,3,2,4,6,1]=>[6,4,2,5,3,1]=>{{1,6},{2,4,5},{3}}=>[6,4,3,5,2,1]=>8
[5,3,2,6,1,4]=>[4,5,2,6,3,1]=>{{1,4,6},{2,5},{3}}=>[4,5,3,6,2,1]=>8
[5,3,2,6,4,1]=>[6,5,2,1,3,4]=>{{1,6},{2,5},{3},{4}}=>[6,5,3,4,2,1]=>8
[5,3,4,1,2,6]=>[2,5,4,1,3,6]=>{{1,2,5},{3,4},{6}}=>[2,5,4,3,1,6]=>5
[5,3,4,1,6,2]=>[5,6,4,1,3,2]=>{{1,5},{2,6},{3,4}}=>[5,6,4,3,1,2]=>9
[5,3,4,2,1,6]=>[5,1,4,2,3,6]=>{{1,5},{2},{3,4},{6}}=>[5,2,4,3,1,6]=>5
[5,3,4,2,6,1]=>[6,5,4,2,3,1]=>{{1,6},{2,5},{3,4}}=>[6,5,4,3,2,1]=>9
[5,3,4,6,1,2]=>[2,6,4,5,3,1]=>{{1,2,6},{3,4,5}}=>[2,6,4,5,3,1]=>7
[5,3,4,6,2,1]=>[6,1,4,5,3,2]=>{{1,6},{2},{3,4,5}}=>[6,2,4,5,3,1]=>7
[5,3,6,1,2,4]=>[2,4,5,6,3,1]=>{{1,2,4,6},{3,5}}=>[2,4,5,6,3,1]=>7
[5,3,6,1,4,2]=>[4,6,5,2,3,1]=>{{1,4},{2,6},{3,5}}=>[4,6,5,1,3,2]=>9
[5,3,6,2,1,4]=>[4,1,5,6,3,2]=>{{1,4,6},{2},{3,5}}=>[4,2,5,6,3,1]=>7
[5,3,6,2,4,1]=>[6,4,5,1,3,2]=>{{1,6},{2,4},{3,5}}=>[6,4,5,2,3,1]=>9
[5,3,6,4,1,2]=>[2,6,5,1,3,4]=>{{1,2,6},{3,5},{4}}=>[2,6,5,4,3,1]=>7
[5,3,6,4,2,1]=>[6,1,5,2,3,4]=>{{1,6},{2},{3,5},{4}}=>[6,2,5,4,3,1]=>7
[5,4,1,2,3,6]=>[2,3,5,1,4,6]=>{{1,2,3,5},{4},{6}}=>[2,3,5,4,1,6]=>4
[5,4,1,2,6,3]=>[2,5,6,1,4,3]=>{{1,2,5},{3,6},{4}}=>[2,5,6,4,1,3]=>7
[5,4,1,3,2,6]=>[3,5,2,1,4,6]=>{{1,3},{2,5},{4},{6}}=>[3,5,1,4,2,6]=>5
[5,4,1,3,6,2]=>[3,6,5,1,4,2]=>{{1,3,5},{2,6},{4}}=>[3,6,5,4,1,2]=>8
[5,4,1,6,2,3]=>[5,3,6,1,4,2]=>{{1,5},{2,3,6},{4}}=>[5,3,6,4,1,2]=>8
[5,4,1,6,3,2]=>[5,6,2,1,4,3]=>{{1,5},{2,6},{3},{4}}=>[5,6,3,4,1,2]=>8
[5,4,2,1,3,6]=>[3,1,5,2,4,6]=>{{1,3,5},{2},{4},{6}}=>[3,2,5,4,1,6]=>4
[5,4,2,1,6,3]=>[5,1,6,2,4,3]=>{{1,5},{2},{3,6},{4}}=>[5,2,6,4,1,3]=>7
[5,4,2,3,1,6]=>[5,3,1,2,4,6]=>{{1,5},{2,3},{4},{6}}=>[5,3,2,4,1,6]=>5
[5,4,2,3,6,1]=>[6,3,5,2,4,1]=>{{1,6},{2,3,5},{4}}=>[6,3,5,4,2,1]=>8
[5,4,2,6,1,3]=>[3,5,6,2,4,1]=>{{1,3,6},{2,5},{4}}=>[3,5,6,4,2,1]=>8
[5,4,2,6,3,1]=>[6,5,1,2,4,3]=>{{1,6},{2,5},{3},{4}}=>[6,5,3,4,2,1]=>8
[5,4,3,1,2,6]=>[2,5,1,3,4,6]=>{{1,2,5},{3},{4},{6}}=>[2,5,3,4,1,6]=>4
[5,4,3,1,6,2]=>[5,6,1,3,4,2]=>{{1,5},{2,6},{3},{4}}=>[5,6,3,4,1,2]=>8
[5,4,3,2,1,6]=>[5,1,2,3,4,6]=>{{1,5},{2},{3},{4},{6}}=>[5,2,3,4,1,6]=>4
[5,4,3,2,6,1]=>[6,5,2,3,4,1]=>{{1,6},{2,5},{3},{4}}=>[6,5,3,4,2,1]=>8
[5,4,3,6,1,2]=>[2,6,5,3,4,1]=>{{1,2,6},{3,5},{4}}=>[2,6,5,4,3,1]=>7
[5,4,3,6,2,1]=>[6,1,5,3,4,2]=>{{1,6},{2},{3,5},{4}}=>[6,2,5,4,3,1]=>7
[5,4,6,1,2,3]=>[2,3,6,5,4,1]=>{{1,2,3,6},{4,5}}=>[2,3,6,5,4,1]=>6
[5,4,6,1,3,2]=>[3,6,2,5,4,1]=>{{1,3},{2,6},{4,5}}=>[3,6,1,5,4,2]=>7
[5,4,6,2,1,3]=>[3,1,6,5,4,2]=>{{1,3,6},{2},{4,5}}=>[3,2,6,5,4,1]=>6
[5,4,6,2,3,1]=>[6,3,1,5,4,2]=>{{1,6},{2,3},{4,5}}=>[6,3,2,5,4,1]=>7
[5,4,6,3,1,2]=>[2,6,1,5,4,3]=>{{1,2,6},{3},{4,5}}=>[2,6,3,5,4,1]=>6
[5,4,6,3,2,1]=>[6,1,2,5,4,3]=>{{1,6},{2},{3},{4,5}}=>[6,2,3,5,4,1]=>6
[5,6,1,2,3,4]=>[2,3,4,6,5,1]=>{{1,2,3,4,6},{5}}=>[2,3,4,6,5,1]=>5
[5,6,1,2,4,3]=>[2,4,6,3,5,1]=>{{1,2,4},{3,6},{5}}=>[2,4,6,1,5,3]=>6
[5,6,1,3,2,4]=>[3,4,2,6,5,1]=>{{1,3},{2,4,6},{5}}=>[3,4,1,6,5,2]=>6
[5,6,1,3,4,2]=>[3,6,4,2,5,1]=>{{1,3,4},{2,6},{5}}=>[3,6,4,1,5,2]=>7
[5,6,1,4,2,3]=>[4,3,6,2,5,1]=>{{1,4},{2,3,6},{5}}=>[4,3,6,1,5,2]=>7
[5,6,1,4,3,2]=>[4,6,2,3,5,1]=>{{1,4},{2,6},{3},{5}}=>[4,6,3,1,5,2]=>7
[5,6,2,1,3,4]=>[3,1,4,6,5,2]=>{{1,3,4,6},{2},{5}}=>[3,2,4,6,5,1]=>5
[5,6,2,1,4,3]=>[4,1,6,3,5,2]=>{{1,4},{2},{3,6},{5}}=>[4,2,6,1,5,3]=>6
[5,6,2,3,1,4]=>[4,3,1,6,5,2]=>{{1,4,6},{2,3},{5}}=>[4,3,2,6,5,1]=>6
[5,6,2,3,4,1]=>[6,3,4,1,5,2]=>{{1,6},{2,3,4},{5}}=>[6,3,4,2,5,1]=>7
[5,6,2,4,1,3]=>[3,4,6,1,5,2]=>{{1,3,6},{2,4},{5}}=>[3,4,6,2,5,1]=>7
[5,6,2,4,3,1]=>[6,4,1,3,5,2]=>{{1,6},{2,4},{3},{5}}=>[6,4,3,2,5,1]=>7
[5,6,3,1,2,4]=>[2,4,1,6,5,3]=>{{1,2,4,6},{3},{5}}=>[2,4,3,6,5,1]=>5
[5,6,3,1,4,2]=>[4,6,1,2,5,3]=>{{1,4},{2,6},{3},{5}}=>[4,6,3,1,5,2]=>7
[5,6,3,2,1,4]=>[4,1,2,6,5,3]=>{{1,4,6},{2},{3},{5}}=>[4,2,3,6,5,1]=>5
[5,6,3,2,4,1]=>[6,4,2,1,5,3]=>{{1,6},{2,4},{3},{5}}=>[6,4,3,2,5,1]=>7
[5,6,3,4,1,2]=>[2,6,4,1,5,3]=>{{1,2,6},{3,4},{5}}=>[2,6,4,3,5,1]=>6
[5,6,3,4,2,1]=>[6,1,4,2,5,3]=>{{1,6},{2},{3,4},{5}}=>[6,2,4,3,5,1]=>6
[5,6,4,1,2,3]=>[2,3,6,1,5,4]=>{{1,2,3,6},{4},{5}}=>[2,3,6,4,5,1]=>5
[5,6,4,1,3,2]=>[3,6,2,1,5,4]=>{{1,3},{2,6},{4},{5}}=>[3,6,1,4,5,2]=>6
[5,6,4,2,1,3]=>[3,1,6,2,5,4]=>{{1,3,6},{2},{4},{5}}=>[3,2,6,4,5,1]=>5
[5,6,4,2,3,1]=>[6,3,1,2,5,4]=>{{1,6},{2,3},{4},{5}}=>[6,3,2,4,5,1]=>6
[5,6,4,3,1,2]=>[2,6,1,3,5,4]=>{{1,2,6},{3},{4},{5}}=>[2,6,3,4,5,1]=>5
[5,6,4,3,2,1]=>[6,1,2,3,5,4]=>{{1,6},{2},{3},{4},{5}}=>[6,2,3,4,5,1]=>5
[6,1,2,3,4,5]=>[2,3,4,5,6,1]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>5
[6,1,2,3,5,4]=>[2,3,5,6,4,1]=>{{1,2,3,5},{4,6}}=>[2,3,5,6,1,4]=>6
[6,1,2,4,3,5]=>[2,4,5,3,6,1]=>{{1,2,4},{3,5,6}}=>[2,4,5,1,6,3]=>6
[6,1,2,4,5,3]=>[2,4,6,5,3,1]=>{{1,2,4,5},{3,6}}=>[2,4,6,5,1,3]=>7
[6,1,2,5,3,4]=>[2,5,4,6,3,1]=>{{1,2,5},{3,4,6}}=>[2,5,4,6,1,3]=>7
[6,1,2,5,4,3]=>[2,5,6,3,4,1]=>{{1,2,5},{3,6},{4}}=>[2,5,6,4,1,3]=>7
[6,1,3,2,4,5]=>[3,4,2,5,6,1]=>{{1,3},{2,4,5,6}}=>[3,4,1,5,6,2]=>6
[6,1,3,2,5,4]=>[3,5,2,6,4,1]=>{{1,3},{2,5},{4,6}}=>[3,5,1,6,2,4]=>7
[6,1,3,4,2,5]=>[3,5,4,2,6,1]=>{{1,3,4},{2,5,6}}=>[3,5,4,1,6,2]=>7
[6,1,3,4,5,2]=>[3,6,4,5,2,1]=>{{1,3,4,5},{2,6}}=>[3,6,4,5,1,2]=>8
[6,1,3,5,2,4]=>[3,4,5,6,2,1]=>{{1,3,5},{2,4,6}}=>[3,4,5,6,1,2]=>8
[6,1,3,5,4,2]=>[3,6,5,2,4,1]=>{{1,3,5},{2,6},{4}}=>[3,6,5,4,1,2]=>8
[6,1,4,2,3,5]=>[4,3,5,2,6,1]=>{{1,4},{2,3,5,6}}=>[4,3,5,1,6,2]=>7
[6,1,4,2,5,3]=>[4,5,6,2,3,1]=>{{1,4},{2,5},{3,6}}=>[4,5,6,1,2,3]=>9
[6,1,4,3,2,5]=>[4,5,2,3,6,1]=>{{1,4},{2,5,6},{3}}=>[4,5,3,1,6,2]=>7
[6,1,4,3,5,2]=>[4,6,5,3,2,1]=>{{1,4},{2,6},{3,5}}=>[4,6,5,1,3,2]=>9
[6,1,4,5,2,3]=>[4,3,6,5,2,1]=>{{1,4,5},{2,3,6}}=>[4,3,6,5,1,2]=>8
[6,1,4,5,3,2]=>[4,6,2,5,3,1]=>{{1,4,5},{2,6},{3}}=>[4,6,3,5,1,2]=>8
[6,1,5,2,3,4]=>[5,3,4,6,2,1]=>{{1,5},{2,3,4,6}}=>[5,3,4,6,1,2]=>8
[6,1,5,2,4,3]=>[5,4,6,3,2,1]=>{{1,5},{2,4},{3,6}}=>[5,4,6,2,1,3]=>9
[6,1,5,3,2,4]=>[5,4,2,6,3,1]=>{{1,5},{2,4,6},{3}}=>[5,4,3,6,1,2]=>8
[6,1,5,3,4,2]=>[5,6,4,2,3,1]=>{{1,5},{2,6},{3,4}}=>[5,6,4,3,1,2]=>9
[6,1,5,4,2,3]=>[5,3,6,2,4,1]=>{{1,5},{2,3,6},{4}}=>[5,3,6,4,1,2]=>8
[6,1,5,4,3,2]=>[5,6,2,3,4,1]=>{{1,5},{2,6},{3},{4}}=>[5,6,3,4,1,2]=>8
[6,2,1,3,4,5]=>[3,1,4,5,6,2]=>{{1,3,4,5,6},{2}}=>[3,2,4,5,6,1]=>5
[6,2,1,3,5,4]=>[3,1,5,6,4,2]=>{{1,3,5},{2},{4,6}}=>[3,2,5,6,1,4]=>6
[6,2,1,4,3,5]=>[4,1,5,3,6,2]=>{{1,4},{2},{3,5,6}}=>[4,2,5,1,6,3]=>6
[6,2,1,4,5,3]=>[4,1,6,5,3,2]=>{{1,4,5},{2},{3,6}}=>[4,2,6,5,1,3]=>7
[6,2,1,5,3,4]=>[5,1,4,6,3,2]=>{{1,5},{2},{3,4,6}}=>[5,2,4,6,1,3]=>7
[6,2,1,5,4,3]=>[5,1,6,3,4,2]=>{{1,5},{2},{3,6},{4}}=>[5,2,6,4,1,3]=>7
[6,2,3,1,4,5]=>[4,3,1,5,6,2]=>{{1,4,5,6},{2,3}}=>[4,3,2,5,6,1]=>6
[6,2,3,1,5,4]=>[5,3,1,6,4,2]=>{{1,5},{2,3},{4,6}}=>[5,3,2,6,1,4]=>7
[6,2,3,4,1,5]=>[5,3,4,1,6,2]=>{{1,5,6},{2,3,4}}=>[5,3,4,2,6,1]=>7
[6,2,3,4,5,1]=>[6,3,4,5,1,2]=>{{1,6},{2,3,4,5}}=>[6,3,4,5,2,1]=>8
[6,2,3,5,1,4]=>[4,3,5,6,1,2]=>{{1,4,6},{2,3,5}}=>[4,3,5,6,2,1]=>8
[6,2,3,5,4,1]=>[6,3,5,1,4,2]=>{{1,6},{2,3,5},{4}}=>[6,3,5,4,2,1]=>8
[6,2,4,1,3,5]=>[3,4,5,1,6,2]=>{{1,3,5,6},{2,4}}=>[3,4,5,2,6,1]=>7
[6,2,4,1,5,3]=>[5,4,6,1,3,2]=>{{1,5},{2,4},{3,6}}=>[5,4,6,2,1,3]=>9
[6,2,4,3,1,5]=>[5,4,1,3,6,2]=>{{1,5,6},{2,4},{3}}=>[5,4,3,2,6,1]=>7
[6,2,4,3,5,1]=>[6,4,5,3,1,2]=>{{1,6},{2,4},{3,5}}=>[6,4,5,2,3,1]=>9
[6,2,4,5,1,3]=>[3,4,6,5,1,2]=>{{1,3,6},{2,4,5}}=>[3,4,6,5,2,1]=>8
[6,2,4,5,3,1]=>[6,4,1,5,3,2]=>{{1,6},{2,4,5},{3}}=>[6,4,3,5,2,1]=>8
[6,2,5,1,3,4]=>[3,5,4,6,1,2]=>{{1,3,4,6},{2,5}}=>[3,5,4,6,2,1]=>8
[6,2,5,1,4,3]=>[4,5,6,3,1,2]=>{{1,4},{2,5},{3,6}}=>[4,5,6,1,2,3]=>9
[6,2,5,3,1,4]=>[4,5,1,6,3,2]=>{{1,4,6},{2,5},{3}}=>[4,5,3,6,2,1]=>8
[6,2,5,3,4,1]=>[6,5,4,1,3,2]=>{{1,6},{2,5},{3,4}}=>[6,5,4,3,2,1]=>9
[6,2,5,4,1,3]=>[3,5,6,1,4,2]=>{{1,3,6},{2,5},{4}}=>[3,5,6,4,2,1]=>8
[6,2,5,4,3,1]=>[6,5,1,3,4,2]=>{{1,6},{2,5},{3},{4}}=>[6,5,3,4,2,1]=>8
[6,3,1,2,4,5]=>[2,4,1,5,6,3]=>{{1,2,4,5,6},{3}}=>[2,4,3,5,6,1]=>5
[6,3,1,2,5,4]=>[2,5,1,6,4,3]=>{{1,2,5},{3},{4,6}}=>[2,5,3,6,1,4]=>6
[6,3,1,4,2,5]=>[4,5,1,2,6,3]=>{{1,4},{2,5,6},{3}}=>[4,5,3,1,6,2]=>7
[6,3,1,4,5,2]=>[4,6,1,5,2,3]=>{{1,4,5},{2,6},{3}}=>[4,6,3,5,1,2]=>8
[6,3,1,5,2,4]=>[5,4,1,6,2,3]=>{{1,5},{2,4,6},{3}}=>[5,4,3,6,1,2]=>8
[6,3,1,5,4,2]=>[5,6,1,2,4,3]=>{{1,5},{2,6},{3},{4}}=>[5,6,3,4,1,2]=>8
[6,3,2,1,4,5]=>[4,1,2,5,6,3]=>{{1,4,5,6},{2},{3}}=>[4,2,3,5,6,1]=>5
[6,3,2,1,5,4]=>[5,1,2,6,4,3]=>{{1,5},{2},{3},{4,6}}=>[5,2,3,6,1,4]=>6
[6,3,2,4,1,5]=>[5,4,2,1,6,3]=>{{1,5,6},{2,4},{3}}=>[5,4,3,2,6,1]=>7
[6,3,2,4,5,1]=>[6,4,2,5,1,3]=>{{1,6},{2,4,5},{3}}=>[6,4,3,5,2,1]=>8
[6,3,2,5,1,4]=>[4,5,2,6,1,3]=>{{1,4,6},{2,5},{3}}=>[4,5,3,6,2,1]=>8
[6,3,2,5,4,1]=>[6,5,2,1,4,3]=>{{1,6},{2,5},{3},{4}}=>[6,5,3,4,2,1]=>8
[6,3,4,1,2,5]=>[2,5,4,1,6,3]=>{{1,2,5,6},{3,4}}=>[2,5,4,3,6,1]=>6
[6,3,4,1,5,2]=>[5,6,4,1,2,3]=>{{1,5},{2,6},{3,4}}=>[5,6,4,3,1,2]=>9
[6,3,4,2,1,5]=>[5,1,4,2,6,3]=>{{1,5,6},{2},{3,4}}=>[5,2,4,3,6,1]=>6
[6,3,4,2,5,1]=>[6,5,4,2,1,3]=>{{1,6},{2,5},{3,4}}=>[6,5,4,3,2,1]=>9
[6,3,4,5,1,2]=>[2,6,4,5,1,3]=>{{1,2,6},{3,4,5}}=>[2,6,4,5,3,1]=>7
[6,3,4,5,2,1]=>[6,1,4,5,2,3]=>{{1,6},{2},{3,4,5}}=>[6,2,4,5,3,1]=>7
[6,3,5,1,2,4]=>[2,4,5,6,1,3]=>{{1,2,4,6},{3,5}}=>[2,4,5,6,3,1]=>7
[6,3,5,1,4,2]=>[4,6,5,2,1,3]=>{{1,4},{2,6},{3,5}}=>[4,6,5,1,3,2]=>9
[6,3,5,2,1,4]=>[4,1,5,6,2,3]=>{{1,4,6},{2},{3,5}}=>[4,2,5,6,3,1]=>7
[6,3,5,2,4,1]=>[6,4,5,1,2,3]=>{{1,6},{2,4},{3,5}}=>[6,4,5,2,3,1]=>9
[6,3,5,4,1,2]=>[2,6,5,1,4,3]=>{{1,2,6},{3,5},{4}}=>[2,6,5,4,3,1]=>7
[6,3,5,4,2,1]=>[6,1,5,2,4,3]=>{{1,6},{2},{3,5},{4}}=>[6,2,5,4,3,1]=>7
[6,4,1,2,3,5]=>[2,3,5,1,6,4]=>{{1,2,3,5,6},{4}}=>[2,3,5,4,6,1]=>5
[6,4,1,2,5,3]=>[2,5,6,1,3,4]=>{{1,2,5},{3,6},{4}}=>[2,5,6,4,1,3]=>7
[6,4,1,3,2,5]=>[3,5,2,1,6,4]=>{{1,3},{2,5,6},{4}}=>[3,5,1,4,6,2]=>6
[6,4,1,3,5,2]=>[3,6,5,1,2,4]=>{{1,3,5},{2,6},{4}}=>[3,6,5,4,1,2]=>8
[6,4,1,5,2,3]=>[5,3,6,1,2,4]=>{{1,5},{2,3,6},{4}}=>[5,3,6,4,1,2]=>8
[6,4,1,5,3,2]=>[5,6,2,1,3,4]=>{{1,5},{2,6},{3},{4}}=>[5,6,3,4,1,2]=>8
[6,4,2,1,3,5]=>[3,1,5,2,6,4]=>{{1,3,5,6},{2},{4}}=>[3,2,5,4,6,1]=>5
[6,4,2,1,5,3]=>[5,1,6,2,3,4]=>{{1,5},{2},{3,6},{4}}=>[5,2,6,4,1,3]=>7
[6,4,2,3,1,5]=>[5,3,1,2,6,4]=>{{1,5,6},{2,3},{4}}=>[5,3,2,4,6,1]=>6
[6,4,2,3,5,1]=>[6,3,5,2,1,4]=>{{1,6},{2,3,5},{4}}=>[6,3,5,4,2,1]=>8
[6,4,2,5,1,3]=>[3,5,6,2,1,4]=>{{1,3,6},{2,5},{4}}=>[3,5,6,4,2,1]=>8
[6,4,2,5,3,1]=>[6,5,1,2,3,4]=>{{1,6},{2,5},{3},{4}}=>[6,5,3,4,2,1]=>8
[6,4,3,1,2,5]=>[2,5,1,3,6,4]=>{{1,2,5,6},{3},{4}}=>[2,5,3,4,6,1]=>5
[6,4,3,1,5,2]=>[5,6,1,3,2,4]=>{{1,5},{2,6},{3},{4}}=>[5,6,3,4,1,2]=>8
[6,4,3,2,1,5]=>[5,1,2,3,6,4]=>{{1,5,6},{2},{3},{4}}=>[5,2,3,4,6,1]=>5
[6,4,3,2,5,1]=>[6,5,2,3,1,4]=>{{1,6},{2,5},{3},{4}}=>[6,5,3,4,2,1]=>8
[6,4,3,5,1,2]=>[2,6,5,3,1,4]=>{{1,2,6},{3,5},{4}}=>[2,6,5,4,3,1]=>7
[6,4,3,5,2,1]=>[6,1,5,3,2,4]=>{{1,6},{2},{3,5},{4}}=>[6,2,5,4,3,1]=>7
[6,4,5,1,2,3]=>[2,3,6,5,1,4]=>{{1,2,3,6},{4,5}}=>[2,3,6,5,4,1]=>6
[6,4,5,1,3,2]=>[3,6,2,5,1,4]=>{{1,3},{2,6},{4,5}}=>[3,6,1,5,4,2]=>7
[6,4,5,2,1,3]=>[3,1,6,5,2,4]=>{{1,3,6},{2},{4,5}}=>[3,2,6,5,4,1]=>6
[6,4,5,2,3,1]=>[6,3,1,5,2,4]=>{{1,6},{2,3},{4,5}}=>[6,3,2,5,4,1]=>7
[6,4,5,3,1,2]=>[2,6,1,5,3,4]=>{{1,2,6},{3},{4,5}}=>[2,6,3,5,4,1]=>6
[6,4,5,3,2,1]=>[6,1,2,5,3,4]=>{{1,6},{2},{3},{4,5}}=>[6,2,3,5,4,1]=>6
[6,5,1,2,3,4]=>[2,3,4,6,1,5]=>{{1,2,3,4,6},{5}}=>[2,3,4,6,5,1]=>5
[6,5,1,2,4,3]=>[2,4,6,3,1,5]=>{{1,2,4},{3,6},{5}}=>[2,4,6,1,5,3]=>6
[6,5,1,3,2,4]=>[3,4,2,6,1,5]=>{{1,3},{2,4,6},{5}}=>[3,4,1,6,5,2]=>6
[6,5,1,3,4,2]=>[3,6,4,2,1,5]=>{{1,3,4},{2,6},{5}}=>[3,6,4,1,5,2]=>7
[6,5,1,4,2,3]=>[4,3,6,2,1,5]=>{{1,4},{2,3,6},{5}}=>[4,3,6,1,5,2]=>7
[6,5,1,4,3,2]=>[4,6,2,3,1,5]=>{{1,4},{2,6},{3},{5}}=>[4,6,3,1,5,2]=>7
[6,5,2,1,3,4]=>[3,1,4,6,2,5]=>{{1,3,4,6},{2},{5}}=>[3,2,4,6,5,1]=>5
[6,5,2,1,4,3]=>[4,1,6,3,2,5]=>{{1,4},{2},{3,6},{5}}=>[4,2,6,1,5,3]=>6
[6,5,2,3,1,4]=>[4,3,1,6,2,5]=>{{1,4,6},{2,3},{5}}=>[4,3,2,6,5,1]=>6
[6,5,2,3,4,1]=>[6,3,4,1,2,5]=>{{1,6},{2,3,4},{5}}=>[6,3,4,2,5,1]=>7
[6,5,2,4,1,3]=>[3,4,6,1,2,5]=>{{1,3,6},{2,4},{5}}=>[3,4,6,2,5,1]=>7
[6,5,2,4,3,1]=>[6,4,1,3,2,5]=>{{1,6},{2,4},{3},{5}}=>[6,4,3,2,5,1]=>7
[6,5,3,1,2,4]=>[2,4,1,6,3,5]=>{{1,2,4,6},{3},{5}}=>[2,4,3,6,5,1]=>5
[6,5,3,1,4,2]=>[4,6,1,2,3,5]=>{{1,4},{2,6},{3},{5}}=>[4,6,3,1,5,2]=>7
[6,5,3,2,1,4]=>[4,1,2,6,3,5]=>{{1,4,6},{2},{3},{5}}=>[4,2,3,6,5,1]=>5
[6,5,3,2,4,1]=>[6,4,2,1,3,5]=>{{1,6},{2,4},{3},{5}}=>[6,4,3,2,5,1]=>7
[6,5,3,4,1,2]=>[2,6,4,1,3,5]=>{{1,2,6},{3,4},{5}}=>[2,6,4,3,5,1]=>6
[6,5,3,4,2,1]=>[6,1,4,2,3,5]=>{{1,6},{2},{3,4},{5}}=>[6,2,4,3,5,1]=>6
[6,5,4,1,2,3]=>[2,3,6,1,4,5]=>{{1,2,3,6},{4},{5}}=>[2,3,6,4,5,1]=>5
[6,5,4,1,3,2]=>[3,6,2,1,4,5]=>{{1,3},{2,6},{4},{5}}=>[3,6,1,4,5,2]=>6
[6,5,4,2,1,3]=>[3,1,6,2,4,5]=>{{1,3,6},{2},{4},{5}}=>[3,2,6,4,5,1]=>5
[6,5,4,2,3,1]=>[6,3,1,2,4,5]=>{{1,6},{2,3},{4},{5}}=>[6,3,2,4,5,1]=>6
[6,5,4,3,1,2]=>[2,6,1,3,4,5]=>{{1,2,6},{3},{4},{5}}=>[2,6,3,4,5,1]=>5
[6,5,4,3,2,1]=>[6,1,2,3,4,5]=>{{1,6},{2},{3},{4},{5}}=>[6,2,3,4,5,1]=>5
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Description
The sorting index of a permutation.
The sorting index counts the total distance that symbols move during a selection sort of a permutation. This sorting algorithm swaps symbol n into index n and then recursively sorts the first n-1 symbols.
Compare this to St000018The number of inversions of a permutation., the number of inversions of a permutation, which is also the total distance that elements move during a bubble sort.
The sorting index counts the total distance that symbols move during a selection sort of a permutation. This sorting algorithm swaps symbol n into index n and then recursively sorts the first n-1 symbols.
Compare this to St000018The number of inversions of a permutation., the number of inversions of a permutation, which is also the total distance that elements move during a bubble sort.
Map
first fundamental transformation
Description
Return the permutation whose cycles are the subsequences between successive left to right maxima.
Map
to permutation
Description
Sends the set partition to the permutation obtained by considering the blocks as increasing cycles.
Map
weak exceedance partition
Description
The set partition induced by the weak exceedances of a permutation.
This is the coarsest set partition that contains all arcs $(i, \pi(i))$ with $i\leq\pi(i)$.
This is the coarsest set partition that contains all arcs $(i, \pi(i))$ with $i\leq\pi(i)$.
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