Identifier
-
Mp00223:
Permutations
—runsort⟶
Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001879: Posets ⟶ ℤ
Values
=>
Cc0014;cc-rep
[1,2,3]=>[1,2,3]=>([(0,2),(2,1)],3)=>2
[2,3,1]=>[1,2,3]=>([(0,2),(2,1)],3)=>2
[3,1,2]=>[1,2,3]=>([(0,2),(2,1)],3)=>2
[3,2,1]=>[1,2,3]=>([(0,2),(2,1)],3)=>2
[1,2,3,4]=>[1,2,3,4]=>([(0,3),(2,1),(3,2)],4)=>3
[1,3,2,4]=>[1,3,2,4]=>([(0,1),(0,2),(1,3),(2,3)],4)=>4
[2,3,4,1]=>[1,2,3,4]=>([(0,3),(2,1),(3,2)],4)=>3
[2,4,1,3]=>[1,3,2,4]=>([(0,1),(0,2),(1,3),(2,3)],4)=>4
[3,4,1,2]=>[1,2,3,4]=>([(0,3),(2,1),(3,2)],4)=>3
[3,4,2,1]=>[1,2,3,4]=>([(0,3),(2,1),(3,2)],4)=>3
[4,1,2,3]=>[1,2,3,4]=>([(0,3),(2,1),(3,2)],4)=>3
[4,1,3,2]=>[1,3,2,4]=>([(0,1),(0,2),(1,3),(2,3)],4)=>4
[4,2,1,3]=>[1,3,2,4]=>([(0,1),(0,2),(1,3),(2,3)],4)=>4
[4,2,3,1]=>[1,2,3,4]=>([(0,3),(2,1),(3,2)],4)=>3
[4,3,1,2]=>[1,2,3,4]=>([(0,3),(2,1),(3,2)],4)=>3
[4,3,2,1]=>[1,2,3,4]=>([(0,3),(2,1),(3,2)],4)=>3
[1,2,3,4,5]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>4
[1,2,4,3,5]=>[1,2,4,3,5]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>5
[1,3,2,4,5]=>[1,3,2,4,5]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>5
[1,3,4,2,5]=>[1,3,4,2,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>6
[1,4,2,3,5]=>[1,4,2,3,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>6
[1,4,3,5,2]=>[1,4,2,3,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>6
[2,1,4,3,5]=>[1,4,2,3,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>6
[2,3,4,5,1]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>4
[2,3,5,1,4]=>[1,4,2,3,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>6
[2,4,3,5,1]=>[1,2,4,3,5]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>5
[2,4,5,1,3]=>[1,3,2,4,5]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>5
[2,5,1,3,4]=>[1,3,4,2,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>6
[3,4,5,1,2]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>4
[3,4,5,2,1]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>4
[3,5,1,2,4]=>[1,2,4,3,5]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>5
[3,5,1,4,2]=>[1,4,2,3,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>6
[3,5,2,1,4]=>[1,4,2,3,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>6
[3,5,2,4,1]=>[1,2,4,3,5]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>5
[4,5,1,2,3]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>4
[4,5,1,3,2]=>[1,3,2,4,5]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>5
[4,5,2,1,3]=>[1,3,2,4,5]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>5
[4,5,2,3,1]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>4
[4,5,3,1,2]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>4
[4,5,3,2,1]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>4
[5,1,2,3,4]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>4
[5,1,2,4,3]=>[1,2,4,3,5]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>5
[5,1,3,2,4]=>[1,3,2,4,5]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>5
[5,1,3,4,2]=>[1,3,4,2,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>6
[5,1,4,2,3]=>[1,4,2,3,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>6
[5,1,4,3,2]=>[1,4,2,3,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>6
[5,2,1,3,4]=>[1,3,4,2,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>6
[5,2,1,4,3]=>[1,4,2,3,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>6
[5,2,3,1,4]=>[1,4,2,3,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>6
[5,2,3,4,1]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>4
[5,2,4,1,3]=>[1,3,2,4,5]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>5
[5,2,4,3,1]=>[1,2,4,3,5]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>5
[5,3,1,2,4]=>[1,2,4,3,5]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>5
[5,3,1,4,2]=>[1,4,2,3,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>6
[5,3,2,1,4]=>[1,4,2,3,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>6
[5,3,2,4,1]=>[1,2,4,3,5]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>5
[5,3,4,1,2]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>4
[5,3,4,2,1]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>4
[5,4,1,2,3]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>4
[5,4,1,3,2]=>[1,3,2,4,5]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>5
[5,4,2,1,3]=>[1,3,2,4,5]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>5
[5,4,2,3,1]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>4
[5,4,3,1,2]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>4
[5,4,3,2,1]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>4
[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)=>6
[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>6
[1,2,4,5,3,6]=>[1,2,4,5,3,6]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>7
[1,2,5,3,4,6]=>[1,2,5,3,4,6]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>7
[1,2,5,4,6,3]=>[1,2,5,3,4,6]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>7
[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>6
[1,3,4,2,5,6]=>[1,3,4,2,5,6]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>7
[1,3,4,5,2,6]=>[1,3,4,5,2,6]=>([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>8
[1,3,5,2,4,6]=>[1,3,5,2,4,6]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>7
[1,3,5,4,6,2]=>[1,3,5,2,4,6]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>7
[1,4,2,3,5,6]=>[1,4,2,3,5,6]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>7
[1,4,2,5,3,6]=>[1,4,2,5,3,6]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>7
[1,4,3,5,6,2]=>[1,4,2,3,5,6]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>7
[1,4,3,6,2,5]=>[1,4,2,5,3,6]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>7
[1,4,5,2,3,6]=>[1,4,5,2,3,6]=>([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)=>8
[1,4,5,3,6,2]=>[1,4,5,2,3,6]=>([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)=>8
[1,5,2,3,4,6]=>[1,5,2,3,4,6]=>([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>8
[1,5,2,4,3,6]=>[1,5,2,4,3,6]=>([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)=>10
[1,5,3,4,6,2]=>[1,5,2,3,4,6]=>([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>8
[1,5,3,6,2,4]=>[1,5,2,4,3,6]=>([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)=>10
[1,5,4,6,2,3]=>[1,5,2,3,4,6]=>([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>8
[1,5,4,6,3,2]=>[1,5,2,3,4,6]=>([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>8
[2,1,3,5,4,6]=>[1,3,5,2,4,6]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>7
[2,1,4,3,5,6]=>[1,4,2,3,5,6]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>7
[2,1,4,5,3,6]=>[1,4,5,2,3,6]=>([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)=>8
[2,1,5,3,4,6]=>[1,5,2,3,4,6]=>([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>8
[2,1,5,4,6,3]=>[1,5,2,3,4,6]=>([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>8
[2,3,1,5,4,6]=>[1,5,2,3,4,6]=>([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>8
[2,3,4,5,6,1]=>[1,2,3,4,5,6]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[2,3,4,6,1,5]=>[1,5,2,3,4,6]=>([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>8
[2,3,5,4,6,1]=>[1,2,3,5,4,6]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)=>6
[2,3,5,6,1,4]=>[1,4,2,3,5,6]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>7
[2,3,6,1,4,5]=>[1,4,5,2,3,6]=>([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)=>8
[2,4,1,5,3,6]=>[1,5,2,4,3,6]=>([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)=>10
[2,4,3,5,6,1]=>[1,2,4,3,5,6]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>6
[2,4,3,6,1,5]=>[1,5,2,4,3,6]=>([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)=>10
[2,4,5,3,6,1]=>[1,2,4,5,3,6]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>7
[2,4,5,6,1,3]=>[1,3,2,4,5,6]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>6
[2,4,6,1,3,5]=>[1,3,5,2,4,6]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>7
[2,5,1,4,3,6]=>[1,4,2,5,3,6]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>7
[2,5,3,4,6,1]=>[1,2,5,3,4,6]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>7
[2,5,3,6,1,4]=>[1,4,2,5,3,6]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>7
[2,5,4,6,3,1]=>[1,2,5,3,4,6]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>7
[2,5,6,1,3,4]=>[1,3,4,2,5,6]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>7
[2,6,1,3,4,5]=>[1,3,4,5,2,6]=>([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>8
[3,1,2,5,4,6]=>[1,2,5,3,4,6]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>7
[3,1,5,4,6,2]=>[1,5,2,3,4,6]=>([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>8
[3,2,1,5,4,6]=>[1,5,2,3,4,6]=>([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>8
[3,2,5,4,6,1]=>[1,2,5,3,4,6]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>7
[3,4,5,6,1,2]=>[1,2,3,4,5,6]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[3,4,5,6,2,1]=>[1,2,3,4,5,6]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[3,4,6,1,2,5]=>[1,2,5,3,4,6]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>7
[3,4,6,1,5,2]=>[1,5,2,3,4,6]=>([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>8
[3,4,6,2,1,5]=>[1,5,2,3,4,6]=>([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>8
[3,4,6,2,5,1]=>[1,2,5,3,4,6]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>7
[3,5,4,6,1,2]=>[1,2,3,5,4,6]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)=>6
[3,5,4,6,2,1]=>[1,2,3,5,4,6]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)=>6
[3,5,6,1,2,4]=>[1,2,4,3,5,6]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>6
[3,5,6,1,4,2]=>[1,4,2,3,5,6]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>7
[3,5,6,2,1,4]=>[1,4,2,3,5,6]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>7
[3,5,6,2,4,1]=>[1,2,4,3,5,6]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>6
[3,6,1,2,4,5]=>[1,2,4,5,3,6]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>7
[3,6,1,4,2,5]=>[1,4,2,5,3,6]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>7
[3,6,1,4,5,2]=>[1,4,5,2,3,6]=>([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)=>8
[3,6,1,5,2,4]=>[1,5,2,4,3,6]=>([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)=>10
[3,6,2,1,4,5]=>[1,4,5,2,3,6]=>([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)=>8
[3,6,2,4,1,5]=>[1,5,2,4,3,6]=>([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)=>10
[3,6,2,4,5,1]=>[1,2,4,5,3,6]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>7
[3,6,2,5,1,4]=>[1,4,2,5,3,6]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>7
[4,5,6,1,2,3]=>[1,2,3,4,5,6]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[4,5,6,1,3,2]=>[1,3,2,4,5,6]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>6
[4,5,6,2,1,3]=>[1,3,2,4,5,6]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>6
[4,5,6,2,3,1]=>[1,2,3,4,5,6]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[4,5,6,3,1,2]=>[1,2,3,4,5,6]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[4,5,6,3,2,1]=>[1,2,3,4,5,6]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[4,6,1,2,3,5]=>[1,2,3,5,4,6]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)=>6
[4,6,1,2,5,3]=>[1,2,5,3,4,6]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>7
[4,6,1,3,5,2]=>[1,3,5,2,4,6]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>7
[4,6,1,5,2,3]=>[1,5,2,3,4,6]=>([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>8
[4,6,1,5,3,2]=>[1,5,2,3,4,6]=>([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>8
[4,6,2,1,3,5]=>[1,3,5,2,4,6]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>7
[4,6,2,1,5,3]=>[1,5,2,3,4,6]=>([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>8
[4,6,2,3,1,5]=>[1,5,2,3,4,6]=>([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>8
[4,6,2,3,5,1]=>[1,2,3,5,4,6]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)=>6
[4,6,2,5,3,1]=>[1,2,5,3,4,6]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>7
[4,6,3,1,2,5]=>[1,2,5,3,4,6]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>7
[4,6,3,1,5,2]=>[1,5,2,3,4,6]=>([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>8
[4,6,3,2,1,5]=>[1,5,2,3,4,6]=>([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>8
[4,6,3,2,5,1]=>[1,2,5,3,4,6]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>7
[4,6,3,5,1,2]=>[1,2,3,5,4,6]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)=>6
[4,6,3,5,2,1]=>[1,2,3,5,4,6]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)=>6
[5,6,1,2,3,4]=>[1,2,3,4,5,6]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[5,6,1,2,4,3]=>[1,2,4,3,5,6]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>6
[5,6,1,3,2,4]=>[1,3,2,4,5,6]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>6
[5,6,1,3,4,2]=>[1,3,4,2,5,6]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>7
[5,6,1,4,2,3]=>[1,4,2,3,5,6]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>7
[5,6,1,4,3,2]=>[1,4,2,3,5,6]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>7
[5,6,2,1,3,4]=>[1,3,4,2,5,6]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>7
[5,6,2,1,4,3]=>[1,4,2,3,5,6]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>7
[5,6,2,3,1,4]=>[1,4,2,3,5,6]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>7
[5,6,2,3,4,1]=>[1,2,3,4,5,6]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[5,6,2,4,1,3]=>[1,3,2,4,5,6]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>6
[5,6,2,4,3,1]=>[1,2,4,3,5,6]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>6
[5,6,3,1,2,4]=>[1,2,4,3,5,6]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>6
[5,6,3,1,4,2]=>[1,4,2,3,5,6]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>7
[5,6,3,2,1,4]=>[1,4,2,3,5,6]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>7
[5,6,3,2,4,1]=>[1,2,4,3,5,6]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>6
[5,6,3,4,1,2]=>[1,2,3,4,5,6]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[5,6,3,4,2,1]=>[1,2,3,4,5,6]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[5,6,4,1,2,3]=>[1,2,3,4,5,6]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[5,6,4,1,3,2]=>[1,3,2,4,5,6]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>6
[5,6,4,2,1,3]=>[1,3,2,4,5,6]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>6
[5,6,4,2,3,1]=>[1,2,3,4,5,6]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[5,6,4,3,1,2]=>[1,2,3,4,5,6]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[5,6,4,3,2,1]=>[1,2,3,4,5,6]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[6,1,2,3,4,5]=>[1,2,3,4,5,6]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[6,1,2,3,5,4]=>[1,2,3,5,4,6]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)=>6
[6,1,2,4,3,5]=>[1,2,4,3,5,6]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>6
[6,1,2,4,5,3]=>[1,2,4,5,3,6]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>7
[6,1,2,5,3,4]=>[1,2,5,3,4,6]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>7
[6,1,2,5,4,3]=>[1,2,5,3,4,6]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>7
[6,1,3,2,4,5]=>[1,3,2,4,5,6]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>6
[6,1,3,4,2,5]=>[1,3,4,2,5,6]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>7
[6,1,3,4,5,2]=>[1,3,4,5,2,6]=>([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>8
[6,1,3,5,2,4]=>[1,3,5,2,4,6]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>7
[6,1,3,5,4,2]=>[1,3,5,2,4,6]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>7
[6,1,4,2,3,5]=>[1,4,2,3,5,6]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>7
[6,1,4,2,5,3]=>[1,4,2,5,3,6]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>7
[6,1,4,3,2,5]=>[1,4,2,5,3,6]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>7
[6,1,4,3,5,2]=>[1,4,2,3,5,6]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>7
[6,1,4,5,2,3]=>[1,4,5,2,3,6]=>([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)=>8
[6,1,4,5,3,2]=>[1,4,5,2,3,6]=>([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)=>8
[6,1,5,2,3,4]=>[1,5,2,3,4,6]=>([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>8
[6,1,5,2,4,3]=>[1,5,2,4,3,6]=>([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)=>10
[6,1,5,3,2,4]=>[1,5,2,4,3,6]=>([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)=>10
[6,1,5,3,4,2]=>[1,5,2,3,4,6]=>([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>8
[6,1,5,4,2,3]=>[1,5,2,3,4,6]=>([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>8
[6,1,5,4,3,2]=>[1,5,2,3,4,6]=>([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>8
[6,2,1,3,4,5]=>[1,3,4,5,2,6]=>([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>8
[6,2,1,3,5,4]=>[1,3,5,2,4,6]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>7
[6,2,1,4,3,5]=>[1,4,2,3,5,6]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>7
[6,2,1,4,5,3]=>[1,4,5,2,3,6]=>([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)=>8
[6,2,1,5,3,4]=>[1,5,2,3,4,6]=>([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>8
[6,2,1,5,4,3]=>[1,5,2,3,4,6]=>([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>8
[6,2,3,1,4,5]=>[1,4,5,2,3,6]=>([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)=>8
[6,2,3,1,5,4]=>[1,5,2,3,4,6]=>([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>8
[6,2,3,4,1,5]=>[1,5,2,3,4,6]=>([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>8
[6,2,3,4,5,1]=>[1,2,3,4,5,6]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[6,2,3,5,1,4]=>[1,4,2,3,5,6]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>7
[6,2,3,5,4,1]=>[1,2,3,5,4,6]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)=>6
[6,2,4,1,3,5]=>[1,3,5,2,4,6]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>7
[6,2,4,1,5,3]=>[1,5,2,4,3,6]=>([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)=>10
[6,2,4,3,1,5]=>[1,5,2,4,3,6]=>([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)=>10
[6,2,4,3,5,1]=>[1,2,4,3,5,6]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>6
[6,2,4,5,1,3]=>[1,3,2,4,5,6]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>6
[6,2,4,5,3,1]=>[1,2,4,5,3,6]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>7
[6,2,5,1,3,4]=>[1,3,4,2,5,6]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>7
[6,2,5,1,4,3]=>[1,4,2,5,3,6]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>7
[6,2,5,3,1,4]=>[1,4,2,5,3,6]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>7
[6,2,5,3,4,1]=>[1,2,5,3,4,6]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>7
[6,2,5,4,3,1]=>[1,2,5,3,4,6]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>7
[6,3,1,2,4,5]=>[1,2,4,5,3,6]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>7
[6,3,1,2,5,4]=>[1,2,5,3,4,6]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>7
[6,3,1,4,2,5]=>[1,4,2,5,3,6]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>7
[6,3,1,4,5,2]=>[1,4,5,2,3,6]=>([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)=>8
[6,3,1,5,2,4]=>[1,5,2,4,3,6]=>([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)=>10
[6,3,1,5,4,2]=>[1,5,2,3,4,6]=>([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>8
[6,3,2,1,4,5]=>[1,4,5,2,3,6]=>([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)=>8
[6,3,2,1,5,4]=>[1,5,2,3,4,6]=>([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>8
[6,3,2,4,1,5]=>[1,5,2,4,3,6]=>([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)=>10
[6,3,2,4,5,1]=>[1,2,4,5,3,6]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>7
[6,3,2,5,1,4]=>[1,4,2,5,3,6]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>7
[6,3,2,5,4,1]=>[1,2,5,3,4,6]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>7
[6,3,4,1,2,5]=>[1,2,5,3,4,6]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>7
[6,3,4,1,5,2]=>[1,5,2,3,4,6]=>([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>8
[6,3,4,2,1,5]=>[1,5,2,3,4,6]=>([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>8
[6,3,4,2,5,1]=>[1,2,5,3,4,6]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>7
[6,3,4,5,1,2]=>[1,2,3,4,5,6]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[6,3,4,5,2,1]=>[1,2,3,4,5,6]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[6,3,5,1,2,4]=>[1,2,4,3,5,6]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>6
[6,3,5,1,4,2]=>[1,4,2,3,5,6]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>7
[6,3,5,2,1,4]=>[1,4,2,3,5,6]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>7
[6,3,5,2,4,1]=>[1,2,4,3,5,6]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>6
[6,3,5,4,1,2]=>[1,2,3,5,4,6]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)=>6
[6,3,5,4,2,1]=>[1,2,3,5,4,6]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)=>6
[6,4,1,2,3,5]=>[1,2,3,5,4,6]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)=>6
[6,4,1,2,5,3]=>[1,2,5,3,4,6]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>7
[6,4,1,3,5,2]=>[1,3,5,2,4,6]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>7
[6,4,1,5,2,3]=>[1,5,2,3,4,6]=>([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>8
[6,4,1,5,3,2]=>[1,5,2,3,4,6]=>([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>8
[6,4,2,1,3,5]=>[1,3,5,2,4,6]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>7
[6,4,2,1,5,3]=>[1,5,2,3,4,6]=>([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>8
[6,4,2,3,1,5]=>[1,5,2,3,4,6]=>([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>8
[6,4,2,3,5,1]=>[1,2,3,5,4,6]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)=>6
[6,4,2,5,3,1]=>[1,2,5,3,4,6]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>7
[6,4,3,1,2,5]=>[1,2,5,3,4,6]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>7
[6,4,3,1,5,2]=>[1,5,2,3,4,6]=>([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>8
[6,4,3,2,1,5]=>[1,5,2,3,4,6]=>([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>8
[6,4,3,2,5,1]=>[1,2,5,3,4,6]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>7
[6,4,3,5,1,2]=>[1,2,3,5,4,6]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)=>6
[6,4,3,5,2,1]=>[1,2,3,5,4,6]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)=>6
[6,4,5,1,2,3]=>[1,2,3,4,5,6]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[6,4,5,1,3,2]=>[1,3,2,4,5,6]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>6
[6,4,5,2,1,3]=>[1,3,2,4,5,6]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>6
[6,4,5,2,3,1]=>[1,2,3,4,5,6]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[6,4,5,3,1,2]=>[1,2,3,4,5,6]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[6,4,5,3,2,1]=>[1,2,3,4,5,6]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[6,5,1,2,3,4]=>[1,2,3,4,5,6]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[6,5,1,2,4,3]=>[1,2,4,3,5,6]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>6
[6,5,1,3,2,4]=>[1,3,2,4,5,6]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>6
[6,5,1,3,4,2]=>[1,3,4,2,5,6]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>7
[6,5,1,4,2,3]=>[1,4,2,3,5,6]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>7
[6,5,1,4,3,2]=>[1,4,2,3,5,6]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>7
[6,5,2,1,3,4]=>[1,3,4,2,5,6]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>7
[6,5,2,1,4,3]=>[1,4,2,3,5,6]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>7
[6,5,2,3,1,4]=>[1,4,2,3,5,6]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>7
[6,5,2,3,4,1]=>[1,2,3,4,5,6]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[6,5,2,4,1,3]=>[1,3,2,4,5,6]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>6
[6,5,2,4,3,1]=>[1,2,4,3,5,6]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>6
[6,5,3,1,2,4]=>[1,2,4,3,5,6]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>6
[6,5,3,1,4,2]=>[1,4,2,3,5,6]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>7
[6,5,3,2,1,4]=>[1,4,2,3,5,6]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>7
[6,5,3,2,4,1]=>[1,2,4,3,5,6]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>6
[6,5,3,4,1,2]=>[1,2,3,4,5,6]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[6,5,4,1,2,3]=>[1,2,3,4,5,6]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[6,5,4,1,3,2]=>[1,3,2,4,5,6]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>6
[6,5,4,2,1,3]=>[1,3,2,4,5,6]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>6
[6,5,4,2,3,1]=>[1,2,3,4,5,6]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[6,5,4,3,1,2]=>[1,2,3,4,5,6]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>5
[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)=>7
[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>7
[1,2,3,5,6,4,7]=>[1,2,3,5,6,4,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[1,2,3,6,4,5,7]=>[1,2,3,6,4,5,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[1,2,3,6,5,7,4]=>[1,2,3,6,4,5,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>7
[1,2,4,5,3,6,7]=>[1,2,4,5,3,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[1,2,4,5,6,3,7]=>[1,2,4,5,6,3,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[1,2,4,6,3,5,7]=>[1,2,4,6,3,5,7]=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>8
[1,2,4,6,5,7,3]=>[1,2,4,6,3,5,7]=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>8
[1,2,5,3,4,6,7]=>[1,2,5,3,4,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[1,2,5,3,6,4,7]=>[1,2,5,3,6,4,7]=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>8
[1,2,5,4,6,7,3]=>[1,2,5,3,4,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[1,2,5,4,7,3,6]=>[1,2,5,3,6,4,7]=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>8
[1,2,5,6,3,4,7]=>[1,2,5,6,3,4,7]=>([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7)=>9
[1,2,5,6,4,7,3]=>[1,2,5,6,3,4,7]=>([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7)=>9
[1,2,6,3,4,5,7]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[1,2,6,3,5,4,7]=>[1,2,6,3,5,4,7]=>([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)=>11
[1,2,6,4,5,7,3]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[1,2,6,4,7,3,5]=>[1,2,6,3,5,4,7]=>([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)=>11
[1,2,6,5,7,3,4]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[1,2,6,5,7,4,3]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)=>7
[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)=>8
[1,3,4,2,5,6,7]=>[1,3,4,2,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[1,3,4,5,2,6,7]=>[1,3,4,5,2,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[1,3,4,5,6,2,7]=>[1,3,4,5,6,2,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[1,3,4,6,2,5,7]=>[1,3,4,6,2,5,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>9
[1,3,4,6,5,7,2]=>[1,3,4,6,2,5,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>9
[1,3,5,2,4,6,7]=>[1,3,5,2,4,6,7]=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>8
[1,3,5,4,6,7,2]=>[1,3,5,2,4,6,7]=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>8
[1,3,5,6,2,4,7]=>[1,3,5,6,2,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[1,3,5,6,4,7,2]=>[1,3,5,6,2,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[1,3,6,2,4,5,7]=>[1,3,6,2,4,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>9
[1,3,6,4,5,7,2]=>[1,3,6,2,4,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>9
[1,3,6,5,7,2,4]=>[1,3,6,2,4,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>9
[1,3,6,5,7,4,2]=>[1,3,6,2,4,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>9
[1,4,2,3,5,6,7]=>[1,4,2,3,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[1,4,2,5,3,6,7]=>[1,4,2,5,3,6,7]=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>8
[1,4,2,5,6,3,7]=>[1,4,2,5,6,3,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>9
[1,4,3,5,6,7,2]=>[1,4,2,3,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[1,4,3,6,7,2,5]=>[1,4,2,5,3,6,7]=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>8
[1,4,3,7,2,5,6]=>[1,4,2,5,6,3,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>9
[1,4,5,2,3,6,7]=>[1,4,5,2,3,6,7]=>([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7)=>9
[1,4,5,2,6,3,7]=>[1,4,5,2,6,3,7]=>([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>9
[1,4,5,3,6,7,2]=>[1,4,5,2,3,6,7]=>([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7)=>9
[1,4,5,3,7,2,6]=>[1,4,5,2,6,3,7]=>([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>9
[1,4,5,6,2,3,7]=>[1,4,5,6,2,3,7]=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>10
[1,4,5,6,3,7,2]=>[1,4,5,6,2,3,7]=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>10
[1,4,6,2,3,5,7]=>[1,4,6,2,3,5,7]=>([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>9
[1,4,6,2,5,3,7]=>[1,4,6,2,5,3,7]=>([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7)=>10
[1,4,6,3,5,7,2]=>[1,4,6,2,3,5,7]=>([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>9
[1,4,6,3,7,2,5]=>[1,4,6,2,5,3,7]=>([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7)=>10
[1,4,6,5,7,2,3]=>[1,4,6,2,3,5,7]=>([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>9
[1,4,6,5,7,3,2]=>[1,4,6,2,3,5,7]=>([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>9
[1,5,2,3,4,6,7]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[1,5,2,3,6,4,7]=>[1,5,2,3,6,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>9
[1,5,2,4,3,6,7]=>[1,5,2,4,3,6,7]=>([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)=>11
[1,5,2,4,6,3,7]=>[1,5,2,4,6,3,7]=>([(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(5,6)],7)=>11
[1,5,2,6,3,4,7]=>[1,5,2,6,3,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[1,5,2,6,4,7,3]=>[1,5,2,6,3,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[1,5,3,2,6,4,7]=>[1,5,2,6,3,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[1,5,3,4,6,7,2]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[1,5,3,4,7,2,6]=>[1,5,2,6,3,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[1,5,3,6,4,7,2]=>[1,5,2,3,6,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>9
[1,5,3,6,7,2,4]=>[1,5,2,4,3,6,7]=>([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)=>11
[1,5,3,7,2,4,6]=>[1,5,2,4,6,3,7]=>([(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(5,6)],7)=>11
[1,5,4,6,7,2,3]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[1,5,4,6,7,3,2]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[1,5,4,7,2,3,6]=>[1,5,2,3,6,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>9
[1,5,4,7,2,6,3]=>[1,5,2,6,3,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[1,5,4,7,3,2,6]=>[1,5,2,6,3,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[1,5,4,7,3,6,2]=>[1,5,2,3,6,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>9
[1,5,6,2,3,4,7]=>[1,5,6,2,3,4,7]=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>10
[1,5,6,2,4,3,7]=>[1,5,6,2,4,3,7]=>([(0,4),(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2)],7)=>12
[1,5,6,3,4,7,2]=>[1,5,6,2,3,4,7]=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>10
[1,5,6,3,7,2,4]=>[1,5,6,2,4,3,7]=>([(0,4),(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2)],7)=>12
[1,5,6,4,7,2,3]=>[1,5,6,2,3,4,7]=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>10
[1,5,6,4,7,3,2]=>[1,5,6,2,3,4,7]=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>10
[1,6,2,3,4,5,7]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[1,6,2,3,5,4,7]=>[1,6,2,3,5,4,7]=>([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)=>12
[1,6,2,4,3,5,7]=>[1,6,2,4,3,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)=>11
[1,6,2,4,5,3,7]=>[1,6,2,4,5,3,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[1,6,2,5,3,4,7]=>[1,6,2,5,3,4,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[1,6,2,5,4,7,3]=>[1,6,2,5,3,4,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[1,6,3,2,5,4,7]=>[1,6,2,5,3,4,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[1,6,3,4,5,7,2]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[1,6,3,4,7,2,5]=>[1,6,2,5,3,4,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[1,6,3,5,4,7,2]=>[1,6,2,3,5,4,7]=>([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)=>12
[1,6,3,5,7,2,4]=>[1,6,2,4,3,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)=>11
[1,6,3,7,2,4,5]=>[1,6,2,4,5,3,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[1,6,4,5,7,2,3]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[1,6,4,5,7,3,2]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[1,6,4,7,2,3,5]=>[1,6,2,3,5,4,7]=>([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)=>12
[1,6,4,7,2,5,3]=>[1,6,2,5,3,4,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[1,6,4,7,3,2,5]=>[1,6,2,5,3,4,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[1,6,4,7,3,5,2]=>[1,6,2,3,5,4,7]=>([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)=>12
[1,6,5,7,2,3,4]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[1,6,5,7,2,4,3]=>[1,6,2,4,3,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)=>11
[1,6,5,7,3,2,4]=>[1,6,2,4,3,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)=>11
[1,6,5,7,3,4,2]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[1,6,5,7,4,2,3]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[1,6,5,7,4,3,2]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[2,1,3,4,6,5,7]=>[1,3,4,6,2,5,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>9
[2,1,3,5,4,6,7]=>[1,3,5,2,4,6,7]=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>8
[2,1,3,5,6,4,7]=>[1,3,5,6,2,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[2,1,3,6,4,5,7]=>[1,3,6,2,4,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>9
[2,1,3,6,5,7,4]=>[1,3,6,2,4,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>9
[2,1,4,3,5,6,7]=>[1,4,2,3,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[2,1,4,5,3,6,7]=>[1,4,5,2,3,6,7]=>([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7)=>9
[2,1,4,5,6,3,7]=>[1,4,5,6,2,3,7]=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>10
[2,1,4,6,3,5,7]=>[1,4,6,2,3,5,7]=>([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>9
[2,1,4,6,5,7,3]=>[1,4,6,2,3,5,7]=>([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>9
[2,1,5,3,4,6,7]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[2,1,5,3,6,4,7]=>[1,5,2,3,6,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>9
[2,1,5,4,6,7,3]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[2,1,5,4,7,3,6]=>[1,5,2,3,6,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>9
[2,1,5,6,3,4,7]=>[1,5,6,2,3,4,7]=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>10
[2,1,5,6,4,7,3]=>[1,5,6,2,3,4,7]=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>10
[2,1,6,3,4,5,7]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[2,1,6,3,5,4,7]=>[1,6,2,3,5,4,7]=>([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)=>12
[2,1,6,4,5,7,3]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[2,1,6,4,7,3,5]=>[1,6,2,3,5,4,7]=>([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)=>12
[2,1,6,5,7,3,4]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[2,1,6,5,7,4,3]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[2,3,1,4,6,5,7]=>[1,4,6,2,3,5,7]=>([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>9
[2,3,1,5,4,6,7]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[2,3,1,5,6,4,7]=>[1,5,6,2,3,4,7]=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>10
[2,3,1,6,4,5,7]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[2,3,1,6,5,7,4]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[2,3,4,1,6,5,7]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[2,3,4,5,6,7,1]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[2,3,4,5,7,1,6]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[2,3,4,6,5,7,1]=>[1,2,3,4,6,5,7]=>([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)=>7
[2,3,4,6,7,1,5]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[2,3,4,7,1,5,6]=>[1,5,6,2,3,4,7]=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>10
[2,3,5,1,6,4,7]=>[1,6,2,3,5,4,7]=>([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)=>12
[2,3,5,4,6,7,1]=>[1,2,3,5,4,6,7]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>7
[2,3,5,4,7,1,6]=>[1,6,2,3,5,4,7]=>([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)=>12
[2,3,5,6,4,7,1]=>[1,2,3,5,6,4,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[2,3,5,6,7,1,4]=>[1,4,2,3,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[2,3,5,7,1,4,6]=>[1,4,6,2,3,5,7]=>([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>9
[2,3,6,1,5,4,7]=>[1,5,2,3,6,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>9
[2,3,6,4,5,7,1]=>[1,2,3,6,4,5,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[2,3,6,4,7,1,5]=>[1,5,2,3,6,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>9
[2,3,6,5,7,4,1]=>[1,2,3,6,4,5,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[2,3,6,7,1,4,5]=>[1,4,5,2,3,6,7]=>([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7)=>9
[2,3,7,1,4,5,6]=>[1,4,5,6,2,3,7]=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>10
[2,4,1,3,6,5,7]=>[1,3,6,2,4,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>9
[2,4,1,5,3,6,7]=>[1,5,2,4,3,6,7]=>([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)=>11
[2,4,1,5,6,3,7]=>[1,5,6,2,4,3,7]=>([(0,4),(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2)],7)=>12
[2,4,1,6,3,5,7]=>[1,6,2,4,3,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)=>11
[2,4,1,6,5,7,3]=>[1,6,2,4,3,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)=>11
[2,4,3,1,6,5,7]=>[1,6,2,4,3,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)=>11
[2,4,3,5,6,7,1]=>[1,2,4,3,5,6,7]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>7
[2,4,3,5,7,1,6]=>[1,6,2,4,3,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)=>11
[2,4,3,6,7,1,5]=>[1,5,2,4,3,6,7]=>([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)=>11
[2,4,3,7,1,5,6]=>[1,5,6,2,4,3,7]=>([(0,4),(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2)],7)=>12
[2,4,5,1,6,3,7]=>[1,6,2,4,5,3,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[2,4,5,3,6,7,1]=>[1,2,4,5,3,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[2,4,5,3,7,1,6]=>[1,6,2,4,5,3,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[2,4,5,6,3,7,1]=>[1,2,4,5,6,3,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[2,4,5,6,7,1,3]=>[1,3,2,4,5,6,7]=>([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)=>7
[2,4,5,7,1,3,6]=>[1,3,6,2,4,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>9
[2,4,6,1,5,3,7]=>[1,5,2,4,6,3,7]=>([(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(5,6)],7)=>11
[2,4,6,3,5,7,1]=>[1,2,4,6,3,5,7]=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>8
[2,4,6,3,7,1,5]=>[1,5,2,4,6,3,7]=>([(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(5,6)],7)=>11
[2,4,6,5,7,1,3]=>[1,3,2,4,6,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)=>8
[2,4,6,5,7,3,1]=>[1,2,4,6,3,5,7]=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>8
[2,4,6,7,1,3,5]=>[1,3,5,2,4,6,7]=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>8
[2,4,7,1,3,5,6]=>[1,3,5,6,2,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[2,5,1,4,3,6,7]=>[1,4,2,5,3,6,7]=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>8
[2,5,1,4,6,3,7]=>[1,4,6,2,5,3,7]=>([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7)=>10
[2,5,1,6,3,4,7]=>[1,6,2,5,3,4,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[2,5,1,6,4,7,3]=>[1,6,2,5,3,4,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[2,5,3,1,6,4,7]=>[1,6,2,5,3,4,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[2,5,3,4,6,7,1]=>[1,2,5,3,4,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[2,5,3,4,7,1,6]=>[1,6,2,5,3,4,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[2,5,3,6,4,7,1]=>[1,2,5,3,6,4,7]=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>8
[2,5,3,6,7,1,4]=>[1,4,2,5,3,6,7]=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>8
[2,5,3,7,1,4,6]=>[1,4,6,2,5,3,7]=>([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7)=>10
[2,5,4,6,7,3,1]=>[1,2,5,3,4,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[2,5,4,7,1,6,3]=>[1,6,2,5,3,4,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[2,5,4,7,3,1,6]=>[1,6,2,5,3,4,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[2,5,4,7,3,6,1]=>[1,2,5,3,6,4,7]=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>8
[2,5,6,1,4,3,7]=>[1,4,2,5,6,3,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>9
[2,5,6,3,4,7,1]=>[1,2,5,6,3,4,7]=>([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7)=>9
[2,5,6,3,7,1,4]=>[1,4,2,5,6,3,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>9
[2,5,6,4,7,3,1]=>[1,2,5,6,3,4,7]=>([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7)=>9
[2,5,6,7,1,3,4]=>[1,3,4,2,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[2,5,7,1,3,4,6]=>[1,3,4,6,2,5,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>9
[2,6,1,4,5,3,7]=>[1,4,5,2,6,3,7]=>([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>9
[2,6,1,5,3,4,7]=>[1,5,2,6,3,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[2,6,1,5,4,7,3]=>[1,5,2,6,3,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[2,6,3,1,5,4,7]=>[1,5,2,6,3,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[2,6,3,4,5,7,1]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[2,6,3,4,7,1,5]=>[1,5,2,6,3,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[2,6,3,5,4,7,1]=>[1,2,6,3,5,4,7]=>([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)=>11
[2,6,3,7,1,4,5]=>[1,4,5,2,6,3,7]=>([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>9
[2,6,4,5,7,3,1]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[2,6,4,7,1,5,3]=>[1,5,2,6,3,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[2,6,4,7,3,1,5]=>[1,5,2,6,3,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[2,6,4,7,3,5,1]=>[1,2,6,3,5,4,7]=>([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)=>11
[2,6,5,7,3,4,1]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[2,6,5,7,4,3,1]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[2,6,7,1,3,4,5]=>[1,3,4,5,2,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[2,7,1,3,4,5,6]=>[1,3,4,5,6,2,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[3,1,2,4,6,5,7]=>[1,2,4,6,3,5,7]=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>8
[3,1,2,5,4,6,7]=>[1,2,5,3,4,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[3,1,2,5,6,4,7]=>[1,2,5,6,3,4,7]=>([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7)=>9
[3,1,2,6,4,5,7]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[3,1,2,6,5,7,4]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[3,1,4,6,5,7,2]=>[1,4,6,2,3,5,7]=>([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>9
[3,1,5,2,6,4,7]=>[1,5,2,6,3,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[3,1,5,4,6,7,2]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[3,1,5,4,7,2,6]=>[1,5,2,6,3,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[3,1,5,6,4,7,2]=>[1,5,6,2,3,4,7]=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>10
[3,1,6,2,5,4,7]=>[1,6,2,5,3,4,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[3,1,6,4,5,7,2]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[3,1,6,4,7,2,5]=>[1,6,2,5,3,4,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[3,1,6,5,7,2,4]=>[1,6,2,4,3,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)=>11
[3,1,6,5,7,4,2]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[3,2,1,4,6,5,7]=>[1,4,6,2,3,5,7]=>([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>9
[3,2,1,5,4,6,7]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[3,2,1,5,6,4,7]=>[1,5,6,2,3,4,7]=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>10
[3,2,1,6,4,5,7]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[3,2,1,6,5,7,4]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[3,2,4,1,6,5,7]=>[1,6,2,4,3,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)=>11
[3,2,4,6,5,7,1]=>[1,2,4,6,3,5,7]=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>8
[3,2,5,1,6,4,7]=>[1,6,2,5,3,4,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[3,2,5,4,6,7,1]=>[1,2,5,3,4,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[3,2,5,4,7,1,6]=>[1,6,2,5,3,4,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[3,2,5,6,4,7,1]=>[1,2,5,6,3,4,7]=>([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7)=>9
[3,2,6,1,5,4,7]=>[1,5,2,6,3,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[3,2,6,4,5,7,1]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[3,2,6,4,7,1,5]=>[1,5,2,6,3,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[3,2,6,5,7,4,1]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[3,4,1,2,6,5,7]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[3,4,1,6,5,7,2]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[3,4,2,1,6,5,7]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[3,4,2,6,5,7,1]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[3,4,5,6,7,1,2]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[3,4,5,6,7,2,1]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[3,4,5,7,1,2,6]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[3,4,5,7,1,6,2]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[3,4,5,7,2,1,6]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[3,4,5,7,2,6,1]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[3,4,6,5,7,1,2]=>[1,2,3,4,6,5,7]=>([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)=>7
[3,4,6,5,7,2,1]=>[1,2,3,4,6,5,7]=>([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)=>7
[3,4,6,7,1,2,5]=>[1,2,5,3,4,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[3,4,6,7,1,5,2]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[3,4,6,7,2,1,5]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[3,4,6,7,2,5,1]=>[1,2,5,3,4,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[3,4,7,1,2,5,6]=>[1,2,5,6,3,4,7]=>([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7)=>9
[3,4,7,1,5,2,6]=>[1,5,2,6,3,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[3,4,7,1,5,6,2]=>[1,5,6,2,3,4,7]=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>10
[3,4,7,1,6,2,5]=>[1,6,2,5,3,4,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[3,4,7,2,1,5,6]=>[1,5,6,2,3,4,7]=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>10
[3,4,7,2,5,1,6]=>[1,6,2,5,3,4,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[3,4,7,2,5,6,1]=>[1,2,5,6,3,4,7]=>([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7)=>9
[3,4,7,2,6,1,5]=>[1,5,2,6,3,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[3,5,1,2,6,4,7]=>[1,2,6,3,5,4,7]=>([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)=>11
[3,5,1,6,4,7,2]=>[1,6,2,3,5,4,7]=>([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)=>12
[3,5,2,1,6,4,7]=>[1,6,2,3,5,4,7]=>([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)=>12
[3,5,2,6,4,7,1]=>[1,2,6,3,5,4,7]=>([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)=>11
[3,5,4,6,7,1,2]=>[1,2,3,5,4,6,7]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>7
[3,5,4,6,7,2,1]=>[1,2,3,5,4,6,7]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>7
[3,5,4,7,1,2,6]=>[1,2,6,3,5,4,7]=>([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)=>11
[3,5,4,7,1,6,2]=>[1,6,2,3,5,4,7]=>([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)=>12
[3,5,4,7,2,1,6]=>[1,6,2,3,5,4,7]=>([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)=>12
[3,5,4,7,2,6,1]=>[1,2,6,3,5,4,7]=>([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)=>11
[3,5,6,4,7,1,2]=>[1,2,3,5,6,4,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[3,5,6,4,7,2,1]=>[1,2,3,5,6,4,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[3,5,6,7,1,2,4]=>[1,2,4,3,5,6,7]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>7
[3,5,6,7,1,4,2]=>[1,4,2,3,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[3,5,6,7,2,1,4]=>[1,4,2,3,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[3,5,6,7,2,4,1]=>[1,2,4,3,5,6,7]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>7
[3,5,7,1,2,4,6]=>[1,2,4,6,3,5,7]=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>8
[3,5,7,1,4,6,2]=>[1,4,6,2,3,5,7]=>([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>9
[3,5,7,1,6,2,4]=>[1,6,2,4,3,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)=>11
[3,5,7,2,1,4,6]=>[1,4,6,2,3,5,7]=>([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>9
[3,5,7,2,4,1,6]=>[1,6,2,4,3,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)=>11
[3,5,7,2,4,6,1]=>[1,2,4,6,3,5,7]=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>8
[3,6,1,2,5,4,7]=>[1,2,5,3,6,4,7]=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>8
[3,6,1,5,4,7,2]=>[1,5,2,3,6,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>9
[3,6,2,1,5,4,7]=>[1,5,2,3,6,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>9
[3,6,2,5,4,7,1]=>[1,2,5,3,6,4,7]=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>8
[3,6,4,5,7,1,2]=>[1,2,3,6,4,5,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[3,6,4,5,7,2,1]=>[1,2,3,6,4,5,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[3,6,4,7,1,2,5]=>[1,2,5,3,6,4,7]=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>8
[3,6,4,7,1,5,2]=>[1,5,2,3,6,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>9
[3,6,4,7,2,1,5]=>[1,5,2,3,6,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>9
[3,6,4,7,2,5,1]=>[1,2,5,3,6,4,7]=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>8
[3,6,5,7,4,1,2]=>[1,2,3,6,4,5,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[3,6,5,7,4,2,1]=>[1,2,3,6,4,5,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[3,6,7,1,2,4,5]=>[1,2,4,5,3,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[3,6,7,1,4,2,5]=>[1,4,2,5,3,6,7]=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>8
[3,6,7,1,4,5,2]=>[1,4,5,2,3,6,7]=>([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7)=>9
[3,6,7,1,5,2,4]=>[1,5,2,4,3,6,7]=>([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)=>11
[3,6,7,2,1,4,5]=>[1,4,5,2,3,6,7]=>([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7)=>9
[3,6,7,2,4,1,5]=>[1,5,2,4,3,6,7]=>([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)=>11
[3,6,7,2,4,5,1]=>[1,2,4,5,3,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[3,6,7,2,5,1,4]=>[1,4,2,5,3,6,7]=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>8
[3,7,1,2,4,5,6]=>[1,2,4,5,6,3,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[3,7,1,4,2,5,6]=>[1,4,2,5,6,3,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>9
[3,7,1,4,5,2,6]=>[1,4,5,2,6,3,7]=>([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>9
[3,7,1,4,5,6,2]=>[1,4,5,6,2,3,7]=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>10
[3,7,1,4,6,2,5]=>[1,4,6,2,5,3,7]=>([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7)=>10
[3,7,1,5,2,4,6]=>[1,5,2,4,6,3,7]=>([(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(5,6)],7)=>11
[3,7,1,5,6,2,4]=>[1,5,6,2,4,3,7]=>([(0,4),(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2)],7)=>12
[3,7,1,6,2,4,5]=>[1,6,2,4,5,3,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[3,7,2,1,4,5,6]=>[1,4,5,6,2,3,7]=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>10
[3,7,2,4,1,5,6]=>[1,5,6,2,4,3,7]=>([(0,4),(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2)],7)=>12
[3,7,2,4,5,1,6]=>[1,6,2,4,5,3,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[3,7,2,4,5,6,1]=>[1,2,4,5,6,3,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[3,7,2,4,6,1,5]=>[1,5,2,4,6,3,7]=>([(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(5,6)],7)=>11
[3,7,2,5,1,4,6]=>[1,4,6,2,5,3,7]=>([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7)=>10
[3,7,2,5,6,1,4]=>[1,4,2,5,6,3,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>9
[3,7,2,6,1,4,5]=>[1,4,5,2,6,3,7]=>([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>9
[4,1,2,3,6,5,7]=>[1,2,3,6,4,5,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[4,1,2,6,5,7,3]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[4,1,3,6,5,7,2]=>[1,3,6,2,4,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>9
[4,1,6,5,7,2,3]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[4,1,6,5,7,3,2]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[4,2,1,3,6,5,7]=>[1,3,6,2,4,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>9
[4,2,1,6,5,7,3]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[4,2,3,1,6,5,7]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[4,2,3,6,5,7,1]=>[1,2,3,6,4,5,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[4,2,6,5,7,3,1]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[4,3,1,2,6,5,7]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[4,3,1,6,5,7,2]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[4,3,2,1,6,5,7]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[4,3,2,6,5,7,1]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[4,3,6,5,7,1,2]=>[1,2,3,6,4,5,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[4,3,6,5,7,2,1]=>[1,2,3,6,4,5,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[4,5,6,7,1,2,3]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[4,5,6,7,1,3,2]=>[1,3,2,4,5,6,7]=>([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)=>7
[4,5,6,7,2,1,3]=>[1,3,2,4,5,6,7]=>([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)=>7
[4,5,6,7,2,3,1]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[4,5,6,7,3,1,2]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[4,5,6,7,3,2,1]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[4,5,7,1,2,3,6]=>[1,2,3,6,4,5,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[4,5,7,1,2,6,3]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[4,5,7,1,3,6,2]=>[1,3,6,2,4,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>9
[4,5,7,1,6,2,3]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[4,5,7,1,6,3,2]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[4,5,7,2,1,3,6]=>[1,3,6,2,4,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>9
[4,5,7,2,1,6,3]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[4,5,7,2,3,1,6]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[4,5,7,2,3,6,1]=>[1,2,3,6,4,5,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[4,5,7,2,6,3,1]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[4,5,7,3,1,2,6]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[4,5,7,3,1,6,2]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[4,5,7,3,2,1,6]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[4,5,7,3,2,6,1]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[4,5,7,3,6,1,2]=>[1,2,3,6,4,5,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[4,5,7,3,6,2,1]=>[1,2,3,6,4,5,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[4,6,5,7,1,2,3]=>[1,2,3,4,6,5,7]=>([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)=>7
[4,6,5,7,1,3,2]=>[1,3,2,4,6,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)=>8
[4,6,5,7,2,1,3]=>[1,3,2,4,6,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)=>8
[4,6,5,7,2,3,1]=>[1,2,3,4,6,5,7]=>([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)=>7
[4,6,5,7,3,1,2]=>[1,2,3,4,6,5,7]=>([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)=>7
[4,6,5,7,3,2,1]=>[1,2,3,4,6,5,7]=>([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)=>7
[4,6,7,1,2,3,5]=>[1,2,3,5,4,6,7]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>7
[4,6,7,1,2,5,3]=>[1,2,5,3,4,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[4,6,7,1,3,5,2]=>[1,3,5,2,4,6,7]=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>8
[4,6,7,1,5,2,3]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[4,6,7,1,5,3,2]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[4,6,7,2,1,3,5]=>[1,3,5,2,4,6,7]=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>8
[4,6,7,2,1,5,3]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[4,6,7,2,3,1,5]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[4,6,7,2,3,5,1]=>[1,2,3,5,4,6,7]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>7
[4,6,7,2,5,3,1]=>[1,2,5,3,4,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[4,6,7,3,1,2,5]=>[1,2,5,3,4,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[4,6,7,3,1,5,2]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[4,6,7,3,2,1,5]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[4,6,7,3,2,5,1]=>[1,2,5,3,4,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[4,6,7,3,5,1,2]=>[1,2,3,5,4,6,7]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>7
[4,6,7,3,5,2,1]=>[1,2,3,5,4,6,7]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>7
[4,7,1,2,3,5,6]=>[1,2,3,5,6,4,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[4,7,1,2,5,3,6]=>[1,2,5,3,6,4,7]=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>8
[4,7,1,2,5,6,3]=>[1,2,5,6,3,4,7]=>([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7)=>9
[4,7,1,2,6,3,5]=>[1,2,6,3,5,4,7]=>([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)=>11
[4,7,1,3,5,6,2]=>[1,3,5,6,2,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[4,7,1,5,2,3,6]=>[1,5,2,3,6,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>9
[4,7,1,5,2,6,3]=>[1,5,2,6,3,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[4,7,1,5,3,2,6]=>[1,5,2,6,3,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[4,7,1,5,3,6,2]=>[1,5,2,3,6,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>9
[4,7,1,5,6,2,3]=>[1,5,6,2,3,4,7]=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>10
[4,7,1,5,6,3,2]=>[1,5,6,2,3,4,7]=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>10
[4,7,1,6,2,3,5]=>[1,6,2,3,5,4,7]=>([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)=>12
[4,7,1,6,2,5,3]=>[1,6,2,5,3,4,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[4,7,1,6,3,2,5]=>[1,6,2,5,3,4,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[4,7,1,6,3,5,2]=>[1,6,2,3,5,4,7]=>([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)=>12
[4,7,2,1,3,5,6]=>[1,3,5,6,2,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[4,7,2,1,5,3,6]=>[1,5,2,3,6,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>9
[4,7,2,1,5,6,3]=>[1,5,6,2,3,4,7]=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>10
[4,7,2,1,6,3,5]=>[1,6,2,3,5,4,7]=>([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)=>12
[4,7,2,3,1,5,6]=>[1,5,6,2,3,4,7]=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>10
[4,7,2,3,5,1,6]=>[1,6,2,3,5,4,7]=>([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)=>12
[4,7,2,3,5,6,1]=>[1,2,3,5,6,4,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[4,7,2,3,6,1,5]=>[1,5,2,3,6,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>9
[4,7,2,5,1,6,3]=>[1,6,2,5,3,4,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[4,7,2,5,3,1,6]=>[1,6,2,5,3,4,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[4,7,2,5,3,6,1]=>[1,2,5,3,6,4,7]=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>8
[4,7,2,5,6,3,1]=>[1,2,5,6,3,4,7]=>([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7)=>9
[4,7,2,6,1,5,3]=>[1,5,2,6,3,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[4,7,2,6,3,1,5]=>[1,5,2,6,3,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[4,7,2,6,3,5,1]=>[1,2,6,3,5,4,7]=>([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)=>11
[4,7,3,1,2,5,6]=>[1,2,5,6,3,4,7]=>([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7)=>9
[4,7,3,1,5,2,6]=>[1,5,2,6,3,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[4,7,3,1,5,6,2]=>[1,5,6,2,3,4,7]=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>10
[4,7,3,1,6,2,5]=>[1,6,2,5,3,4,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[4,7,3,2,1,5,6]=>[1,5,6,2,3,4,7]=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>10
[4,7,3,2,5,1,6]=>[1,6,2,5,3,4,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[4,7,3,2,5,6,1]=>[1,2,5,6,3,4,7]=>([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7)=>9
[4,7,3,2,6,1,5]=>[1,5,2,6,3,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[4,7,3,5,1,2,6]=>[1,2,6,3,5,4,7]=>([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)=>11
[4,7,3,5,1,6,2]=>[1,6,2,3,5,4,7]=>([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)=>12
[4,7,3,5,2,1,6]=>[1,6,2,3,5,4,7]=>([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)=>12
[4,7,3,5,2,6,1]=>[1,2,6,3,5,4,7]=>([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)=>11
[4,7,3,5,6,1,2]=>[1,2,3,5,6,4,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[4,7,3,5,6,2,1]=>[1,2,3,5,6,4,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[4,7,3,6,1,2,5]=>[1,2,5,3,6,4,7]=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>8
[4,7,3,6,1,5,2]=>[1,5,2,3,6,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>9
[4,7,3,6,2,1,5]=>[1,5,2,3,6,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>9
[4,7,3,6,2,5,1]=>[1,2,5,3,6,4,7]=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>8
[5,6,7,1,2,3,4]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[5,6,7,1,2,4,3]=>[1,2,4,3,5,6,7]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>7
[5,6,7,1,3,2,4]=>[1,3,2,4,5,6,7]=>([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)=>7
[5,6,7,1,3,4,2]=>[1,3,4,2,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[5,6,7,1,4,2,3]=>[1,4,2,3,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[5,6,7,1,4,3,2]=>[1,4,2,3,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[5,6,7,2,1,3,4]=>[1,3,4,2,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[5,6,7,2,1,4,3]=>[1,4,2,3,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[5,6,7,2,3,1,4]=>[1,4,2,3,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[5,6,7,2,3,4,1]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[5,6,7,2,4,1,3]=>[1,3,2,4,5,6,7]=>([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)=>7
[5,6,7,2,4,3,1]=>[1,2,4,3,5,6,7]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>7
[5,6,7,3,1,2,4]=>[1,2,4,3,5,6,7]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>7
[5,6,7,3,1,4,2]=>[1,4,2,3,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[5,6,7,3,2,1,4]=>[1,4,2,3,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[5,6,7,3,2,4,1]=>[1,2,4,3,5,6,7]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>7
[5,6,7,3,4,1,2]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[5,6,7,3,4,2,1]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[5,6,7,4,1,2,3]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[5,6,7,4,1,3,2]=>[1,3,2,4,5,6,7]=>([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)=>7
[5,6,7,4,2,1,3]=>[1,3,2,4,5,6,7]=>([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)=>7
[5,6,7,4,2,3,1]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[5,6,7,4,3,1,2]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[5,6,7,4,3,2,1]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[5,7,1,2,3,4,6]=>[1,2,3,4,6,5,7]=>([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)=>7
[5,7,1,2,3,6,4]=>[1,2,3,6,4,5,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[5,7,1,2,4,6,3]=>[1,2,4,6,3,5,7]=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>8
[5,7,1,2,6,3,4]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[5,7,1,2,6,4,3]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[5,7,1,3,2,4,6]=>[1,3,2,4,6,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)=>8
[5,7,1,3,4,6,2]=>[1,3,4,6,2,5,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>9
[5,7,1,3,6,2,4]=>[1,3,6,2,4,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>9
[5,7,1,3,6,4,2]=>[1,3,6,2,4,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>9
[5,7,1,4,6,2,3]=>[1,4,6,2,3,5,7]=>([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>9
[5,7,1,4,6,3,2]=>[1,4,6,2,3,5,7]=>([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>9
[5,7,1,6,2,3,4]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[5,7,1,6,2,4,3]=>[1,6,2,4,3,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)=>11
[5,7,1,6,3,2,4]=>[1,6,2,4,3,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)=>11
[5,7,1,6,3,4,2]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[5,7,1,6,4,2,3]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[5,7,1,6,4,3,2]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[5,7,2,1,3,4,6]=>[1,3,4,6,2,5,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>9
[5,7,2,1,3,6,4]=>[1,3,6,2,4,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>9
[5,7,2,1,4,6,3]=>[1,4,6,2,3,5,7]=>([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>9
[5,7,2,1,6,3,4]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[5,7,2,1,6,4,3]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[5,7,2,3,1,4,6]=>[1,4,6,2,3,5,7]=>([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>9
[5,7,2,3,1,6,4]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[5,7,2,3,4,1,6]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[5,7,2,3,4,6,1]=>[1,2,3,4,6,5,7]=>([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)=>7
[5,7,2,3,6,4,1]=>[1,2,3,6,4,5,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[5,7,2,4,1,3,6]=>[1,3,6,2,4,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>9
[5,7,2,4,1,6,3]=>[1,6,2,4,3,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)=>11
[5,7,2,4,3,1,6]=>[1,6,2,4,3,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)=>11
[5,7,2,4,6,1,3]=>[1,3,2,4,6,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)=>8
[5,7,2,4,6,3,1]=>[1,2,4,6,3,5,7]=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>8
[5,7,2,6,3,4,1]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[5,7,2,6,4,3,1]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[5,7,3,1,2,4,6]=>[1,2,4,6,3,5,7]=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>8
[5,7,3,1,2,6,4]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[5,7,3,1,4,6,2]=>[1,4,6,2,3,5,7]=>([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>9
[5,7,3,1,6,2,4]=>[1,6,2,4,3,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)=>11
[5,7,3,1,6,4,2]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[5,7,3,2,1,4,6]=>[1,4,6,2,3,5,7]=>([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>9
[5,7,3,2,1,6,4]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[5,7,3,2,4,1,6]=>[1,6,2,4,3,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)=>11
[5,7,3,2,4,6,1]=>[1,2,4,6,3,5,7]=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>8
[5,7,3,2,6,4,1]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[5,7,3,4,1,2,6]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[5,7,3,4,1,6,2]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[5,7,3,4,2,1,6]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[5,7,3,4,2,6,1]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[5,7,3,4,6,1,2]=>[1,2,3,4,6,5,7]=>([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)=>7
[5,7,3,4,6,2,1]=>[1,2,3,4,6,5,7]=>([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)=>7
[5,7,3,6,4,1,2]=>[1,2,3,6,4,5,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[5,7,3,6,4,2,1]=>[1,2,3,6,4,5,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[5,7,4,1,2,3,6]=>[1,2,3,6,4,5,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[5,7,4,1,2,6,3]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[5,7,4,1,3,6,2]=>[1,3,6,2,4,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>9
[5,7,4,1,6,2,3]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[5,7,4,1,6,3,2]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[5,7,4,2,1,3,6]=>[1,3,6,2,4,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>9
[5,7,4,2,1,6,3]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[5,7,4,2,3,1,6]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[5,7,4,2,3,6,1]=>[1,2,3,6,4,5,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[5,7,4,2,6,3,1]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[5,7,4,3,1,2,6]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[5,7,4,3,1,6,2]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[5,7,4,3,2,1,6]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[5,7,4,3,2,6,1]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[5,7,4,3,6,1,2]=>[1,2,3,6,4,5,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[5,7,4,3,6,2,1]=>[1,2,3,6,4,5,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[5,7,4,6,1,2,3]=>[1,2,3,4,6,5,7]=>([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)=>7
[5,7,4,6,1,3,2]=>[1,3,2,4,6,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)=>8
[5,7,4,6,2,1,3]=>[1,3,2,4,6,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)=>8
[5,7,4,6,2,3,1]=>[1,2,3,4,6,5,7]=>([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)=>7
[5,7,4,6,3,1,2]=>[1,2,3,4,6,5,7]=>([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)=>7
[5,7,4,6,3,2,1]=>[1,2,3,4,6,5,7]=>([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)=>7
[6,7,1,2,3,4,5]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[6,7,1,2,3,5,4]=>[1,2,3,5,4,6,7]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>7
[6,7,1,2,4,3,5]=>[1,2,4,3,5,6,7]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>7
[6,7,1,2,4,5,3]=>[1,2,4,5,3,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[6,7,1,2,5,3,4]=>[1,2,5,3,4,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[6,7,1,2,5,4,3]=>[1,2,5,3,4,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[6,7,1,3,2,4,5]=>[1,3,2,4,5,6,7]=>([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)=>7
[6,7,1,3,4,2,5]=>[1,3,4,2,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[6,7,1,3,4,5,2]=>[1,3,4,5,2,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[6,7,1,3,5,2,4]=>[1,3,5,2,4,6,7]=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>8
[6,7,1,3,5,4,2]=>[1,3,5,2,4,6,7]=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>8
[6,7,1,4,2,3,5]=>[1,4,2,3,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[6,7,1,4,2,5,3]=>[1,4,2,5,3,6,7]=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>8
[6,7,1,4,3,2,5]=>[1,4,2,5,3,6,7]=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>8
[6,7,1,4,3,5,2]=>[1,4,2,3,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[6,7,1,4,5,2,3]=>[1,4,5,2,3,6,7]=>([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7)=>9
[6,7,1,4,5,3,2]=>[1,4,5,2,3,6,7]=>([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7)=>9
[6,7,1,5,2,3,4]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[6,7,1,5,2,4,3]=>[1,5,2,4,3,6,7]=>([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)=>11
[6,7,1,5,3,2,4]=>[1,5,2,4,3,6,7]=>([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)=>11
[6,7,1,5,3,4,2]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[6,7,1,5,4,2,3]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[6,7,1,5,4,3,2]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[6,7,2,1,3,4,5]=>[1,3,4,5,2,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[6,7,2,1,3,5,4]=>[1,3,5,2,4,6,7]=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>8
[6,7,2,1,4,3,5]=>[1,4,2,3,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[6,7,2,1,4,5,3]=>[1,4,5,2,3,6,7]=>([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7)=>9
[6,7,2,1,5,3,4]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[6,7,2,1,5,4,3]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[6,7,2,3,1,4,5]=>[1,4,5,2,3,6,7]=>([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7)=>9
[6,7,2,3,1,5,4]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[6,7,2,3,4,1,5]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[6,7,2,3,4,5,1]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[6,7,2,3,5,1,4]=>[1,4,2,3,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[6,7,2,3,5,4,1]=>[1,2,3,5,4,6,7]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>7
[6,7,2,4,1,3,5]=>[1,3,5,2,4,6,7]=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>8
[6,7,2,4,1,5,3]=>[1,5,2,4,3,6,7]=>([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)=>11
[6,7,2,4,3,1,5]=>[1,5,2,4,3,6,7]=>([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)=>11
[6,7,2,4,3,5,1]=>[1,2,4,3,5,6,7]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>7
[6,7,2,4,5,1,3]=>[1,3,2,4,5,6,7]=>([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)=>7
[6,7,2,4,5,3,1]=>[1,2,4,5,3,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[6,7,2,5,1,3,4]=>[1,3,4,2,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[6,7,2,5,1,4,3]=>[1,4,2,5,3,6,7]=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>8
[6,7,2,5,3,1,4]=>[1,4,2,5,3,6,7]=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>8
[6,7,2,5,3,4,1]=>[1,2,5,3,4,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[6,7,2,5,4,3,1]=>[1,2,5,3,4,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[6,7,3,1,2,4,5]=>[1,2,4,5,3,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[6,7,3,1,2,5,4]=>[1,2,5,3,4,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[6,7,3,1,4,2,5]=>[1,4,2,5,3,6,7]=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>8
[6,7,3,1,4,5,2]=>[1,4,5,2,3,6,7]=>([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7)=>9
[6,7,3,1,5,2,4]=>[1,5,2,4,3,6,7]=>([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)=>11
[6,7,3,1,5,4,2]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[6,7,3,2,1,4,5]=>[1,4,5,2,3,6,7]=>([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7)=>9
[6,7,3,2,1,5,4]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[6,7,3,2,4,1,5]=>[1,5,2,4,3,6,7]=>([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)=>11
[6,7,3,2,4,5,1]=>[1,2,4,5,3,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[6,7,3,2,5,1,4]=>[1,4,2,5,3,6,7]=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>8
[6,7,3,2,5,4,1]=>[1,2,5,3,4,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[6,7,3,4,1,2,5]=>[1,2,5,3,4,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[6,7,3,4,1,5,2]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[6,7,3,4,2,1,5]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[6,7,3,4,2,5,1]=>[1,2,5,3,4,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[6,7,3,4,5,1,2]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[6,7,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[6,7,3,5,1,2,4]=>[1,2,4,3,5,6,7]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>7
[6,7,3,5,1,4,2]=>[1,4,2,3,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[6,7,3,5,2,1,4]=>[1,4,2,3,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[6,7,3,5,2,4,1]=>[1,2,4,3,5,6,7]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>7
[6,7,3,5,4,1,2]=>[1,2,3,5,4,6,7]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>7
[6,7,3,5,4,2,1]=>[1,2,3,5,4,6,7]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>7
[6,7,4,1,2,3,5]=>[1,2,3,5,4,6,7]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>7
[6,7,4,1,2,5,3]=>[1,2,5,3,4,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[6,7,4,1,3,5,2]=>[1,3,5,2,4,6,7]=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>8
[6,7,4,1,5,2,3]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[6,7,4,1,5,3,2]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[6,7,4,2,1,3,5]=>[1,3,5,2,4,6,7]=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>8
[6,7,4,2,1,5,3]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[6,7,4,2,3,1,5]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[6,7,4,2,3,5,1]=>[1,2,3,5,4,6,7]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>7
[6,7,4,2,5,3,1]=>[1,2,5,3,4,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[6,7,4,3,1,2,5]=>[1,2,5,3,4,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[6,7,4,3,1,5,2]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[6,7,4,3,2,1,5]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[6,7,4,3,2,5,1]=>[1,2,5,3,4,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[6,7,4,3,5,1,2]=>[1,2,3,5,4,6,7]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>7
[6,7,4,3,5,2,1]=>[1,2,3,5,4,6,7]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>7
[6,7,4,5,1,2,3]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[6,7,4,5,1,3,2]=>[1,3,2,4,5,6,7]=>([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)=>7
[6,7,4,5,2,1,3]=>[1,3,2,4,5,6,7]=>([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)=>7
[6,7,4,5,2,3,1]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[6,7,4,5,3,1,2]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[6,7,4,5,3,2,1]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[6,7,5,1,2,3,4]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[6,7,5,1,2,4,3]=>[1,2,4,3,5,6,7]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>7
[6,7,5,1,3,2,4]=>[1,3,2,4,5,6,7]=>([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)=>7
[6,7,5,1,3,4,2]=>[1,3,4,2,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[6,7,5,1,4,2,3]=>[1,4,2,3,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[6,7,5,1,4,3,2]=>[1,4,2,3,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[6,7,5,2,1,3,4]=>[1,3,4,2,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[6,7,5,2,1,4,3]=>[1,4,2,3,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[6,7,5,2,3,1,4]=>[1,4,2,3,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[6,7,5,2,3,4,1]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[6,7,5,2,4,1,3]=>[1,3,2,4,5,6,7]=>([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)=>7
[6,7,5,2,4,3,1]=>[1,2,4,3,5,6,7]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>7
[6,7,5,3,1,2,4]=>[1,2,4,3,5,6,7]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>7
[6,7,5,3,1,4,2]=>[1,4,2,3,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[6,7,5,3,2,1,4]=>[1,4,2,3,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[6,7,5,3,2,4,1]=>[1,2,4,3,5,6,7]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>7
[6,7,5,3,4,1,2]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[6,7,5,3,4,2,1]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[6,7,5,4,1,2,3]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[6,7,5,4,1,3,2]=>[1,3,2,4,5,6,7]=>([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)=>7
[6,7,5,4,2,1,3]=>[1,3,2,4,5,6,7]=>([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)=>7
[6,7,5,4,2,3,1]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[6,7,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[7,1,2,3,4,5,6]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[7,1,2,3,4,6,5]=>[1,2,3,4,6,5,7]=>([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)=>7
[7,1,2,3,5,4,6]=>[1,2,3,5,4,6,7]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>7
[7,1,2,3,5,6,4]=>[1,2,3,5,6,4,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[7,1,2,3,6,4,5]=>[1,2,3,6,4,5,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[7,1,2,3,6,5,4]=>[1,2,3,6,4,5,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[7,1,2,4,3,5,6]=>[1,2,4,3,5,6,7]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>7
[7,1,2,4,5,3,6]=>[1,2,4,5,3,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[7,1,2,4,5,6,3]=>[1,2,4,5,6,3,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[7,1,2,4,6,3,5]=>[1,2,4,6,3,5,7]=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>8
[7,1,2,4,6,5,3]=>[1,2,4,6,3,5,7]=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>8
[7,1,2,5,3,4,6]=>[1,2,5,3,4,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[7,1,2,5,3,6,4]=>[1,2,5,3,6,4,7]=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>8
[7,1,2,5,4,3,6]=>[1,2,5,3,6,4,7]=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>8
[7,1,2,5,4,6,3]=>[1,2,5,3,4,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[7,1,2,5,6,3,4]=>[1,2,5,6,3,4,7]=>([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7)=>9
[7,1,2,5,6,4,3]=>[1,2,5,6,3,4,7]=>([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7)=>9
[7,1,2,6,3,4,5]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[7,1,2,6,3,5,4]=>[1,2,6,3,5,4,7]=>([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)=>11
[7,1,2,6,4,3,5]=>[1,2,6,3,5,4,7]=>([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)=>11
[7,1,2,6,4,5,3]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[7,1,2,6,5,3,4]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[7,1,2,6,5,4,3]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[7,1,3,2,4,5,6]=>[1,3,2,4,5,6,7]=>([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)=>7
[7,1,3,2,4,6,5]=>[1,3,2,4,6,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)=>8
[7,1,3,4,2,5,6]=>[1,3,4,2,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[7,1,3,4,5,2,6]=>[1,3,4,5,2,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[7,1,3,4,5,6,2]=>[1,3,4,5,6,2,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[7,1,3,4,6,2,5]=>[1,3,4,6,2,5,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>9
[7,1,3,4,6,5,2]=>[1,3,4,6,2,5,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>9
[7,1,3,5,2,4,6]=>[1,3,5,2,4,6,7]=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>8
[7,1,3,5,4,6,2]=>[1,3,5,2,4,6,7]=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>8
[7,1,3,5,6,2,4]=>[1,3,5,6,2,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[7,1,3,5,6,4,2]=>[1,3,5,6,2,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[7,1,3,6,2,4,5]=>[1,3,6,2,4,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>9
[7,1,3,6,4,5,2]=>[1,3,6,2,4,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>9
[7,1,3,6,5,2,4]=>[1,3,6,2,4,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>9
[7,1,3,6,5,4,2]=>[1,3,6,2,4,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>9
[7,1,4,2,3,5,6]=>[1,4,2,3,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[7,1,4,2,5,3,6]=>[1,4,2,5,3,6,7]=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>8
[7,1,4,2,5,6,3]=>[1,4,2,5,6,3,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>9
[7,1,4,3,2,5,6]=>[1,4,2,5,6,3,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>9
[7,1,4,3,5,6,2]=>[1,4,2,3,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[7,1,4,3,6,2,5]=>[1,4,2,5,3,6,7]=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>8
[7,1,4,5,2,3,6]=>[1,4,5,2,3,6,7]=>([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7)=>9
[7,1,4,5,2,6,3]=>[1,4,5,2,6,3,7]=>([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>9
[7,1,4,5,3,2,6]=>[1,4,5,2,6,3,7]=>([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>9
[7,1,4,5,3,6,2]=>[1,4,5,2,3,6,7]=>([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7)=>9
[7,1,4,5,6,2,3]=>[1,4,5,6,2,3,7]=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>10
[7,1,4,5,6,3,2]=>[1,4,5,6,2,3,7]=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>10
[7,1,4,6,2,3,5]=>[1,4,6,2,3,5,7]=>([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>9
[7,1,4,6,2,5,3]=>[1,4,6,2,5,3,7]=>([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7)=>10
[7,1,4,6,3,2,5]=>[1,4,6,2,5,3,7]=>([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7)=>10
[7,1,4,6,3,5,2]=>[1,4,6,2,3,5,7]=>([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>9
[7,1,4,6,5,2,3]=>[1,4,6,2,3,5,7]=>([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>9
[7,1,4,6,5,3,2]=>[1,4,6,2,3,5,7]=>([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>9
[7,1,5,2,3,4,6]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[7,1,5,2,3,6,4]=>[1,5,2,3,6,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>9
[7,1,5,2,4,3,6]=>[1,5,2,4,3,6,7]=>([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)=>11
[7,1,5,2,4,6,3]=>[1,5,2,4,6,3,7]=>([(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(5,6)],7)=>11
[7,1,5,2,6,3,4]=>[1,5,2,6,3,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[7,1,5,2,6,4,3]=>[1,5,2,6,3,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[7,1,5,3,2,4,6]=>[1,5,2,4,6,3,7]=>([(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(5,6)],7)=>11
[7,1,5,3,2,6,4]=>[1,5,2,6,3,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[7,1,5,3,4,2,6]=>[1,5,2,6,3,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[7,1,5,3,4,6,2]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[7,1,5,3,6,2,4]=>[1,5,2,4,3,6,7]=>([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)=>11
[7,1,5,3,6,4,2]=>[1,5,2,3,6,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>9
[7,1,5,4,2,3,6]=>[1,5,2,3,6,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>9
[7,1,5,4,2,6,3]=>[1,5,2,6,3,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[7,1,5,4,3,2,6]=>[1,5,2,6,3,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[7,1,5,4,3,6,2]=>[1,5,2,3,6,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>9
[7,1,5,4,6,2,3]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[7,1,5,4,6,3,2]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[7,1,5,6,2,3,4]=>[1,5,6,2,3,4,7]=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>10
[7,1,5,6,2,4,3]=>[1,5,6,2,4,3,7]=>([(0,4),(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2)],7)=>12
[7,1,5,6,3,2,4]=>[1,5,6,2,4,3,7]=>([(0,4),(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2)],7)=>12
[7,1,5,6,3,4,2]=>[1,5,6,2,3,4,7]=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>10
[7,1,5,6,4,2,3]=>[1,5,6,2,3,4,7]=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>10
[7,1,5,6,4,3,2]=>[1,5,6,2,3,4,7]=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>10
[7,1,6,2,3,4,5]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[7,1,6,2,3,5,4]=>[1,6,2,3,5,4,7]=>([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)=>12
[7,1,6,2,4,3,5]=>[1,6,2,4,3,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)=>11
[7,1,6,2,4,5,3]=>[1,6,2,4,5,3,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[7,1,6,2,5,3,4]=>[1,6,2,5,3,4,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[7,1,6,2,5,4,3]=>[1,6,2,5,3,4,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[7,1,6,3,2,4,5]=>[1,6,2,4,5,3,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[7,1,6,3,2,5,4]=>[1,6,2,5,3,4,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[7,1,6,3,4,2,5]=>[1,6,2,5,3,4,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[7,1,6,3,4,5,2]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[7,1,6,3,5,2,4]=>[1,6,2,4,3,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)=>11
[7,1,6,3,5,4,2]=>[1,6,2,3,5,4,7]=>([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)=>12
[7,1,6,4,2,3,5]=>[1,6,2,3,5,4,7]=>([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)=>12
[7,1,6,4,2,5,3]=>[1,6,2,5,3,4,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[7,1,6,4,3,2,5]=>[1,6,2,5,3,4,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[7,1,6,4,3,5,2]=>[1,6,2,3,5,4,7]=>([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)=>12
[7,1,6,4,5,2,3]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[7,1,6,4,5,3,2]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[7,1,6,5,2,3,4]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[7,1,6,5,2,4,3]=>[1,6,2,4,3,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)=>11
[7,1,6,5,3,2,4]=>[1,6,2,4,3,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)=>11
[7,1,6,5,3,4,2]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[7,1,6,5,4,2,3]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[7,1,6,5,4,3,2]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[7,2,1,3,4,5,6]=>[1,3,4,5,6,2,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[7,2,1,3,4,6,5]=>[1,3,4,6,2,5,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>9
[7,2,1,3,5,4,6]=>[1,3,5,2,4,6,7]=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>8
[7,2,1,3,5,6,4]=>[1,3,5,6,2,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[7,2,1,3,6,4,5]=>[1,3,6,2,4,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>9
[7,2,1,3,6,5,4]=>[1,3,6,2,4,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>9
[7,2,1,4,3,5,6]=>[1,4,2,3,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[7,2,1,4,5,3,6]=>[1,4,5,2,3,6,7]=>([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7)=>9
[7,2,1,4,5,6,3]=>[1,4,5,6,2,3,7]=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>10
[7,2,1,4,6,3,5]=>[1,4,6,2,3,5,7]=>([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>9
[7,2,1,4,6,5,3]=>[1,4,6,2,3,5,7]=>([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>9
[7,2,1,5,3,4,6]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[7,2,1,5,3,6,4]=>[1,5,2,3,6,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>9
[7,2,1,5,4,3,6]=>[1,5,2,3,6,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>9
[7,2,1,5,4,6,3]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[7,2,1,5,6,3,4]=>[1,5,6,2,3,4,7]=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>10
[7,2,1,5,6,4,3]=>[1,5,6,2,3,4,7]=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>10
[7,2,1,6,3,4,5]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[7,2,1,6,3,5,4]=>[1,6,2,3,5,4,7]=>([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)=>12
[7,2,1,6,4,3,5]=>[1,6,2,3,5,4,7]=>([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)=>12
[7,2,1,6,4,5,3]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[7,2,1,6,5,3,4]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[7,2,1,6,5,4,3]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[7,2,3,1,4,5,6]=>[1,4,5,6,2,3,7]=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>10
[7,2,3,1,4,6,5]=>[1,4,6,2,3,5,7]=>([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>9
[7,2,3,1,5,4,6]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[7,2,3,1,5,6,4]=>[1,5,6,2,3,4,7]=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>10
[7,2,3,1,6,4,5]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[7,2,3,1,6,5,4]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[7,2,3,4,1,5,6]=>[1,5,6,2,3,4,7]=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>10
[7,2,3,4,1,6,5]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[7,2,3,4,5,1,6]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[7,2,3,4,5,6,1]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[7,2,3,4,6,1,5]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[7,2,3,4,6,5,1]=>[1,2,3,4,6,5,7]=>([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)=>7
[7,2,3,5,1,4,6]=>[1,4,6,2,3,5,7]=>([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>9
[7,2,3,5,1,6,4]=>[1,6,2,3,5,4,7]=>([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)=>12
[7,2,3,5,4,1,6]=>[1,6,2,3,5,4,7]=>([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)=>12
[7,2,3,5,4,6,1]=>[1,2,3,5,4,6,7]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>7
[7,2,3,5,6,1,4]=>[1,4,2,3,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[7,2,3,5,6,4,1]=>[1,2,3,5,6,4,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[7,2,3,6,1,4,5]=>[1,4,5,2,3,6,7]=>([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7)=>9
[7,2,3,6,1,5,4]=>[1,5,2,3,6,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>9
[7,2,3,6,4,1,5]=>[1,5,2,3,6,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>9
[7,2,3,6,4,5,1]=>[1,2,3,6,4,5,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[7,2,3,6,5,4,1]=>[1,2,3,6,4,5,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[7,2,4,1,3,5,6]=>[1,3,5,6,2,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[7,2,4,1,3,6,5]=>[1,3,6,2,4,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>9
[7,2,4,1,5,3,6]=>[1,5,2,4,3,6,7]=>([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)=>11
[7,2,4,1,5,6,3]=>[1,5,6,2,4,3,7]=>([(0,4),(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2)],7)=>12
[7,2,4,1,6,3,5]=>[1,6,2,4,3,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)=>11
[7,2,4,1,6,5,3]=>[1,6,2,4,3,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)=>11
[7,2,4,3,1,5,6]=>[1,5,6,2,4,3,7]=>([(0,4),(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2)],7)=>12
[7,2,4,3,1,6,5]=>[1,6,2,4,3,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)=>11
[7,2,4,3,5,1,6]=>[1,6,2,4,3,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)=>11
[7,2,4,3,5,6,1]=>[1,2,4,3,5,6,7]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>7
[7,2,4,3,6,1,5]=>[1,5,2,4,3,6,7]=>([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)=>11
[7,2,4,5,1,3,6]=>[1,3,6,2,4,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>9
[7,2,4,5,1,6,3]=>[1,6,2,4,5,3,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[7,2,4,5,3,1,6]=>[1,6,2,4,5,3,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[7,2,4,5,3,6,1]=>[1,2,4,5,3,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[7,2,4,5,6,1,3]=>[1,3,2,4,5,6,7]=>([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)=>7
[7,2,4,5,6,3,1]=>[1,2,4,5,6,3,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[7,2,4,6,1,3,5]=>[1,3,5,2,4,6,7]=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>8
[7,2,4,6,1,5,3]=>[1,5,2,4,6,3,7]=>([(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(5,6)],7)=>11
[7,2,4,6,3,1,5]=>[1,5,2,4,6,3,7]=>([(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(5,6)],7)=>11
[7,2,4,6,3,5,1]=>[1,2,4,6,3,5,7]=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>8
[7,2,4,6,5,1,3]=>[1,3,2,4,6,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)=>8
[7,2,4,6,5,3,1]=>[1,2,4,6,3,5,7]=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>8
[7,2,5,1,3,4,6]=>[1,3,4,6,2,5,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>9
[7,2,5,1,4,3,6]=>[1,4,2,5,3,6,7]=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>8
[7,2,5,1,4,6,3]=>[1,4,6,2,5,3,7]=>([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7)=>10
[7,2,5,1,6,3,4]=>[1,6,2,5,3,4,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[7,2,5,1,6,4,3]=>[1,6,2,5,3,4,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[7,2,5,3,1,4,6]=>[1,4,6,2,5,3,7]=>([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7)=>10
[7,2,5,3,1,6,4]=>[1,6,2,5,3,4,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[7,2,5,3,4,1,6]=>[1,6,2,5,3,4,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[7,2,5,3,4,6,1]=>[1,2,5,3,4,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[7,2,5,3,6,1,4]=>[1,4,2,5,3,6,7]=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>8
[7,2,5,3,6,4,1]=>[1,2,5,3,6,4,7]=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>8
[7,2,5,4,1,6,3]=>[1,6,2,5,3,4,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[7,2,5,4,3,1,6]=>[1,6,2,5,3,4,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[7,2,5,4,3,6,1]=>[1,2,5,3,6,4,7]=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>8
[7,2,5,4,6,3,1]=>[1,2,5,3,4,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[7,2,5,6,1,3,4]=>[1,3,4,2,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[7,2,5,6,1,4,3]=>[1,4,2,5,6,3,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>9
[7,2,5,6,3,1,4]=>[1,4,2,5,6,3,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>9
[7,2,5,6,3,4,1]=>[1,2,5,6,3,4,7]=>([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7)=>9
[7,2,5,6,4,3,1]=>[1,2,5,6,3,4,7]=>([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7)=>9
[7,2,6,1,3,4,5]=>[1,3,4,5,2,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[7,2,6,1,4,5,3]=>[1,4,5,2,6,3,7]=>([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>9
[7,2,6,1,5,3,4]=>[1,5,2,6,3,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[7,2,6,1,5,4,3]=>[1,5,2,6,3,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[7,2,6,3,1,4,5]=>[1,4,5,2,6,3,7]=>([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>9
[7,2,6,3,1,5,4]=>[1,5,2,6,3,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[7,2,6,3,4,1,5]=>[1,5,2,6,3,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[7,2,6,3,4,5,1]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[7,2,6,3,5,4,1]=>[1,2,6,3,5,4,7]=>([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)=>11
[7,2,6,4,1,5,3]=>[1,5,2,6,3,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[7,2,6,4,3,1,5]=>[1,5,2,6,3,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[7,2,6,4,3,5,1]=>[1,2,6,3,5,4,7]=>([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)=>11
[7,2,6,4,5,3,1]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[7,2,6,5,3,4,1]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[7,2,6,5,4,3,1]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[7,3,1,2,4,5,6]=>[1,2,4,5,6,3,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[7,3,1,2,4,6,5]=>[1,2,4,6,3,5,7]=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>8
[7,3,1,2,5,4,6]=>[1,2,5,3,4,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[7,3,1,2,5,6,4]=>[1,2,5,6,3,4,7]=>([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7)=>9
[7,3,1,2,6,4,5]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[7,3,1,2,6,5,4]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[7,3,1,4,2,5,6]=>[1,4,2,5,6,3,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>9
[7,3,1,4,5,2,6]=>[1,4,5,2,6,3,7]=>([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>9
[7,3,1,4,5,6,2]=>[1,4,5,6,2,3,7]=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>10
[7,3,1,4,6,2,5]=>[1,4,6,2,5,3,7]=>([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7)=>10
[7,3,1,4,6,5,2]=>[1,4,6,2,3,5,7]=>([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>9
[7,3,1,5,2,4,6]=>[1,5,2,4,6,3,7]=>([(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(5,6)],7)=>11
[7,3,1,5,2,6,4]=>[1,5,2,6,3,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[7,3,1,5,4,2,6]=>[1,5,2,6,3,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[7,3,1,5,4,6,2]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[7,3,1,5,6,2,4]=>[1,5,6,2,4,3,7]=>([(0,4),(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2)],7)=>12
[7,3,1,5,6,4,2]=>[1,5,6,2,3,4,7]=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>10
[7,3,1,6,2,4,5]=>[1,6,2,4,5,3,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[7,3,1,6,2,5,4]=>[1,6,2,5,3,4,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[7,3,1,6,4,2,5]=>[1,6,2,5,3,4,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[7,3,1,6,4,5,2]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[7,3,1,6,5,2,4]=>[1,6,2,4,3,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)=>11
[7,3,1,6,5,4,2]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[7,3,2,1,4,5,6]=>[1,4,5,6,2,3,7]=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>10
[7,3,2,1,4,6,5]=>[1,4,6,2,3,5,7]=>([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>9
[7,3,2,1,5,4,6]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[7,3,2,1,5,6,4]=>[1,5,6,2,3,4,7]=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>10
[7,3,2,1,6,4,5]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[7,3,2,1,6,5,4]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[7,3,2,4,1,5,6]=>[1,5,6,2,4,3,7]=>([(0,4),(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2)],7)=>12
[7,3,2,4,1,6,5]=>[1,6,2,4,3,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)=>11
[7,3,2,4,5,1,6]=>[1,6,2,4,5,3,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[7,3,2,4,5,6,1]=>[1,2,4,5,6,3,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[7,3,2,4,6,1,5]=>[1,5,2,4,6,3,7]=>([(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(5,6)],7)=>11
[7,3,2,4,6,5,1]=>[1,2,4,6,3,5,7]=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>8
[7,3,2,5,1,4,6]=>[1,4,6,2,5,3,7]=>([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7)=>10
[7,3,2,5,1,6,4]=>[1,6,2,5,3,4,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[7,3,2,5,4,1,6]=>[1,6,2,5,3,4,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[7,3,2,5,4,6,1]=>[1,2,5,3,4,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[7,3,2,5,6,1,4]=>[1,4,2,5,6,3,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>9
[7,3,2,5,6,4,1]=>[1,2,5,6,3,4,7]=>([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7)=>9
[7,3,2,6,1,4,5]=>[1,4,5,2,6,3,7]=>([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>9
[7,3,2,6,1,5,4]=>[1,5,2,6,3,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[7,3,2,6,4,1,5]=>[1,5,2,6,3,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[7,3,2,6,4,5,1]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[7,3,2,6,5,4,1]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[7,3,4,1,2,5,6]=>[1,2,5,6,3,4,7]=>([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7)=>9
[7,3,4,1,2,6,5]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[7,3,4,1,5,2,6]=>[1,5,2,6,3,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[7,3,4,1,5,6,2]=>[1,5,6,2,3,4,7]=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>10
[7,3,4,1,6,2,5]=>[1,6,2,5,3,4,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[7,3,4,1,6,5,2]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[7,3,4,2,1,5,6]=>[1,5,6,2,3,4,7]=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>10
[7,3,4,2,1,6,5]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[7,3,4,2,5,1,6]=>[1,6,2,5,3,4,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[7,3,4,2,5,6,1]=>[1,2,5,6,3,4,7]=>([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7)=>9
[7,3,4,2,6,1,5]=>[1,5,2,6,3,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[7,3,4,2,6,5,1]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[7,3,4,5,1,2,6]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[7,3,4,5,1,6,2]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[7,3,4,5,2,1,6]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[7,3,4,5,2,6,1]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[7,3,4,5,6,1,2]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[7,3,4,5,6,2,1]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[7,3,4,6,1,2,5]=>[1,2,5,3,4,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[7,3,4,6,1,5,2]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[7,3,4,6,2,1,5]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[7,3,4,6,2,5,1]=>[1,2,5,3,4,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[7,3,4,6,5,1,2]=>[1,2,3,4,6,5,7]=>([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)=>7
[7,3,4,6,5,2,1]=>[1,2,3,4,6,5,7]=>([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)=>7
[7,3,5,1,2,4,6]=>[1,2,4,6,3,5,7]=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>8
[7,3,5,1,2,6,4]=>[1,2,6,3,5,4,7]=>([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)=>11
[7,3,5,1,4,6,2]=>[1,4,6,2,3,5,7]=>([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>9
[7,3,5,1,6,2,4]=>[1,6,2,4,3,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)=>11
[7,3,5,1,6,4,2]=>[1,6,2,3,5,4,7]=>([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)=>12
[7,3,5,2,1,4,6]=>[1,4,6,2,3,5,7]=>([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>9
[7,3,5,2,1,6,4]=>[1,6,2,3,5,4,7]=>([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)=>12
[7,3,5,2,4,1,6]=>[1,6,2,4,3,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)=>11
[7,3,5,2,4,6,1]=>[1,2,4,6,3,5,7]=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>8
[7,3,5,2,6,4,1]=>[1,2,6,3,5,4,7]=>([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)=>11
[7,3,5,4,1,2,6]=>[1,2,6,3,5,4,7]=>([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)=>11
[7,3,5,4,1,6,2]=>[1,6,2,3,5,4,7]=>([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)=>12
[7,3,5,4,2,1,6]=>[1,6,2,3,5,4,7]=>([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)=>12
[7,3,5,4,2,6,1]=>[1,2,6,3,5,4,7]=>([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)=>11
[7,3,5,4,6,1,2]=>[1,2,3,5,4,6,7]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>7
[7,3,5,4,6,2,1]=>[1,2,3,5,4,6,7]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>7
[7,3,5,6,1,2,4]=>[1,2,4,3,5,6,7]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>7
[7,3,5,6,1,4,2]=>[1,4,2,3,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[7,3,5,6,2,1,4]=>[1,4,2,3,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[7,3,5,6,2,4,1]=>[1,2,4,3,5,6,7]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>7
[7,3,5,6,4,1,2]=>[1,2,3,5,6,4,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[7,3,5,6,4,2,1]=>[1,2,3,5,6,4,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[7,3,6,1,2,4,5]=>[1,2,4,5,3,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[7,3,6,1,2,5,4]=>[1,2,5,3,6,4,7]=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>8
[7,3,6,1,4,2,5]=>[1,4,2,5,3,6,7]=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>8
[7,3,6,1,4,5,2]=>[1,4,5,2,3,6,7]=>([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7)=>9
[7,3,6,1,5,2,4]=>[1,5,2,4,3,6,7]=>([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)=>11
[7,3,6,1,5,4,2]=>[1,5,2,3,6,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>9
[7,3,6,2,1,4,5]=>[1,4,5,2,3,6,7]=>([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7)=>9
[7,3,6,2,1,5,4]=>[1,5,2,3,6,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>9
[7,3,6,2,4,1,5]=>[1,5,2,4,3,6,7]=>([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)=>11
[7,3,6,2,4,5,1]=>[1,2,4,5,3,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[7,3,6,2,5,1,4]=>[1,4,2,5,3,6,7]=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>8
[7,3,6,2,5,4,1]=>[1,2,5,3,6,4,7]=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>8
[7,3,6,4,1,2,5]=>[1,2,5,3,6,4,7]=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>8
[7,3,6,4,1,5,2]=>[1,5,2,3,6,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>9
[7,3,6,4,2,1,5]=>[1,5,2,3,6,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>9
[7,3,6,4,2,5,1]=>[1,2,5,3,6,4,7]=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>8
[7,3,6,4,5,1,2]=>[1,2,3,6,4,5,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[7,3,6,4,5,2,1]=>[1,2,3,6,4,5,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[7,3,6,5,4,1,2]=>[1,2,3,6,4,5,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[7,3,6,5,4,2,1]=>[1,2,3,6,4,5,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[7,4,1,2,3,5,6]=>[1,2,3,5,6,4,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[7,4,1,2,3,6,5]=>[1,2,3,6,4,5,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[7,4,1,2,5,3,6]=>[1,2,5,3,6,4,7]=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>8
[7,4,1,2,5,6,3]=>[1,2,5,6,3,4,7]=>([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7)=>9
[7,4,1,2,6,3,5]=>[1,2,6,3,5,4,7]=>([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)=>11
[7,4,1,2,6,5,3]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[7,4,1,3,5,6,2]=>[1,3,5,6,2,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[7,4,1,3,6,5,2]=>[1,3,6,2,4,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>9
[7,4,1,5,2,3,6]=>[1,5,2,3,6,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>9
[7,4,1,5,2,6,3]=>[1,5,2,6,3,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[7,4,1,5,3,2,6]=>[1,5,2,6,3,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[7,4,1,5,3,6,2]=>[1,5,2,3,6,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>9
[7,4,1,5,6,2,3]=>[1,5,6,2,3,4,7]=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>10
[7,4,1,5,6,3,2]=>[1,5,6,2,3,4,7]=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>10
[7,4,1,6,2,3,5]=>[1,6,2,3,5,4,7]=>([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)=>12
[7,4,1,6,2,5,3]=>[1,6,2,5,3,4,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[7,4,1,6,3,2,5]=>[1,6,2,5,3,4,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[7,4,1,6,3,5,2]=>[1,6,2,3,5,4,7]=>([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)=>12
[7,4,1,6,5,2,3]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[7,4,1,6,5,3,2]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[7,4,2,1,3,5,6]=>[1,3,5,6,2,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[7,4,2,1,3,6,5]=>[1,3,6,2,4,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>9
[7,4,2,1,5,3,6]=>[1,5,2,3,6,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>9
[7,4,2,1,5,6,3]=>[1,5,6,2,3,4,7]=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>10
[7,4,2,1,6,3,5]=>[1,6,2,3,5,4,7]=>([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)=>12
[7,4,2,1,6,5,3]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[7,4,2,3,1,5,6]=>[1,5,6,2,3,4,7]=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>10
[7,4,2,3,1,6,5]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[7,4,2,3,5,1,6]=>[1,6,2,3,5,4,7]=>([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)=>12
[7,4,2,3,5,6,1]=>[1,2,3,5,6,4,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[7,4,2,3,6,1,5]=>[1,5,2,3,6,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>9
[7,4,2,3,6,5,1]=>[1,2,3,6,4,5,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[7,4,2,5,1,6,3]=>[1,6,2,5,3,4,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[7,4,2,5,3,1,6]=>[1,6,2,5,3,4,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[7,4,2,5,3,6,1]=>[1,2,5,3,6,4,7]=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>8
[7,4,2,5,6,3,1]=>[1,2,5,6,3,4,7]=>([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7)=>9
[7,4,2,6,1,5,3]=>[1,5,2,6,3,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[7,4,2,6,3,1,5]=>[1,5,2,6,3,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[7,4,2,6,3,5,1]=>[1,2,6,3,5,4,7]=>([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)=>11
[7,4,2,6,5,3,1]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[7,4,3,1,2,5,6]=>[1,2,5,6,3,4,7]=>([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7)=>9
[7,4,3,1,2,6,5]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[7,4,3,1,5,2,6]=>[1,5,2,6,3,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[7,4,3,1,5,6,2]=>[1,5,6,2,3,4,7]=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>10
[7,4,3,1,6,2,5]=>[1,6,2,5,3,4,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[7,4,3,1,6,5,2]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[7,4,3,2,1,5,6]=>[1,5,6,2,3,4,7]=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>10
[7,4,3,2,1,6,5]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[7,4,3,2,5,1,6]=>[1,6,2,5,3,4,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>13
[7,4,3,2,5,6,1]=>[1,2,5,6,3,4,7]=>([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7)=>9
[7,4,3,2,6,1,5]=>[1,5,2,6,3,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>9
[7,4,3,2,6,5,1]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[7,4,3,5,1,2,6]=>[1,2,6,3,5,4,7]=>([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)=>11
[7,4,3,5,1,6,2]=>[1,6,2,3,5,4,7]=>([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)=>12
[7,4,3,5,2,1,6]=>[1,6,2,3,5,4,7]=>([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)=>12
[7,4,3,5,2,6,1]=>[1,2,6,3,5,4,7]=>([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)=>11
[7,4,3,5,6,1,2]=>[1,2,3,5,6,4,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[7,4,3,5,6,2,1]=>[1,2,3,5,6,4,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[7,4,3,6,1,2,5]=>[1,2,5,3,6,4,7]=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>8
[7,4,3,6,1,5,2]=>[1,5,2,3,6,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>9
[7,4,3,6,2,1,5]=>[1,5,2,3,6,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>9
[7,4,3,6,2,5,1]=>[1,2,5,3,6,4,7]=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>8
[7,4,3,6,5,1,2]=>[1,2,3,6,4,5,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[7,4,3,6,5,2,1]=>[1,2,3,6,4,5,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[7,4,5,1,2,3,6]=>[1,2,3,6,4,5,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[7,4,5,1,2,6,3]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[7,4,5,1,3,6,2]=>[1,3,6,2,4,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>9
[7,4,5,1,6,2,3]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[7,4,5,1,6,3,2]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[7,4,5,2,1,3,6]=>[1,3,6,2,4,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>9
[7,4,5,2,1,6,3]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[7,4,5,2,3,1,6]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[7,4,5,2,3,6,1]=>[1,2,3,6,4,5,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[7,4,5,2,6,3,1]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[7,4,5,3,1,2,6]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[7,4,5,3,1,6,2]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[7,4,5,3,2,1,6]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[7,4,5,3,2,6,1]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[7,4,5,3,6,1,2]=>[1,2,3,6,4,5,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[7,4,5,3,6,2,1]=>[1,2,3,6,4,5,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[7,4,5,6,1,2,3]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[7,4,5,6,1,3,2]=>[1,3,2,4,5,6,7]=>([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)=>7
[7,4,5,6,2,1,3]=>[1,3,2,4,5,6,7]=>([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)=>7
[7,4,5,6,2,3,1]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[7,4,5,6,3,1,2]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[7,4,5,6,3,2,1]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[7,4,6,1,2,3,5]=>[1,2,3,5,4,6,7]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>7
[7,4,6,1,2,5,3]=>[1,2,5,3,4,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[7,4,6,1,3,5,2]=>[1,3,5,2,4,6,7]=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>8
[7,4,6,1,5,2,3]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[7,4,6,1,5,3,2]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[7,4,6,2,1,3,5]=>[1,3,5,2,4,6,7]=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>8
[7,4,6,2,1,5,3]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[7,4,6,2,3,1,5]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[7,4,6,2,3,5,1]=>[1,2,3,5,4,6,7]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>7
[7,4,6,2,5,3,1]=>[1,2,5,3,4,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[7,4,6,3,1,2,5]=>[1,2,5,3,4,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[7,4,6,3,1,5,2]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[7,4,6,3,2,1,5]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[7,4,6,3,2,5,1]=>[1,2,5,3,4,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[7,4,6,3,5,1,2]=>[1,2,3,5,4,6,7]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>7
[7,4,6,3,5,2,1]=>[1,2,3,5,4,6,7]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>7
[7,4,6,5,1,2,3]=>[1,2,3,4,6,5,7]=>([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)=>7
[7,4,6,5,1,3,2]=>[1,3,2,4,6,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)=>8
[7,4,6,5,2,1,3]=>[1,3,2,4,6,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)=>8
[7,4,6,5,2,3,1]=>[1,2,3,4,6,5,7]=>([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)=>7
[7,4,6,5,3,1,2]=>[1,2,3,4,6,5,7]=>([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)=>7
[7,4,6,5,3,2,1]=>[1,2,3,4,6,5,7]=>([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)=>7
[7,5,1,2,3,4,6]=>[1,2,3,4,6,5,7]=>([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)=>7
[7,5,1,2,3,6,4]=>[1,2,3,6,4,5,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[7,5,1,2,4,6,3]=>[1,2,4,6,3,5,7]=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>8
[7,5,1,2,6,3,4]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[7,5,1,2,6,4,3]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[7,5,1,3,2,4,6]=>[1,3,2,4,6,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)=>8
[7,5,1,3,4,6,2]=>[1,3,4,6,2,5,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>9
[7,5,1,3,6,2,4]=>[1,3,6,2,4,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>9
[7,5,1,3,6,4,2]=>[1,3,6,2,4,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>9
[7,5,1,4,6,2,3]=>[1,4,6,2,3,5,7]=>([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>9
[7,5,1,4,6,3,2]=>[1,4,6,2,3,5,7]=>([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>9
[7,5,1,6,2,3,4]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[7,5,1,6,2,4,3]=>[1,6,2,4,3,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)=>11
[7,5,1,6,3,2,4]=>[1,6,2,4,3,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)=>11
[7,5,1,6,3,4,2]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[7,5,1,6,4,2,3]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[7,5,1,6,4,3,2]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[7,5,2,1,3,4,6]=>[1,3,4,6,2,5,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>9
[7,5,2,1,3,6,4]=>[1,3,6,2,4,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>9
[7,5,2,1,4,6,3]=>[1,4,6,2,3,5,7]=>([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>9
[7,5,2,1,6,3,4]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[7,5,2,1,6,4,3]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[7,5,2,3,1,4,6]=>[1,4,6,2,3,5,7]=>([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>9
[7,5,2,3,1,6,4]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[7,5,2,3,4,1,6]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[7,5,2,3,4,6,1]=>[1,2,3,4,6,5,7]=>([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)=>7
[7,5,2,3,6,4,1]=>[1,2,3,6,4,5,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[7,5,2,4,1,3,6]=>[1,3,6,2,4,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>9
[7,5,2,4,1,6,3]=>[1,6,2,4,3,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)=>11
[7,5,2,4,3,1,6]=>[1,6,2,4,3,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)=>11
[7,5,2,4,6,1,3]=>[1,3,2,4,6,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)=>8
[7,5,2,4,6,3,1]=>[1,2,4,6,3,5,7]=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>8
[7,5,2,6,3,4,1]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[7,5,2,6,4,3,1]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[7,5,3,1,2,4,6]=>[1,2,4,6,3,5,7]=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>8
[7,5,3,1,2,6,4]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[7,5,3,1,4,6,2]=>[1,4,6,2,3,5,7]=>([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>9
[7,5,3,1,6,2,4]=>[1,6,2,4,3,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)=>11
[7,5,3,1,6,4,2]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[7,5,3,2,1,4,6]=>[1,4,6,2,3,5,7]=>([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>9
[7,5,3,2,1,6,4]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[7,5,3,2,4,1,6]=>[1,6,2,4,3,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)=>11
[7,5,3,2,4,6,1]=>[1,2,4,6,3,5,7]=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>8
[7,5,3,2,6,4,1]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[7,5,3,4,1,2,6]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[7,5,3,4,1,6,2]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[7,5,3,4,2,1,6]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[7,5,3,4,2,6,1]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[7,5,3,4,6,1,2]=>[1,2,3,4,6,5,7]=>([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)=>7
[7,5,3,4,6,2,1]=>[1,2,3,4,6,5,7]=>([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)=>7
[7,5,3,6,4,1,2]=>[1,2,3,6,4,5,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[7,5,3,6,4,2,1]=>[1,2,3,6,4,5,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[7,5,4,1,2,3,6]=>[1,2,3,6,4,5,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[7,5,4,1,2,6,3]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[7,5,4,1,3,6,2]=>[1,3,6,2,4,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>9
[7,5,4,1,6,2,3]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[7,5,4,1,6,3,2]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[7,5,4,2,1,3,6]=>[1,3,6,2,4,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>9
[7,5,4,2,1,6,3]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[7,5,4,2,3,1,6]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[7,5,4,2,3,6,1]=>[1,2,3,6,4,5,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[7,5,4,2,6,3,1]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[7,5,4,3,1,2,6]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[7,5,4,3,1,6,2]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[7,5,4,3,2,1,6]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>10
[7,5,4,3,2,6,1]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>9
[7,5,4,3,6,1,2]=>[1,2,3,6,4,5,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[7,5,4,3,6,2,1]=>[1,2,3,6,4,5,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>8
[7,5,4,6,1,2,3]=>[1,2,3,4,6,5,7]=>([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)=>7
[7,5,4,6,1,3,2]=>[1,3,2,4,6,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)=>8
[7,5,4,6,2,1,3]=>[1,3,2,4,6,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)=>8
[7,5,4,6,2,3,1]=>[1,2,3,4,6,5,7]=>([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)=>7
[7,5,4,6,3,1,2]=>[1,2,3,4,6,5,7]=>([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)=>7
[7,5,4,6,3,2,1]=>[1,2,3,4,6,5,7]=>([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)=>7
[7,5,6,1,2,3,4]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[7,5,6,1,2,4,3]=>[1,2,4,3,5,6,7]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>7
[7,5,6,1,3,2,4]=>[1,3,2,4,5,6,7]=>([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)=>7
[7,5,6,1,3,4,2]=>[1,3,4,2,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[7,5,6,1,4,2,3]=>[1,4,2,3,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[7,5,6,1,4,3,2]=>[1,4,2,3,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[7,5,6,2,1,3,4]=>[1,3,4,2,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[7,5,6,2,1,4,3]=>[1,4,2,3,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[7,5,6,2,3,1,4]=>[1,4,2,3,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[7,5,6,2,3,4,1]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[7,5,6,2,4,1,3]=>[1,3,2,4,5,6,7]=>([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)=>7
[7,5,6,2,4,3,1]=>[1,2,4,3,5,6,7]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>7
[7,5,6,3,1,2,4]=>[1,2,4,3,5,6,7]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>7
[7,5,6,3,1,4,2]=>[1,4,2,3,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[7,5,6,3,2,1,4]=>[1,4,2,3,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[7,5,6,3,2,4,1]=>[1,2,4,3,5,6,7]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>7
[7,5,6,3,4,1,2]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[7,5,6,3,4,2,1]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[7,5,6,4,1,2,3]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[7,5,6,4,1,3,2]=>[1,3,2,4,5,6,7]=>([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)=>7
[7,5,6,4,2,1,3]=>[1,3,2,4,5,6,7]=>([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)=>7
[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[7,5,6,4,3,1,2]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[7,5,6,4,3,2,1]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[7,6,1,2,3,4,5]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[7,6,1,2,3,5,4]=>[1,2,3,5,4,6,7]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>7
[7,6,1,2,4,3,5]=>[1,2,4,3,5,6,7]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>7
[7,6,1,2,4,5,3]=>[1,2,4,5,3,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[7,6,1,2,5,3,4]=>[1,2,5,3,4,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[7,6,1,2,5,4,3]=>[1,2,5,3,4,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[7,6,1,3,2,4,5]=>[1,3,2,4,5,6,7]=>([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)=>7
[7,6,1,3,4,2,5]=>[1,3,4,2,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[7,6,1,3,4,5,2]=>[1,3,4,5,2,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[7,6,1,3,5,2,4]=>[1,3,5,2,4,6,7]=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>8
[7,6,1,3,5,4,2]=>[1,3,5,2,4,6,7]=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>8
[7,6,1,4,2,3,5]=>[1,4,2,3,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[7,6,1,4,2,5,3]=>[1,4,2,5,3,6,7]=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>8
[7,6,1,4,3,2,5]=>[1,4,2,5,3,6,7]=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>8
[7,6,1,4,3,5,2]=>[1,4,2,3,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[7,6,1,4,5,2,3]=>[1,4,5,2,3,6,7]=>([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7)=>9
[7,6,1,4,5,3,2]=>[1,4,5,2,3,6,7]=>([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7)=>9
[7,6,1,5,2,3,4]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[7,6,1,5,2,4,3]=>[1,5,2,4,3,6,7]=>([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)=>11
[7,6,1,5,3,2,4]=>[1,5,2,4,3,6,7]=>([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)=>11
[7,6,1,5,3,4,2]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[7,6,1,5,4,2,3]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[7,6,1,5,4,3,2]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[7,6,2,1,3,4,5]=>[1,3,4,5,2,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[7,6,2,1,3,5,4]=>[1,3,5,2,4,6,7]=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>8
[7,6,2,1,4,3,5]=>[1,4,2,3,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[7,6,2,1,4,5,3]=>[1,4,5,2,3,6,7]=>([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7)=>9
[7,6,2,1,5,3,4]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[7,6,2,1,5,4,3]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[7,6,2,3,1,4,5]=>[1,4,5,2,3,6,7]=>([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7)=>9
[7,6,2,3,1,5,4]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[7,6,2,3,4,1,5]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[7,6,2,3,4,5,1]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[7,6,2,3,5,1,4]=>[1,4,2,3,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[7,6,2,3,5,4,1]=>[1,2,3,5,4,6,7]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>7
[7,6,2,4,1,3,5]=>[1,3,5,2,4,6,7]=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>8
[7,6,2,4,1,5,3]=>[1,5,2,4,3,6,7]=>([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)=>11
[7,6,2,4,3,1,5]=>[1,5,2,4,3,6,7]=>([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)=>11
[7,6,2,4,3,5,1]=>[1,2,4,3,5,6,7]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>7
[7,6,2,4,5,1,3]=>[1,3,2,4,5,6,7]=>([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)=>7
[7,6,2,4,5,3,1]=>[1,2,4,5,3,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[7,6,2,5,1,3,4]=>[1,3,4,2,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[7,6,2,5,1,4,3]=>[1,4,2,5,3,6,7]=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>8
[7,6,2,5,3,1,4]=>[1,4,2,5,3,6,7]=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>8
[7,6,2,5,3,4,1]=>[1,2,5,3,4,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[7,6,2,5,4,3,1]=>[1,2,5,3,4,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[7,6,3,1,2,4,5]=>[1,2,4,5,3,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[7,6,3,1,2,5,4]=>[1,2,5,3,4,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[7,6,3,1,4,2,5]=>[1,4,2,5,3,6,7]=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>8
[7,6,3,1,4,5,2]=>[1,4,5,2,3,6,7]=>([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7)=>9
[7,6,3,1,5,2,4]=>[1,5,2,4,3,6,7]=>([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)=>11
[7,6,3,1,5,4,2]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[7,6,3,2,1,4,5]=>[1,4,5,2,3,6,7]=>([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7)=>9
[7,6,3,2,1,5,4]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[7,6,3,2,4,1,5]=>[1,5,2,4,3,6,7]=>([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)=>11
[7,6,3,2,4,5,1]=>[1,2,4,5,3,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[7,6,3,2,5,1,4]=>[1,4,2,5,3,6,7]=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>8
[7,6,3,2,5,4,1]=>[1,2,5,3,4,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[7,6,3,4,1,2,5]=>[1,2,5,3,4,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[7,6,3,4,1,5,2]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[7,6,3,4,2,1,5]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[7,6,3,4,2,5,1]=>[1,2,5,3,4,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[7,6,3,4,5,1,2]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[7,6,3,5,1,2,4]=>[1,2,4,3,5,6,7]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>7
[7,6,3,5,1,4,2]=>[1,4,2,3,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[7,6,3,5,2,1,4]=>[1,4,2,3,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[7,6,3,5,2,4,1]=>[1,2,4,3,5,6,7]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>7
[7,6,3,5,4,1,2]=>[1,2,3,5,4,6,7]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>7
[7,6,3,5,4,2,1]=>[1,2,3,5,4,6,7]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>7
[7,6,4,1,2,3,5]=>[1,2,3,5,4,6,7]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>7
[7,6,4,1,2,5,3]=>[1,2,5,3,4,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[7,6,4,1,3,5,2]=>[1,3,5,2,4,6,7]=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>8
[7,6,4,1,5,2,3]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[7,6,4,1,5,3,2]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[7,6,4,2,1,3,5]=>[1,3,5,2,4,6,7]=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>8
[7,6,4,2,1,5,3]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[7,6,4,2,3,1,5]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[7,6,4,2,3,5,1]=>[1,2,3,5,4,6,7]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>7
[7,6,4,2,5,3,1]=>[1,2,5,3,4,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[7,6,4,3,1,2,5]=>[1,2,5,3,4,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[7,6,4,3,1,5,2]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[7,6,4,3,2,1,5]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>9
[7,6,4,3,2,5,1]=>[1,2,5,3,4,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>8
[7,6,4,3,5,1,2]=>[1,2,3,5,4,6,7]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>7
[7,6,4,3,5,2,1]=>[1,2,3,5,4,6,7]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>7
[7,6,4,5,1,2,3]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[7,6,4,5,1,3,2]=>[1,3,2,4,5,6,7]=>([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)=>7
[7,6,4,5,2,1,3]=>[1,3,2,4,5,6,7]=>([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)=>7
[7,6,4,5,2,3,1]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[7,6,4,5,3,1,2]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[7,6,4,5,3,2,1]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[7,6,5,1,2,3,4]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[7,6,5,1,2,4,3]=>[1,2,4,3,5,6,7]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>7
[7,6,5,1,3,2,4]=>[1,3,2,4,5,6,7]=>([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)=>7
[7,6,5,1,3,4,2]=>[1,3,4,2,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[7,6,5,1,4,2,3]=>[1,4,2,3,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[7,6,5,1,4,3,2]=>[1,4,2,3,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[7,6,5,2,1,3,4]=>[1,3,4,2,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[7,6,5,2,1,4,3]=>[1,4,2,3,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[7,6,5,2,3,1,4]=>[1,4,2,3,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[7,6,5,2,3,4,1]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[7,6,5,2,4,1,3]=>[1,3,2,4,5,6,7]=>([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)=>7
[7,6,5,2,4,3,1]=>[1,2,4,3,5,6,7]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>7
[7,6,5,3,1,2,4]=>[1,2,4,3,5,6,7]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>7
[7,6,5,3,1,4,2]=>[1,4,2,3,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[7,6,5,3,2,1,4]=>[1,4,2,3,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>8
[7,6,5,3,2,4,1]=>[1,2,4,3,5,6,7]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>7
[7,6,5,3,4,1,2]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[7,6,5,3,4,2,1]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[7,6,5,4,1,2,3]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[7,6,5,4,1,3,2]=>[1,3,2,4,5,6,7]=>([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)=>7
[7,6,5,4,2,1,3]=>[1,3,2,4,5,6,7]=>([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)=>7
[7,6,5,4,2,3,1]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[7,6,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>6
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Description
The number of indecomposable summands of the top of the first syzygy of the dual of the regular module in the incidence algebra of the lattice.
Map
permutation poset
Description
Sends a permutation to its permutation poset.
For a permutation $\pi$ of length $n$, this poset has vertices
$$\{ (i,\pi(i))\ :\ 1 \leq i \leq n \}$$
and the cover relation is given by $(w, x) \leq (y, z)$ if $w \leq y$ and $x \leq z$.
For example, the permutation $[3,1,5,4,2]$ is mapped to the poset with cover relations
$$\{ (2, 1) \prec (5, 2),\ (2, 1) \prec (4, 4),\ (2, 1) \prec (3, 5),\ (1, 3) \prec (4, 4),\ (1, 3) \prec (3, 5) \}.$$
For a permutation $\pi$ of length $n$, this poset has vertices
$$\{ (i,\pi(i))\ :\ 1 \leq i \leq n \}$$
and the cover relation is given by $(w, x) \leq (y, z)$ if $w \leq y$ and $x \leq z$.
For example, the permutation $[3,1,5,4,2]$ is mapped to the poset with cover relations
$$\{ (2, 1) \prec (5, 2),\ (2, 1) \prec (4, 4),\ (2, 1) \prec (3, 5),\ (1, 3) \prec (4, 4),\ (1, 3) \prec (3, 5) \}.$$
Map
runsort
Description
The permutation obtained by sorting the increasing runs lexicographically.
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