Identifier
Mp00049:
Ordered trees
—to binary tree: left brother = left child⟶
Binary trees
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
Images
=>
Cc0021;cc-rep-0Cc0010;cc-rep-1Cc0020;cc-rep-3
[[]]=>[.,.]=>[1]=>([],1)
[[],[]]=>[[.,.],.]=>[1,2]=>([],2)
[[[]]]=>[.,[.,.]]=>[2,1]=>([(0,1)],2)
[[],[],[]]=>[[[.,.],.],.]=>[1,2,3]=>([],3)
[[],[[]]]=>[[.,.],[.,.]]=>[1,3,2]=>([(1,2)],3)
[[[]],[]]=>[[.,[.,.]],.]=>[2,1,3]=>([(1,2)],3)
[[[],[]]]=>[.,[[.,.],.]]=>[2,3,1]=>([(0,2),(1,2)],3)
[[[[]]]]=>[.,[.,[.,.]]]=>[3,2,1]=>([(0,1),(0,2),(1,2)],3)
[[],[],[],[]]=>[[[[.,.],.],.],.]=>[1,2,3,4]=>([],4)
[[],[],[[]]]=>[[[.,.],.],[.,.]]=>[1,2,4,3]=>([(2,3)],4)
[[],[[]],[]]=>[[[.,.],[.,.]],.]=>[1,3,2,4]=>([(2,3)],4)
[[],[[],[]]]=>[[.,.],[[.,.],.]]=>[1,3,4,2]=>([(1,3),(2,3)],4)
[[],[[[]]]]=>[[.,.],[.,[.,.]]]=>[1,4,3,2]=>([(1,2),(1,3),(2,3)],4)
[[[]],[],[]]=>[[[.,[.,.]],.],.]=>[2,1,3,4]=>([(2,3)],4)
[[[]],[[]]]=>[[.,[.,.]],[.,.]]=>[2,1,4,3]=>([(0,3),(1,2)],4)
[[[],[]],[]]=>[[.,[[.,.],.]],.]=>[2,3,1,4]=>([(1,3),(2,3)],4)
[[[[]]],[]]=>[[.,[.,[.,.]]],.]=>[3,2,1,4]=>([(1,2),(1,3),(2,3)],4)
[[[],[],[]]]=>[.,[[[.,.],.],.]]=>[2,3,4,1]=>([(0,3),(1,3),(2,3)],4)
[[[],[[]]]]=>[.,[[.,.],[.,.]]]=>[2,4,3,1]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[[[]],[]]]=>[.,[[.,[.,.]],.]]=>[3,2,4,1]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[[[],[]]]]=>[.,[.,[[.,.],.]]]=>[3,4,2,1]=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[[[[[]]]]]=>[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[[],[],[],[],[]]=>[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>([],5)
[[],[],[],[[]]]=>[[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]=>([(3,4)],5)
[[],[],[[]],[]]=>[[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]=>([(3,4)],5)
[[],[],[[],[]]]=>[[[.,.],.],[[.,.],.]]=>[1,2,4,5,3]=>([(2,4),(3,4)],5)
[[],[],[[[]]]]=>[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]=>([(2,3),(2,4),(3,4)],5)
[[],[[]],[],[]]=>[[[[.,.],[.,.]],.],.]=>[1,3,2,4,5]=>([(3,4)],5)
[[],[[]],[[]]]=>[[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]=>([(1,4),(2,3)],5)
[[],[[],[]],[]]=>[[[.,.],[[.,.],.]],.]=>[1,3,4,2,5]=>([(2,4),(3,4)],5)
[[],[[[]]],[]]=>[[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5]=>([(2,3),(2,4),(3,4)],5)
[[],[[],[],[]]]=>[[.,.],[[[.,.],.],.]]=>[1,3,4,5,2]=>([(1,4),(2,4),(3,4)],5)
[[],[[],[[]]]]=>[[.,.],[[.,.],[.,.]]]=>[1,3,5,4,2]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[],[[[]],[]]]=>[[.,.],[[.,[.,.]],.]]=>[1,4,3,5,2]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[],[[[],[]]]]=>[[.,.],[.,[[.,.],.]]]=>[1,4,5,3,2]=>([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[],[[[[]]]]]=>[[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[[]],[],[],[]]=>[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>([(3,4)],5)
[[[]],[],[[]]]=>[[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]=>([(1,4),(2,3)],5)
[[[]],[[]],[]]=>[[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5]=>([(1,4),(2,3)],5)
[[[]],[[],[]]]=>[[.,[.,.]],[[.,.],.]]=>[2,1,4,5,3]=>([(0,1),(2,4),(3,4)],5)
[[[]],[[[]]]]=>[[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]=>([(0,1),(2,3),(2,4),(3,4)],5)
[[[],[]],[],[]]=>[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>([(2,4),(3,4)],5)
[[[[]]],[],[]]=>[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>([(2,3),(2,4),(3,4)],5)
[[[],[]],[[]]]=>[[.,[[.,.],.]],[.,.]]=>[2,3,1,5,4]=>([(0,1),(2,4),(3,4)],5)
[[[[]]],[[]]]=>[[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4]=>([(0,1),(2,3),(2,4),(3,4)],5)
[[[],[],[]],[]]=>[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>([(1,4),(2,4),(3,4)],5)
[[[],[[]]],[]]=>[[.,[[.,.],[.,.]]],.]=>[2,4,3,1,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[[[]],[]],[]]=>[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[[[],[]]],[]]=>[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[[[[]]]],[]]=>[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[[],[],[],[]]]=>[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[[],[],[[]]]]=>[.,[[[.,.],.],[.,.]]]=>[2,3,5,4,1]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[[],[[]],[]]]=>[.,[[[.,.],[.,.]],.]]=>[2,4,3,5,1]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[[],[[],[]]]]=>[.,[[.,.],[[.,.],.]]]=>[2,4,5,3,1]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[[],[[[]]]]]=>[.,[[.,.],[.,[.,.]]]]=>[2,5,4,3,1]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[[[]],[],[]]]=>[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[[[]],[[]]]]=>[.,[[.,[.,.]],[.,.]]]=>[3,2,5,4,1]=>([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
[[[[],[]],[]]]=>[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[[[[]]],[]]]=>[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[[[],[],[]]]]=>[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[[[],[[]]]]]=>[.,[.,[[.,.],[.,.]]]]=>[3,5,4,2,1]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[[[[]],[]]]]=>[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[[[[],[]]]]]=>[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[[[[[]]]]]]=>[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[],[],[],[],[],[]]=>[[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>([],6)
[[],[],[],[],[[]]]=>[[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5]=>([(4,5)],6)
[[],[],[],[[]],[]]=>[[[[[.,.],.],.],[.,.]],.]=>[1,2,3,5,4,6]=>([(4,5)],6)
[[],[],[],[[],[]]]=>[[[[.,.],.],.],[[.,.],.]]=>[1,2,3,5,6,4]=>([(3,5),(4,5)],6)
[[],[],[],[[[]]]]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]=>([(3,4),(3,5),(4,5)],6)
[[],[],[[]],[],[]]=>[[[[[.,.],.],[.,.]],.],.]=>[1,2,4,3,5,6]=>([(4,5)],6)
[[],[],[[]],[[]]]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]=>([(2,5),(3,4)],6)
[[],[],[[],[]],[]]=>[[[[.,.],.],[[.,.],.]],.]=>[1,2,4,5,3,6]=>([(3,5),(4,5)],6)
[[],[],[[[]]],[]]=>[[[[.,.],.],[.,[.,.]]],.]=>[1,2,5,4,3,6]=>([(3,4),(3,5),(4,5)],6)
[[],[],[[],[],[]]]=>[[[.,.],.],[[[.,.],.],.]]=>[1,2,4,5,6,3]=>([(2,5),(3,5),(4,5)],6)
[[],[],[[],[[]]]]=>[[[.,.],.],[[.,.],[.,.]]]=>[1,2,4,6,5,3]=>([(2,5),(3,4),(3,5),(4,5)],6)
[[],[],[[[]],[]]]=>[[[.,.],.],[[.,[.,.]],.]]=>[1,2,5,4,6,3]=>([(2,5),(3,4),(3,5),(4,5)],6)
[[],[],[[[],[]]]]=>[[[.,.],.],[.,[[.,.],.]]]=>[1,2,5,6,4,3]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[],[],[[[[]]]]]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[],[[]],[],[],[]]=>[[[[[.,.],[.,.]],.],.],.]=>[1,3,2,4,5,6]=>([(4,5)],6)
[[],[[]],[],[[]]]=>[[[[.,.],[.,.]],.],[.,.]]=>[1,3,2,4,6,5]=>([(2,5),(3,4)],6)
[[],[[]],[[]],[]]=>[[[[.,.],[.,.]],[.,.]],.]=>[1,3,2,5,4,6]=>([(2,5),(3,4)],6)
[[],[[]],[[],[]]]=>[[[.,.],[.,.]],[[.,.],.]]=>[1,3,2,5,6,4]=>([(1,2),(3,5),(4,5)],6)
[[],[[]],[[[]]]]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]=>([(1,2),(3,4),(3,5),(4,5)],6)
[[],[[],[]],[],[]]=>[[[[.,.],[[.,.],.]],.],.]=>[1,3,4,2,5,6]=>([(3,5),(4,5)],6)
[[],[[[]]],[],[]]=>[[[[.,.],[.,[.,.]]],.],.]=>[1,4,3,2,5,6]=>([(3,4),(3,5),(4,5)],6)
[[],[[],[]],[[]]]=>[[[.,.],[[.,.],.]],[.,.]]=>[1,3,4,2,6,5]=>([(1,2),(3,5),(4,5)],6)
[[],[[[]]],[[]]]=>[[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]=>([(1,2),(3,4),(3,5),(4,5)],6)
[[],[[],[],[]],[]]=>[[[.,.],[[[.,.],.],.]],.]=>[1,3,4,5,2,6]=>([(2,5),(3,5),(4,5)],6)
[[],[[],[[]]],[]]=>[[[.,.],[[.,.],[.,.]]],.]=>[1,3,5,4,2,6]=>([(2,5),(3,4),(3,5),(4,5)],6)
[[],[[[]],[]],[]]=>[[[.,.],[[.,[.,.]],.]],.]=>[1,4,3,5,2,6]=>([(2,5),(3,4),(3,5),(4,5)],6)
[[],[[[],[]]],[]]=>[[[.,.],[.,[[.,.],.]]],.]=>[1,4,5,3,2,6]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[],[[[[]]]],[]]=>[[[.,.],[.,[.,[.,.]]]],.]=>[1,5,4,3,2,6]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[],[[],[],[],[]]]=>[[.,.],[[[[.,.],.],.],.]]=>[1,3,4,5,6,2]=>([(1,5),(2,5),(3,5),(4,5)],6)
[[],[[],[],[[]]]]=>[[.,.],[[[.,.],.],[.,.]]]=>[1,3,4,6,5,2]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[],[[],[[]],[]]]=>[[.,.],[[[.,.],[.,.]],.]]=>[1,3,5,4,6,2]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[],[[],[[],[]]]]=>[[.,.],[[.,.],[[.,.],.]]]=>[1,3,5,6,4,2]=>([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[],[[],[[[]]]]]=>[[.,.],[[.,.],[.,[.,.]]]]=>[1,3,6,5,4,2]=>([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[],[[[]],[],[]]]=>[[.,.],[[[.,[.,.]],.],.]]=>[1,4,3,5,6,2]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[],[[[]],[[]]]]=>[[.,.],[[.,[.,.]],[.,.]]]=>[1,4,3,6,5,2]=>([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
[[],[[[],[]],[]]]=>[[.,.],[[.,[[.,.],.]],.]]=>[1,4,5,3,6,2]=>([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[],[[[[]]],[]]]=>[[.,.],[[.,[.,[.,.]]],.]]=>[1,5,4,3,6,2]=>([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[],[[[],[],[]]]]=>[[.,.],[.,[[[.,.],.],.]]]=>[1,4,5,6,3,2]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[],[[[],[[]]]]]=>[[.,.],[.,[[.,.],[.,.]]]]=>[1,4,6,5,3,2]=>([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[],[[[[]],[]]]]=>[[.,.],[.,[[.,[.,.]],.]]]=>[1,5,4,6,3,2]=>([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[],[[[[],[]]]]]=>[[.,.],[.,[.,[[.,.],.]]]]=>[1,5,6,4,3,2]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[],[[[[[]]]]]]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[[]],[],[],[],[]]=>[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>([(4,5)],6)
[[[]],[],[],[[]]]=>[[[[.,[.,.]],.],.],[.,.]]=>[2,1,3,4,6,5]=>([(2,5),(3,4)],6)
[[[]],[],[[]],[]]=>[[[[.,[.,.]],.],[.,.]],.]=>[2,1,3,5,4,6]=>([(2,5),(3,4)],6)
[[[]],[],[[],[]]]=>[[[.,[.,.]],.],[[.,.],.]]=>[2,1,3,5,6,4]=>([(1,2),(3,5),(4,5)],6)
[[[]],[],[[[]]]]=>[[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]=>([(1,2),(3,4),(3,5),(4,5)],6)
[[[]],[[]],[],[]]=>[[[[.,[.,.]],[.,.]],.],.]=>[2,1,4,3,5,6]=>([(2,5),(3,4)],6)
[[[]],[[]],[[]]]=>[[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]=>([(0,5),(1,4),(2,3)],6)
[[[]],[[],[]],[]]=>[[[.,[.,.]],[[.,.],.]],.]=>[2,1,4,5,3,6]=>([(1,2),(3,5),(4,5)],6)
[[[]],[[[]]],[]]=>[[[.,[.,.]],[.,[.,.]]],.]=>[2,1,5,4,3,6]=>([(1,2),(3,4),(3,5),(4,5)],6)
[[[]],[[],[],[]]]=>[[.,[.,.]],[[[.,.],.],.]]=>[2,1,4,5,6,3]=>([(0,1),(2,5),(3,5),(4,5)],6)
[[[]],[[],[[]]]]=>[[.,[.,.]],[[.,.],[.,.]]]=>[2,1,4,6,5,3]=>([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
[[[]],[[[]],[]]]=>[[.,[.,.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3]=>([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
[[[]],[[[],[]]]]=>[[.,[.,.]],[.,[[.,.],.]]]=>[2,1,5,6,4,3]=>([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[[]],[[[[]]]]]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]=>([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[[],[]],[],[],[]]=>[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>([(3,5),(4,5)],6)
[[[[]]],[],[],[]]=>[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>([(3,4),(3,5),(4,5)],6)
[[[],[]],[],[[]]]=>[[[.,[[.,.],.]],.],[.,.]]=>[2,3,1,4,6,5]=>([(1,2),(3,5),(4,5)],6)
[[[[]]],[],[[]]]=>[[[.,[.,[.,.]]],.],[.,.]]=>[3,2,1,4,6,5]=>([(1,2),(3,4),(3,5),(4,5)],6)
[[[],[]],[[]],[]]=>[[[.,[[.,.],.]],[.,.]],.]=>[2,3,1,5,4,6]=>([(1,2),(3,5),(4,5)],6)
[[[[]]],[[]],[]]=>[[[.,[.,[.,.]]],[.,.]],.]=>[3,2,1,5,4,6]=>([(1,2),(3,4),(3,5),(4,5)],6)
[[[],[]],[[],[]]]=>[[.,[[.,.],.]],[[.,.],.]]=>[2,3,1,5,6,4]=>([(0,5),(1,5),(2,4),(3,4)],6)
[[[],[]],[[[]]]]=>[[.,[[.,.],.]],[.,[.,.]]]=>[2,3,1,6,5,4]=>([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
[[[[]]],[[],[]]]=>[[.,[.,[.,.]]],[[.,.],.]]=>[3,2,1,5,6,4]=>([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
[[[[]]],[[[]]]]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]=>([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
[[[],[],[]],[],[]]=>[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>([(2,5),(3,5),(4,5)],6)
[[[],[[]]],[],[]]=>[[[.,[[.,.],[.,.]]],.],.]=>[2,4,3,1,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6)
[[[[]],[]],[],[]]=>[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6)
[[[[],[]]],[],[]]=>[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[[[[]]]],[],[]]=>[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[[],[],[]],[[]]]=>[[.,[[[.,.],.],.]],[.,.]]=>[2,3,4,1,6,5]=>([(0,1),(2,5),(3,5),(4,5)],6)
[[[],[[]]],[[]]]=>[[.,[[.,.],[.,.]]],[.,.]]=>[2,4,3,1,6,5]=>([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
[[[[]],[]],[[]]]=>[[.,[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,6,5]=>([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
[[[[],[]]],[[]]]=>[[.,[.,[[.,.],.]]],[.,.]]=>[3,4,2,1,6,5]=>([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[[[[]]]],[[]]]=>[[.,[.,[.,[.,.]]]],[.,.]]=>[4,3,2,1,6,5]=>([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[[],[],[],[]],[]]=>[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>([(1,5),(2,5),(3,5),(4,5)],6)
[[[],[],[[]]],[]]=>[[.,[[[.,.],.],[.,.]]],.]=>[2,3,5,4,1,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[[],[[]],[]],[]]=>[[.,[[[.,.],[.,.]],.]],.]=>[2,4,3,5,1,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[[],[[],[]]],[]]=>[[.,[[.,.],[[.,.],.]]],.]=>[2,4,5,3,1,6]=>([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[[],[[[]]]],[]]=>[[.,[[.,.],[.,[.,.]]]],.]=>[2,5,4,3,1,6]=>([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[[[]],[],[]],[]]=>[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[[[]],[[]]],[]]=>[[.,[[.,[.,.]],[.,.]]],.]=>[3,2,5,4,1,6]=>([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
[[[[],[]],[]],[]]=>[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[[[[]]],[]],[]]=>[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[[[],[],[]]],[]]=>[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[[[],[[]]]],[]]=>[[.,[.,[[.,.],[.,.]]]],.]=>[3,5,4,2,1,6]=>([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[[[[]],[]]],[]]=>[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[[[[],[]]]],[]]=>[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[[[[[]]]]],[]]=>[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[[],[],[],[],[]]]=>[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
[[[],[],[],[[]]]]=>[.,[[[[.,.],.],.],[.,.]]]=>[2,3,4,6,5,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[[],[],[[]],[]]]=>[.,[[[[.,.],.],[.,.]],.]]=>[2,3,5,4,6,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[[],[],[[],[]]]]=>[.,[[[.,.],.],[[.,.],.]]]=>[2,3,5,6,4,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[[],[],[[[]]]]]=>[.,[[[.,.],.],[.,[.,.]]]]=>[2,3,6,5,4,1]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[[],[[]],[],[]]]=>[.,[[[[.,.],[.,.]],.],.]]=>[2,4,3,5,6,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[[],[[]],[[]]]]=>[.,[[[.,.],[.,.]],[.,.]]]=>[2,4,3,6,5,1]=>([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
[[[],[[],[]],[]]]=>[.,[[[.,.],[[.,.],.]],.]]=>[2,4,5,3,6,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[[],[[[]]],[]]]=>[.,[[[.,.],[.,[.,.]]],.]]=>[2,5,4,3,6,1]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[[],[[],[],[]]]]=>[.,[[.,.],[[[.,.],.],.]]]=>[2,4,5,6,3,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[[],[[],[[]]]]]=>[.,[[.,.],[[.,.],[.,.]]]]=>[2,4,6,5,3,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[[],[[[]],[]]]]=>[.,[[.,.],[[.,[.,.]],.]]]=>[2,5,4,6,3,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[[],[[[],[]]]]]=>[.,[[.,.],[.,[[.,.],.]]]]=>[2,5,6,4,3,1]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[[],[[[[]]]]]]=>[.,[[.,.],[.,[.,[.,.]]]]]=>[2,6,5,4,3,1]=>([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[[[]],[],[],[]]]=>[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[[[]],[],[[]]]]=>[.,[[[.,[.,.]],.],[.,.]]]=>[3,2,4,6,5,1]=>([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
[[[[]],[[]],[]]]=>[.,[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1]=>([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
[[[[]],[[],[]]]]=>[.,[[.,[.,.]],[[.,.],.]]]=>[3,2,5,6,4,1]=>([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[[[]],[[[]]]]]=>[.,[[.,[.,.]],[.,[.,.]]]]=>[3,2,6,5,4,1]=>([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[[[],[]],[],[]]]=>[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[[[[]]],[],[]]]=>[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[[[],[]],[[]]]]=>[.,[[.,[[.,.],.]],[.,.]]]=>[3,4,2,6,5,1]=>([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[[[[]]],[[]]]]=>[.,[[.,[.,[.,.]]],[.,.]]]=>[4,3,2,6,5,1]=>([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[[[],[],[]],[]]]=>[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[[[],[[]]],[]]]=>[.,[[.,[[.,.],[.,.]]],.]]=>[3,5,4,2,6,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[[[[]],[]],[]]]=>[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[[[[],[]]],[]]]=>[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[[[[[]]]],[]]]=>[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[[[],[],[],[]]]]=>[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[[[],[],[[]]]]]=>[.,[.,[[[.,.],.],[.,.]]]]=>[3,4,6,5,2,1]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[[[],[[]],[]]]]=>[.,[.,[[[.,.],[.,.]],.]]]=>[3,5,4,6,2,1]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[[[],[[],[]]]]]=>[.,[.,[[.,.],[[.,.],.]]]]=>[3,5,6,4,2,1]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[[[],[[[]]]]]]=>[.,[.,[[.,.],[.,[.,.]]]]]=>[3,6,5,4,2,1]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[[[[]],[],[]]]]=>[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[[[[]],[[]]]]]=>[.,[.,[[.,[.,.]],[.,.]]]]=>[4,3,6,5,2,1]=>([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[[[[],[]],[]]]]=>[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[[[[[]]],[]]]]=>[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[[[[],[],[]]]]]=>[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[[[[],[[]]]]]]=>[.,[.,[.,[[.,.],[.,.]]]]]=>[4,6,5,3,2,1]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[[[[[]],[]]]]]=>[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[[[[[],[]]]]]]=>[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[[[[[[]]]]]]]=>[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[],[],[],[],[],[],[]]=>[[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>([],7)
[[],[],[],[],[],[[]]]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[1,2,3,4,5,7,6]=>([(5,6)],7)
[[],[],[],[],[[]],[]]=>[[[[[[.,.],.],.],.],[.,.]],.]=>[1,2,3,4,6,5,7]=>([(5,6)],7)
[[],[],[],[],[[],[]]]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[1,2,3,4,6,7,5]=>([(4,6),(5,6)],7)
[[],[],[],[],[[[]]]]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]=>([(4,5),(4,6),(5,6)],7)
[[],[],[],[[]],[],[]]=>[[[[[[.,.],.],.],[.,.]],.],.]=>[1,2,3,5,4,6,7]=>([(5,6)],7)
[[],[],[],[[]],[[]]]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]=>([(3,6),(4,5)],7)
[[],[],[],[[],[]],[]]=>[[[[[.,.],.],.],[[.,.],.]],.]=>[1,2,3,5,6,4,7]=>([(4,6),(5,6)],7)
[[],[],[],[[[]]],[]]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,2,3,6,5,4,7]=>([(4,5),(4,6),(5,6)],7)
[[],[],[],[[],[],[]]]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[1,2,3,5,6,7,4]=>([(3,6),(4,6),(5,6)],7)
[[],[],[],[[],[[]]]]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,2,3,5,7,6,4]=>([(3,6),(4,5),(4,6),(5,6)],7)
[[],[],[],[[[]],[]]]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,2,3,6,5,7,4]=>([(3,6),(4,5),(4,6),(5,6)],7)
[[],[],[],[[[],[]]]]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,2,3,6,7,5,4]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[],[],[[[[]]]]]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]=>([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[],[[]],[],[],[]]=>[[[[[[.,.],.],[.,.]],.],.],.]=>[1,2,4,3,5,6,7]=>([(5,6)],7)
[[],[],[[]],[],[[]]]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,2,4,3,5,7,6]=>([(3,6),(4,5)],7)
[[],[],[[]],[[]],[]]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,2,4,3,6,5,7]=>([(3,6),(4,5)],7)
[[],[],[[]],[[],[]]]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,2,4,3,6,7,5]=>([(2,3),(4,6),(5,6)],7)
[[],[],[[]],[[[]]]]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]=>([(2,3),(4,5),(4,6),(5,6)],7)
[[],[],[[],[]],[],[]]=>[[[[[.,.],.],[[.,.],.]],.],.]=>[1,2,4,5,3,6,7]=>([(4,6),(5,6)],7)
[[],[],[[[]]],[],[]]=>[[[[[.,.],.],[.,[.,.]]],.],.]=>[1,2,5,4,3,6,7]=>([(4,5),(4,6),(5,6)],7)
[[],[],[[],[]],[[]]]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,2,4,5,3,7,6]=>([(2,3),(4,6),(5,6)],7)
[[],[],[[[]]],[[]]]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,2,5,4,3,7,6]=>([(2,3),(4,5),(4,6),(5,6)],7)
[[],[],[[],[],[]],[]]=>[[[[.,.],.],[[[.,.],.],.]],.]=>[1,2,4,5,6,3,7]=>([(3,6),(4,6),(5,6)],7)
[[],[],[[],[[]]],[]]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,2,4,6,5,3,7]=>([(3,6),(4,5),(4,6),(5,6)],7)
[[],[],[[[]],[]],[]]=>[[[[.,.],.],[[.,[.,.]],.]],.]=>[1,2,5,4,6,3,7]=>([(3,6),(4,5),(4,6),(5,6)],7)
[[],[],[[[],[]]],[]]=>[[[[.,.],.],[.,[[.,.],.]]],.]=>[1,2,5,6,4,3,7]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[],[[[[]]]],[]]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,2,6,5,4,3,7]=>([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[],[[],[],[],[]]]=>[[[.,.],.],[[[[.,.],.],.],.]]=>[1,2,4,5,6,7,3]=>([(2,6),(3,6),(4,6),(5,6)],7)
[[],[],[[],[],[[]]]]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,2,4,5,7,6,3]=>([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[],[],[[],[[]],[]]]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,2,4,6,5,7,3]=>([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[],[],[[],[[],[]]]]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,2,4,6,7,5,3]=>([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[],[[],[[[]]]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,2,4,7,6,5,3]=>([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[],[[[]],[],[]]]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,2,5,4,6,7,3]=>([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[],[],[[[]],[[]]]]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,2,5,4,7,6,3]=>([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
[[],[],[[[],[]],[]]]=>[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,2,5,6,4,7,3]=>([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[],[[[[]]],[]]]=>[[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,2,6,5,4,7,3]=>([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[],[[[],[],[]]]]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[1,2,5,6,7,4,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[],[[[],[[]]]]]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,2,5,7,6,4,3]=>([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[],[[[[]],[]]]]=>[[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,2,6,5,7,4,3]=>([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[],[[[[],[]]]]]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,2,6,7,5,4,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[],[[[[[]]]]]]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]=>([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[]],[],[],[],[]]=>[[[[[[.,.],[.,.]],.],.],.],.]=>[1,3,2,4,5,6,7]=>([(5,6)],7)
[[],[[]],[],[],[[]]]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,3,2,4,5,7,6]=>([(3,6),(4,5)],7)
[[],[[]],[],[[]],[]]=>[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,3,2,4,6,5,7]=>([(3,6),(4,5)],7)
[[],[[]],[],[[],[]]]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,3,2,4,6,7,5]=>([(2,3),(4,6),(5,6)],7)
[[],[[]],[],[[[]]]]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5]=>([(2,3),(4,5),(4,6),(5,6)],7)
[[],[[]],[[]],[],[]]=>[[[[[.,.],[.,.]],[.,.]],.],.]=>[1,3,2,5,4,6,7]=>([(3,6),(4,5)],7)
[[],[[]],[[]],[[]]]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]=>([(1,6),(2,5),(3,4)],7)
[[],[[]],[[],[]],[]]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,3,2,5,6,4,7]=>([(2,3),(4,6),(5,6)],7)
[[],[[]],[[[]]],[]]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,3,2,6,5,4,7]=>([(2,3),(4,5),(4,6),(5,6)],7)
[[],[[]],[[],[],[]]]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,3,2,5,6,7,4]=>([(1,2),(3,6),(4,6),(5,6)],7)
[[],[[]],[[],[[]]]]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,3,2,5,7,6,4]=>([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[]],[[[]],[]]]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,3,2,6,5,7,4]=>([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[]],[[[],[]]]]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,3,2,6,7,5,4]=>([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[]],[[[[]]]]]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]=>([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[],[]],[],[],[]]=>[[[[[.,.],[[.,.],.]],.],.],.]=>[1,3,4,2,5,6,7]=>([(4,6),(5,6)],7)
[[],[[[]]],[],[],[]]=>[[[[[.,.],[.,[.,.]]],.],.],.]=>[1,4,3,2,5,6,7]=>([(4,5),(4,6),(5,6)],7)
[[],[[],[]],[],[[]]]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,3,4,2,5,7,6]=>([(2,3),(4,6),(5,6)],7)
[[],[[[]]],[],[[]]]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,4,3,2,5,7,6]=>([(2,3),(4,5),(4,6),(5,6)],7)
[[],[[],[]],[[]],[]]=>[[[[.,.],[[.,.],.]],[.,.]],.]=>[1,3,4,2,6,5,7]=>([(2,3),(4,6),(5,6)],7)
[[],[[[]]],[[]],[]]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,4,3,2,6,5,7]=>([(2,3),(4,5),(4,6),(5,6)],7)
[[],[[],[]],[[],[]]]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,3,4,2,6,7,5]=>([(1,6),(2,6),(3,5),(4,5)],7)
[[],[[],[]],[[[]]]]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,3,4,2,7,6,5]=>([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
[[],[[[]]],[[],[]]]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,4,3,2,6,7,5]=>([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
[[],[[[]]],[[[]]]]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]=>([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7)
[[],[[],[],[]],[],[]]=>[[[[.,.],[[[.,.],.],.]],.],.]=>[1,3,4,5,2,6,7]=>([(3,6),(4,6),(5,6)],7)
[[],[[],[[]]],[],[]]=>[[[[.,.],[[.,.],[.,.]]],.],.]=>[1,3,5,4,2,6,7]=>([(3,6),(4,5),(4,6),(5,6)],7)
[[],[[[]],[]],[],[]]=>[[[[.,.],[[.,[.,.]],.]],.],.]=>[1,4,3,5,2,6,7]=>([(3,6),(4,5),(4,6),(5,6)],7)
[[],[[[],[]]],[],[]]=>[[[[.,.],[.,[[.,.],.]]],.],.]=>[1,4,5,3,2,6,7]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[[[]]]],[],[]]=>[[[[.,.],[.,[.,[.,.]]]],.],.]=>[1,5,4,3,2,6,7]=>([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[],[],[]],[[]]]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,3,4,5,2,7,6]=>([(1,2),(3,6),(4,6),(5,6)],7)
[[],[[],[[]]],[[]]]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,3,5,4,2,7,6]=>([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[[]],[]],[[]]]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,4,3,5,2,7,6]=>([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[[],[]]],[[]]]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,4,5,3,2,7,6]=>([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[[[]]]],[[]]]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,5,4,3,2,7,6]=>([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[],[],[],[]],[]]=>[[[.,.],[[[[.,.],.],.],.]],.]=>[1,3,4,5,6,2,7]=>([(2,6),(3,6),(4,6),(5,6)],7)
[[],[[],[],[[]]],[]]=>[[[.,.],[[[.,.],.],[.,.]]],.]=>[1,3,4,6,5,2,7]=>([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[],[[]],[]],[]]=>[[[.,.],[[[.,.],[.,.]],.]],.]=>[1,3,5,4,6,2,7]=>([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[],[[],[]]],[]]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[1,3,5,6,4,2,7]=>([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[],[[[]]]],[]]=>[[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,3,6,5,4,2,7]=>([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[[]],[],[]],[]]=>[[[.,.],[[[.,[.,.]],.],.]],.]=>[1,4,3,5,6,2,7]=>([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[[]],[[]]],[]]=>[[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,4,3,6,5,2,7]=>([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
[[],[[[],[]],[]],[]]=>[[[.,.],[[.,[[.,.],.]],.]],.]=>[1,4,5,3,6,2,7]=>([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[[[]]],[]],[]]=>[[[.,.],[[.,[.,[.,.]]],.]],.]=>[1,5,4,3,6,2,7]=>([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[[],[],[]]],[]]=>[[[.,.],[.,[[[.,.],.],.]]],.]=>[1,4,5,6,3,2,7]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[[],[[]]]],[]]=>[[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,4,6,5,3,2,7]=>([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[[[]],[]]],[]]=>[[[.,.],[.,[[.,[.,.]],.]]],.]=>[1,5,4,6,3,2,7]=>([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[[[],[]]]],[]]=>[[[.,.],[.,[.,[[.,.],.]]]],.]=>[1,5,6,4,3,2,7]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[[[[]]]]],[]]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[1,6,5,4,3,2,7]=>([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[],[],[],[],[]]]=>[[.,.],[[[[[.,.],.],.],.],.]]=>[1,3,4,5,6,7,2]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
[[],[[],[],[],[[]]]]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,3,4,5,7,6,2]=>([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[],[],[[]],[]]]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,3,4,6,5,7,2]=>([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[],[],[[],[]]]]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,3,4,6,7,5,2]=>([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[],[],[[[]]]]]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,3,4,7,6,5,2]=>([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[],[[]],[],[]]]=>[[.,.],[[[[.,.],[.,.]],.],.]]=>[1,3,5,4,6,7,2]=>([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[],[[]],[[]]]]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,3,5,4,7,6,2]=>([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
[[],[[],[[],[]],[]]]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,3,5,6,4,7,2]=>([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[],[[[]]],[]]]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,3,6,5,4,7,2]=>([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[],[[],[],[]]]]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,3,5,6,7,4,2]=>([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[],[[],[[]]]]]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,3,5,7,6,4,2]=>([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[],[[[]],[]]]]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,3,6,5,7,4,2]=>([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[],[[[],[]]]]]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,3,6,7,5,4,2]=>([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[],[[[[]]]]]]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,3,7,6,5,4,2]=>([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[[]],[],[],[]]]=>[[.,.],[[[[.,[.,.]],.],.],.]]=>[1,4,3,5,6,7,2]=>([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[[]],[],[[]]]]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,4,3,5,7,6,2]=>([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
[[],[[[]],[[]],[]]]=>[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,4,3,6,5,7,2]=>([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
[[],[[[]],[[],[]]]]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,4,3,6,7,5,2]=>([(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[[]],[[[]]]]]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,4,3,7,6,5,2]=>([(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[[],[]],[],[]]]=>[[.,.],[[[.,[[.,.],.]],.],.]]=>[1,4,5,3,6,7,2]=>([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[[[]]],[],[]]]=>[[.,.],[[[.,[.,[.,.]]],.],.]]=>[1,5,4,3,6,7,2]=>([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[[],[]],[[]]]]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,4,5,3,7,6,2]=>([(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[[[]]],[[]]]]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,5,4,3,7,6,2]=>([(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[[],[],[]],[]]]=>[[.,.],[[.,[[[.,.],.],.]],.]]=>[1,4,5,6,3,7,2]=>([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[[],[[]]],[]]]=>[[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,4,6,5,3,7,2]=>([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[[[]],[]],[]]]=>[[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,5,4,6,3,7,2]=>([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[[[],[]]],[]]]=>[[.,.],[[.,[.,[[.,.],.]]],.]]=>[1,5,6,4,3,7,2]=>([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[[[[]]]],[]]]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,6,5,4,3,7,2]=>([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[[],[],[],[]]]]=>[[.,.],[.,[[[[.,.],.],.],.]]]=>[1,4,5,6,7,3,2]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[[],[],[[]]]]]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,4,5,7,6,3,2]=>([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[[],[[]],[]]]]=>[[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,4,6,5,7,3,2]=>([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[[],[[],[]]]]]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,4,6,7,5,3,2]=>([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[[],[[[]]]]]]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,4,7,6,5,3,2]=>([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[[[]],[],[]]]]=>[[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,5,4,6,7,3,2]=>([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[[[]],[[]]]]]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,5,4,7,6,3,2]=>([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[[[],[]],[]]]]=>[[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,5,6,4,7,3,2]=>([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[[[[]]],[]]]]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,6,5,4,7,3,2]=>([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[[[],[],[]]]]]=>[[.,.],[.,[.,[[[.,.],.],.]]]]=>[1,5,6,7,4,3,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[[[],[[]]]]]]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,5,7,6,4,3,2]=>([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[[[[]],[]]]]]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[1,6,5,7,4,3,2]=>([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[[[[],[]]]]]]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[1,6,7,5,4,3,2]=>([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[[[[[[]]]]]]]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,7,6,5,4,3,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[]],[],[],[],[],[]]=>[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>([(5,6)],7)
[[[]],[],[],[],[[]]]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>[2,1,3,4,5,7,6]=>([(3,6),(4,5)],7)
[[[]],[],[],[[]],[]]=>[[[[[.,[.,.]],.],.],[.,.]],.]=>[2,1,3,4,6,5,7]=>([(3,6),(4,5)],7)
[[[]],[],[],[[],[]]]=>[[[[.,[.,.]],.],.],[[.,.],.]]=>[2,1,3,4,6,7,5]=>([(2,3),(4,6),(5,6)],7)
[[[]],[],[],[[[]]]]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[2,1,3,4,7,6,5]=>([(2,3),(4,5),(4,6),(5,6)],7)
[[[]],[],[[]],[],[]]=>[[[[[.,[.,.]],.],[.,.]],.],.]=>[2,1,3,5,4,6,7]=>([(3,6),(4,5)],7)
[[[]],[],[[]],[[]]]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[2,1,3,5,4,7,6]=>([(1,6),(2,5),(3,4)],7)
[[[]],[],[[],[]],[]]=>[[[[.,[.,.]],.],[[.,.],.]],.]=>[2,1,3,5,6,4,7]=>([(2,3),(4,6),(5,6)],7)
[[[]],[],[[[]]],[]]=>[[[[.,[.,.]],.],[.,[.,.]]],.]=>[2,1,3,6,5,4,7]=>([(2,3),(4,5),(4,6),(5,6)],7)
[[[]],[],[[],[],[]]]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[2,1,3,5,6,7,4]=>([(1,2),(3,6),(4,6),(5,6)],7)
[[[]],[],[[],[[]]]]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[2,1,3,5,7,6,4]=>([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
[[[]],[],[[[]],[]]]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[2,1,3,6,5,7,4]=>([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
[[[]],[],[[[],[]]]]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[2,1,3,6,7,5,4]=>([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[]],[],[[[[]]]]]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[2,1,3,7,6,5,4]=>([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[]],[[]],[],[],[]]=>[[[[[.,[.,.]],[.,.]],.],.],.]=>[2,1,4,3,5,6,7]=>([(3,6),(4,5)],7)
[[[]],[[]],[],[[]]]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[2,1,4,3,5,7,6]=>([(1,6),(2,5),(3,4)],7)
[[[]],[[]],[[]],[]]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>[2,1,4,3,6,5,7]=>([(1,6),(2,5),(3,4)],7)
[[[]],[[]],[[],[]]]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[2,1,4,3,6,7,5]=>([(0,3),(1,2),(4,6),(5,6)],7)
[[[]],[[]],[[[]]]]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]=>([(0,3),(1,2),(4,5),(4,6),(5,6)],7)
[[[]],[[],[]],[],[]]=>[[[[.,[.,.]],[[.,.],.]],.],.]=>[2,1,4,5,3,6,7]=>([(2,3),(4,6),(5,6)],7)
[[[]],[[[]]],[],[]]=>[[[[.,[.,.]],[.,[.,.]]],.],.]=>[2,1,5,4,3,6,7]=>([(2,3),(4,5),(4,6),(5,6)],7)
[[[]],[[],[]],[[]]]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[2,1,4,5,3,7,6]=>([(0,3),(1,2),(4,6),(5,6)],7)
[[[]],[[[]]],[[]]]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[2,1,5,4,3,7,6]=>([(0,3),(1,2),(4,5),(4,6),(5,6)],7)
[[[]],[[],[],[]],[]]=>[[[.,[.,.]],[[[.,.],.],.]],.]=>[2,1,4,5,6,3,7]=>([(1,2),(3,6),(4,6),(5,6)],7)
[[[]],[[],[[]]],[]]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[2,1,4,6,5,3,7]=>([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
[[[]],[[[]],[]],[]]=>[[[.,[.,.]],[[.,[.,.]],.]],.]=>[2,1,5,4,6,3,7]=>([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
[[[]],[[[],[]]],[]]=>[[[.,[.,.]],[.,[[.,.],.]]],.]=>[2,1,5,6,4,3,7]=>([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[]],[[[[]]]],[]]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[2,1,6,5,4,3,7]=>([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[]],[[],[],[],[]]]=>[[.,[.,.]],[[[[.,.],.],.],.]]=>[2,1,4,5,6,7,3]=>([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
[[[]],[[],[],[[]]]]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[2,1,4,5,7,6,3]=>([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[[]],[[],[[]],[]]]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[2,1,4,6,5,7,3]=>([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[[]],[[],[[],[]]]]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[2,1,4,6,7,5,3]=>([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[]],[[],[[[]]]]]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[2,1,4,7,6,5,3]=>([(0,1),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[]],[[[]],[],[]]]=>[[.,[.,.]],[[[.,[.,.]],.],.]]=>[2,1,5,4,6,7,3]=>([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[[]],[[[]],[[]]]]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[2,1,5,4,7,6,3]=>([(0,1),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
[[[]],[[[],[]],[]]]=>[[.,[.,.]],[[.,[[.,.],.]],.]]=>[2,1,5,6,4,7,3]=>([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[]],[[[[]]],[]]]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[2,1,6,5,4,7,3]=>([(0,1),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[]],[[[],[],[]]]]=>[[.,[.,.]],[.,[[[.,.],.],.]]]=>[2,1,5,6,7,4,3]=>([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[]],[[[],[[]]]]]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[2,1,5,7,6,4,3]=>([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[]],[[[[]],[]]]]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[2,1,6,5,7,4,3]=>([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[]],[[[[],[]]]]]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[2,1,6,7,5,4,3]=>([(0,1),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[]],[[[[[]]]]]]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]=>([(0,1),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[]],[],[],[],[]]=>[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>([(4,6),(5,6)],7)
[[[[]]],[],[],[],[]]=>[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>([(4,5),(4,6),(5,6)],7)
[[[],[]],[],[],[[]]]=>[[[[.,[[.,.],.]],.],.],[.,.]]=>[2,3,1,4,5,7,6]=>([(2,3),(4,6),(5,6)],7)
[[[[]]],[],[],[[]]]=>[[[[.,[.,[.,.]]],.],.],[.,.]]=>[3,2,1,4,5,7,6]=>([(2,3),(4,5),(4,6),(5,6)],7)
[[[],[]],[],[[]],[]]=>[[[[.,[[.,.],.]],.],[.,.]],.]=>[2,3,1,4,6,5,7]=>([(2,3),(4,6),(5,6)],7)
[[[[]]],[],[[]],[]]=>[[[[.,[.,[.,.]]],.],[.,.]],.]=>[3,2,1,4,6,5,7]=>([(2,3),(4,5),(4,6),(5,6)],7)
[[[],[]],[],[[],[]]]=>[[[.,[[.,.],.]],.],[[.,.],.]]=>[2,3,1,4,6,7,5]=>([(1,6),(2,6),(3,5),(4,5)],7)
[[[],[]],[],[[[]]]]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>[2,3,1,4,7,6,5]=>([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
[[[[]]],[],[[],[]]]=>[[[.,[.,[.,.]]],.],[[.,.],.]]=>[3,2,1,4,6,7,5]=>([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
[[[[]]],[],[[[]]]]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[3,2,1,4,7,6,5]=>([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7)
[[[],[]],[[]],[],[]]=>[[[[.,[[.,.],.]],[.,.]],.],.]=>[2,3,1,5,4,6,7]=>([(2,3),(4,6),(5,6)],7)
[[[[]]],[[]],[],[]]=>[[[[.,[.,[.,.]]],[.,.]],.],.]=>[3,2,1,5,4,6,7]=>([(2,3),(4,5),(4,6),(5,6)],7)
[[[],[]],[[]],[[]]]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[2,3,1,5,4,7,6]=>([(0,3),(1,2),(4,6),(5,6)],7)
[[[[]]],[[]],[[]]]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[3,2,1,5,4,7,6]=>([(0,3),(1,2),(4,5),(4,6),(5,6)],7)
[[[],[]],[[],[]],[]]=>[[[.,[[.,.],.]],[[.,.],.]],.]=>[2,3,1,5,6,4,7]=>([(1,6),(2,6),(3,5),(4,5)],7)
[[[],[]],[[[]]],[]]=>[[[.,[[.,.],.]],[.,[.,.]]],.]=>[2,3,1,6,5,4,7]=>([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
[[[[]]],[[],[]],[]]=>[[[.,[.,[.,.]]],[[.,.],.]],.]=>[3,2,1,5,6,4,7]=>([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
[[[[]]],[[[]]],[]]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[3,2,1,6,5,4,7]=>([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7)
[[[],[]],[[],[],[]]]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[2,3,1,5,6,7,4]=>([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
[[[],[]],[[],[[]]]]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[2,3,1,5,7,6,4]=>([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
[[[],[]],[[[]],[]]]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[2,3,1,6,5,7,4]=>([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
[[[],[]],[[[],[]]]]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[2,3,1,6,7,5,4]=>([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7)
[[[],[]],[[[[]]]]]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[2,3,1,7,6,5,4]=>([(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[]]],[[],[],[]]]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[3,2,1,5,6,7,4]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7)
[[[[]]],[[],[[]]]]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[3,2,1,5,7,6,4]=>([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
[[[[]]],[[[]],[]]]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[3,2,1,6,5,7,4]=>([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
[[[[]]],[[[],[]]]]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[3,2,1,6,7,5,4]=>([(0,1),(0,2),(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[]]],[[[[]]]]]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]=>([(0,1),(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[],[]],[],[],[]]=>[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>([(3,6),(4,6),(5,6)],7)
[[[],[[]]],[],[],[]]=>[[[[.,[[.,.],[.,.]]],.],.],.]=>[2,4,3,1,5,6,7]=>([(3,6),(4,5),(4,6),(5,6)],7)
[[[[]],[]],[],[],[]]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>([(3,6),(4,5),(4,6),(5,6)],7)
[[[[],[]]],[],[],[]]=>[[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[]]]],[],[],[]]=>[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[],[]],[],[[]]]=>[[[.,[[[.,.],.],.]],.],[.,.]]=>[2,3,4,1,5,7,6]=>([(1,2),(3,6),(4,6),(5,6)],7)
[[[],[[]]],[],[[]]]=>[[[.,[[.,.],[.,.]]],.],[.,.]]=>[2,4,3,1,5,7,6]=>([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
[[[[]],[]],[],[[]]]=>[[[.,[[.,[.,.]],.]],.],[.,.]]=>[3,2,4,1,5,7,6]=>([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
[[[[],[]]],[],[[]]]=>[[[.,[.,[[.,.],.]]],.],[.,.]]=>[3,4,2,1,5,7,6]=>([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[]]]],[],[[]]]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[4,3,2,1,5,7,6]=>([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[],[]],[[]],[]]=>[[[.,[[[.,.],.],.]],[.,.]],.]=>[2,3,4,1,6,5,7]=>([(1,2),(3,6),(4,6),(5,6)],7)
[[[],[[]]],[[]],[]]=>[[[.,[[.,.],[.,.]]],[.,.]],.]=>[2,4,3,1,6,5,7]=>([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
[[[[]],[]],[[]],[]]=>[[[.,[[.,[.,.]],.]],[.,.]],.]=>[3,2,4,1,6,5,7]=>([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
[[[[],[]]],[[]],[]]=>[[[.,[.,[[.,.],.]]],[.,.]],.]=>[3,4,2,1,6,5,7]=>([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[]]]],[[]],[]]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[4,3,2,1,6,5,7]=>([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[],[]],[[],[]]]=>[[.,[[[.,.],.],.]],[[.,.],.]]=>[2,3,4,1,6,7,5]=>([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
[[[],[],[]],[[[]]]]=>[[.,[[[.,.],.],.]],[.,[.,.]]]=>[2,3,4,1,7,6,5]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7)
[[[],[[]]],[[],[]]]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[2,4,3,1,6,7,5]=>([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
[[[],[[]]],[[[]]]]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[2,4,3,1,7,6,5]=>([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
[[[[]],[]],[[],[]]]=>[[.,[[.,[.,.]],.]],[[.,.],.]]=>[3,2,4,1,6,7,5]=>([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
[[[[]],[]],[[[]]]]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[3,2,4,1,7,6,5]=>([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
[[[[],[]]],[[],[]]]=>[[.,[.,[[.,.],.]]],[[.,.],.]]=>[3,4,2,1,6,7,5]=>([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7)
[[[[],[]]],[[[]]]]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[3,4,2,1,7,6,5]=>([(0,1),(0,2),(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[]]]],[[],[]]]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[4,3,2,1,6,7,5]=>([(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[]]]],[[[]]]]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[4,3,2,1,7,6,5]=>([(0,1),(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[],[],[]],[],[]]=>[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>([(2,6),(3,6),(4,6),(5,6)],7)
[[[],[],[[]]],[],[]]=>[[[.,[[[.,.],.],[.,.]]],.],.]=>[2,3,5,4,1,6,7]=>([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[[]],[]],[],[]]=>[[[.,[[[.,.],[.,.]],.]],.],.]=>[2,4,3,5,1,6,7]=>([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[[],[]]],[],[]]=>[[[.,[[.,.],[[.,.],.]]],.],.]=>[2,4,5,3,1,6,7]=>([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[[[]]]],[],[]]=>[[[.,[[.,.],[.,[.,.]]]],.],.]=>[2,5,4,3,1,6,7]=>([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[]],[],[]],[],[]]=>[[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[[[]],[[]]],[],[]]=>[[[.,[[.,[.,.]],[.,.]]],.],.]=>[3,2,5,4,1,6,7]=>([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
[[[[],[]],[]],[],[]]=>[[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[]]],[]],[],[]]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[],[],[]]],[],[]]=>[[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[],[[]]]],[],[]]=>[[[.,[.,[[.,.],[.,.]]]],.],.]=>[3,5,4,2,1,6,7]=>([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[]],[]]],[],[]]=>[[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[],[]]]],[],[]]=>[[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[[]]]]],[],[]]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[],[],[]],[[]]]=>[[.,[[[[.,.],.],.],.]],[.,.]]=>[2,3,4,5,1,7,6]=>([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
[[[],[],[[]]],[[]]]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>[2,3,5,4,1,7,6]=>([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[[]],[]],[[]]]=>[[.,[[[.,.],[.,.]],.]],[.,.]]=>[2,4,3,5,1,7,6]=>([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[[],[]]],[[]]]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>[2,4,5,3,1,7,6]=>([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[[[]]]],[[]]]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[2,5,4,3,1,7,6]=>([(0,1),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[]],[],[]],[[]]]=>[[.,[[[.,[.,.]],.],.]],[.,.]]=>[3,2,4,5,1,7,6]=>([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[[[]],[[]]],[[]]]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[3,2,5,4,1,7,6]=>([(0,1),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
[[[[],[]],[]],[[]]]=>[[.,[[.,[[.,.],.]],.]],[.,.]]=>[3,4,2,5,1,7,6]=>([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[]]],[]],[[]]]=>[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[4,3,2,5,1,7,6]=>([(0,1),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[],[],[]]],[[]]]=>[[.,[.,[[[.,.],.],.]]],[.,.]]=>[3,4,5,2,1,7,6]=>([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[],[[]]]],[[]]]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[3,5,4,2,1,7,6]=>([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[]],[]]],[[]]]=>[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[4,3,5,2,1,7,6]=>([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[],[]]]],[[]]]=>[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[4,5,3,2,1,7,6]=>([(0,1),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[[]]]]],[[]]]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[5,4,3,2,1,7,6]=>([(0,1),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[],[],[],[]],[]]=>[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
[[[],[],[],[[]]],[]]=>[[.,[[[[.,.],.],.],[.,.]]],.]=>[2,3,4,6,5,1,7]=>([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[],[[]],[]],[]]=>[[.,[[[[.,.],.],[.,.]],.]],.]=>[2,3,5,4,6,1,7]=>([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[],[[],[]]],[]]=>[[.,[[[.,.],.],[[.,.],.]]],.]=>[2,3,5,6,4,1,7]=>([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[],[[[]]]],[]]=>[[.,[[[.,.],.],[.,[.,.]]]],.]=>[2,3,6,5,4,1,7]=>([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[[]],[],[]],[]]=>[[.,[[[[.,.],[.,.]],.],.]],.]=>[2,4,3,5,6,1,7]=>([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[[]],[[]]],[]]=>[[.,[[[.,.],[.,.]],[.,.]]],.]=>[2,4,3,6,5,1,7]=>([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
[[[],[[],[]],[]],[]]=>[[.,[[[.,.],[[.,.],.]],.]],.]=>[2,4,5,3,6,1,7]=>([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[[[]]],[]],[]]=>[[.,[[[.,.],[.,[.,.]]],.]],.]=>[2,5,4,3,6,1,7]=>([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[[],[],[]]],[]]=>[[.,[[.,.],[[[.,.],.],.]]],.]=>[2,4,5,6,3,1,7]=>([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[[],[[]]]],[]]=>[[.,[[.,.],[[.,.],[.,.]]]],.]=>[2,4,6,5,3,1,7]=>([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[[[]],[]]],[]]=>[[.,[[.,.],[[.,[.,.]],.]]],.]=>[2,5,4,6,3,1,7]=>([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[[[],[]]]],[]]=>[[.,[[.,.],[.,[[.,.],.]]]],.]=>[2,5,6,4,3,1,7]=>([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[[[[]]]]],[]]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[2,6,5,4,3,1,7]=>([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[]],[],[],[]],[]]=>[[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[[[]],[],[[]]],[]]=>[[.,[[[.,[.,.]],.],[.,.]]],.]=>[3,2,4,6,5,1,7]=>([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
[[[[]],[[]],[]],[]]=>[[.,[[[.,[.,.]],[.,.]],.]],.]=>[3,2,5,4,6,1,7]=>([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
[[[[]],[[],[]]],[]]=>[[.,[[.,[.,.]],[[.,.],.]]],.]=>[3,2,5,6,4,1,7]=>([(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[]],[[[]]]],[]]=>[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[3,2,6,5,4,1,7]=>([(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[],[]],[],[]],[]]=>[[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[]]],[],[]],[]]=>[[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[],[]],[[]]],[]]=>[[.,[[.,[[.,.],.]],[.,.]]],.]=>[3,4,2,6,5,1,7]=>([(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[]]],[[]]],[]]=>[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[4,3,2,6,5,1,7]=>([(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[],[],[]],[]],[]]=>[[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[],[[]]],[]],[]]=>[[.,[[.,[[.,.],[.,.]]],.]],.]=>[3,5,4,2,6,1,7]=>([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[]],[]],[]],[]]=>[[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[],[]]],[]],[]]=>[[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[[]]]],[]],[]]=>[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[],[],[],[]]],[]]=>[[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[],[],[[]]]],[]]=>[[.,[.,[[[.,.],.],[.,.]]]],.]=>[3,4,6,5,2,1,7]=>([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[],[[]],[]]],[]]=>[[.,[.,[[[.,.],[.,.]],.]]],.]=>[3,5,4,6,2,1,7]=>([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[],[[],[]]]],[]]=>[[.,[.,[[.,.],[[.,.],.]]]],.]=>[3,5,6,4,2,1,7]=>([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[],[[[]]]]],[]]=>[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[3,6,5,4,2,1,7]=>([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[]],[],[]]],[]]=>[[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[]],[[]]]],[]]=>[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[4,3,6,5,2,1,7]=>([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[],[]],[]]],[]]=>[[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[[]]],[]]],[]]=>[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[],[],[]]]],[]]=>[[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[],[[]]]]],[]]=>[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[4,6,5,3,2,1,7]=>([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[[]],[]]]],[]]=>[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[[],[]]]]],[]]=>[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[[[]]]]]],[]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[],[],[],[],[]]]=>[.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
[[[],[],[],[],[[]]]]=>[.,[[[[[.,.],.],.],.],[.,.]]]=>[2,3,4,5,7,6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[],[],[[]],[]]]=>[.,[[[[[.,.],.],.],[.,.]],.]]=>[2,3,4,6,5,7,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[],[],[[],[]]]]=>[.,[[[[.,.],.],.],[[.,.],.]]]=>[2,3,4,6,7,5,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[],[],[[[]]]]]=>[.,[[[[.,.],.],.],[.,[.,.]]]]=>[2,3,4,7,6,5,1]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[],[[]],[],[]]]=>[.,[[[[[.,.],.],[.,.]],.],.]]=>[2,3,5,4,6,7,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[],[[]],[[]]]]=>[.,[[[[.,.],.],[.,.]],[.,.]]]=>[2,3,5,4,7,6,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
[[[],[],[[],[]],[]]]=>[.,[[[[.,.],.],[[.,.],.]],.]]=>[2,3,5,6,4,7,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[],[[[]]],[]]]=>[.,[[[[.,.],.],[.,[.,.]]],.]]=>[2,3,6,5,4,7,1]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[],[[],[],[]]]]=>[.,[[[.,.],.],[[[.,.],.],.]]]=>[2,3,5,6,7,4,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[],[[],[[]]]]]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[2,3,5,7,6,4,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[],[[[]],[]]]]=>[.,[[[.,.],.],[[.,[.,.]],.]]]=>[2,3,6,5,7,4,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[],[[[],[]]]]]=>[.,[[[.,.],.],[.,[[.,.],.]]]]=>[2,3,6,7,5,4,1]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[],[[[[]]]]]]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[2,3,7,6,5,4,1]=>([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[[]],[],[],[]]]=>[.,[[[[[.,.],[.,.]],.],.],.]]=>[2,4,3,5,6,7,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[[]],[],[[]]]]=>[.,[[[[.,.],[.,.]],.],[.,.]]]=>[2,4,3,5,7,6,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
[[[],[[]],[[]],[]]]=>[.,[[[[.,.],[.,.]],[.,.]],.]]=>[2,4,3,6,5,7,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
[[[],[[]],[[],[]]]]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[2,4,3,6,7,5,1]=>([(0,6),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[[]],[[[]]]]]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[2,4,3,7,6,5,1]=>([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[[],[]],[],[]]]=>[.,[[[[.,.],[[.,.],.]],.],.]]=>[2,4,5,3,6,7,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[[[]]],[],[]]]=>[.,[[[[.,.],[.,[.,.]]],.],.]]=>[2,5,4,3,6,7,1]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[[],[]],[[]]]]=>[.,[[[.,.],[[.,.],.]],[.,.]]]=>[2,4,5,3,7,6,1]=>([(0,6),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[[[]]],[[]]]]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[2,5,4,3,7,6,1]=>([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[[],[],[]],[]]]=>[.,[[[.,.],[[[.,.],.],.]],.]]=>[2,4,5,6,3,7,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[[],[[]]],[]]]=>[.,[[[.,.],[[.,.],[.,.]]],.]]=>[2,4,6,5,3,7,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[[[]],[]],[]]]=>[.,[[[.,.],[[.,[.,.]],.]],.]]=>[2,5,4,6,3,7,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[[[],[]]],[]]]=>[.,[[[.,.],[.,[[.,.],.]]],.]]=>[2,5,6,4,3,7,1]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[[[[]]]],[]]]=>[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[2,6,5,4,3,7,1]=>([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[[],[],[],[]]]]=>[.,[[.,.],[[[[.,.],.],.],.]]]=>[2,4,5,6,7,3,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[[],[],[[]]]]]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>[2,4,5,7,6,3,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[[],[[]],[]]]]=>[.,[[.,.],[[[.,.],[.,.]],.]]]=>[2,4,6,5,7,3,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[[],[[],[]]]]]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>[2,4,6,7,5,3,1]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[[],[[[]]]]]]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[2,4,7,6,5,3,1]=>([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[[[]],[],[]]]]=>[.,[[.,.],[[[.,[.,.]],.],.]]]=>[2,5,4,6,7,3,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[[[]],[[]]]]]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[2,5,4,7,6,3,1]=>([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[[[],[]],[]]]]=>[.,[[.,.],[[.,[[.,.],.]],.]]]=>[2,5,6,4,7,3,1]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[[[[]]],[]]]]=>[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[2,6,5,4,7,3,1]=>([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[[[],[],[]]]]]=>[.,[[.,.],[.,[[[.,.],.],.]]]]=>[2,5,6,7,4,3,1]=>([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[[[],[[]]]]]]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[2,5,7,6,4,3,1]=>([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[[[[]],[]]]]]=>[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[2,6,5,7,4,3,1]=>([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[[[[],[]]]]]]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[2,6,7,5,4,3,1]=>([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[],[[[[[]]]]]]]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[2,7,6,5,4,3,1]=>([(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[]],[],[],[],[]]]=>[.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[[[]],[],[],[[]]]]=>[.,[[[[.,[.,.]],.],.],[.,.]]]=>[3,2,4,5,7,6,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
[[[[]],[],[[]],[]]]=>[.,[[[[.,[.,.]],.],[.,.]],.]]=>[3,2,4,6,5,7,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
[[[[]],[],[[],[]]]]=>[.,[[[.,[.,.]],.],[[.,.],.]]]=>[3,2,4,6,7,5,1]=>([(0,6),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[]],[],[[[]]]]]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[3,2,4,7,6,5,1]=>([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[]],[[]],[],[]]]=>[.,[[[[.,[.,.]],[.,.]],.],.]]=>[3,2,5,4,6,7,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
[[[[]],[[]],[[]]]]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[3,2,5,4,7,6,1]=>([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
[[[[]],[[],[]],[]]]=>[.,[[[.,[.,.]],[[.,.],.]],.]]=>[3,2,5,6,4,7,1]=>([(0,6),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[]],[[[]]],[]]]=>[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[3,2,6,5,4,7,1]=>([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[]],[[],[],[]]]]=>[.,[[.,[.,.]],[[[.,.],.],.]]]=>[3,2,5,6,7,4,1]=>([(0,1),(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[]],[[],[[]]]]]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[3,2,5,7,6,4,1]=>([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[]],[[[]],[]]]]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[3,2,6,5,7,4,1]=>([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[]],[[[],[]]]]]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[3,2,6,7,5,4,1]=>([(0,1),(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[]],[[[[]]]]]]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[3,2,7,6,5,4,1]=>([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[],[]],[],[],[]]]=>[.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[]]],[],[],[]]]=>[.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[],[]],[],[[]]]]=>[.,[[[.,[[.,.],.]],.],[.,.]]]=>[3,4,2,5,7,6,1]=>([(0,6),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[]]],[],[[]]]]=>[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[4,3,2,5,7,6,1]=>([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[],[]],[[]],[]]]=>[.,[[[.,[[.,.],.]],[.,.]],.]]=>[3,4,2,6,5,7,1]=>([(0,6),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[]]],[[]],[]]]=>[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[4,3,2,6,5,7,1]=>([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[],[]],[[],[]]]]=>[.,[[.,[[.,.],.]],[[.,.],.]]]=>[3,4,2,6,7,5,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
[[[[],[]],[[[]]]]]=>[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[3,4,2,7,6,5,1]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
[[[[[]]],[[],[]]]]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[4,3,2,6,7,5,1]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
[[[[[]]],[[[]]]]]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[4,3,2,7,6,5,1]=>([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[[[],[],[]],[],[]]]=>[.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[],[[]]],[],[]]]=>[.,[[[.,[[.,.],[.,.]]],.],.]]=>[3,5,4,2,6,7,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[]],[]],[],[]]]=>[.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[],[]]],[],[]]]=>[.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[[]]]],[],[]]]=>[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[],[],[]],[[]]]]=>[.,[[.,[[[.,.],.],.]],[.,.]]]=>[3,4,5,2,7,6,1]=>([(0,1),(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[],[[]]],[[]]]]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[3,5,4,2,7,6,1]=>([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[]],[]],[[]]]]=>[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[4,3,5,2,7,6,1]=>([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[],[]]],[[]]]]=>[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[4,5,3,2,7,6,1]=>([(0,1),(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[[]]]],[[]]]]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[5,4,3,2,7,6,1]=>([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[],[],[],[]],[]]]=>[.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[],[],[[]]],[]]]=>[.,[[.,[[[.,.],.],[.,.]]],.]]=>[3,4,6,5,2,7,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[],[[]],[]],[]]]=>[.,[[.,[[[.,.],[.,.]],.]],.]]=>[3,5,4,6,2,7,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[],[[],[]]],[]]]=>[.,[[.,[[.,.],[[.,.],.]]],.]]=>[3,5,6,4,2,7,1]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[],[[[]]]],[]]]=>[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[3,6,5,4,2,7,1]=>([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[]],[],[]],[]]]=>[.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[]],[[]]],[]]]=>[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[4,3,6,5,2,7,1]=>([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[],[]],[]],[]]]=>[.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[[]]],[]],[]]]=>[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[],[],[]]],[]]]=>[.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[],[[]]]],[]]]=>[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[4,6,5,3,2,7,1]=>([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[[]],[]]],[]]]=>[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[[],[]]]],[]]]=>[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[[[]]]]],[]]]=>[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>([(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[],[],[],[],[]]]]=>[.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[],[],[],[[]]]]]=>[.,[.,[[[[.,.],.],.],[.,.]]]]=>[3,4,5,7,6,2,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[],[],[[]],[]]]]=>[.,[.,[[[[.,.],.],[.,.]],.]]]=>[3,4,6,5,7,2,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[],[],[[],[]]]]]=>[.,[.,[[[.,.],.],[[.,.],.]]]]=>[3,4,6,7,5,2,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[],[],[[[]]]]]]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[3,4,7,6,5,2,1]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[],[[]],[],[]]]]=>[.,[.,[[[[.,.],[.,.]],.],.]]]=>[3,5,4,6,7,2,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[],[[]],[[]]]]]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[3,5,4,7,6,2,1]=>([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[],[[],[]],[]]]]=>[.,[.,[[[.,.],[[.,.],.]],.]]]=>[3,5,6,4,7,2,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[],[[[]]],[]]]]=>[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[3,6,5,4,7,2,1]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[],[[],[],[]]]]]=>[.,[.,[[.,.],[[[.,.],.],.]]]]=>[3,5,6,7,4,2,1]=>([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[],[[],[[]]]]]]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[3,5,7,6,4,2,1]=>([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[],[[[]],[]]]]]=>[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[3,6,5,7,4,2,1]=>([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[],[[[],[]]]]]]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[3,6,7,5,4,2,1]=>([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[],[[[[]]]]]]]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[3,7,6,5,4,2,1]=>([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[]],[],[],[]]]]=>[.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[]],[],[[]]]]]=>[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[4,3,5,7,6,2,1]=>([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[]],[[]],[]]]]=>[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[4,3,6,5,7,2,1]=>([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[]],[[],[]]]]]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[4,3,6,7,5,2,1]=>([(0,1),(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[]],[[[]]]]]]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[4,3,7,6,5,2,1]=>([(0,1),(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[],[]],[],[]]]]=>[.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[[]]],[],[]]]]=>[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[],[]],[[]]]]]=>[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[4,5,3,7,6,2,1]=>([(0,1),(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[[]]],[[]]]]]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[5,4,3,7,6,2,1]=>([(0,1),(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[],[],[]],[]]]]=>[.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[],[[]]],[]]]]=>[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[4,6,5,3,7,2,1]=>([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[[]],[]],[]]]]=>[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[[],[]]],[]]]]=>[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[[[]]]],[]]]]=>[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[],[],[],[]]]]]=>[.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[],[],[[]]]]]]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[4,5,7,6,3,2,1]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[],[[]],[]]]]]=>[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[4,6,5,7,3,2,1]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[],[[],[]]]]]]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[4,6,7,5,3,2,1]=>([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[],[[[]]]]]]]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[4,7,6,5,3,2,1]=>([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[[]],[],[]]]]]=>[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[[]],[[]]]]]]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[5,4,7,6,3,2,1]=>([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[[],[]],[]]]]]=>[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[[[]]],[]]]]]=>[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[[],[],[]]]]]]=>[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[[],[[]]]]]]]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[5,7,6,4,3,2,1]=>([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[[[]],[]]]]]]=>[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[[[],[]]]]]]]=>[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[[[[[]]]]]]]]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[],[],[],[],[],[],[],[]]=>[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>([],8)
[[],[],[[]],[[]],[],[]]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,2,4,3,6,5,7,8]=>([(4,7),(5,6)],8)
[[],[[]],[],[],[[]],[]]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,3,2,4,5,7,6,8]=>([(4,7),(5,6)],8)
[[],[[],[]],[[],[]],[]]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[1,3,4,2,6,7,5,8]=>([(2,7),(3,7),(4,6),(5,6)],8)
[[],[[[]]],[[[]]],[]]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,4,3,2,7,6,5,8]=>([(2,6),(2,7),(3,4),(3,5),(4,5),(6,7)],8)
[[[]],[],[],[],[],[[]]]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,8,7]=>([(4,7),(5,6)],8)
[[[]],[[]],[[]],[[]]]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]=>([(0,7),(1,6),(2,5),(3,4)],8)
[[[]],[[]],[[[[]]]]]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]=>([(0,3),(1,2),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[[]],[[[[]]]],[[]]]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[2,1,6,5,4,3,8,7]=>([(0,3),(1,2),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[[]],[[[[[[]]]]]]]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]=>([(0,1),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[[],[]],[],[],[[],[]]]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[2,3,1,4,5,7,8,6]=>([(2,7),(3,7),(4,6),(5,6)],8)
[[[[]]],[],[],[[[]]]]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[3,2,1,4,5,8,7,6]=>([(2,6),(2,7),(3,4),(3,5),(4,5),(6,7)],8)
[[[[[]]]],[[]],[[]]]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[4,3,2,1,6,5,8,7]=>([(0,3),(1,2),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[[],[],[]],[[],[],[]]]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[2,3,4,1,6,7,8,5]=>([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6)],8)
[[[],[[]]],[[[]],[]]]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[2,4,3,1,7,6,8,5]=>([(0,7),(1,6),(2,3),(2,6),(3,6),(4,5),(4,7),(5,7)],8)
[[[[]],[]],[[],[[]]]]=>[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[3,2,4,1,6,8,7,5]=>([(0,7),(1,6),(2,3),(2,6),(3,6),(4,5),(4,7),(5,7)],8)
[[[[],[]]],[[[],[]]]]=>[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[3,4,2,1,7,8,6,5]=>([(0,6),(0,7),(1,4),(1,5),(2,4),(2,5),(3,6),(3,7),(4,5),(6,7)],8)
[[[[[]]]],[[[[]]]]]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[4,3,2,1,8,7,6,5]=>([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4),(5,6),(5,7),(6,7)],8)
[[[[[[[]]]]]],[[]]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[6,5,4,3,2,1,8,7]=>([(0,1),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[[[[[[[[]]]]]]]]]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
Map
to binary tree: left brother = left child
Description
Return a binary tree of size $n-1$ (where $n$ is the size of $t$, and where $t$ is an ordered tree) by the following recursive rule:
- if $x$ is the left brother of $y$ in $t$, then $x$ becomes the left child of $y$;
- if $x$ is the last child of $y$ in $t$, then $x$ becomes the right child of $y$,
and removing the root of $t$.
- if $x$ is the left brother of $y$ in $t$, then $x$ becomes the left child of $y$;
- if $x$ is the last child of $y$ in $t$, then $x$ becomes the right child of $y$,
and removing the root of $t$.
Map
to 312-avoiding permutation
Description
Return a 312-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
Map
graph of inversions
Description
The graph of inversions of a permutation.
For a permutation of $\{1,\dots,n\}$, this is the graph with vertices $\{1,\dots,n\}$, where $(i,j)$ is an edge if and only if it is an inversion of the permutation.
For a permutation of $\{1,\dots,n\}$, this is the graph with vertices $\{1,\dots,n\}$, where $(i,j)$ is an edge if and only if it is an inversion of the permutation.
searching the database
Sorry, this map was not found in the database.