Gold Mine Solver

Gold Mine is yet another ingenious puzzle from SmartGames. Here you help a dwarf in a cave to get to one or more piles of gold by placing transparent tiles with ladders. (The position of the dwarf and the gold is fixed by the puzzle.)

An example solution from the rulebook:

We are going to use a bottom-up approach.

Representation

The cave is a 7x4 grid where most cells are connected horizontally, but no cells are connected vertically (by default):

  1 2 3 4 5 6 7
1 _______ _____
2 ___ _____ ___
3 _ _____ _____
4 _____ ___ ___

So a position is a pair of coordinates in this range:

position(X-Y) :- between(1, 7, X), between(1, 4, Y).

A puzzle always fixes the position of the dwarf and the gold, so we can represent it as puzzle(N, Dwarf, Golds), where N is the problem’s number. For example:

puzzle(1, 5-4, [7-4]).
puzzle(26, 5-2, [4-1,5-1,2-3]).
puzzle(48, 1-1, [5-2,2-3,6-3]).

There are 3 ladder tiles, two of which can be rotated in two ways:

Type 1:
..||..

Type 2:
||..||..   or  ..||..||

Type 3:
||             ||..
..||       or    ||

These can be described as ladder(Type-Rotation, Position), where the first argument can take the values

• 1-n/a (rotation is N/A)

• 2-left or 2-right (depending on which side the ladders are skewed to)

• 3-bottom or 3-top (depending on the position of the cell without a ladder)

So the possible values are described by the following rule:

direction(1, n/a).
direction(2, left).
direction(2, right).
direction(3, bottom).
direction(3, top).

The second argument is the anchor position of the ladder tile, for which we will always use the top-left cell of the tile.

Connections

We need to know which cells are connected to a given cell. This is partly defined by the cave, but we also need to take the ladders into account. These will be handled by the connected(Ladders, Pos, Adjacent) rule.

We can move left in the cave if we are not in the first column, and if we are not at the left end of a “room”:

connected(_, X-Y, X1-Y) :-
    X > 1, X1 is X - 1,
    \+ member(X-Y, [5-1,3-2,6-2,2-3,5-3,4-4,6-4]).

Similarly for moving right:

connected(_, X-Y, X1-Y) :-
    X < 7, X1 is X + 1,
    \+ member(X-Y, [4-1,2-2,5-2,1-3,4-3,3-4,5-4]).

Moving up or down is a bit more complex. We can move up if there is a ladder at the current cell, and we can move down if there is a ladder at the target cell. We are going to use the DY variable to show the relative y-coordinate where the ladder needs to be. Otherwise it is just a switch-case on the ladder type:

connected(Ladders, X-Y, X-Y1) :-
    ( Y > 1, Y1 is Y - 1, DY = 0
    ; Y < 4, Y1 is Y + 1, DY = 1
    ),
    ( member(ladder(1-_, Lx-Ly), Ladders),
      Lx =:= X - 1, Ly =:= Y + DY
    ; member(ladder(2-left, Lx-Ly), Ladders),
      ( Lx =:= X ; Lx =:= X - 2 ), Ly =:= Y + DY
    ; member(ladder(2-right, Lx-Ly), Ladders),
      ( Lx =:= X - 1 ; Lx =:= X - 3 ), Ly =:= Y + DY
    ; member(ladder(3-_, Lx-Ly), Ladders),
      ( Lx =:= X, Ly =:= Y + DY ; Lx =:= X - 1, Ly =:= Y + DY - 1 )
    ).

Occupancy

Tiles cannot be placed on top of each other, so we need to be able to decide whether a given cell is already occupied by a cell. Here the dwarf and gold tiles also count, but they are the easiest to handle. We represent them by their position, which is the only cell they occupy:

occupies(X-Y, X-Y).

A type-1 ladder occupies its anchor position and also two cells to the right:

occupies(ladder(1-_, X-Y), X1-Y) :- between(0, 2, DX), X1 is X + DX.

Similarly for a type-2 ladder (with three cells to the right):

occupies(ladder(2-_, X-Y), X1-Y) :- between(0, 3, DX), X1 is X + DX.

A type-3 ladder always occupies the anchor position and the cell to the right and below:

occupies(ladder(3-_, X-Y), X-Y).
occupies(ladder(3-_, X-Y), X1-Y1) :- X1 is X + 1, Y1 is Y + 1.

Depending on its orientation, it also occupies the cell either below to the right of the anchor position:

occupies(ladder(3-bottom, X-Y), X-Y1) :- Y1 is Y + 1.
occupies(ladder(3-top, X-Y), X1-Y) :- X1 is X + 1.

Placement

Now we can place ladders. The place(Tiles, Type Tiles1) rule adds a ladder of the given type to the input list of tiles:

place(Tiles, Type, [Ladder|Tiles]) :-
    \+ member(ladder(Type-_,_), Tiles),
    direction(Type, Dir),
    position(Pos),
    Ladder = ladder(Type-Dir, Pos),
    forall(occupies(Ladder, P), position(P)),
    \+ ( occupies(Ladder, P1),
         member(T, Tiles),
         occupies(T, P2),
         P1 = P2
       ).

In other words:

1. First it checks if this tile is not already placed.

2. It chooses a suitable direction for the tile.

3. It chooses a suitable position for the tile.

4. It checks that all cells occupied by the tile are valid positions (not outside the board).

5. It checks that no cell occupied by the ladder tile is already occupied by another tile.

Solver

We have a rule for connectedness, but we also need a rule to decide whether there is a path between two cells.

Obviously, position Pos2 can be reached from Pos1 when the two are connected:

reaches(Ladders, Pos1, Pos2, _) :- connected(Ladders, Pos1, Pos2).

It can also be reached if there is another position P that is connected to Pos1 and can reach Pos2. Here we need to be careful, and note the positions we have already visited, lest we get in an infinite cycle:

reaches(Ladders, Pos1, Pos2, Visited) :-
    connected(Ladders, Pos1, P),
    \+ member(P, Visited),
    reaches(Ladders, P, Pos2, [P|Visited]).

Finally, we can write our solver. It places the dwarf, the piles of gold, the three ladders, and checks that the dwarf can reach the gold:

solve(Dwarf, Golds, Ladders) :-
    place([Dwarf|Golds], 1, T1),
    place(T1, 2, T2),
    place(T2, 3, Tiles),
    findall(L, ( member(L, Tiles), L = ladder(_,_) ), Ladders),
    forall(member(Gold, Golds), reaches(Ladders, Dwarf, Gold, [])).

(Since Tiles contains the positions for the dwarf and the gold as well, we remove them before the final check.)

Tests

?- puzzle(1, D, G), solve(D, G, L).
L = [ladder(3-top, 5-3), ladder(2-right, 1-4), ladder(1-n/a, 2-3)]

?- puzzle(26, D, G), solve(D, G, L).
L = [ladder(3-top, 6-2), ladder(2-left, 3-3), ladder(1-n/a, 2-2)]

?- puzzle(48, D, G), solve(D, G, L).
L = [ladder(3-top, 4-3), ladder(2-right, 1-4), ladder(1-n/a, 2-2)]

Nice!

Experiments

A natural question to ask is how many puzzles are there? By “puzzles” I mean unambiguous puzzles, of course. First note that the dwarf and the piles of gold are not different at all, so a puzzle is just a list of 2 to 4 positions that are to be connected by the ladders:

unambiguous(Items, Solution) :-
    between(2, 4, N),
    length(Items, N),
    maplist(position, Items),
    sorted(Items),
    Items = [Dwarf|Golds],
    findall(Ladders, solve(Dwarf, Golds, Ladders), [Solution]).

Here we require that these “items” are sorted, so each case is only checked once. We arbitrarily set the dwarf as the first item, and check if there is only a single solution.

The sorted/1 rule is quite trivial:

sorted([_]).
sorted([X,Y|Xs]) :- X @< Y, sorted([Y|Xs]).

This runs for a long time …

?- unambiguous(P, S), write(P), write(' -> '), write(S), nl, fail.
[1-2,1-3] -> [ladder(3-bottom,2-2),ladder(2-left,1-4),ladder(1-n/a,3-2)]
[1-4,6-4] -> [ladder(3-top,6-3),ladder(2-right,2-3),ladder(1-n/a,2-4)]
[2-2,6-2] -> [ladder(3-bottom,1-2),ladder(2-right,4-3),ladder(1-n/a,3-2)]
[2-2,7-2] -> [ladder(3-bottom,1-2),ladder(2-right,4-3),ladder(1-n/a,3-2)]
[2-3,6-4] -> [ladder(3-top,6-3),ladder(2-right,4-2),ladder(1-n/a,3-3)]
[2-3,7-4] -> [ladder(3-top,2-2),ladder(2-right,3-4),ladder(1-n/a,4-3)]
[2-4,6-3] -> [ladder(3-top,4-2),ladder(2-left,3-4),ladder(1-n/a,2-3)]
[5-4,6-3] -> [ladder(3-top,4-2),ladder(2-right,1-4),ladder(1-n/a,2-3)]
[5-4,7-4] -> [ladder(3-top,5-3),ladder(2-right,1-4),ladder(1-n/a,2-3)]
[1-1,1-2,1-3] -> [ladder(3-bottom,2-2),ladder(2-left,1-4),ladder(1-n/a,3-2)]
[1-1,1-2,6-2] -> [ladder(3-bottom,2-2),ladder(2-right,4-3),ladder(1-n/a,3-2)]
[1-1,1-2,7-2] -> [ladder(3-bottom,2-2),ladder(2-right,4-3),ladder(1-n/a,3-2)]
[1-1,1-3,5-1] -> [ladder(3-bottom,3-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-1,1-3,6-1] -> [ladder(3-bottom,3-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-1,1-3,6-3] -> [ladder(3-top,4-2),ladder(2-left,1-4),ladder(1-n/a,2-3)]
[1-1,1-3,7-1] -> [ladder(3-bottom,3-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-1,1-3,7-3] -> [ladder(3-top,4-2),ladder(2-left,1-4),ladder(1-n/a,2-3)]
[1-1,2-2,3-4] -> [ladder(3-bottom,1-3),ladder(2-left,2-3),ladder(1-n/a,3-2)]
[1-1,2-2,6-2] -> [ladder(3-bottom,1-2),ladder(2-right,4-3),ladder(1-n/a,3-2)]
[1-1,2-2,7-2] -> [ladder(3-bottom,1-2),ladder(2-right,4-3),ladder(1-n/a,3-2)]
[1-1,2-4,5-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[1-1,2-4,6-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[1-1,2-4,6-3] -> [ladder(3-top,4-2),ladder(2-left,3-4),ladder(1-n/a,2-3)]
[1-1,2-4,7-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[1-1,3-4,4-2] -> [ladder(3-bottom,1-3),ladder(2-left,2-3),ladder(1-n/a,1-2)]
[1-1,5-2,6-4] -> [ladder(3-top,6-3),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[1-1,5-4,6-3] -> [ladder(3-top,4-2),ladder(2-right,1-4),ladder(1-n/a,2-3)]
[1-1,6-1,6-2] -> [ladder(3-top,4-1),ladder(2-right,4-3),ladder(1-n/a,2-2)]
[1-1,6-2,7-1] -> [ladder(3-top,4-1),ladder(2-right,4-3),ladder(1-n/a,2-2)]
[1-2,1-3,2-1] -> [ladder(3-bottom,2-2),ladder(2-left,1-4),ladder(1-n/a,3-2)]
[1-2,1-3,3-1] -> [ladder(3-bottom,2-2),ladder(2-left,1-4),ladder(1-n/a,3-2)]
[1-2,1-3,4-1] -> [ladder(3-bottom,2-2),ladder(2-left,1-4),ladder(1-n/a,3-2)]
[1-2,1-3,4-3] -> [ladder(3-bottom,2-2),ladder(2-left,1-4),ladder(1-n/a,3-2)]
[1-2,1-4,3-4] -> [ladder(3-top,1-3),ladder(2-left,2-2),ladder(1-n/a,3-3)]
[1-2,2-1,6-2] -> [ladder(3-bottom,2-2),ladder(2-right,4-3),ladder(1-n/a,3-2)]
[1-2,2-1,7-2] -> [ladder(3-bottom,2-2),ladder(2-right,4-3),ladder(1-n/a,3-2)]
[1-2,2-3,3-2] -> [ladder(3-top,1-1),ladder(2-left,4-2),ladder(1-n/a,3-3)]
[1-2,2-3,3-4] -> [ladder(3-bottom,1-3),ladder(2-left,2-2),ladder(1-n/a,3-3)]
[1-2,2-3,5-1] -> [ladder(3-top,1-1),ladder(2-left,3-2),ladder(1-n/a,3-3)]
[1-2,2-3,6-1] -> [ladder(3-top,1-1),ladder(2-left,3-2),ladder(1-n/a,3-3)]
[1-2,2-3,7-1] -> [ladder(3-top,1-1),ladder(2-left,3-2),ladder(1-n/a,3-3)]
[1-2,2-4,5-1] -> [ladder(3-top,2-3),ladder(2-left,4-3),ladder(1-n/a,4-2)]
[1-2,2-4,6-1] -> [ladder(3-top,2-3),ladder(2-left,4-3),ladder(1-n/a,4-2)]
[1-2,2-4,7-1] -> [ladder(3-top,2-3),ladder(2-left,4-3),ladder(1-n/a,4-2)]
[1-2,2-4,7-3] -> [ladder(3-top,2-3),ladder(2-left,2-2),ladder(1-n/a,4-3)]
[1-2,3-3,5-1] -> [ladder(3-bottom,2-3),ladder(2-left,4-3),ladder(1-n/a,4-2)]
[1-2,3-3,6-1] -> [ladder(3-bottom,2-3),ladder(2-left,4-3),ladder(1-n/a,4-2)]
[1-2,3-3,7-1] -> [ladder(3-bottom,2-3),ladder(2-left,4-3),ladder(1-n/a,4-2)]
[1-2,3-3,7-3] -> [ladder(3-bottom,2-3),ladder(2-left,2-2),ladder(1-n/a,4-3)]
[1-2,3-4,5-1] -> [ladder(3-bottom,1-3),ladder(2-left,2-3),ladder(1-n/a,4-2)]
[1-2,3-4,6-1] -> [ladder(3-bottom,1-3),ladder(2-left,2-3),ladder(1-n/a,4-2)]
[1-2,3-4,7-1] -> [ladder(3-bottom,1-3),ladder(2-left,2-3),ladder(1-n/a,4-2)]
[1-2,4-3,6-3] -> [ladder(3-bottom,5-3),ladder(2-left,2-2),ladder(1-n/a,1-3)]
[1-2,5-1,6-3] -> [ladder(3-bottom,5-3),ladder(2-right,1-3),ladder(1-n/a,4-2)]
[1-2,5-2,5-4] -> [ladder(3-top,3-2),ladder(2-right,1-4),ladder(1-n/a,1-3)]
[1-2,5-4,7-3] -> [ladder(3-bottom,3-3),ladder(2-left,2-2),ladder(1-n/a,4-3)]
[1-2,6-1,6-3] -> [ladder(3-bottom,5-3),ladder(2-right,1-3),ladder(1-n/a,4-2)]
[1-2,6-3,7-1] -> [ladder(3-bottom,5-3),ladder(2-right,1-3),ladder(1-n/a,4-2)]
[1-3,2-1,5-1] -> [ladder(3-bottom,3-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-3,2-1,6-1] -> [ladder(3-bottom,3-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-3,2-1,6-3] -> [ladder(3-top,4-2),ladder(2-left,1-4),ladder(1-n/a,2-3)]
[1-3,2-1,7-1] -> [ladder(3-bottom,3-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-3,2-1,7-3] -> [ladder(3-top,4-2),ladder(2-left,1-4),ladder(1-n/a,2-3)]
[1-3,2-3,7-3] -> [ladder(3-top,2-2),ladder(2-left,1-4),ladder(1-n/a,4-3)]
[1-3,3-1,5-1] -> [ladder(3-bottom,3-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-3,3-1,6-1] -> [ladder(3-bottom,3-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-3,3-1,6-3] -> [ladder(3-top,4-2),ladder(2-left,1-4),ladder(1-n/a,2-3)]
[1-3,3-1,7-1] -> [ladder(3-bottom,3-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-3,3-1,7-3] -> [ladder(3-top,4-2),ladder(2-left,1-4),ladder(1-n/a,2-3)]
[1-3,3-3,5-1] -> [ladder(3-top,4-3),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-3,3-3,6-1] -> [ladder(3-top,4-3),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-3,3-3,7-1] -> [ladder(3-top,4-3),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-3,4-1,5-1] -> [ladder(3-bottom,3-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-3,4-1,6-1] -> [ladder(3-bottom,3-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-3,4-1,6-3] -> [ladder(3-top,4-2),ladder(2-left,1-4),ladder(1-n/a,2-3)]
[1-3,4-1,7-1] -> [ladder(3-bottom,3-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-3,4-1,7-3] -> [ladder(3-top,4-2),ladder(2-left,1-4),ladder(1-n/a,2-3)]
[1-3,4-2,6-3] -> [ladder(3-bottom,5-3),ladder(2-left,1-4),ladder(1-n/a,2-3)]
[1-3,5-2,6-3] -> [ladder(3-bottom,5-3),ladder(2-left,1-4),ladder(1-n/a,2-3)]
[1-3,6-3,7-4] -> [ladder(3-bottom,5-3),ladder(2-left,1-4),ladder(1-n/a,2-3)]
[1-4,2-3,6-2] -> [ladder(3-top,2-2),ladder(2-right,4-3),ladder(1-n/a,2-4)]
[1-4,2-3,7-2] -> [ladder(3-top,2-2),ladder(2-right,4-3),ladder(1-n/a,2-4)]
[1-4,2-4,6-3] -> [ladder(3-top,4-2),ladder(2-left,3-4),ladder(1-n/a,2-3)]
[1-4,3-2,6-4] -> [ladder(3-top,6-3),ladder(2-right,2-3),ladder(1-n/a,2-4)]
[1-4,4-2,6-4] -> [ladder(3-top,6-3),ladder(2-right,2-3),ladder(1-n/a,2-4)]
[1-4,5-2,6-4] -> [ladder(3-top,6-3),ladder(2-right,2-3),ladder(1-n/a,2-4)]
[1-4,6-2,6-4] -> [ladder(3-top,6-3),ladder(2-right,2-3),ladder(1-n/a,2-4)]
[1-4,6-2,7-3] -> [ladder(3-bottom,6-3),ladder(2-right,2-3),ladder(1-n/a,2-4)]
[1-4,6-4,7-2] -> [ladder(3-top,6-3),ladder(2-right,2-3),ladder(1-n/a,2-4)]
[2-1,2-2,3-4] -> [ladder(3-bottom,1-3),ladder(2-left,2-3),ladder(1-n/a,3-2)]
[2-1,2-2,6-2] -> [ladder(3-bottom,1-2),ladder(2-right,4-3),ladder(1-n/a,3-2)]
[2-1,2-2,7-2] -> [ladder(3-bottom,1-2),ladder(2-right,4-3),ladder(1-n/a,3-2)]
[2-1,2-4,5-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[2-1,2-4,6-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[2-1,2-4,6-3] -> [ladder(3-top,4-2),ladder(2-left,3-4),ladder(1-n/a,2-3)]
[2-1,2-4,7-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[2-1,3-4,4-2] -> [ladder(3-bottom,1-3),ladder(2-left,2-3),ladder(1-n/a,1-2)]
[2-1,4-2,6-3] -> [ladder(3-bottom,5-3),ladder(2-right,1-3),ladder(1-n/a,1-2)]
[2-1,5-2,6-4] -> [ladder(3-top,6-3),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[2-1,5-4,6-3] -> [ladder(3-top,4-2),ladder(2-right,1-4),ladder(1-n/a,2-3)]
[2-1,6-1,6-2] -> [ladder(3-top,4-1),ladder(2-right,4-3),ladder(1-n/a,2-2)]
[2-1,6-2,7-1] -> [ladder(3-top,4-1),ladder(2-right,4-3),ladder(1-n/a,2-2)]
[2-2,2-4,5-1] -> [ladder(3-top,2-3),ladder(2-left,4-3),ladder(1-n/a,4-2)]
[2-2,2-4,6-1] -> [ladder(3-top,2-3),ladder(2-left,4-3),ladder(1-n/a,4-2)]
[2-2,2-4,7-1] -> [ladder(3-top,2-3),ladder(2-left,4-3),ladder(1-n/a,4-2)]
[2-2,3-1,3-4] -> [ladder(3-bottom,1-3),ladder(2-left,2-3),ladder(1-n/a,3-2)]
[2-2,3-1,6-2] -> [ladder(3-bottom,1-2),ladder(2-right,4-3),ladder(1-n/a,3-2)]
[2-2,3-1,7-2] -> [ladder(3-bottom,1-2),ladder(2-right,4-3),ladder(1-n/a,3-2)]
[2-2,3-2,5-4] -> [ladder(3-bottom,1-2),ladder(2-right,1-4),ladder(1-n/a,3-3)]
[2-2,3-3,6-2] -> [ladder(3-bottom,1-2),ladder(2-right,4-3),ladder(1-n/a,3-2)]
[2-2,3-3,7-2] -> [ladder(3-bottom,1-2),ladder(2-right,4-3),ladder(1-n/a,3-2)]
[2-2,3-4,4-1] -> [ladder(3-bottom,1-3),ladder(2-left,2-3),ladder(1-n/a,3-2)]
[2-2,3-4,5-1] -> [ladder(3-bottom,1-3),ladder(2-left,2-3),ladder(1-n/a,4-2)]
[2-2,3-4,6-1] -> [ladder(3-bottom,1-3),ladder(2-left,2-3),ladder(1-n/a,4-2)]
[2-2,3-4,7-1] -> [ladder(3-bottom,1-3),ladder(2-left,2-3),ladder(1-n/a,4-2)]
[2-2,4-1,6-2] -> [ladder(3-bottom,1-2),ladder(2-right,4-3),ladder(1-n/a,3-2)]
[2-2,4-1,7-2] -> [ladder(3-bottom,1-2),ladder(2-right,4-3),ladder(1-n/a,3-2)]
[2-2,4-2,5-4] -> [ladder(3-bottom,1-2),ladder(2-right,1-4),ladder(1-n/a,3-3)]
[2-2,5-1,6-3] -> [ladder(3-bottom,5-3),ladder(2-right,1-3),ladder(1-n/a,4-2)]
[2-2,6-1,6-3] -> [ladder(3-bottom,5-3),ladder(2-right,1-3),ladder(1-n/a,4-2)]
[2-2,6-2,7-2] -> [ladder(3-bottom,1-2),ladder(2-right,4-3),ladder(1-n/a,3-2)]
[2-2,6-3,7-1] -> [ladder(3-bottom,5-3),ladder(2-right,1-3),ladder(1-n/a,4-2)]
[2-3,2-4,7-3] -> [ladder(3-top,2-2),ladder(2-left,3-4),ladder(1-n/a,4-3)]
[2-3,3-2,6-4] -> [ladder(3-top,6-3),ladder(2-right,4-2),ladder(1-n/a,3-3)]
[2-3,4-2,7-4] -> [ladder(3-top,2-2),ladder(2-right,3-4),ladder(1-n/a,4-3)]
[2-3,5-1,6-2] -> [ladder(3-top,6-1),ladder(2-right,2-2),ladder(1-n/a,3-3)]
[2-3,5-1,6-4] -> [ladder(3-top,6-3),ladder(2-right,4-2),ladder(1-n/a,3-3)]
[2-3,5-2,7-4] -> [ladder(3-top,2-2),ladder(2-right,3-4),ladder(1-n/a,4-3)]
[2-3,6-1,6-4] -> [ladder(3-top,6-3),ladder(2-right,4-2),ladder(1-n/a,3-3)]
[2-3,6-4,7-1] -> [ladder(3-top,6-3),ladder(2-right,4-2),ladder(1-n/a,3-3)]
[2-3,7-3,7-4] -> [ladder(3-top,2-2),ladder(2-right,3-4),ladder(1-n/a,4-3)]
[2-4,3-1,5-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[2-4,3-1,6-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[2-4,3-1,6-3] -> [ladder(3-top,4-2),ladder(2-left,3-4),ladder(1-n/a,2-3)]
[2-4,3-1,7-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[2-4,3-2,6-3] -> [ladder(3-top,4-2),ladder(2-left,3-4),ladder(1-n/a,2-3)]
[2-4,4-1,5-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[2-4,4-1,6-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[2-4,4-1,6-3] -> [ladder(3-top,4-2),ladder(2-left,3-4),ladder(1-n/a,2-3)]
[2-4,4-1,7-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[2-4,6-3,7-3] -> [ladder(3-top,4-2),ladder(2-left,3-4),ladder(1-n/a,2-3)]
[3-1,3-4,4-2] -> [ladder(3-bottom,1-3),ladder(2-left,2-3),ladder(1-n/a,1-2)]
[3-1,5-2,6-4] -> [ladder(3-top,6-3),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[3-1,5-4,6-3] -> [ladder(3-top,4-2),ladder(2-right,1-4),ladder(1-n/a,2-3)]
[3-1,6-1,6-2] -> [ladder(3-top,4-1),ladder(2-right,4-3),ladder(1-n/a,2-2)]
[3-1,6-2,7-1] -> [ladder(3-top,4-1),ladder(2-right,4-3),ladder(1-n/a,2-2)]
[3-2,5-4,6-3] -> [ladder(3-top,4-2),ladder(2-right,1-4),ladder(1-n/a,2-3)]
[3-2,5-4,7-4] -> [ladder(3-top,5-3),ladder(2-right,1-4),ladder(1-n/a,2-3)]
[3-3,5-1,6-3] -> [ladder(3-top,4-3),ladder(2-right,1-4),ladder(1-n/a,4-2)]
[3-3,5-2,6-2] -> [ladder(3-bottom,1-2),ladder(2-right,4-3),ladder(1-n/a,2-2)]
[3-3,5-2,7-2] -> [ladder(3-bottom,1-2),ladder(2-right,4-3),ladder(1-n/a,2-2)]
[3-3,6-1,6-3] -> [ladder(3-top,4-3),ladder(2-right,1-4),ladder(1-n/a,4-2)]
[3-3,6-3,7-1] -> [ladder(3-top,4-3),ladder(2-right,1-4),ladder(1-n/a,4-2)]
[3-4,4-1,4-2] -> [ladder(3-bottom,1-3),ladder(2-left,2-3),ladder(1-n/a,1-2)]
[3-4,5-1,6-3] -> [ladder(3-bottom,1-3),ladder(2-right,2-3),ladder(1-n/a,4-2)]
[3-4,6-1,6-3] -> [ladder(3-bottom,1-3),ladder(2-right,2-3),ladder(1-n/a,4-2)]
[3-4,6-3,7-1] -> [ladder(3-bottom,1-3),ladder(2-right,2-3),ladder(1-n/a,4-2)]
[4-1,5-2,6-4] -> [ladder(3-top,6-3),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[4-1,5-4,6-3] -> [ladder(3-top,4-2),ladder(2-right,1-4),ladder(1-n/a,2-3)]
[4-2,5-1,6-4] -> [ladder(3-top,6-3),ladder(2-right,2-3),ladder(1-n/a,5-2)]
[4-2,5-1,7-4] -> [ladder(3-top,6-2),ladder(2-right,3-4),ladder(1-n/a,4-3)]
[4-2,5-4,7-4] -> [ladder(3-top,5-3),ladder(2-right,1-4),ladder(1-n/a,2-3)]
[4-2,6-1,6-4] -> [ladder(3-top,6-3),ladder(2-right,2-3),ladder(1-n/a,5-2)]
[4-2,6-4,7-1] -> [ladder(3-top,6-3),ladder(2-right,2-3),ladder(1-n/a,5-2)]
[5-1,5-2,7-4] -> [ladder(3-top,6-2),ladder(2-right,3-4),ladder(1-n/a,4-3)]
[5-1,5-4,7-2] -> [ladder(3-bottom,3-3),ladder(2-right,4-3),ladder(1-n/a,4-2)]
[5-1,6-2,7-4] -> [ladder(3-top,6-1),ladder(2-right,3-4),ladder(1-n/a,5-3)]
[5-2,5-4,7-4] -> [ladder(3-top,5-3),ladder(2-right,1-4),ladder(1-n/a,2-3)]
[5-2,6-1,7-4] -> [ladder(3-top,6-2),ladder(2-right,3-4),ladder(1-n/a,4-3)]
[5-2,7-1,7-4] -> [ladder(3-top,6-2),ladder(2-right,3-4),ladder(1-n/a,4-3)]
[5-4,6-1,7-2] -> [ladder(3-bottom,3-3),ladder(2-right,4-3),ladder(1-n/a,4-2)]
[5-4,6-3,7-3] -> [ladder(3-top,4-2),ladder(2-right,1-4),ladder(1-n/a,2-3)]
[5-4,7-1,7-2] -> [ladder(3-bottom,3-3),ladder(2-right,4-3),ladder(1-n/a,4-2)]
[5-4,7-3,7-4] -> [ladder(3-top,5-3),ladder(2-right,1-4),ladder(1-n/a,2-3)]
[1-1,1-2,1-3,2-1] -> [ladder(3-bottom,2-2),ladder(2-left,1-4),ladder(1-n/a,3-2)]
[1-1,1-2,1-3,3-1] -> [ladder(3-bottom,2-2),ladder(2-left,1-4),ladder(1-n/a,3-2)]
[1-1,1-2,1-3,4-1] -> [ladder(3-bottom,2-2),ladder(2-left,1-4),ladder(1-n/a,3-2)]
[1-1,1-2,1-3,4-3] -> [ladder(3-bottom,2-2),ladder(2-left,1-4),ladder(1-n/a,3-2)]
[1-1,1-2,1-4,3-4] -> [ladder(3-top,1-3),ladder(2-left,2-2),ladder(1-n/a,3-3)]
[1-1,1-2,1-4,6-3] -> [ladder(3-top,4-2),ladder(2-right,1-3),ladder(1-n/a,2-4)]
[1-1,1-2,2-1,6-2] -> [ladder(3-bottom,2-2),ladder(2-right,4-3),ladder(1-n/a,3-2)]
[1-1,1-2,2-1,7-2] -> [ladder(3-bottom,2-2),ladder(2-right,4-3),ladder(1-n/a,3-2)]
[1-1,1-2,2-2,3-3] -> [ladder(3-bottom,2-3),ladder(2-left,4-3),ladder(1-n/a,3-2)]
[1-1,1-2,2-2,3-4] -> [ladder(3-bottom,1-3),ladder(2-left,2-3),ladder(1-n/a,3-2)]
[1-1,1-2,2-2,5-4] -> [ladder(3-top,3-2),ladder(2-right,1-4),ladder(1-n/a,1-3)]
[1-1,1-2,2-3,3-4] -> [ladder(3-bottom,1-3),ladder(2-left,2-2),ladder(1-n/a,3-3)]
[1-1,1-2,2-4,7-3] -> [ladder(3-top,2-3),ladder(2-left,2-2),ladder(1-n/a,4-3)]
[1-1,1-2,3-1,6-2] -> [ladder(3-bottom,2-2),ladder(2-right,4-3),ladder(1-n/a,3-2)]
[1-1,1-2,3-1,7-2] -> [ladder(3-bottom,2-2),ladder(2-right,4-3),ladder(1-n/a,3-2)]
[1-1,1-2,3-3,5-2] -> [ladder(3-bottom,2-3),ladder(2-left,4-3),ladder(1-n/a,2-2)]
[1-1,1-2,3-3,7-3] -> [ladder(3-bottom,2-3),ladder(2-left,2-2),ladder(1-n/a,4-3)]
[1-1,1-2,3-4,5-2] -> [ladder(3-bottom,1-3),ladder(2-left,2-3),ladder(1-n/a,2-2)]
[1-1,1-2,4-1,6-2] -> [ladder(3-bottom,2-2),ladder(2-right,4-3),ladder(1-n/a,3-2)]
[1-1,1-2,4-1,7-2] -> [ladder(3-bottom,2-2),ladder(2-right,4-3),ladder(1-n/a,3-2)]
[1-1,1-2,4-3,6-3] -> [ladder(3-bottom,5-3),ladder(2-left,2-2),ladder(1-n/a,1-3)]
[1-1,1-2,5-1,7-3] -> [ladder(3-bottom,2-2),ladder(2-left,3-2),ladder(1-n/a,4-3)]
[1-1,1-2,5-2,5-4] -> [ladder(3-top,3-2),ladder(2-right,1-4),ladder(1-n/a,1-3)]
[1-1,1-2,5-2,6-3] -> [ladder(3-bottom,5-3),ladder(2-right,1-3),ladder(1-n/a,2-2)]
[1-1,1-2,5-4,7-3] -> [ladder(3-bottom,3-3),ladder(2-left,2-2),ladder(1-n/a,4-3)]
[1-1,1-2,6-1,7-3] -> [ladder(3-bottom,2-2),ladder(2-left,3-2),ladder(1-n/a,4-3)]
[1-1,1-2,6-2,7-2] -> [ladder(3-bottom,2-2),ladder(2-right,4-3),ladder(1-n/a,3-2)]
[1-1,1-2,7-1,7-3] -> [ladder(3-bottom,2-2),ladder(2-left,3-2),ladder(1-n/a,4-3)]
[1-1,1-3,2-1,5-1] -> [ladder(3-bottom,3-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-1,1-3,2-1,6-1] -> [ladder(3-bottom,3-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-1,1-3,2-1,6-3] -> [ladder(3-top,4-2),ladder(2-left,1-4),ladder(1-n/a,2-3)]
[1-1,1-3,2-1,7-1] -> [ladder(3-bottom,3-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-1,1-3,2-1,7-3] -> [ladder(3-top,4-2),ladder(2-left,1-4),ladder(1-n/a,2-3)]
[1-1,1-3,2-3,3-2] -> [ladder(3-top,3-1),ladder(2-left,1-4),ladder(1-n/a,3-3)]
[1-1,1-3,2-3,5-1] -> [ladder(3-bottom,3-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-1,1-3,2-3,6-1] -> [ladder(3-bottom,3-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-1,1-3,2-3,7-1] -> [ladder(3-bottom,3-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-1,1-3,3-1,5-1] -> [ladder(3-bottom,3-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-1,1-3,3-1,6-1] -> [ladder(3-bottom,3-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-1,1-3,3-1,6-3] -> [ladder(3-top,4-2),ladder(2-left,1-4),ladder(1-n/a,2-3)]
[1-1,1-3,3-1,7-1] -> [ladder(3-bottom,3-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-1,1-3,3-1,7-3] -> [ladder(3-top,4-2),ladder(2-left,1-4),ladder(1-n/a,2-3)]
[1-1,1-3,3-2,4-2] -> [ladder(3-top,1-2),ladder(2-left,1-4),ladder(1-n/a,3-3)]
[1-1,1-3,3-2,6-3] -> [ladder(3-top,4-2),ladder(2-left,1-4),ladder(1-n/a,2-3)]
[1-1,1-3,3-2,7-3] -> [ladder(3-top,4-2),ladder(2-left,1-4),ladder(1-n/a,2-3)]
[1-1,1-3,4-1,5-1] -> [ladder(3-bottom,3-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-1,1-3,4-1,6-1] -> [ladder(3-bottom,3-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-1,1-3,4-1,6-3] -> [ladder(3-top,4-2),ladder(2-left,1-4),ladder(1-n/a,2-3)]
[1-1,1-3,4-1,7-1] -> [ladder(3-bottom,3-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-1,1-3,4-1,7-3] -> [ladder(3-top,4-2),ladder(2-left,1-4),ladder(1-n/a,2-3)]
[1-1,1-3,5-1,6-1] -> [ladder(3-bottom,3-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-1,1-3,5-1,7-1] -> [ladder(3-bottom,3-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-1,1-3,6-1,7-1] -> [ladder(3-bottom,3-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-1,1-3,6-3,7-3] -> [ladder(3-top,4-2),ladder(2-left,1-4),ladder(1-n/a,2-3)]
[1-1,1-4,2-2,6-3] -> [ladder(3-top,4-2),ladder(2-right,1-3),ladder(1-n/a,2-4)]
[1-1,1-4,2-3,4-3] -> [ladder(3-top,2-2),ladder(2-left,4-2),ladder(1-n/a,2-4)]
[1-1,1-4,2-4,5-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[1-1,1-4,2-4,6-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[1-1,1-4,2-4,6-3] -> [ladder(3-top,4-2),ladder(2-left,3-4),ladder(1-n/a,2-3)]
[1-1,1-4,2-4,7-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[1-1,1-4,3-2,3-4] -> [ladder(3-top,1-3),ladder(2-left,4-2),ladder(1-n/a,3-3)]
[1-1,2-1,2-2,3-4] -> [ladder(3-bottom,1-3),ladder(2-left,2-3),ladder(1-n/a,3-2)]
[1-1,2-1,2-2,6-2] -> [ladder(3-bottom,1-2),ladder(2-right,4-3),ladder(1-n/a,3-2)]
[1-1,2-1,2-2,7-2] -> [ladder(3-bottom,1-2),ladder(2-right,4-3),ladder(1-n/a,3-2)]
[1-1,2-1,2-4,5-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[1-1,2-1,2-4,6-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[1-1,2-1,2-4,6-3] -> [ladder(3-top,4-2),ladder(2-left,3-4),ladder(1-n/a,2-3)]
[1-1,2-1,2-4,7-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[1-1,2-1,3-4,4-2] -> [ladder(3-bottom,1-3),ladder(2-left,2-3),ladder(1-n/a,1-2)]
[1-1,2-1,4-2,6-3] -> [ladder(3-bottom,5-3),ladder(2-right,1-3),ladder(1-n/a,1-2)]
[1-1,2-1,5-2,6-4] -> [ladder(3-top,6-3),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[1-1,2-1,5-4,6-3] -> [ladder(3-top,4-2),ladder(2-right,1-4),ladder(1-n/a,2-3)]
[1-1,2-1,6-1,6-2] -> [ladder(3-top,4-1),ladder(2-right,4-3),ladder(1-n/a,2-2)]
[1-1,2-1,6-2,7-1] -> [ladder(3-top,4-1),ladder(2-right,4-3),ladder(1-n/a,2-2)]
[1-1,2-2,2-4,3-2] -> [ladder(3-bottom,1-2),ladder(2-left,3-4),ladder(1-n/a,3-3)]
[1-1,2-2,2-4,4-2] -> [ladder(3-bottom,1-2),ladder(2-left,3-4),ladder(1-n/a,3-3)]
[1-1,2-2,3-1,3-4] -> [ladder(3-bottom,1-3),ladder(2-left,2-3),ladder(1-n/a,3-2)]
[1-1,2-2,3-1,6-2] -> [ladder(3-bottom,1-2),ladder(2-right,4-3),ladder(1-n/a,3-2)]
[1-1,2-2,3-1,7-2] -> [ladder(3-bottom,1-2),ladder(2-right,4-3),ladder(1-n/a,3-2)]
[1-1,2-2,3-2,5-4] -> [ladder(3-bottom,1-2),ladder(2-right,1-4),ladder(1-n/a,3-3)]
[1-1,2-2,3-3,6-2] -> [ladder(3-bottom,1-2),ladder(2-right,4-3),ladder(1-n/a,3-2)]
[1-1,2-2,3-3,7-2] -> [ladder(3-bottom,1-2),ladder(2-right,4-3),ladder(1-n/a,3-2)]
[1-1,2-2,3-4,4-1] -> [ladder(3-bottom,1-3),ladder(2-left,2-3),ladder(1-n/a,3-2)]
[1-1,2-2,4-1,6-2] -> [ladder(3-bottom,1-2),ladder(2-right,4-3),ladder(1-n/a,3-2)]
[1-1,2-2,4-1,7-2] -> [ladder(3-bottom,1-2),ladder(2-right,4-3),ladder(1-n/a,3-2)]
[1-1,2-2,4-2,5-4] -> [ladder(3-bottom,1-2),ladder(2-right,1-4),ladder(1-n/a,3-3)]
[1-1,2-2,6-2,7-2] -> [ladder(3-bottom,1-2),ladder(2-right,4-3),ladder(1-n/a,3-2)]
[1-1,2-2,6-3,7-4] -> [ladder(3-bottom,5-3),ladder(2-right,1-3),ladder(1-n/a,3-2)]
[1-1,2-3,2-4,3-2] -> [ladder(3-top,3-1),ladder(2-left,3-4),ladder(1-n/a,3-3)]
[1-1,2-3,2-4,5-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[1-1,2-3,2-4,6-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[1-1,2-3,2-4,7-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[1-1,2-3,3-2,3-4] -> [ladder(3-bottom,1-3),ladder(2-left,4-2),ladder(1-n/a,3-3)]
[1-1,2-3,5-1,5-2] -> [ladder(3-top,6-2),ladder(2-left,3-3),ladder(1-n/a,2-2)]
[1-1,2-3,5-1,6-2] -> [ladder(3-top,6-1),ladder(2-right,2-2),ladder(1-n/a,3-3)]
[1-1,2-3,5-1,6-3] -> [ladder(3-top,6-2),ladder(2-right,2-2),ladder(1-n/a,3-3)]
[1-1,2-3,5-1,7-2] -> [ladder(3-bottom,6-2),ladder(2-right,2-2),ladder(1-n/a,3-3)]
[1-1,2-3,5-2,6-1] -> [ladder(3-top,6-2),ladder(2-left,3-3),ladder(1-n/a,2-2)]
[1-1,2-3,5-2,6-2] -> [ladder(3-bottom,3-3),ladder(2-right,4-3),ladder(1-n/a,2-2)]
[1-1,2-3,5-2,6-3] -> [ladder(3-top,4-3),ladder(2-right,1-4),ladder(1-n/a,2-2)]
[1-1,2-3,5-2,7-1] -> [ladder(3-top,6-2),ladder(2-left,3-3),ladder(1-n/a,2-2)]
[1-1,2-3,5-2,7-2] -> [ladder(3-bottom,3-3),ladder(2-right,4-3),ladder(1-n/a,2-2)]
[1-1,2-3,6-1,6-3] -> [ladder(3-top,6-2),ladder(2-right,2-2),ladder(1-n/a,3-3)]
[1-1,2-3,6-1,7-2] -> [ladder(3-bottom,6-2),ladder(2-right,2-2),ladder(1-n/a,3-3)]
[1-1,2-3,6-3,7-1] -> [ladder(3-top,6-2),ladder(2-right,2-2),ladder(1-n/a,3-3)]
[1-1,2-4,3-1,5-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[1-1,2-4,3-1,6-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[1-1,2-4,3-1,6-3] -> [ladder(3-top,4-2),ladder(2-left,3-4),ladder(1-n/a,2-3)]
[1-1,2-4,3-1,7-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[1-1,2-4,3-2,6-3] -> [ladder(3-top,4-2),ladder(2-left,3-4),ladder(1-n/a,2-3)]
[1-1,2-4,3-2,7-3] -> [ladder(3-top,4-2),ladder(2-left,3-4),ladder(1-n/a,2-3)]
[1-1,2-4,4-1,5-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[1-1,2-4,4-1,6-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[1-1,2-4,4-1,6-3] -> [ladder(3-top,4-2),ladder(2-left,3-4),ladder(1-n/a,2-3)]
[1-1,2-4,4-1,7-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[1-1,2-4,5-1,6-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[1-1,2-4,5-1,7-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[1-1,2-4,6-1,7-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[1-1,2-4,6-3,7-3] -> [ladder(3-top,4-2),ladder(2-left,3-4),ladder(1-n/a,2-3)]
[1-1,3-1,3-4,4-2] -> [ladder(3-bottom,1-3),ladder(2-left,2-3),ladder(1-n/a,1-2)]
[1-1,3-1,5-2,6-4] -> [ladder(3-top,6-3),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[1-1,3-1,5-4,6-3] -> [ladder(3-top,4-2),ladder(2-right,1-4),ladder(1-n/a,2-3)]
[1-1,3-1,6-1,6-2] -> [ladder(3-top,4-1),ladder(2-right,4-3),ladder(1-n/a,2-2)]
[1-1,3-1,6-2,7-1] -> [ladder(3-top,4-1),ladder(2-right,4-3),ladder(1-n/a,2-2)]
[1-1,3-2,5-4,6-3] -> [ladder(3-top,4-2),ladder(2-right,1-4),ladder(1-n/a,2-3)]
[1-1,3-3,5-2,6-2] -> [ladder(3-bottom,1-2),ladder(2-right,4-3),ladder(1-n/a,2-2)]
[1-1,3-3,5-2,6-3] -> [ladder(3-top,4-3),ladder(2-right,1-4),ladder(1-n/a,2-2)]
[1-1,3-3,5-2,7-2] -> [ladder(3-bottom,1-2),ladder(2-right,4-3),ladder(1-n/a,2-2)]
[1-1,3-4,4-1,4-2] -> [ladder(3-bottom,1-3),ladder(2-left,2-3),ladder(1-n/a,1-2)]
[1-1,3-4,4-2,5-2] -> [ladder(3-bottom,1-3),ladder(2-left,2-3),ladder(1-n/a,1-2)]
[1-1,3-4,5-2,6-3] -> [ladder(3-bottom,1-3),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[1-1,4-1,5-2,6-4] -> [ladder(3-top,6-3),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[1-1,4-1,5-4,6-3] -> [ladder(3-top,4-2),ladder(2-right,1-4),ladder(1-n/a,2-3)]
[1-1,4-2,6-3,7-4] -> [ladder(3-bottom,5-3),ladder(2-right,1-3),ladder(1-n/a,1-2)]
[1-1,5-1,5-2,6-2] -> [ladder(3-top,6-1),ladder(2-right,4-3),ladder(1-n/a,2-2)]
[1-1,5-1,5-2,6-3] -> [ladder(3-top,6-2),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[1-1,5-1,5-2,7-2] -> [ladder(3-bottom,6-2),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[1-1,5-1,6-2,7-3] -> [ladder(3-top,6-1),ladder(2-right,2-2),ladder(1-n/a,4-3)]
[1-1,5-1,7-2,7-3] -> [ladder(3-top,5-2),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[1-1,5-2,5-4,6-2] -> [ladder(3-bottom,3-3),ladder(2-right,4-3),ladder(1-n/a,2-2)]
[1-1,5-2,5-4,7-2] -> [ladder(3-bottom,3-3),ladder(2-right,4-3),ladder(1-n/a,2-2)]
[1-1,5-2,6-1,6-3] -> [ladder(3-top,6-2),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[1-1,5-2,6-1,7-2] -> [ladder(3-bottom,6-2),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[1-1,5-2,6-2,6-4] -> [ladder(3-top,6-3),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[1-1,5-2,6-2,7-3] -> [ladder(3-bottom,6-3),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[1-1,5-2,6-3,7-1] -> [ladder(3-top,6-2),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[1-1,5-2,6-4,7-2] -> [ladder(3-top,6-3),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[1-1,5-2,7-2,7-3] -> [ladder(3-bottom,6-3),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[1-1,5-4,6-3,7-3] -> [ladder(3-top,4-2),ladder(2-right,1-4),ladder(1-n/a,2-3)]
[1-1,6-1,6-2,7-1] -> [ladder(3-top,4-1),ladder(2-right,4-3),ladder(1-n/a,2-2)]
[1-1,6-1,6-2,7-2] -> [ladder(3-top,4-1),ladder(2-right,4-3),ladder(1-n/a,2-2)]
[1-1,6-1,7-2,7-3] -> [ladder(3-top,5-2),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[1-1,6-2,7-1,7-2] -> [ladder(3-top,4-1),ladder(2-right,4-3),ladder(1-n/a,2-2)]
[1-2,1-3,2-1,3-1] -> [ladder(3-bottom,2-2),ladder(2-left,1-4),ladder(1-n/a,3-2)]
[1-2,1-3,2-1,4-1] -> [ladder(3-bottom,2-2),ladder(2-left,1-4),ladder(1-n/a,3-2)]
[1-2,1-3,2-1,4-3] -> [ladder(3-bottom,2-2),ladder(2-left,1-4),ladder(1-n/a,3-2)]
[1-2,1-3,3-1,4-1] -> [ladder(3-bottom,2-2),ladder(2-left,1-4),ladder(1-n/a,3-2)]
[1-2,1-3,3-1,4-3] -> [ladder(3-bottom,2-2),ladder(2-left,1-4),ladder(1-n/a,3-2)]
[1-2,1-3,4-1,4-3] -> [ladder(3-bottom,2-2),ladder(2-left,1-4),ladder(1-n/a,3-2)]
[1-2,1-4,2-1,3-4] -> [ladder(3-top,1-3),ladder(2-left,2-2),ladder(1-n/a,3-3)]
[1-2,1-4,2-1,6-3] -> [ladder(3-top,4-2),ladder(2-right,1-3),ladder(1-n/a,2-4)]
[1-2,1-4,2-3,3-3] -> [ladder(3-top,4-3),ladder(2-left,2-2),ladder(1-n/a,2-4)]
[1-2,1-4,2-3,4-3] -> [ladder(3-top,2-2),ladder(2-left,4-2),ladder(1-n/a,2-4)]
[1-2,1-4,2-4,5-1] -> [ladder(3-top,2-3),ladder(2-left,4-3),ladder(1-n/a,4-2)]
[1-2,1-4,2-4,6-1] -> [ladder(3-top,2-3),ladder(2-left,4-3),ladder(1-n/a,4-2)]
[1-2,1-4,2-4,7-1] -> [ladder(3-top,2-3),ladder(2-left,4-3),ladder(1-n/a,4-2)]
[1-2,1-4,2-4,7-3] -> [ladder(3-top,2-3),ladder(2-left,2-2),ladder(1-n/a,4-3)]
[1-2,1-4,3-1,3-4] -> [ladder(3-top,1-3),ladder(2-left,2-2),ladder(1-n/a,3-3)]
[1-2,1-4,3-1,6-3] -> [ladder(3-top,4-2),ladder(2-right,1-3),ladder(1-n/a,2-4)]
[1-2,1-4,3-2,4-3] -> [ladder(3-bottom,2-2),ladder(2-left,4-2),ladder(1-n/a,2-4)]
[1-2,1-4,3-3,5-1] -> [ladder(3-bottom,2-3),ladder(2-left,4-3),ladder(1-n/a,4-2)]
[1-2,1-4,3-3,6-1] -> [ladder(3-bottom,2-3),ladder(2-left,4-3),ladder(1-n/a,4-2)]
[1-2,1-4,3-3,7-1] -> [ladder(3-bottom,2-3),ladder(2-left,4-3),ladder(1-n/a,4-2)]
[1-2,1-4,3-3,7-3] -> [ladder(3-bottom,2-3),ladder(2-left,2-2),ladder(1-n/a,4-3)]
[1-2,1-4,3-4,4-1] -> [ladder(3-top,1-3),ladder(2-left,2-2),ladder(1-n/a,3-3)]
[1-2,1-4,4-1,6-3] -> [ladder(3-top,4-2),ladder(2-right,1-3),ladder(1-n/a,2-4)]
[1-2,1-4,4-2,6-3] -> [ladder(3-bottom,5-3),ladder(2-right,1-3),ladder(1-n/a,2-4)]
[1-2,1-4,4-3,5-1] -> [ladder(3-bottom,2-2),ladder(2-left,3-2),ladder(1-n/a,2-4)]
[1-2,1-4,4-3,6-1] -> [ladder(3-bottom,2-2),ladder(2-left,3-2),ladder(1-n/a,2-4)]
[1-2,1-4,4-3,7-1] -> [ladder(3-bottom,2-2),ladder(2-left,3-2),ladder(1-n/a,2-4)]
[1-2,1-4,5-1,7-3] -> [ladder(3-bottom,2-3),ladder(2-left,3-3),ladder(1-n/a,4-2)]
[1-2,1-4,5-2,6-3] -> [ladder(3-bottom,5-3),ladder(2-right,1-3),ladder(1-n/a,2-4)]
[1-2,1-4,6-1,7-3] -> [ladder(3-bottom,2-3),ladder(2-left,3-3),ladder(1-n/a,4-2)]
[1-2,1-4,6-3,7-4] -> [ladder(3-bottom,5-3),ladder(2-right,1-3),ladder(1-n/a,2-4)]
[1-2,1-4,7-1,7-3] -> [ladder(3-bottom,2-3),ladder(2-left,3-3),ladder(1-n/a,4-2)]
[1-2,2-1,2-2,3-3] -> [ladder(3-bottom,2-3),ladder(2-left,4-3),ladder(1-n/a,3-2)]
[1-2,2-1,2-2,3-4] -> [ladder(3-bottom,1-3),ladder(2-left,2-3),ladder(1-n/a,3-2)]
[1-2,2-1,2-2,5-4] -> [ladder(3-top,3-2),ladder(2-right,1-4),ladder(1-n/a,1-3)]
[1-2,2-1,2-3,3-4] -> [ladder(3-bottom,1-3),ladder(2-left,2-2),ladder(1-n/a,3-3)]
[1-2,2-1,2-4,7-3] -> [ladder(3-top,2-3),ladder(2-left,2-2),ladder(1-n/a,4-3)]
[1-2,2-1,3-1,6-2] -> [ladder(3-bottom,2-2),ladder(2-right,4-3),ladder(1-n/a,3-2)]
[1-2,2-1,3-1,7-2] -> [ladder(3-bottom,2-2),ladder(2-right,4-3),ladder(1-n/a,3-2)]
[1-2,2-1,3-3,5-2] -> [ladder(3-bottom,2-3),ladder(2-left,4-3),ladder(1-n/a,2-2)]
[1-2,2-1,3-3,7-3] -> [ladder(3-bottom,2-3),ladder(2-left,2-2),ladder(1-n/a,4-3)]
[1-2,2-1,3-4,5-2] -> [ladder(3-bottom,1-3),ladder(2-left,2-3),ladder(1-n/a,2-2)]
[1-2,2-1,4-1,6-2] -> [ladder(3-bottom,2-2),ladder(2-right,4-3),ladder(1-n/a,3-2)]
[1-2,2-1,4-1,7-2] -> [ladder(3-bottom,2-2),ladder(2-right,4-3),ladder(1-n/a,3-2)]
[1-2,2-1,4-3,6-3] -> [ladder(3-bottom,5-3),ladder(2-left,2-2),ladder(1-n/a,1-3)]
[1-2,2-1,5-1,7-3] -> [ladder(3-bottom,2-2),ladder(2-left,3-2),ladder(1-n/a,4-3)]
[1-2,2-1,5-2,5-4] -> [ladder(3-top,3-2),ladder(2-right,1-4),ladder(1-n/a,1-3)]
[1-2,2-1,5-2,6-3] -> [ladder(3-bottom,5-3),ladder(2-right,1-3),ladder(1-n/a,2-2)]
[1-2,2-1,5-4,7-3] -> [ladder(3-bottom,3-3),ladder(2-left,2-2),ladder(1-n/a,4-3)]
[1-2,2-1,6-1,7-3] -> [ladder(3-bottom,2-2),ladder(2-left,3-2),ladder(1-n/a,4-3)]
[1-2,2-1,6-2,7-2] -> [ladder(3-bottom,2-2),ladder(2-right,4-3),ladder(1-n/a,3-2)]
[1-2,2-1,7-1,7-3] -> [ladder(3-bottom,2-2),ladder(2-left,3-2),ladder(1-n/a,4-3)]
[1-2,2-2,2-4,5-1] -> [ladder(3-top,2-3),ladder(2-left,4-3),ladder(1-n/a,4-2)]
[1-2,2-2,2-4,6-1] -> [ladder(3-top,2-3),ladder(2-left,4-3),ladder(1-n/a,4-2)]
[1-2,2-2,2-4,7-1] -> [ladder(3-top,2-3),ladder(2-left,4-3),ladder(1-n/a,4-2)]
[1-2,2-2,3-1,3-3] -> [ladder(3-bottom,2-3),ladder(2-left,4-3),ladder(1-n/a,3-2)]
[1-2,2-2,3-1,3-4] -> [ladder(3-bottom,1-3),ladder(2-left,2-3),ladder(1-n/a,3-2)]
[1-2,2-2,3-1,5-4] -> [ladder(3-top,3-2),ladder(2-right,1-4),ladder(1-n/a,1-3)]
[1-2,2-2,3-3,4-1] -> [ladder(3-bottom,2-3),ladder(2-left,4-3),ladder(1-n/a,3-2)]
[1-2,2-2,3-3,5-1] -> [ladder(3-bottom,2-3),ladder(2-left,4-3),ladder(1-n/a,4-2)]
[1-2,2-2,3-3,6-1] -> [ladder(3-bottom,2-3),ladder(2-left,4-3),ladder(1-n/a,4-2)]
[1-2,2-2,3-3,7-1] -> [ladder(3-bottom,2-3),ladder(2-left,4-3),ladder(1-n/a,4-2)]
[1-2,2-2,3-4,4-1] -> [ladder(3-bottom,1-3),ladder(2-left,2-3),ladder(1-n/a,3-2)]
[1-2,2-2,3-4,5-1] -> [ladder(3-bottom,1-3),ladder(2-left,2-3),ladder(1-n/a,4-2)]
[1-2,2-2,3-4,6-1] -> [ladder(3-bottom,1-3),ladder(2-left,2-3),ladder(1-n/a,4-2)]
[1-2,2-2,3-4,7-1] -> [ladder(3-bottom,1-3),ladder(2-left,2-3),ladder(1-n/a,4-2)]
[1-2,2-2,4-1,5-4] -> [ladder(3-top,3-2),ladder(2-right,1-4),ladder(1-n/a,1-3)]
[1-2,2-2,5-1,6-3] -> [ladder(3-bottom,5-3),ladder(2-right,1-3),ladder(1-n/a,4-2)]
[1-2,2-2,5-2,5-4] -> [ladder(3-top,3-2),ladder(2-right,1-4),ladder(1-n/a,1-3)]
[1-2,2-2,6-1,6-3] -> [ladder(3-bottom,5-3),ladder(2-right,1-3),ladder(1-n/a,4-2)]
[1-2,2-2,6-3,7-1] -> [ladder(3-bottom,5-3),ladder(2-right,1-3),ladder(1-n/a,4-2)]
[1-2,2-3,3-1,3-2] -> [ladder(3-top,1-1),ladder(2-left,4-2),ladder(1-n/a,3-3)]
[1-2,2-3,3-1,3-4] -> [ladder(3-bottom,1-3),ladder(2-left,2-2),ladder(1-n/a,3-3)]
[1-2,2-3,3-1,5-1] -> [ladder(3-top,1-1),ladder(2-left,3-2),ladder(1-n/a,3-3)]
[1-2,2-3,3-1,6-1] -> [ladder(3-top,1-1),ladder(2-left,3-2),ladder(1-n/a,3-3)]
[1-2,2-3,3-1,7-1] -> [ladder(3-top,1-1),ladder(2-left,3-2),ladder(1-n/a,3-3)]
[1-2,2-3,3-2,4-1] -> [ladder(3-top,1-1),ladder(2-left,4-2),ladder(1-n/a,3-3)]
[1-2,2-3,3-4,4-1] -> [ladder(3-bottom,1-3),ladder(2-left,2-2),ladder(1-n/a,3-3)]
[1-2,2-3,4-1,5-1] -> [ladder(3-top,1-1),ladder(2-left,3-2),ladder(1-n/a,3-3)]
[1-2,2-3,4-1,6-1] -> [ladder(3-top,1-1),ladder(2-left,3-2),ladder(1-n/a,3-3)]
[1-2,2-3,4-1,7-1] -> [ladder(3-top,1-1),ladder(2-left,3-2),ladder(1-n/a,3-3)]
[1-2,2-3,5-1,6-1] -> [ladder(3-top,1-1),ladder(2-left,3-2),ladder(1-n/a,3-3)]
[1-2,2-3,5-1,7-1] -> [ladder(3-top,1-1),ladder(2-left,3-2),ladder(1-n/a,3-3)]
[1-2,2-3,5-4,7-3] -> [ladder(3-bottom,3-3),ladder(2-left,2-2),ladder(1-n/a,4-3)]
[1-2,2-3,6-1,7-1] -> [ladder(3-top,1-1),ladder(2-left,3-2),ladder(1-n/a,3-3)]
[1-2,2-4,3-1,7-3] -> [ladder(3-top,2-3),ladder(2-left,2-2),ladder(1-n/a,4-3)]
[1-2,2-4,3-2,5-1] -> [ladder(3-top,2-3),ladder(2-left,4-3),ladder(1-n/a,4-2)]
[1-2,2-4,3-2,6-1] -> [ladder(3-top,2-3),ladder(2-left,4-3),ladder(1-n/a,4-2)]
[1-2,2-4,3-2,7-1] -> [ladder(3-top,2-3),ladder(2-left,4-3),ladder(1-n/a,4-2)]
[1-2,2-4,4-1,7-3] -> [ladder(3-top,2-3),ladder(2-left,2-2),ladder(1-n/a,4-3)]
[1-2,2-4,5-1,6-1] -> [ladder(3-top,2-3),ladder(2-left,4-3),ladder(1-n/a,4-2)]
[1-2,2-4,5-1,7-1] -> [ladder(3-top,2-3),ladder(2-left,4-3),ladder(1-n/a,4-2)]
[1-2,2-4,6-1,7-1] -> [ladder(3-top,2-3),ladder(2-left,4-3),ladder(1-n/a,4-2)]
[1-2,3-1,3-3,5-2] -> [ladder(3-bottom,2-3),ladder(2-left,4-3),ladder(1-n/a,2-2)]
[1-2,3-1,3-3,7-3] -> [ladder(3-bottom,2-3),ladder(2-left,2-2),ladder(1-n/a,4-3)]
[1-2,3-1,3-4,5-2] -> [ladder(3-bottom,1-3),ladder(2-left,2-3),ladder(1-n/a,2-2)]
[1-2,3-1,4-3,6-3] -> [ladder(3-bottom,5-3),ladder(2-left,2-2),ladder(1-n/a,1-3)]
[1-2,3-1,5-2,5-4] -> [ladder(3-top,3-2),ladder(2-right,1-4),ladder(1-n/a,1-3)]
[1-2,3-1,5-2,6-3] -> [ladder(3-bottom,5-3),ladder(2-right,1-3),ladder(1-n/a,2-2)]
[1-2,3-1,5-4,7-3] -> [ladder(3-bottom,3-3),ladder(2-left,2-2),ladder(1-n/a,4-3)]
[1-2,3-2,3-3,5-1] -> [ladder(3-bottom,2-3),ladder(2-left,4-3),ladder(1-n/a,4-2)]
[1-2,3-2,3-3,6-1] -> [ladder(3-bottom,2-3),ladder(2-left,4-3),ladder(1-n/a,4-2)]
[1-2,3-2,3-3,7-1] -> [ladder(3-bottom,2-3),ladder(2-left,4-3),ladder(1-n/a,4-2)]
[1-2,3-2,3-4,5-1] -> [ladder(3-bottom,1-3),ladder(2-left,2-3),ladder(1-n/a,4-2)]
[1-2,3-2,3-4,6-1] -> [ladder(3-bottom,1-3),ladder(2-left,2-3),ladder(1-n/a,4-2)]
[1-2,3-2,3-4,7-1] -> [ladder(3-bottom,1-3),ladder(2-left,2-3),ladder(1-n/a,4-2)]
[1-2,3-2,5-1,6-3] -> [ladder(3-bottom,5-3),ladder(2-right,1-3),ladder(1-n/a,4-2)]
[1-2,3-2,6-1,6-3] -> [ladder(3-bottom,5-3),ladder(2-right,1-3),ladder(1-n/a,4-2)]
[1-2,3-2,6-3,7-1] -> [ladder(3-bottom,5-3),ladder(2-right,1-3),ladder(1-n/a,4-2)]
[1-2,3-3,4-1,5-2] -> [ladder(3-bottom,2-3),ladder(2-left,4-3),ladder(1-n/a,2-2)]
[1-2,3-3,4-1,7-3] -> [ladder(3-bottom,2-3),ladder(2-left,2-2),ladder(1-n/a,4-3)]
[1-2,3-3,5-1,6-1] -> [ladder(3-bottom,2-3),ladder(2-left,4-3),ladder(1-n/a,4-2)]
[1-2,3-3,5-1,7-1] -> [ladder(3-bottom,2-3),ladder(2-left,4-3),ladder(1-n/a,4-2)]
[1-2,3-3,6-1,7-1] -> [ladder(3-bottom,2-3),ladder(2-left,4-3),ladder(1-n/a,4-2)]
[1-2,3-4,4-1,5-2] -> [ladder(3-bottom,1-3),ladder(2-left,2-3),ladder(1-n/a,2-2)]
[1-2,3-4,5-1,6-1] -> [ladder(3-bottom,1-3),ladder(2-left,2-3),ladder(1-n/a,4-2)]
[1-2,3-4,5-1,7-1] -> [ladder(3-bottom,1-3),ladder(2-left,2-3),ladder(1-n/a,4-2)]
[1-2,3-4,6-1,7-1] -> [ladder(3-bottom,1-3),ladder(2-left,2-3),ladder(1-n/a,4-2)]
[1-2,4-1,4-3,6-3] -> [ladder(3-bottom,5-3),ladder(2-left,2-2),ladder(1-n/a,1-3)]
[1-2,4-1,5-2,5-4] -> [ladder(3-top,3-2),ladder(2-right,1-4),ladder(1-n/a,1-3)]
[1-2,4-1,5-2,6-3] -> [ladder(3-bottom,5-3),ladder(2-right,1-3),ladder(1-n/a,2-2)]
[1-2,4-1,5-4,7-3] -> [ladder(3-bottom,3-3),ladder(2-left,2-2),ladder(1-n/a,4-3)]
[1-2,4-3,6-3,7-3] -> [ladder(3-bottom,5-3),ladder(2-left,2-2),ladder(1-n/a,1-3)]
[1-2,4-3,6-3,7-4] -> [ladder(3-bottom,5-3),ladder(2-left,2-2),ladder(1-n/a,1-3)]
[1-2,5-1,6-1,6-3] -> [ladder(3-bottom,5-3),ladder(2-right,1-3),ladder(1-n/a,4-2)]
[1-2,5-1,6-3,7-1] -> [ladder(3-bottom,5-3),ladder(2-right,1-3),ladder(1-n/a,4-2)]
[1-2,5-1,6-3,7-3] -> [ladder(3-bottom,5-3),ladder(2-right,1-3),ladder(1-n/a,4-2)]
[1-2,5-1,6-3,7-4] -> [ladder(3-bottom,5-3),ladder(2-right,1-3),ladder(1-n/a,4-2)]
[1-2,6-1,6-3,7-1] -> [ladder(3-bottom,5-3),ladder(2-right,1-3),ladder(1-n/a,4-2)]
[1-2,6-1,6-3,7-3] -> [ladder(3-bottom,5-3),ladder(2-right,1-3),ladder(1-n/a,4-2)]
[1-2,6-1,6-3,7-4] -> [ladder(3-bottom,5-3),ladder(2-right,1-3),ladder(1-n/a,4-2)]
[1-2,6-3,7-1,7-3] -> [ladder(3-bottom,5-3),ladder(2-right,1-3),ladder(1-n/a,4-2)]
[1-2,6-3,7-1,7-4] -> [ladder(3-bottom,5-3),ladder(2-right,1-3),ladder(1-n/a,4-2)]
[1-3,2-1,2-3,3-2] -> [ladder(3-top,3-1),ladder(2-left,1-4),ladder(1-n/a,3-3)]
[1-3,2-1,2-3,5-1] -> [ladder(3-bottom,3-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-3,2-1,2-3,6-1] -> [ladder(3-bottom,3-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-3,2-1,2-3,7-1] -> [ladder(3-bottom,3-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-3,2-1,3-1,5-1] -> [ladder(3-bottom,3-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-3,2-1,3-1,6-1] -> [ladder(3-bottom,3-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-3,2-1,3-1,6-3] -> [ladder(3-top,4-2),ladder(2-left,1-4),ladder(1-n/a,2-3)]
[1-3,2-1,3-1,7-1] -> [ladder(3-bottom,3-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-3,2-1,3-1,7-3] -> [ladder(3-top,4-2),ladder(2-left,1-4),ladder(1-n/a,2-3)]
[1-3,2-1,3-2,4-2] -> [ladder(3-top,1-2),ladder(2-left,1-4),ladder(1-n/a,3-3)]
[1-3,2-1,3-2,6-3] -> [ladder(3-top,4-2),ladder(2-left,1-4),ladder(1-n/a,2-3)]
[1-3,2-1,3-2,7-3] -> [ladder(3-top,4-2),ladder(2-left,1-4),ladder(1-n/a,2-3)]
[1-3,2-1,4-1,5-1] -> [ladder(3-bottom,3-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-3,2-1,4-1,6-1] -> [ladder(3-bottom,3-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-3,2-1,4-1,6-3] -> [ladder(3-top,4-2),ladder(2-left,1-4),ladder(1-n/a,2-3)]
[1-3,2-1,4-1,7-1] -> [ladder(3-bottom,3-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-3,2-1,4-1,7-3] -> [ladder(3-top,4-2),ladder(2-left,1-4),ladder(1-n/a,2-3)]
[1-3,2-1,5-1,6-1] -> [ladder(3-bottom,3-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-3,2-1,5-1,7-1] -> [ladder(3-bottom,3-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-3,2-1,6-1,7-1] -> [ladder(3-bottom,3-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-3,2-1,6-3,7-3] -> [ladder(3-top,4-2),ladder(2-left,1-4),ladder(1-n/a,2-3)]
[1-3,2-3,3-1,5-1] -> [ladder(3-bottom,3-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-3,2-3,3-1,6-1] -> [ladder(3-bottom,3-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-3,2-3,3-1,7-1] -> [ladder(3-bottom,3-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-3,2-3,3-3,5-1] -> [ladder(3-top,4-3),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-3,2-3,3-3,6-1] -> [ladder(3-top,4-3),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-3,2-3,3-3,7-1] -> [ladder(3-top,4-3),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-3,2-3,4-1,5-1] -> [ladder(3-bottom,3-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-3,2-3,4-1,6-1] -> [ladder(3-bottom,3-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-3,2-3,4-1,7-1] -> [ladder(3-bottom,3-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-3,2-3,4-2,5-1] -> [ladder(3-top,5-2),ladder(2-left,1-4),ladder(1-n/a,3-3)]
[1-3,2-3,4-2,7-3] -> [ladder(3-top,2-2),ladder(2-left,1-4),ladder(1-n/a,4-3)]
[1-3,2-3,4-3,5-1] -> [ladder(3-top,2-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-3,2-3,4-3,6-1] -> [ladder(3-top,2-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-3,2-3,4-3,7-1] -> [ladder(3-top,2-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-3,2-3,5-2,7-3] -> [ladder(3-top,2-2),ladder(2-left,1-4),ladder(1-n/a,4-3)]
[1-3,3-1,3-2,4-2] -> [ladder(3-top,1-2),ladder(2-left,1-4),ladder(1-n/a,3-3)]
[1-3,3-1,3-2,5-2] -> [ladder(3-top,1-2),ladder(2-left,1-4),ladder(1-n/a,3-3)]
[1-3,3-1,3-2,6-3] -> [ladder(3-top,4-2),ladder(2-left,1-4),ladder(1-n/a,2-3)]
[1-3,3-1,3-2,7-3] -> [ladder(3-top,4-2),ladder(2-left,1-4),ladder(1-n/a,2-3)]
[1-3,3-1,4-1,5-1] -> [ladder(3-bottom,3-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-3,3-1,4-1,6-1] -> [ladder(3-bottom,3-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-3,3-1,4-1,6-3] -> [ladder(3-top,4-2),ladder(2-left,1-4),ladder(1-n/a,2-3)]
[1-3,3-1,4-1,7-1] -> [ladder(3-bottom,3-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-3,3-1,4-1,7-3] -> [ladder(3-top,4-2),ladder(2-left,1-4),ladder(1-n/a,2-3)]
[1-3,3-1,5-1,6-1] -> [ladder(3-bottom,3-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-3,3-1,5-1,7-1] -> [ladder(3-bottom,3-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-3,3-1,6-1,7-1] -> [ladder(3-bottom,3-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-3,3-1,6-3,7-3] -> [ladder(3-top,4-2),ladder(2-left,1-4),ladder(1-n/a,2-3)]
[1-3,3-2,3-3,5-1] -> [ladder(3-top,4-3),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-3,3-2,3-3,6-1] -> [ladder(3-top,4-3),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-3,3-2,3-3,7-1] -> [ladder(3-top,4-3),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-3,3-2,4-1,4-2] -> [ladder(3-top,1-2),ladder(2-left,1-4),ladder(1-n/a,3-3)]
[1-3,3-2,4-1,5-2] -> [ladder(3-top,1-2),ladder(2-left,1-4),ladder(1-n/a,3-3)]
[1-3,3-2,4-1,6-3] -> [ladder(3-top,4-2),ladder(2-left,1-4),ladder(1-n/a,2-3)]
[1-3,3-2,4-1,7-3] -> [ladder(3-top,4-2),ladder(2-left,1-4),ladder(1-n/a,2-3)]
[1-3,3-2,4-2,6-3] -> [ladder(3-bottom,5-3),ladder(2-left,1-4),ladder(1-n/a,2-3)]
[1-3,3-2,4-3,5-1] -> [ladder(3-bottom,2-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-3,3-2,4-3,6-1] -> [ladder(3-bottom,2-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-3,3-2,4-3,7-1] -> [ladder(3-bottom,2-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-3,3-2,5-2,6-3] -> [ladder(3-bottom,5-3),ladder(2-left,1-4),ladder(1-n/a,2-3)]
[1-3,3-2,6-3,7-4] -> [ladder(3-bottom,5-3),ladder(2-left,1-4),ladder(1-n/a,2-3)]
[1-3,3-3,5-1,6-1] -> [ladder(3-top,4-3),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-3,3-3,5-1,7-1] -> [ladder(3-top,4-3),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-3,3-3,6-1,7-1] -> [ladder(3-top,4-3),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-3,4-1,5-1,6-1] -> [ladder(3-bottom,3-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-3,4-1,5-1,7-1] -> [ladder(3-bottom,3-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-3,4-1,6-1,7-1] -> [ladder(3-bottom,3-2),ladder(2-left,1-4),ladder(1-n/a,4-2)]
[1-3,4-1,6-3,7-3] -> [ladder(3-top,4-2),ladder(2-left,1-4),ladder(1-n/a,2-3)]
[1-3,4-2,5-2,6-3] -> [ladder(3-bottom,5-3),ladder(2-left,1-4),ladder(1-n/a,2-3)]
[1-3,4-2,6-3,7-3] -> [ladder(3-bottom,5-3),ladder(2-left,1-4),ladder(1-n/a,2-3)]
[1-3,4-2,6-3,7-4] -> [ladder(3-bottom,5-3),ladder(2-left,1-4),ladder(1-n/a,2-3)]
[1-3,5-2,6-3,7-3] -> [ladder(3-bottom,5-3),ladder(2-left,1-4),ladder(1-n/a,2-3)]
[1-3,5-2,6-3,7-4] -> [ladder(3-bottom,5-3),ladder(2-left,1-4),ladder(1-n/a,2-3)]
[1-3,6-3,7-3,7-4] -> [ladder(3-bottom,5-3),ladder(2-left,1-4),ladder(1-n/a,2-3)]
[1-4,2-1,2-2,6-3] -> [ladder(3-top,4-2),ladder(2-right,1-3),ladder(1-n/a,2-4)]
[1-4,2-1,2-3,4-3] -> [ladder(3-top,2-2),ladder(2-left,4-2),ladder(1-n/a,2-4)]
[1-4,2-1,2-4,5-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[1-4,2-1,2-4,6-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[1-4,2-1,2-4,6-3] -> [ladder(3-top,4-2),ladder(2-left,3-4),ladder(1-n/a,2-3)]
[1-4,2-1,2-4,7-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[1-4,2-1,3-2,3-4] -> [ladder(3-top,1-3),ladder(2-left,4-2),ladder(1-n/a,3-3)]
[1-4,2-2,2-4,5-1] -> [ladder(3-top,2-3),ladder(2-left,4-3),ladder(1-n/a,4-2)]
[1-4,2-2,2-4,6-1] -> [ladder(3-top,2-3),ladder(2-left,4-3),ladder(1-n/a,4-2)]
[1-4,2-2,2-4,7-1] -> [ladder(3-top,2-3),ladder(2-left,4-3),ladder(1-n/a,4-2)]
[1-4,2-2,3-1,6-3] -> [ladder(3-top,4-2),ladder(2-right,1-3),ladder(1-n/a,2-4)]
[1-4,2-2,3-2,4-3] -> [ladder(3-bottom,1-2),ladder(2-left,4-2),ladder(1-n/a,2-4)]
[1-4,2-2,4-1,6-3] -> [ladder(3-top,4-2),ladder(2-right,1-3),ladder(1-n/a,2-4)]
[1-4,2-2,4-2,6-3] -> [ladder(3-bottom,5-3),ladder(2-right,1-3),ladder(1-n/a,2-4)]
[1-4,2-2,4-3,5-1] -> [ladder(3-bottom,1-2),ladder(2-left,3-2),ladder(1-n/a,2-4)]
[1-4,2-2,4-3,6-1] -> [ladder(3-bottom,1-2),ladder(2-left,3-2),ladder(1-n/a,2-4)]
[1-4,2-2,4-3,7-1] -> [ladder(3-bottom,1-2),ladder(2-left,3-2),ladder(1-n/a,2-4)]
[1-4,2-2,5-1,7-3] -> [ladder(3-bottom,2-3),ladder(2-left,3-3),ladder(1-n/a,4-2)]
[1-4,2-2,5-2,6-3] -> [ladder(3-bottom,5-3),ladder(2-right,1-3),ladder(1-n/a,2-4)]
[1-4,2-2,6-1,7-3] -> [ladder(3-bottom,2-3),ladder(2-left,3-3),ladder(1-n/a,4-2)]
[1-4,2-2,6-3,7-4] -> [ladder(3-bottom,5-3),ladder(2-right,1-3),ladder(1-n/a,2-4)]
[1-4,2-2,7-1,7-3] -> [ladder(3-bottom,2-3),ladder(2-left,3-3),ladder(1-n/a,4-2)]
[1-4,2-3,2-4,7-3] -> [ladder(3-top,2-2),ladder(2-left,3-4),ladder(1-n/a,4-3)]
[1-4,2-3,3-1,3-2] -> [ladder(3-top,4-3),ladder(2-left,4-2),ladder(1-n/a,2-4)]
[1-4,2-3,3-1,4-3] -> [ladder(3-top,2-2),ladder(2-left,4-2),ladder(1-n/a,2-4)]
[1-4,2-3,3-1,7-3] -> [ladder(3-bottom,2-1),ladder(2-left,3-3),ladder(1-n/a,2-4)]
[1-4,2-3,3-2,4-1] -> [ladder(3-top,4-3),ladder(2-left,4-2),ladder(1-n/a,2-4)]
[1-4,2-3,4-1,4-3] -> [ladder(3-top,2-2),ladder(2-left,4-2),ladder(1-n/a,2-4)]
[1-4,2-3,4-2,6-2] -> [ladder(3-top,2-2),ladder(2-right,4-3),ladder(1-n/a,2-4)]
[1-4,2-3,4-2,7-2] -> [ladder(3-top,2-2),ladder(2-right,4-3),ladder(1-n/a,2-4)]
[1-4,2-3,5-1,5-2] -> [ladder(3-top,6-2),ladder(2-left,3-3),ladder(1-n/a,2-4)]
[1-4,2-3,5-1,7-3] -> [ladder(3-bottom,4-1),ladder(2-left,3-3),ladder(1-n/a,2-4)]
[1-4,2-3,5-2,6-1] -> [ladder(3-top,6-2),ladder(2-left,3-3),ladder(1-n/a,2-4)]
[1-4,2-3,5-2,6-2] -> [ladder(3-top,2-2),ladder(2-right,4-3),ladder(1-n/a,2-4)]
[1-4,2-3,5-2,7-1] -> [ladder(3-top,6-2),ladder(2-left,3-3),ladder(1-n/a,2-4)]
[1-4,2-3,5-2,7-2] -> [ladder(3-top,2-2),ladder(2-right,4-3),ladder(1-n/a,2-4)]
[1-4,2-3,6-2,7-2] -> [ladder(3-top,2-2),ladder(2-right,4-3),ladder(1-n/a,2-4)]
[1-4,2-4,3-1,5-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[1-4,2-4,3-1,6-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[1-4,2-4,3-1,6-3] -> [ladder(3-top,4-2),ladder(2-left,3-4),ladder(1-n/a,2-3)]
[1-4,2-4,3-1,7-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[1-4,2-4,3-2,6-3] -> [ladder(3-top,4-2),ladder(2-left,3-4),ladder(1-n/a,2-3)]
[1-4,2-4,4-1,5-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[1-4,2-4,4-1,6-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[1-4,2-4,4-1,6-3] -> [ladder(3-top,4-2),ladder(2-left,3-4),ladder(1-n/a,2-3)]
[1-4,2-4,4-1,7-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[1-4,2-4,6-3,7-3] -> [ladder(3-top,4-2),ladder(2-left,3-4),ladder(1-n/a,2-3)]
[1-4,3-1,3-2,3-4] -> [ladder(3-top,1-3),ladder(2-left,4-2),ladder(1-n/a,3-3)]
[1-4,3-1,4-2,6-3] -> [ladder(3-bottom,2-1),ladder(2-right,2-3),ladder(1-n/a,2-4)]
[1-4,3-1,5-2,6-3] -> [ladder(3-bottom,2-1),ladder(2-right,2-3),ladder(1-n/a,2-4)]
[1-4,3-2,3-4,4-1] -> [ladder(3-top,1-3),ladder(2-left,4-2),ladder(1-n/a,3-3)]
[1-4,3-2,4-2,6-4] -> [ladder(3-top,6-3),ladder(2-right,2-3),ladder(1-n/a,2-4)]
[1-4,3-2,5-2,6-4] -> [ladder(3-top,6-3),ladder(2-right,2-3),ladder(1-n/a,2-4)]
[1-4,3-2,6-2,6-4] -> [ladder(3-top,6-3),ladder(2-right,2-3),ladder(1-n/a,2-4)]
[1-4,3-2,6-2,7-3] -> [ladder(3-bottom,6-3),ladder(2-right,2-3),ladder(1-n/a,2-4)]
[1-4,3-2,6-4,7-2] -> [ladder(3-top,6-3),ladder(2-right,2-3),ladder(1-n/a,2-4)]
[1-4,3-3,3-4,5-1] -> [ladder(3-top,1-3),ladder(2-left,4-3),ladder(1-n/a,4-2)]
[1-4,3-3,3-4,6-1] -> [ladder(3-top,1-3),ladder(2-left,4-3),ladder(1-n/a,4-2)]
[1-4,3-3,3-4,7-1] -> [ladder(3-top,1-3),ladder(2-left,4-3),ladder(1-n/a,4-2)]
[1-4,3-3,4-2,6-1] -> [ladder(3-top,4-1),ladder(2-left,4-3),ladder(1-n/a,2-4)]
[1-4,3-3,4-2,7-1] -> [ladder(3-top,4-1),ladder(2-left,4-3),ladder(1-n/a,2-4)]
[1-4,3-4,5-1,7-3] -> [ladder(3-top,1-3),ladder(2-left,3-3),ladder(1-n/a,4-2)]
[1-4,3-4,6-1,7-3] -> [ladder(3-top,1-3),ladder(2-left,3-3),ladder(1-n/a,4-2)]
[1-4,3-4,7-1,7-3] -> [ladder(3-top,1-3),ladder(2-left,3-3),ladder(1-n/a,4-2)]
[1-4,4-2,5-1,6-3] -> [ladder(3-top,6-2),ladder(2-right,2-3),ladder(1-n/a,2-4)]
[1-4,4-2,5-1,7-3] -> [ladder(3-top,5-2),ladder(2-right,2-3),ladder(1-n/a,2-4)]
[1-4,4-2,5-2,6-4] -> [ladder(3-top,6-3),ladder(2-right,2-3),ladder(1-n/a,2-4)]
[1-4,4-2,6-2,6-4] -> [ladder(3-top,6-3),ladder(2-right,2-3),ladder(1-n/a,2-4)]
[1-4,4-2,6-2,7-3] -> [ladder(3-bottom,6-3),ladder(2-right,2-3),ladder(1-n/a,2-4)]
[1-4,4-2,6-4,7-2] -> [ladder(3-top,6-3),ladder(2-right,2-3),ladder(1-n/a,2-4)]
[1-4,5-1,5-2,6-3] -> [ladder(3-top,6-2),ladder(2-right,2-3),ladder(1-n/a,2-4)]
[1-4,5-1,5-2,7-2] -> [ladder(3-bottom,6-2),ladder(2-right,2-3),ladder(1-n/a,2-4)]
[1-4,5-1,6-3,7-3] -> [ladder(3-bottom,4-1),ladder(2-right,2-3),ladder(1-n/a,2-4)]
[1-4,5-1,7-2,7-3] -> [ladder(3-top,5-2),ladder(2-right,2-3),ladder(1-n/a,2-4)]
[1-4,5-2,6-1,6-3] -> [ladder(3-top,6-2),ladder(2-right,2-3),ladder(1-n/a,2-4)]
[1-4,5-2,6-1,7-2] -> [ladder(3-bottom,6-2),ladder(2-right,2-3),ladder(1-n/a,2-4)]
[1-4,5-2,6-2,6-4] -> [ladder(3-top,6-3),ladder(2-right,2-3),ladder(1-n/a,2-4)]
[1-4,5-2,6-2,7-3] -> [ladder(3-bottom,6-3),ladder(2-right,2-3),ladder(1-n/a,2-4)]
[1-4,5-2,6-3,7-1] -> [ladder(3-top,6-2),ladder(2-right,2-3),ladder(1-n/a,2-4)]
[1-4,5-2,6-4,7-2] -> [ladder(3-top,6-3),ladder(2-right,2-3),ladder(1-n/a,2-4)]
[1-4,5-2,7-1,7-2] -> [ladder(3-bottom,6-2),ladder(2-right,2-3),ladder(1-n/a,2-4)]
[1-4,5-2,7-2,7-3] -> [ladder(3-bottom,6-3),ladder(2-right,2-3),ladder(1-n/a,2-4)]
[1-4,6-1,7-2,7-3] -> [ladder(3-top,5-2),ladder(2-right,2-3),ladder(1-n/a,2-4)]
[1-4,6-2,6-4,7-2] -> [ladder(3-top,6-3),ladder(2-right,2-3),ladder(1-n/a,2-4)]
[1-4,6-2,7-2,7-3] -> [ladder(3-bottom,6-3),ladder(2-right,2-3),ladder(1-n/a,2-4)]
[1-4,7-1,7-2,7-3] -> [ladder(3-top,5-2),ladder(2-right,2-3),ladder(1-n/a,2-4)]
[2-1,2-2,2-4,3-2] -> [ladder(3-bottom,1-2),ladder(2-left,3-4),ladder(1-n/a,3-3)]
[2-1,2-2,2-4,4-2] -> [ladder(3-bottom,1-2),ladder(2-left,3-4),ladder(1-n/a,3-3)]
[2-1,2-2,3-1,3-4] -> [ladder(3-bottom,1-3),ladder(2-left,2-3),ladder(1-n/a,3-2)]
[2-1,2-2,3-1,6-2] -> [ladder(3-bottom,1-2),ladder(2-right,4-3),ladder(1-n/a,3-2)]
[2-1,2-2,3-1,7-2] -> [ladder(3-bottom,1-2),ladder(2-right,4-3),ladder(1-n/a,3-2)]
[2-1,2-2,3-2,5-4] -> [ladder(3-bottom,1-2),ladder(2-right,1-4),ladder(1-n/a,3-3)]
[2-1,2-2,3-3,6-2] -> [ladder(3-bottom,1-2),ladder(2-right,4-3),ladder(1-n/a,3-2)]
[2-1,2-2,3-3,7-2] -> [ladder(3-bottom,1-2),ladder(2-right,4-3),ladder(1-n/a,3-2)]
[2-1,2-2,3-4,4-1] -> [ladder(3-bottom,1-3),ladder(2-left,2-3),ladder(1-n/a,3-2)]
[2-1,2-2,4-1,6-2] -> [ladder(3-bottom,1-2),ladder(2-right,4-3),ladder(1-n/a,3-2)]
[2-1,2-2,4-1,7-2] -> [ladder(3-bottom,1-2),ladder(2-right,4-3),ladder(1-n/a,3-2)]
[2-1,2-2,4-2,5-4] -> [ladder(3-bottom,1-2),ladder(2-right,1-4),ladder(1-n/a,3-3)]
[2-1,2-2,6-2,7-2] -> [ladder(3-bottom,1-2),ladder(2-right,4-3),ladder(1-n/a,3-2)]
[2-1,2-2,6-3,7-4] -> [ladder(3-bottom,5-3),ladder(2-right,1-3),ladder(1-n/a,3-2)]
[2-1,2-3,2-4,3-2] -> [ladder(3-top,3-1),ladder(2-left,3-4),ladder(1-n/a,3-3)]
[2-1,2-3,2-4,5-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[2-1,2-3,2-4,6-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[2-1,2-3,2-4,7-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[2-1,2-3,3-2,3-4] -> [ladder(3-bottom,1-3),ladder(2-left,4-2),ladder(1-n/a,3-3)]
[2-1,2-3,5-1,5-2] -> [ladder(3-top,6-2),ladder(2-left,3-3),ladder(1-n/a,2-2)]
[2-1,2-3,5-1,6-2] -> [ladder(3-top,6-1),ladder(2-right,2-2),ladder(1-n/a,3-3)]
[2-1,2-3,5-1,6-3] -> [ladder(3-top,6-2),ladder(2-right,2-2),ladder(1-n/a,3-3)]
[2-1,2-3,5-1,7-2] -> [ladder(3-bottom,6-2),ladder(2-right,2-2),ladder(1-n/a,3-3)]
[2-1,2-3,5-2,6-1] -> [ladder(3-top,6-2),ladder(2-left,3-3),ladder(1-n/a,2-2)]
[2-1,2-3,5-2,6-2] -> [ladder(3-bottom,3-3),ladder(2-right,4-3),ladder(1-n/a,2-2)]
[2-1,2-3,5-2,6-3] -> [ladder(3-top,4-3),ladder(2-right,1-4),ladder(1-n/a,2-2)]
[2-1,2-3,5-2,7-1] -> [ladder(3-top,6-2),ladder(2-left,3-3),ladder(1-n/a,2-2)]
[2-1,2-3,5-2,7-2] -> [ladder(3-bottom,3-3),ladder(2-right,4-3),ladder(1-n/a,2-2)]
[2-1,2-3,6-1,6-3] -> [ladder(3-top,6-2),ladder(2-right,2-2),ladder(1-n/a,3-3)]
[2-1,2-3,6-1,7-2] -> [ladder(3-bottom,6-2),ladder(2-right,2-2),ladder(1-n/a,3-3)]
[2-1,2-3,6-3,7-1] -> [ladder(3-top,6-2),ladder(2-right,2-2),ladder(1-n/a,3-3)]
[2-1,2-4,3-1,5-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[2-1,2-4,3-1,6-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[2-1,2-4,3-1,6-3] -> [ladder(3-top,4-2),ladder(2-left,3-4),ladder(1-n/a,2-3)]
[2-1,2-4,3-1,7-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[2-1,2-4,3-2,6-3] -> [ladder(3-top,4-2),ladder(2-left,3-4),ladder(1-n/a,2-3)]
[2-1,2-4,3-2,7-3] -> [ladder(3-top,4-2),ladder(2-left,3-4),ladder(1-n/a,2-3)]
[2-1,2-4,4-1,5-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[2-1,2-4,4-1,6-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[2-1,2-4,4-1,6-3] -> [ladder(3-top,4-2),ladder(2-left,3-4),ladder(1-n/a,2-3)]
[2-1,2-4,4-1,7-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[2-1,2-4,5-1,6-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[2-1,2-4,5-1,7-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[2-1,2-4,6-1,7-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[2-1,2-4,6-3,7-3] -> [ladder(3-top,4-2),ladder(2-left,3-4),ladder(1-n/a,2-3)]
[2-1,3-1,3-4,4-2] -> [ladder(3-bottom,1-3),ladder(2-left,2-3),ladder(1-n/a,1-2)]
[2-1,3-1,4-2,6-3] -> [ladder(3-bottom,5-3),ladder(2-right,1-3),ladder(1-n/a,1-2)]
[2-1,3-1,5-2,6-4] -> [ladder(3-top,6-3),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[2-1,3-1,5-4,6-3] -> [ladder(3-top,4-2),ladder(2-right,1-4),ladder(1-n/a,2-3)]
[2-1,3-1,6-1,6-2] -> [ladder(3-top,4-1),ladder(2-right,4-3),ladder(1-n/a,2-2)]
[2-1,3-1,6-2,7-1] -> [ladder(3-top,4-1),ladder(2-right,4-3),ladder(1-n/a,2-2)]
[2-1,3-2,5-4,6-3] -> [ladder(3-top,4-2),ladder(2-right,1-4),ladder(1-n/a,2-3)]
[2-1,3-3,5-2,6-2] -> [ladder(3-bottom,1-2),ladder(2-right,4-3),ladder(1-n/a,2-2)]
[2-1,3-3,5-2,6-3] -> [ladder(3-top,4-3),ladder(2-right,1-4),ladder(1-n/a,2-2)]
[2-1,3-3,5-2,7-2] -> [ladder(3-bottom,1-2),ladder(2-right,4-3),ladder(1-n/a,2-2)]
[2-1,3-4,4-1,4-2] -> [ladder(3-bottom,1-3),ladder(2-left,2-3),ladder(1-n/a,1-2)]
[2-1,3-4,4-2,5-2] -> [ladder(3-bottom,1-3),ladder(2-left,2-3),ladder(1-n/a,1-2)]
[2-1,3-4,5-2,6-3] -> [ladder(3-bottom,1-3),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[2-1,4-1,4-2,6-3] -> [ladder(3-bottom,5-3),ladder(2-right,1-3),ladder(1-n/a,1-2)]
[2-1,4-1,5-2,6-4] -> [ladder(3-top,6-3),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[2-1,4-1,5-4,6-3] -> [ladder(3-top,4-2),ladder(2-right,1-4),ladder(1-n/a,2-3)]
[2-1,4-2,5-2,6-3] -> [ladder(3-bottom,5-3),ladder(2-right,1-3),ladder(1-n/a,1-2)]
[2-1,4-2,6-3,7-3] -> [ladder(3-bottom,5-3),ladder(2-right,1-3),ladder(1-n/a,1-2)]
[2-1,4-2,6-3,7-4] -> [ladder(3-bottom,5-3),ladder(2-right,1-3),ladder(1-n/a,1-2)]
[2-1,5-1,5-2,6-2] -> [ladder(3-top,6-1),ladder(2-right,4-3),ladder(1-n/a,2-2)]
[2-1,5-1,5-2,6-3] -> [ladder(3-top,6-2),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[2-1,5-1,5-2,7-2] -> [ladder(3-bottom,6-2),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[2-1,5-1,6-2,7-3] -> [ladder(3-top,6-1),ladder(2-right,2-2),ladder(1-n/a,4-3)]
[2-1,5-1,7-2,7-3] -> [ladder(3-top,5-2),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[2-1,5-2,5-4,6-2] -> [ladder(3-bottom,3-3),ladder(2-right,4-3),ladder(1-n/a,2-2)]
[2-1,5-2,5-4,7-2] -> [ladder(3-bottom,3-3),ladder(2-right,4-3),ladder(1-n/a,2-2)]
[2-1,5-2,6-1,6-3] -> [ladder(3-top,6-2),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[2-1,5-2,6-1,7-2] -> [ladder(3-bottom,6-2),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[2-1,5-2,6-2,6-4] -> [ladder(3-top,6-3),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[2-1,5-2,6-2,7-3] -> [ladder(3-bottom,6-3),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[2-1,5-2,6-3,7-1] -> [ladder(3-top,6-2),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[2-1,5-2,6-4,7-2] -> [ladder(3-top,6-3),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[2-1,5-2,7-2,7-3] -> [ladder(3-bottom,6-3),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[2-1,5-4,6-3,7-3] -> [ladder(3-top,4-2),ladder(2-right,1-4),ladder(1-n/a,2-3)]
[2-1,6-1,6-2,7-1] -> [ladder(3-top,4-1),ladder(2-right,4-3),ladder(1-n/a,2-2)]
[2-1,6-1,6-2,7-2] -> [ladder(3-top,4-1),ladder(2-right,4-3),ladder(1-n/a,2-2)]
[2-1,6-1,7-2,7-3] -> [ladder(3-top,5-2),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[2-1,6-2,7-1,7-2] -> [ladder(3-top,4-1),ladder(2-right,4-3),ladder(1-n/a,2-2)]
[2-2,2-4,3-1,3-2] -> [ladder(3-bottom,1-2),ladder(2-left,3-4),ladder(1-n/a,3-3)]
[2-2,2-4,3-1,4-2] -> [ladder(3-bottom,1-2),ladder(2-left,3-4),ladder(1-n/a,3-3)]
[2-2,2-4,3-2,4-1] -> [ladder(3-bottom,1-2),ladder(2-left,3-4),ladder(1-n/a,3-3)]
[2-2,2-4,3-2,5-1] -> [ladder(3-top,2-3),ladder(2-left,4-3),ladder(1-n/a,4-2)]
[2-2,2-4,3-2,6-1] -> [ladder(3-top,2-3),ladder(2-left,4-3),ladder(1-n/a,4-2)]
[2-2,2-4,3-2,7-1] -> [ladder(3-top,2-3),ladder(2-left,4-3),ladder(1-n/a,4-2)]
[2-2,2-4,4-1,4-2] -> [ladder(3-bottom,1-2),ladder(2-left,3-4),ladder(1-n/a,3-3)]
[2-2,2-4,5-1,6-1] -> [ladder(3-top,2-3),ladder(2-left,4-3),ladder(1-n/a,4-2)]
[2-2,2-4,5-1,7-1] -> [ladder(3-top,2-3),ladder(2-left,4-3),ladder(1-n/a,4-2)]
[2-2,2-4,6-1,7-1] -> [ladder(3-top,2-3),ladder(2-left,4-3),ladder(1-n/a,4-2)]
[2-2,3-1,3-2,5-4] -> [ladder(3-bottom,1-2),ladder(2-right,1-4),ladder(1-n/a,3-3)]
[2-2,3-1,3-3,6-2] -> [ladder(3-bottom,1-2),ladder(2-right,4-3),ladder(1-n/a,3-2)]
[2-2,3-1,3-3,7-2] -> [ladder(3-bottom,1-2),ladder(2-right,4-3),ladder(1-n/a,3-2)]
[2-2,3-1,3-4,4-1] -> [ladder(3-bottom,1-3),ladder(2-left,2-3),ladder(1-n/a,3-2)]
[2-2,3-1,4-1,6-2] -> [ladder(3-bottom,1-2),ladder(2-right,4-3),ladder(1-n/a,3-2)]
[2-2,3-1,4-1,7-2] -> [ladder(3-bottom,1-2),ladder(2-right,4-3),ladder(1-n/a,3-2)]
[2-2,3-1,4-2,5-4] -> [ladder(3-bottom,1-2),ladder(2-right,1-4),ladder(1-n/a,3-3)]
[2-2,3-1,6-2,7-2] -> [ladder(3-bottom,1-2),ladder(2-right,4-3),ladder(1-n/a,3-2)]
[2-2,3-1,6-3,7-4] -> [ladder(3-bottom,5-3),ladder(2-right,1-3),ladder(1-n/a,3-2)]
[2-2,3-2,3-3,7-3] -> [ladder(3-bottom,1-2),ladder(2-left,4-2),ladder(1-n/a,4-3)]
[2-2,3-2,3-4,5-1] -> [ladder(3-bottom,1-3),ladder(2-left,2-3),ladder(1-n/a,4-2)]
[2-2,3-2,3-4,6-1] -> [ladder(3-bottom,1-3),ladder(2-left,2-3),ladder(1-n/a,4-2)]
[2-2,3-2,3-4,7-1] -> [ladder(3-bottom,1-3),ladder(2-left,2-3),ladder(1-n/a,4-2)]
[2-2,3-2,4-1,5-4] -> [ladder(3-bottom,1-2),ladder(2-right,1-4),ladder(1-n/a,3-3)]
[2-2,3-2,4-2,5-4] -> [ladder(3-bottom,1-2),ladder(2-right,1-4),ladder(1-n/a,3-3)]
[2-2,3-2,5-1,6-3] -> [ladder(3-bottom,5-3),ladder(2-right,1-3),ladder(1-n/a,4-2)]
[2-2,3-2,5-2,5-4] -> [ladder(3-bottom,1-2),ladder(2-right,1-4),ladder(1-n/a,3-3)]
[2-2,3-2,6-1,6-3] -> [ladder(3-bottom,5-3),ladder(2-right,1-3),ladder(1-n/a,4-2)]
[2-2,3-2,6-3,7-1] -> [ladder(3-bottom,5-3),ladder(2-right,1-3),ladder(1-n/a,4-2)]
[2-2,3-3,4-1,6-2] -> [ladder(3-bottom,1-2),ladder(2-right,4-3),ladder(1-n/a,3-2)]
[2-2,3-3,4-1,7-2] -> [ladder(3-bottom,1-2),ladder(2-right,4-3),ladder(1-n/a,3-2)]
[2-2,3-3,5-1,7-3] -> [ladder(3-bottom,1-2),ladder(2-left,3-2),ladder(1-n/a,4-3)]
[2-2,3-3,6-1,7-3] -> [ladder(3-bottom,1-2),ladder(2-left,3-2),ladder(1-n/a,4-3)]
[2-2,3-3,6-2,7-2] -> [ladder(3-bottom,1-2),ladder(2-right,4-3),ladder(1-n/a,3-2)]
[2-2,3-3,7-1,7-3] -> [ladder(3-bottom,1-2),ladder(2-left,3-2),ladder(1-n/a,4-3)]
[2-2,3-4,5-1,6-1] -> [ladder(3-bottom,1-3),ladder(2-left,2-3),ladder(1-n/a,4-2)]
[2-2,3-4,5-1,7-1] -> [ladder(3-bottom,1-3),ladder(2-left,2-3),ladder(1-n/a,4-2)]
[2-2,3-4,6-1,7-1] -> [ladder(3-bottom,1-3),ladder(2-left,2-3),ladder(1-n/a,4-2)]
[2-2,4-1,4-2,5-4] -> [ladder(3-bottom,1-2),ladder(2-right,1-4),ladder(1-n/a,3-3)]
[2-2,4-1,6-2,7-2] -> [ladder(3-bottom,1-2),ladder(2-right,4-3),ladder(1-n/a,3-2)]
[2-2,4-1,6-3,7-4] -> [ladder(3-bottom,5-3),ladder(2-right,1-3),ladder(1-n/a,3-2)]
[2-2,4-2,5-2,5-4] -> [ladder(3-bottom,1-2),ladder(2-right,1-4),ladder(1-n/a,3-3)]
[2-2,5-1,6-1,6-3] -> [ladder(3-bottom,5-3),ladder(2-right,1-3),ladder(1-n/a,4-2)]
[2-2,5-1,6-3,7-1] -> [ladder(3-bottom,5-3),ladder(2-right,1-3),ladder(1-n/a,4-2)]
[2-2,5-1,6-3,7-3] -> [ladder(3-bottom,5-3),ladder(2-right,1-3),ladder(1-n/a,4-2)]
[2-2,5-1,6-3,7-4] -> [ladder(3-bottom,5-3),ladder(2-right,1-3),ladder(1-n/a,4-2)]
[2-2,6-1,6-3,7-1] -> [ladder(3-bottom,5-3),ladder(2-right,1-3),ladder(1-n/a,4-2)]
[2-2,6-1,6-3,7-3] -> [ladder(3-bottom,5-3),ladder(2-right,1-3),ladder(1-n/a,4-2)]
[2-2,6-1,6-3,7-4] -> [ladder(3-bottom,5-3),ladder(2-right,1-3),ladder(1-n/a,4-2)]
[2-2,6-3,7-1,7-3] -> [ladder(3-bottom,5-3),ladder(2-right,1-3),ladder(1-n/a,4-2)]
[2-2,6-3,7-1,7-4] -> [ladder(3-bottom,5-3),ladder(2-right,1-3),ladder(1-n/a,4-2)]
[2-3,2-4,3-1,5-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[2-3,2-4,3-1,6-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[2-3,2-4,3-1,7-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[2-3,2-4,4-1,5-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[2-3,2-4,4-1,6-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[2-3,2-4,4-1,7-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[2-3,2-4,4-2,5-1] -> [ladder(3-top,5-2),ladder(2-left,3-4),ladder(1-n/a,3-3)]
[2-3,2-4,4-2,7-3] -> [ladder(3-top,2-2),ladder(2-left,3-4),ladder(1-n/a,4-3)]
[2-3,2-4,4-3,5-1] -> [ladder(3-top,2-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[2-3,2-4,4-3,6-1] -> [ladder(3-top,2-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[2-3,2-4,4-3,7-1] -> [ladder(3-top,2-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[2-3,2-4,5-2,7-3] -> [ladder(3-top,2-2),ladder(2-left,3-4),ladder(1-n/a,4-3)]
[2-3,3-1,3-2,3-4] -> [ladder(3-bottom,1-3),ladder(2-left,4-2),ladder(1-n/a,3-3)]
[2-3,3-1,3-2,7-3] -> [ladder(3-bottom,3-3),ladder(2-left,4-2),ladder(1-n/a,4-3)]
[2-3,3-1,5-1,5-2] -> [ladder(3-top,6-2),ladder(2-left,3-3),ladder(1-n/a,2-2)]
[2-3,3-1,5-1,6-2] -> [ladder(3-top,6-1),ladder(2-right,2-2),ladder(1-n/a,3-3)]
[2-3,3-1,5-1,6-3] -> [ladder(3-top,6-2),ladder(2-right,2-2),ladder(1-n/a,3-3)]
[2-3,3-1,5-1,7-2] -> [ladder(3-bottom,6-2),ladder(2-right,2-2),ladder(1-n/a,3-3)]
[2-3,3-1,5-2,6-1] -> [ladder(3-top,6-2),ladder(2-left,3-3),ladder(1-n/a,2-2)]
[2-3,3-1,5-2,6-2] -> [ladder(3-bottom,3-3),ladder(2-right,4-3),ladder(1-n/a,2-2)]
[2-3,3-1,5-2,6-3] -> [ladder(3-top,4-3),ladder(2-right,1-4),ladder(1-n/a,2-2)]
[2-3,3-1,5-2,7-1] -> [ladder(3-top,6-2),ladder(2-left,3-3),ladder(1-n/a,2-2)]
[2-3,3-1,5-2,7-2] -> [ladder(3-bottom,3-3),ladder(2-right,4-3),ladder(1-n/a,2-2)]
[2-3,3-1,6-1,6-3] -> [ladder(3-top,6-2),ladder(2-right,2-2),ladder(1-n/a,3-3)]
[2-3,3-1,6-1,7-2] -> [ladder(3-bottom,6-2),ladder(2-right,2-2),ladder(1-n/a,3-3)]
[2-3,3-1,6-3,7-1] -> [ladder(3-top,6-2),ladder(2-right,2-2),ladder(1-n/a,3-3)]
[2-3,3-2,3-4,4-1] -> [ladder(3-bottom,1-3),ladder(2-left,4-2),ladder(1-n/a,3-3)]
[2-3,3-2,4-1,7-3] -> [ladder(3-bottom,3-3),ladder(2-left,4-2),ladder(1-n/a,4-3)]
[2-3,3-2,5-1,6-3] -> [ladder(3-top,4-3),ladder(2-right,1-4),ladder(1-n/a,4-2)]
[2-3,3-2,5-1,6-4] -> [ladder(3-top,6-3),ladder(2-right,4-2),ladder(1-n/a,3-3)]
[2-3,3-2,5-1,7-2] -> [ladder(3-bottom,3-3),ladder(2-right,4-3),ladder(1-n/a,4-2)]
[2-3,3-2,6-1,6-3] -> [ladder(3-top,4-3),ladder(2-right,1-4),ladder(1-n/a,4-2)]
[2-3,3-2,6-1,6-4] -> [ladder(3-top,6-3),ladder(2-right,4-2),ladder(1-n/a,3-3)]
[2-3,3-2,6-1,7-2] -> [ladder(3-bottom,3-3),ladder(2-right,4-3),ladder(1-n/a,4-2)]
[2-3,3-2,6-3,7-1] -> [ladder(3-top,4-3),ladder(2-right,1-4),ladder(1-n/a,4-2)]
[2-3,3-2,6-4,7-1] -> [ladder(3-top,6-3),ladder(2-right,4-2),ladder(1-n/a,3-3)]
[2-3,3-2,7-1,7-2] -> [ladder(3-bottom,3-3),ladder(2-right,4-3),ladder(1-n/a,4-2)]
[2-3,3-3,3-4,5-1] -> [ladder(3-bottom,1-3),ladder(2-left,4-3),ladder(1-n/a,4-2)]
[2-3,3-3,3-4,6-1] -> [ladder(3-bottom,1-3),ladder(2-left,4-3),ladder(1-n/a,4-2)]
[2-3,3-3,3-4,7-1] -> [ladder(3-bottom,1-3),ladder(2-left,4-3),ladder(1-n/a,4-2)]
[2-3,3-3,5-1,6-3] -> [ladder(3-top,4-3),ladder(2-right,1-4),ladder(1-n/a,4-2)]
[2-3,3-3,5-1,7-3] -> [ladder(3-top,4-3),ladder(2-right,1-4),ladder(1-n/a,4-2)]
[2-3,3-3,6-1,6-3] -> [ladder(3-top,4-3),ladder(2-right,1-4),ladder(1-n/a,4-2)]
[2-3,3-3,6-1,7-3] -> [ladder(3-top,4-3),ladder(2-right,1-4),ladder(1-n/a,4-2)]
[2-3,3-3,6-3,7-1] -> [ladder(3-top,4-3),ladder(2-right,1-4),ladder(1-n/a,4-2)]
[2-3,3-3,7-1,7-3] -> [ladder(3-top,4-3),ladder(2-right,1-4),ladder(1-n/a,4-2)]
[2-3,3-4,5-1,7-3] -> [ladder(3-bottom,1-3),ladder(2-left,3-3),ladder(1-n/a,4-2)]
[2-3,3-4,6-1,7-3] -> [ladder(3-bottom,1-3),ladder(2-left,3-3),ladder(1-n/a,4-2)]
[2-3,3-4,7-1,7-3] -> [ladder(3-bottom,1-3),ladder(2-left,3-3),ladder(1-n/a,4-2)]
[2-3,4-1,5-1,5-2] -> [ladder(3-top,6-2),ladder(2-left,3-3),ladder(1-n/a,2-2)]
[2-3,4-1,5-1,6-2] -> [ladder(3-top,6-1),ladder(2-right,2-2),ladder(1-n/a,3-3)]
[2-3,4-1,5-1,6-3] -> [ladder(3-top,6-2),ladder(2-right,2-2),ladder(1-n/a,3-3)]
[2-3,4-1,5-1,7-2] -> [ladder(3-bottom,6-2),ladder(2-right,2-2),ladder(1-n/a,3-3)]
[2-3,4-1,5-2,6-1] -> [ladder(3-top,6-2),ladder(2-left,3-3),ladder(1-n/a,2-2)]
[2-3,4-1,5-2,6-2] -> [ladder(3-bottom,3-3),ladder(2-right,4-3),ladder(1-n/a,2-2)]
[2-3,4-1,5-2,6-3] -> [ladder(3-top,4-3),ladder(2-right,1-4),ladder(1-n/a,2-2)]
[2-3,4-1,5-2,7-1] -> [ladder(3-top,6-2),ladder(2-left,3-3),ladder(1-n/a,2-2)]
[2-3,4-1,5-2,7-2] -> [ladder(3-bottom,3-3),ladder(2-right,4-3),ladder(1-n/a,2-2)]
[2-3,4-1,6-1,6-3] -> [ladder(3-top,6-2),ladder(2-right,2-2),ladder(1-n/a,3-3)]
[2-3,4-1,6-1,7-2] -> [ladder(3-bottom,6-2),ladder(2-right,2-2),ladder(1-n/a,3-3)]
[2-3,4-1,6-3,7-1] -> [ladder(3-top,6-2),ladder(2-right,2-2),ladder(1-n/a,3-3)]
[2-3,4-2,5-2,7-4] -> [ladder(3-top,2-2),ladder(2-right,3-4),ladder(1-n/a,4-3)]
[2-3,4-2,7-3,7-4] -> [ladder(3-top,2-2),ladder(2-right,3-4),ladder(1-n/a,4-3)]
[2-3,5-1,5-4,7-2] -> [ladder(3-bottom,3-3),ladder(2-right,4-3),ladder(1-n/a,4-2)]
[2-3,5-1,6-1,6-4] -> [ladder(3-top,6-3),ladder(2-right,4-2),ladder(1-n/a,3-3)]
[2-3,5-1,6-3,7-3] -> [ladder(3-top,4-3),ladder(2-right,1-4),ladder(1-n/a,4-2)]
[2-3,5-1,6-4,7-1] -> [ladder(3-top,6-3),ladder(2-right,4-2),ladder(1-n/a,3-3)]
[2-3,5-2,7-3,7-4] -> [ladder(3-top,2-2),ladder(2-right,3-4),ladder(1-n/a,4-3)]
[2-3,5-4,6-1,7-2] -> [ladder(3-bottom,3-3),ladder(2-right,4-3),ladder(1-n/a,4-2)]
[2-3,5-4,7-1,7-2] -> [ladder(3-bottom,3-3),ladder(2-right,4-3),ladder(1-n/a,4-2)]
[2-3,6-1,6-3,7-3] -> [ladder(3-top,4-3),ladder(2-right,1-4),ladder(1-n/a,4-2)]
[2-3,6-1,6-4,7-1] -> [ladder(3-top,6-3),ladder(2-right,4-2),ladder(1-n/a,3-3)]
[2-3,6-3,7-1,7-3] -> [ladder(3-top,4-3),ladder(2-right,1-4),ladder(1-n/a,4-2)]
[2-4,3-1,3-2,6-3] -> [ladder(3-top,4-2),ladder(2-left,3-4),ladder(1-n/a,2-3)]
[2-4,3-1,3-2,7-3] -> [ladder(3-top,4-2),ladder(2-left,3-4),ladder(1-n/a,2-3)]
[2-4,3-1,4-1,5-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[2-4,3-1,4-1,6-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[2-4,3-1,4-1,6-3] -> [ladder(3-top,4-2),ladder(2-left,3-4),ladder(1-n/a,2-3)]
[2-4,3-1,4-1,7-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[2-4,3-1,5-1,6-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[2-4,3-1,5-1,7-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[2-4,3-1,6-1,7-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[2-4,3-1,6-3,7-3] -> [ladder(3-top,4-2),ladder(2-left,3-4),ladder(1-n/a,2-3)]
[2-4,3-2,4-1,6-3] -> [ladder(3-top,4-2),ladder(2-left,3-4),ladder(1-n/a,2-3)]
[2-4,3-2,4-1,7-3] -> [ladder(3-top,4-2),ladder(2-left,3-4),ladder(1-n/a,2-3)]
[2-4,3-2,4-2,7-3] -> [ladder(3-bottom,2-2),ladder(2-left,3-4),ladder(1-n/a,4-3)]
[2-4,3-2,4-3,5-1] -> [ladder(3-bottom,2-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[2-4,3-2,4-3,6-1] -> [ladder(3-bottom,2-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[2-4,3-2,4-3,7-1] -> [ladder(3-bottom,2-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[2-4,3-2,5-2,7-3] -> [ladder(3-bottom,2-2),ladder(2-left,3-4),ladder(1-n/a,4-3)]
[2-4,3-2,6-3,7-3] -> [ladder(3-top,4-2),ladder(2-left,3-4),ladder(1-n/a,2-3)]
[2-4,3-3,4-3,5-2] -> [ladder(3-bottom,1-2),ladder(2-left,3-4),ladder(1-n/a,2-2)]
[2-4,4-1,5-1,6-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[2-4,4-1,5-1,7-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[2-4,4-1,6-1,7-1] -> [ladder(3-bottom,3-2),ladder(2-left,3-4),ladder(1-n/a,4-2)]
[2-4,4-1,6-3,7-3] -> [ladder(3-top,4-2),ladder(2-left,3-4),ladder(1-n/a,2-3)]
[3-1,3-2,5-4,6-3] -> [ladder(3-top,4-2),ladder(2-right,1-4),ladder(1-n/a,2-3)]
[3-1,3-3,5-2,6-2] -> [ladder(3-bottom,1-2),ladder(2-right,4-3),ladder(1-n/a,2-2)]
[3-1,3-3,5-2,6-3] -> [ladder(3-top,4-3),ladder(2-right,1-4),ladder(1-n/a,2-2)]
[3-1,3-3,5-2,7-2] -> [ladder(3-bottom,1-2),ladder(2-right,4-3),ladder(1-n/a,2-2)]
[3-1,3-4,4-1,4-2] -> [ladder(3-bottom,1-3),ladder(2-left,2-3),ladder(1-n/a,1-2)]
[3-1,3-4,4-2,5-2] -> [ladder(3-bottom,1-3),ladder(2-left,2-3),ladder(1-n/a,1-2)]
[3-1,3-4,5-2,6-3] -> [ladder(3-bottom,1-3),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[3-1,4-1,5-2,6-4] -> [ladder(3-top,6-3),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[3-1,4-1,5-4,6-3] -> [ladder(3-top,4-2),ladder(2-right,1-4),ladder(1-n/a,2-3)]
[3-1,4-2,6-3,7-4] -> [ladder(3-bottom,5-3),ladder(2-right,1-3),ladder(1-n/a,1-2)]
[3-1,5-1,5-2,6-2] -> [ladder(3-top,6-1),ladder(2-right,4-3),ladder(1-n/a,2-2)]
[3-1,5-1,5-2,6-3] -> [ladder(3-top,6-2),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[3-1,5-1,5-2,7-2] -> [ladder(3-bottom,6-2),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[3-1,5-1,6-2,7-3] -> [ladder(3-top,6-1),ladder(2-right,2-2),ladder(1-n/a,4-3)]
[3-1,5-1,7-2,7-3] -> [ladder(3-top,5-2),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[3-1,5-2,5-4,6-2] -> [ladder(3-bottom,3-3),ladder(2-right,4-3),ladder(1-n/a,2-2)]
[3-1,5-2,5-4,7-2] -> [ladder(3-bottom,3-3),ladder(2-right,4-3),ladder(1-n/a,2-2)]
[3-1,5-2,6-1,6-3] -> [ladder(3-top,6-2),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[3-1,5-2,6-1,7-2] -> [ladder(3-bottom,6-2),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[3-1,5-2,6-2,6-4] -> [ladder(3-top,6-3),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[3-1,5-2,6-2,7-3] -> [ladder(3-bottom,6-3),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[3-1,5-2,6-3,7-1] -> [ladder(3-top,6-2),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[3-1,5-2,6-4,7-2] -> [ladder(3-top,6-3),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[3-1,5-2,7-2,7-3] -> [ladder(3-bottom,6-3),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[3-1,5-4,6-3,7-3] -> [ladder(3-top,4-2),ladder(2-right,1-4),ladder(1-n/a,2-3)]
[3-1,6-1,6-2,7-1] -> [ladder(3-top,4-1),ladder(2-right,4-3),ladder(1-n/a,2-2)]
[3-1,6-1,6-2,7-2] -> [ladder(3-top,4-1),ladder(2-right,4-3),ladder(1-n/a,2-2)]
[3-1,6-1,7-2,7-3] -> [ladder(3-top,5-2),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[3-1,6-2,7-1,7-2] -> [ladder(3-top,4-1),ladder(2-right,4-3),ladder(1-n/a,2-2)]
[3-2,3-3,5-1,6-3] -> [ladder(3-top,4-3),ladder(2-right,1-4),ladder(1-n/a,4-2)]
[3-2,3-3,5-1,7-3] -> [ladder(3-top,4-3),ladder(2-right,1-4),ladder(1-n/a,4-2)]
[3-2,3-3,6-1,6-3] -> [ladder(3-top,4-3),ladder(2-right,1-4),ladder(1-n/a,4-2)]
[3-2,3-3,6-1,7-3] -> [ladder(3-top,4-3),ladder(2-right,1-4),ladder(1-n/a,4-2)]
[3-2,3-3,6-3,7-1] -> [ladder(3-top,4-3),ladder(2-right,1-4),ladder(1-n/a,4-2)]
[3-2,3-3,7-1,7-3] -> [ladder(3-top,4-3),ladder(2-right,1-4),ladder(1-n/a,4-2)]
[3-2,3-4,5-1,6-3] -> [ladder(3-bottom,1-3),ladder(2-right,2-3),ladder(1-n/a,4-2)]
[3-2,3-4,6-1,6-3] -> [ladder(3-bottom,1-3),ladder(2-right,2-3),ladder(1-n/a,4-2)]
[3-2,3-4,6-3,7-1] -> [ladder(3-bottom,1-3),ladder(2-right,2-3),ladder(1-n/a,4-2)]
[3-2,4-1,5-4,6-3] -> [ladder(3-top,4-2),ladder(2-right,1-4),ladder(1-n/a,2-3)]
[3-2,4-2,5-1,6-4] -> [ladder(3-top,6-3),ladder(2-right,2-3),ladder(1-n/a,5-2)]
[3-2,4-2,5-1,7-4] -> [ladder(3-top,6-2),ladder(2-right,3-4),ladder(1-n/a,4-3)]
[3-2,4-2,5-4,7-4] -> [ladder(3-top,5-3),ladder(2-right,1-4),ladder(1-n/a,2-3)]
[3-2,4-2,6-1,6-4] -> [ladder(3-top,6-3),ladder(2-right,2-3),ladder(1-n/a,5-2)]
[3-2,4-2,6-4,7-1] -> [ladder(3-top,6-3),ladder(2-right,2-3),ladder(1-n/a,5-2)]
[3-2,5-1,5-2,7-4] -> [ladder(3-top,6-2),ladder(2-right,3-4),ladder(1-n/a,4-3)]
[3-2,5-1,5-4,7-2] -> [ladder(3-bottom,3-3),ladder(2-right,4-3),ladder(1-n/a,4-2)]
[3-2,5-1,5-4,7-3] -> [ladder(3-bottom,3-3),ladder(2-right,4-2),ladder(1-n/a,4-3)]
[3-2,5-1,6-4,7-2] -> [ladder(3-top,6-3),ladder(2-right,2-3),ladder(1-n/a,4-2)]
[3-2,5-2,5-4,7-4] -> [ladder(3-top,5-3),ladder(2-right,1-4),ladder(1-n/a,2-3)]
[3-2,5-2,6-1,7-4] -> [ladder(3-top,6-2),ladder(2-right,3-4),ladder(1-n/a,4-3)]
[3-2,5-2,7-1,7-4] -> [ladder(3-top,6-2),ladder(2-right,3-4),ladder(1-n/a,4-3)]
[3-2,5-4,6-1,7-2] -> [ladder(3-bottom,3-3),ladder(2-right,4-3),ladder(1-n/a,4-2)]
[3-2,5-4,6-1,7-3] -> [ladder(3-bottom,3-3),ladder(2-right,4-2),ladder(1-n/a,4-3)]
[3-2,5-4,6-3,7-3] -> [ladder(3-top,4-2),ladder(2-right,1-4),ladder(1-n/a,2-3)]
[3-2,5-4,7-1,7-2] -> [ladder(3-bottom,3-3),ladder(2-right,4-3),ladder(1-n/a,4-2)]
[3-2,5-4,7-1,7-3] -> [ladder(3-bottom,3-3),ladder(2-right,4-2),ladder(1-n/a,4-3)]
[3-2,5-4,7-3,7-4] -> [ladder(3-top,5-3),ladder(2-right,1-4),ladder(1-n/a,2-3)]
[3-2,6-1,6-4,7-2] -> [ladder(3-top,6-3),ladder(2-right,2-3),ladder(1-n/a,4-2)]
[3-2,6-4,7-1,7-2] -> [ladder(3-top,6-3),ladder(2-right,2-3),ladder(1-n/a,4-2)]
[3-3,4-1,5-2,6-2] -> [ladder(3-bottom,1-2),ladder(2-right,4-3),ladder(1-n/a,2-2)]
[3-3,4-1,5-2,6-3] -> [ladder(3-top,4-3),ladder(2-right,1-4),ladder(1-n/a,2-2)]
[3-3,4-1,5-2,7-2] -> [ladder(3-bottom,1-2),ladder(2-right,4-3),ladder(1-n/a,2-2)]
[3-3,4-3,5-2,5-4] -> [ladder(3-bottom,1-2),ladder(2-right,1-4),ladder(1-n/a,2-2)]
[3-3,5-1,6-1,6-3] -> [ladder(3-top,4-3),ladder(2-right,1-4),ladder(1-n/a,4-2)]
[3-3,5-1,6-3,7-1] -> [ladder(3-top,4-3),ladder(2-right,1-4),ladder(1-n/a,4-2)]
[3-3,5-1,6-3,7-3] -> [ladder(3-top,4-3),ladder(2-right,1-4),ladder(1-n/a,4-2)]
[3-3,5-2,6-2,7-2] -> [ladder(3-bottom,1-2),ladder(2-right,4-3),ladder(1-n/a,2-2)]
[3-3,6-1,6-3,7-1] -> [ladder(3-top,4-3),ladder(2-right,1-4),ladder(1-n/a,4-2)]
[3-3,6-1,6-3,7-3] -> [ladder(3-top,4-3),ladder(2-right,1-4),ladder(1-n/a,4-2)]
[3-3,6-3,7-1,7-3] -> [ladder(3-top,4-3),ladder(2-right,1-4),ladder(1-n/a,4-2)]
[3-4,4-1,4-2,5-2] -> [ladder(3-bottom,1-3),ladder(2-left,2-3),ladder(1-n/a,1-2)]
[3-4,4-1,5-2,6-3] -> [ladder(3-bottom,1-3),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[3-4,5-1,6-1,6-3] -> [ladder(3-bottom,1-3),ladder(2-right,2-3),ladder(1-n/a,4-2)]
[3-4,5-1,6-3,7-1] -> [ladder(3-bottom,1-3),ladder(2-right,2-3),ladder(1-n/a,4-2)]
[3-4,5-1,6-3,7-3] -> [ladder(3-bottom,1-3),ladder(2-right,2-3),ladder(1-n/a,4-2)]
[3-4,6-1,6-3,7-1] -> [ladder(3-bottom,1-3),ladder(2-right,2-3),ladder(1-n/a,4-2)]
[3-4,6-1,6-3,7-3] -> [ladder(3-bottom,1-3),ladder(2-right,2-3),ladder(1-n/a,4-2)]
[3-4,6-3,7-1,7-3] -> [ladder(3-bottom,1-3),ladder(2-right,2-3),ladder(1-n/a,4-2)]
[4-1,4-2,6-3,7-4] -> [ladder(3-bottom,5-3),ladder(2-right,1-3),ladder(1-n/a,1-2)]
[4-1,5-1,5-2,6-2] -> [ladder(3-top,6-1),ladder(2-right,4-3),ladder(1-n/a,2-2)]
[4-1,5-1,5-2,6-3] -> [ladder(3-top,6-2),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[4-1,5-1,5-2,7-2] -> [ladder(3-bottom,6-2),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[4-1,5-1,6-2,7-3] -> [ladder(3-top,6-1),ladder(2-right,2-2),ladder(1-n/a,4-3)]
[4-1,5-1,7-2,7-3] -> [ladder(3-top,5-2),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[4-1,5-2,5-4,6-2] -> [ladder(3-bottom,3-3),ladder(2-right,4-3),ladder(1-n/a,2-2)]
[4-1,5-2,5-4,7-2] -> [ladder(3-bottom,3-3),ladder(2-right,4-3),ladder(1-n/a,2-2)]
[4-1,5-2,6-1,6-3] -> [ladder(3-top,6-2),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[4-1,5-2,6-1,7-2] -> [ladder(3-bottom,6-2),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[4-1,5-2,6-2,6-4] -> [ladder(3-top,6-3),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[4-1,5-2,6-2,7-3] -> [ladder(3-bottom,6-3),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[4-1,5-2,6-3,7-1] -> [ladder(3-top,6-2),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[4-1,5-2,6-4,7-2] -> [ladder(3-top,6-3),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[4-1,5-2,7-2,7-3] -> [ladder(3-bottom,6-3),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[4-1,5-4,6-3,7-3] -> [ladder(3-top,4-2),ladder(2-right,1-4),ladder(1-n/a,2-3)]
[4-1,6-1,7-2,7-3] -> [ladder(3-top,5-2),ladder(2-right,2-3),ladder(1-n/a,2-2)]
[4-2,5-1,5-2,7-4] -> [ladder(3-top,6-2),ladder(2-right,3-4),ladder(1-n/a,4-3)]
[4-2,5-1,6-1,6-4] -> [ladder(3-top,6-3),ladder(2-right,2-3),ladder(1-n/a,5-2)]
[4-2,5-1,6-1,7-4] -> [ladder(3-top,6-2),ladder(2-right,3-4),ladder(1-n/a,4-3)]
[4-2,5-1,6-4,7-1] -> [ladder(3-top,6-3),ladder(2-right,2-3),ladder(1-n/a,5-2)]
[4-2,5-1,7-1,7-4] -> [ladder(3-top,6-2),ladder(2-right,3-4),ladder(1-n/a,4-3)]
[4-2,5-2,5-4,7-4] -> [ladder(3-top,5-3),ladder(2-right,1-4),ladder(1-n/a,2-3)]
[4-2,5-2,6-1,7-4] -> [ladder(3-top,6-2),ladder(2-right,3-4),ladder(1-n/a,4-3)]
[4-2,5-2,7-1,7-4] -> [ladder(3-top,6-2),ladder(2-right,3-4),ladder(1-n/a,4-3)]
[4-2,5-4,7-3,7-4] -> [ladder(3-top,5-3),ladder(2-right,1-4),ladder(1-n/a,2-3)]
[4-2,6-1,6-4,7-1] -> [ladder(3-top,6-3),ladder(2-right,2-3),ladder(1-n/a,5-2)]
[4-2,6-1,7-3,7-4] -> [ladder(3-top,4-1),ladder(2-right,3-4),ladder(1-n/a,4-3)]
[4-2,7-1,7-3,7-4] -> [ladder(3-top,4-1),ladder(2-right,3-4),ladder(1-n/a,4-3)]
[5-1,5-2,6-1,7-4] -> [ladder(3-top,6-2),ladder(2-right,3-4),ladder(1-n/a,4-3)]
[5-1,5-2,7-1,7-4] -> [ladder(3-top,6-2),ladder(2-right,3-4),ladder(1-n/a,4-3)]
[5-1,5-4,6-1,7-2] -> [ladder(3-bottom,3-3),ladder(2-right,4-3),ladder(1-n/a,4-2)]
[5-1,5-4,7-1,7-2] -> [ladder(3-bottom,3-3),ladder(2-right,4-3),ladder(1-n/a,4-2)]
[5-2,5-4,7-3,7-4] -> [ladder(3-top,5-3),ladder(2-right,1-4),ladder(1-n/a,2-3)]
[5-2,6-1,7-1,7-4] -> [ladder(3-top,6-2),ladder(2-right,3-4),ladder(1-n/a,4-3)]
[5-4,6-1,7-1,7-2] -> [ladder(3-bottom,3-3),ladder(2-right,4-3),ladder(1-n/a,4-2)]

There are 965 puzzles: 9 with 1 pile of gold, 165 with 2 piles of gold, and 791 with 3 piles of gold.

That’s quite a lot … how many puzzle candidates are there? It’s just the number of combinations:

• C(7 * 4, 2) = 378 (so 2.4% is unambiguous)

• C(7 * 4, 3) = 3276 (so 5% is unambiguous)

• C(7 * 4, 4) = 20475 (so 3.9% is unambiguous)

In overall, almost 4% of all combinations are unambiguous.

The whole program

position(X-Y) :- between(1, 7, X), between(1, 4, Y).

puzzle(1, 5-4, [7-4]).
puzzle(26, 5-2, [4-1,5-1,2-3]).
puzzle(48, 1-1, [5-2,2-3,6-3]).

direction(1, n/a).
direction(2, left).
direction(2, right).
direction(3, bottom).
direction(3, top).

connected(_, X-Y, X1-Y) :-
    X > 1, X1 is X - 1,
    \+ member(X-Y, [5-1,3-2,6-2,2-3,5-3,4-4,6-4]).
connected(_, X-Y, X1-Y) :-
    X < 7, X1 is X + 1,
    \+ member(X-Y, [4-1,2-2,5-2,1-3,4-3,3-4,5-4]).
connected(Ladders, X-Y, X-Y1) :-
    ( Y > 1, Y1 is Y - 1, DY = 0
    ; Y < 4, Y1 is Y + 1, DY = 1
    ),
    ( member(ladder(1-_, Lx-Ly), Ladders),
      Lx =:= X - 1, Ly =:= Y + DY
    ; member(ladder(2-left, Lx-Ly), Ladders),
      ( Lx =:= X ; Lx =:= X - 2 ), Ly =:= Y + DY
    ; member(ladder(2-right, Lx-Ly), Ladders),
      ( Lx =:= X - 1 ; Lx =:= X - 3 ), Ly =:= Y + DY
    ; member(ladder(3-_, Lx-Ly), Ladders),
      ( Lx =:= X, Ly =:= Y + DY ; Lx =:= X - 1, Ly =:= Y + DY - 1 )
    ).

occupies(X-Y, X-Y).
occupies(ladder(1-_, X-Y), X1-Y) :- between(0, 2, DX), X1 is X + DX.
occupies(ladder(2-_, X-Y), X1-Y) :- between(0, 3, DX), X1 is X + DX.
occupies(ladder(3-_, X-Y), X-Y).
occupies(ladder(3-_, X-Y), X1-Y1) :- X1 is X + 1, Y1 is Y + 1.
occupies(ladder(3-bottom, X-Y), X-Y1) :- Y1 is Y + 1.
occupies(ladder(3-top, X-Y), X1-Y) :- X1 is X + 1.

place(Tiles, Type, [Ladder|Tiles]) :-
    \+ member(ladder(Type-_,_), Tiles),
    direction(Type, Dir),
    position(Pos),
    Ladder = ladder(Type-Dir, Pos),
    forall(occupies(Ladder, P), position(P)),
    \+ ( occupies(Ladder, P1),
         member(T, Tiles),
         occupies(T, P2),
         P1 = P2
       ).

reaches(Ladders, Pos1, Pos2, _) :- connected(Ladders, Pos1, Pos2).
reaches(Ladders, Pos1, Pos2, Visited) :-
    connected(Ladders, Pos1, P),
    \+ member(P, Visited),
    reaches(Ladders, P, Pos2, [P|Visited]).

solve(Dwarf, Golds, Ladders) :-
    place([Dwarf|Golds], 1, T1),
    place(T1, 2, T2),
    place(T2, 3, Tiles),
    findall(L, ( member(L, Tiles), L = ladder(_,_) ), Ladders),
    forall(member(Gold, Golds), reaches(Ladders, Dwarf, Gold, [])).

unambiguous(Items, Solution) :-
    between(2, 4, N),
    length(Items, N),
    maplist(position, Items),
    sorted(Items),
    Items = [Dwarf|Golds],
    findall(Ladders, solve(Dwarf, Golds, Ladders), [Solution]).

sorted([_]).
sorted([X,Y|Xs]) :- X @< Y, sorted([Y|Xs]).