DWITE Online Computer Programming Contest, December 2008, Problem 5

Let's try to break out from the confines of the over-simplified 2D problems, and add some depth to the otherwise typical maze problems.

The input will contain 5 sets of data. Each set starts with a single integer ~2 \le n \le 5~ followed by ~n*n~ lines, describing a cube space. # for solid space; . for free space; A for start; B for end.

The output will contain 5 lines – each the shortest distance between A and B in the input maze.

The maze traversal is done only through free space, in any of the 6 directions. There are no diagonal movements.

Sample input explanation; first set: is a ~2*2*2~ empty cube, with A and B in two opposite corners. There are 6 different ways to get from A to B in 3 steps. There are also 3 different ways to get from A to B in 7 steps (without backtracking), but since we are looking for the shortest distance, the latter is of less interest.

Sample input explanation; second set: is also a ~2*2*2~ cube, but filled space forces only a single path to be available. Think of the path this way, starting at A: right, up one layer, down. Also 3 steps.

Sample input explanation; third set: is a ~3*3*3~ cube. A and B are on empty layers, but they are separated by a mostly filled layer, with a single opening in its "bottom-right" corner.

Sample Input

2
A.
..
..
.B
2
A.
##
#.
#B
3
A..
...
...
###
###
##.
B..
...
...

Sample Output

3
3
10

Problem Resource: DWITE