A sheet of paper is folded left-to-right then up-to-down N times. Then you cut out a few shapes and unfold the sheet.
The task is to determine how many parts the sheet will break up to.
Explanations
Lets look at the example. It is a sheet of two pieces. One piece is one or more connected #'s. Note that cells adjacent diagonally are not connected.
### #.. #.#
Unfolding works as follow: 1) Down-to-up
#.# #.. ### ### #.. #.#
2) Right-to-left
#.##.# ..##.. ###### ###### ..##.. #.##.#
3) Go to 1, repeat N-1 times.
In this case N=1, so after unfolding there will be 5 pieces (four in the corners and one in the center).
Note that there are always as many horizontal folds as vertical ones: the number N of folds is really a number of double folds, once in each direction.
Input
Line 1: Single integer N. Line 2: Two space-separated integers W and H represent width and height of the folded sheet respectively. Next H lines:W characters, where . is hole and # is paper.
