• 45

Goal

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.
Output
Line 1: An integer M – the number of parts.
Constraints
1 ≤ W, H ≤ 100
1 ≤ N ≤ 10000
1 ≤ M ≤ 2³¹
Example
Input
1
3 3
###
#..
#.#
Output
5

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