Mirror Box

2000ms

262144K

Description:

You are given a box full of mirrors. Box consists of grid of size n × m. Each cell of the grid contains a mirror put in the shape of '\' or ' / ' (45 degree to the horizontal or vertical line). But mirrors in some cells have been destroyed. You want to put new mirrors into these grids so that the following two conditions are satisfied:

If you put a light ray horizontally/vertically into the middle of any unit segment that is side of some border cell, the light will go out from the neighboring unit segment to the segment you put the ray in.
each unit segment of the grid of the mirror box can be penetrated by at least one light ray horizontally/vertically put into the box according to the rules of the previous paragraph

$\text{[math]}$

After you tried putting some mirrors, you find out that there are many ways of doing so. How many possible ways are there? The answer might be large, so please find the result modulo prime number MOD.

Input:

The first line contains three integers n, m, MOD (1 ≤ n, m ≤ 100, 3 ≤ MOD ≤ 10⁹ + 7, MOD is prime), m, n indicates the dimensions of a box and MOD is the number to module the answer.

The following n lines each contains a string of length m. Each string contains only ' / ', '\', '*', where '*' denotes that the mirror in that grid has been destroyed.

It is guaranteed that the number of '*' is no more than 200.