Description

You are given an $n \times m$ grid. Some of the cells are obstacles, the others are empty. Choose a non-negative integer $k$ and color all empty cells with $k+1$ colors $0, 1, 2, \ldots k$. You can not color two cells in the same row or same column with the same non-zero color.

You are given two non-negative integers $c$ and $d$. For a coloring plan, define $z$ as the number of the cells with color $0$. Define the cost of the plan is $ck+dz$.

Find the minimum cost.

Input Format

The first line contains four integers $n$, $m$ ($1\leq n, m\leq 250$), $c$ and $d$ ($0\leq c, d\leq 10 ^ 9$).

The $i$-th line of the next $n$ lines contains a string of $m$ characters. The $j$-th character is * if the cell in the $i$-th row and the $j$-th column is an obstacle. The $j$-th character is . if the cell in the $i$-th row and the $j$-th column is empty.

Output Format

Output a line with a single number, representing the answer.

3 4 2 1
.***
*..*
**..

4

3 4 1 2
.***
*..*
**..

2

Hint

Source: The 2022 ICPC Asia Xi'an Regional Contest Problem B.

Author: csy2005.