Maximum flow and matchings
Filling with domino
Given the size of the playing field n × m, some cells of which are already paved. To fill the free neighboring cells with domino of dimensions 1 × 2 worth a units. To fill one free square cell 1 × 1 worth b units.
Determine the minimum sum of money to fill all the field.
The first line contains four numbers n, m, a, b (1 ≤ n, m ≤ 100, a, b are integers not greater than 1000 by absolute value). Each of the next n lines contains m symbols: character "." (point) means the filled cell of the field, the character "\*" (star) means the free cell.
Find the minimum sum of money to fill all free cells of the field (and only them).
Input example #1
2 3 3 2 .** .*.
Output example #1
Input example #2
3 4 5 3 *..* **** ***.
Output example #2