Description
You've got an n × m
A picture is a barcode if the following conditions are fulfilled:
- All pixels in each column are of the same color.
- The width of each monochrome vertical line is at least x and at most y pixels. In other words, if we group all neighbouring columns of the pixels with equal color, the size of each group can not be less than x or greater than y.
Input
The first line contains four space-separated integers n, m, x and y (1 ≤ n, m, x, y ≤ 1000; x ≤ y).
Then follow n lines, describing the original image. Each of these lines contains exactly m characters. Character "." represents a white pixel and "#" represents a black pixel. The picture description doesn't have any other characters besides "." and "#".
Output
In the first line print the minimum number of pixels to repaint. It is guaranteed that the answer exists.
Sample Input
Input
6 5 1 2 ##.#. .###. ###.. #...# .##.# ###..
Output
11
Input
2 5 1 1 ##### .....
Output
5
Hint
In the first test sample the picture after changing some colors can looks as follows:
.##.. .##.. .##.. .##.. .##.. .##..
In the second test sample the picture after changing some colors can looks as follows: