You've got an *n* × *m* pixel picture. Each pixel can be white or black. Your task is to change the colors of as few pixels as possible to obtain a barcode picture.

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*.
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 "#".
n, m, k, a, b = map(int, input().split())
matrix = [input() for _ in range(n)]

# count the number of white and black cells in each column
cnt_w = [[0]*m for _ in range(n)]
cnt_b = [[0]*m for _ in range(n)]
for i in range(n):
    for j in range(m):
        if matrix[i][j] == 'W':
            cnt_w[i][j] = 1
        else:
            cnt_b[i][j] = 1
for j in range(m):
    for i in range(1, n):
        cnt_w[i][j] += cnt_w[i-1][j]
        cnt_b[i
