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 "#".
def main():
    n, m, x, y = map(int, input().split())
 
    col = [0] * m
    for i in range(n):
        row = input()
        for j in range(m):
            if row[j] == '.':
                col[j] += 1
 
    acc = [0]
    for j in range(m):
        acc.append(acc[-1] + col[j])
 
    dp = [[0]*(m+1), [0]*(m+1)]
 
    for j in range(1, m+1):
        dp[0][j] = float('infinity')
        dp[1][j] = float('infinity')
        for k in range(x, y+1):
            if j-k >= 0:
                wp = acc[j] - acc[j-k]
                bp = k * n - wp
                dp[0][j] = min(dp[0][j], dp[1][j-k] + wp)
                dp[1][j] = min(dp[1][j], dp[0][j-k] + bp)
 
    print(min(dp[0][m], dp[1][m]))
 
 
if __name__ == "__main__":
    main()