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 min_pixels_to_repaint(n, m, x, y, picture):
    count = 0
    for j in range(m):
        column = [picture[i][j] for i in range(n)]
        i = 0
        while i < n:
            if column[i] == '#':
                # Count the number of consecutive black pixels
                black_pixels = 0
                while i < n and column[i] == '#':
                    black_pixels += 1
                    i += 1
                # Update the count based on the width of the black pixels
                if black_pixels < x:
                    count += x - black_pixels
                elif black_pixels > y:
                    count += black_pixels - y
            else:
                # Count the number of consecutive white pixels
                white_pixels = 0
                while i < n and column[i] == '.':
                    white_pixels += 1
                    i += 1
                # Update the count based on the width of the white pixels
                if white_pixels < x:
                    count += x - white_pixels
                elif white_pixels > y:
                    count += white_pixels - y
    return count

# Read input
n, m, x, y = map(int, input().split())
picture = []
for _ in range(n):
    row = input().strip()
    picture.append(row)

# Call the function and print the result
result = min_pixels_to_repaint(n, m, x, y, picture)
print(result)
