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 "#".
import math
ans = 99999999
l = 0

def solve(arr, num, i, same, prev):
    global ans, x, y, l
    if i >= len(arr):
        ans = min(ans, num)
        return
    if prev == "#":
        solve(arr, num + (l - arr[i]), i + 1, 1, ".")
        if same + 1 <= y and same + 1 >= x:            
            solve(arr, num + arr[i], i + 1, same + 1, "#")
    elif prev == ".":
        solve(arr, num + arr[i], i + 1, 1, "#")
        if same + 1 <= y and same + 1 >= x:
            solve(arr, num + l - arr[i], i + 1, same + 1, ".")
    else:
        solve(arr, num + (l - arr[i]), i + 1, 1, ".")
        solve(arr, num + arr[i], i + 1, 1, "#")
        
f = input().split(" ")
n = int(f[0])
mat = []
arr = []
for i in range(n):
    o = input()
    o = [x for x in o]
    mat.append(o)
for i in range(len(mat[0])):
    num = 0
    for j in range(len(mat)):
        if mat[j][i] == ".":
            num += 1
    arr.append(num)
x = int(f[2])
y = int(f[3])
l = len(mat)
solve(arr, 0, 0, 0, "")
print(ans)