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 .

输入描述:

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 "#".

输出描述:

In the first line print the minimum number of pixels to repaint. It is guaranteed that the answer exists.

备注:

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: .#.#..#.#.