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Problems

Annoying painting tool

Annoying painting tool

Time limit 1 second
Memory limit 128 MiB

Maybe you wonder what an annoying painting tool is? First of all, the painting tool we speak of supports only black and white. Therefore, a picture consists of a rectangular area of pixels, which are either black or white. Second, there is only one operation how to change the colour of pixels:

Select a rectangular area of r rows and c columns of pixels, which is completely inside the picture. As a result of the operation, each pixel inside the selected rectangle changes its colour (from black to white, or from white to black).

Initially, all pixels are white. To create a picture, the operation described above can be applied several times. Can you paint a certain picture which you have in mind?

Input data

Contains several test cases. Each test case starts with one line containing four integers n, m, r and c (1rn100, 1cm100). The following n lines each describe one row of pixels of the painting you want to create. The i-th line consists of m characters describing the desired pixel values of the i-th row in the finished painting ('0' indicates white, '1' indicates black).

The last test case is followed by a line containing four zeros.

Output data

For each test case, print the minimum number of operations needed to create the painting, or -1 if it is impossible.

Examples

Input example #1
3 3 1 1
010
101
010
4 3 2 1
011
110
011
110
3 4 2 2
0110
0111
0000
0 0 0 0
Output example #1
4
6
-1
Source University of Ulm Local Contest 2007.07.06