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 \textbf{r} rows and \textbf{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? \InputFile Contains several test cases. Each test case starts with one line containing four integers \textbf{n}, \textbf{m}, \textbf{r} and \textbf{c} (\textbf{1} ≤ \textbf{r} ≤ \textbf{n} ≤ \textbf{100}, \textbf{1} ≤ \textbf{c} ≤ \textbf{m} ≤ \textbf{100}). The following \textbf{n} lines each describe one row of pixels of the painting you want to create. The \textbf{i}-th line consists of \textbf{m} characters describing the desired pixel values of the \textbf{i}-th row in the finished painting ('\textbf{0}' indicates white, '\textbf{1}' indicates black). The last test case is followed by a line containing four zeros. \OutputFile For each test case, print the minimum number of operations needed to create the painting, or -\textbf{1} if it is impossible.