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 The input contains several test cases. Each test case starts with one line containing four integers n, m, randc. (1≤r≤n≤100,1≤c≤m≤100),Thefollowingnlineseachdescribeonerowofpixels 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 For each test case, print the minimum number of operations needed to create the painting, or ‘-1’ if it is impossible. Sample Input 3311 010 101 010 4321 011 110 011 110 3422 0110 0111 0000 0000 Sample Output 4 6 -1