# Even Parity

We have a grid of size N × N . Each cell of the grid initially contains a zero(0) or a one(1). The parity of a cell is the number of 1s surrounding that cell. A cell is surrounded by at most 4 cells (top, bottom, left, right). Suppose we have a grid of size 4 × 4: 1 0 1 0 Theparityofeachcellwouldbe 1 3 1 2 1111 2321 0100 2121 0000 0100 For this problem, you have to change some of the 0s to 1s so that the parity of every cell becomes even. We are interested in the minimum number of transformations of 0 to 1 that is needed to achieve the desired requirement. Input The first line of input is an integer T (T < 30) that indicates the number of test cases. Each case starts with a positive integer N (1 ≤ N ≤ 15). Each of the next N lines contain N integers (0/1) each. The integers are separated by a single space character. Output For each case, output the case number followed by the minimum number of transformations required. If it’s impossible to achieve the desired result, then output ‘-1’ instead. Sample Input 3 3 000 000 000 3 000 100 000 3 111 111 000 Sample Output Case 1: 0 Case 2: 3 Case 3: -1