You are given an integer (k) and a matrix (v) with (n) rows and (m) columns. The element in row (i) and column (j) is denoted by (v_{i,j}). A cell ((x, y)) is called a peak if its value is greater than or equal to the sum of the values in all other cells in row (x) and column (y). Formally, ((x, y)) is a peak if () v_{x,y} \ge \sum_{\substack{1 \le i \le n \\i \neq x}} v_{i,y} + \sum_{\substack{1 \le j \le m \\j \neq y}} v_{x,j}. () You may perform the following operation any number of times (possibly zero): Choose four integers (x_l), (x_r), (y_l), and (y_r) ((1 \le x_l \le x_r \le n), (1 \le y_l \le y_r \le m)). Subtract (1) from (v_{i,j}) for every (x_l \le i \le x_r) and (y_l \le j \le y_r). Find the minimum number of operations required to obtain a matrix with at least (k) peaks. Each test contains multiple test cases. The first line contains the number of test cases (t) ((1 \le t \le 10^4)). The description of the test cases follows. The first line of each test case contains three integers (n), (m), and (k) ((1 \le n, m \le 10^5), (1 \le k \le n \cdot m), (n \cdot m \le 10^5)) — the number of rows, the number of columns, and the required number of peaks. The (i)-th of the next (n) lines contains (m) integers (v_{i,1}, v_{i,2}, \ldots, v_{i,m}) ((-10^9 \le v_{i,j} \le 10^9)). It is guaranteed that the sum of (n \cdot m) over all test cases does not exceed (10^5). For each test case, output a single integer — the minimum number of operations required to obtain at least (k) peaks. If there is no solution, print a single integer (-1). For the first test case, you can perform the following two operations: choose ((x_l, x_r, y_l, y_r) = (1, 3, 2, 3)); choose ((x_l, x_r, y_l, y_r) = (2, 3, 1, 3)). After these operations, the matrix will be: The seven peaks are highlighted in green. For ex