You are given a binary grid(^{\text{∗}}) (G) of dimensions (n \times m). Let us define a rectangle as a tuple ((u,d,l,r)) that satisfies the following conditions: (1 \le \boldsymbol{u < d} \le n); (1 \le \boldsymbol{l < r} \le m); Cells ((u,l)), ((u,r)), ((d,l)), ((d,r)) all contain a (1). Then, the area of a rectangle ((u,d,l,r)) is defined as ((d-u+1) \cdot (r-l+1)). For example, consider the following binary grid given below. ()\begin{matrix} 1 & 0 & 1 & 0 & 1 \\ 1 & 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 & 1 \end{matrix}() Here, you may see two rectangles ((1,2,1,3)) and ((1,3,3,5))(^{\text{†}}), each of which has area (6) and (9), respectively. For each cell ((i,j)), find the minimum area of any rectangle ((u,d,l,r)) such that (u \le i \le d) and (l \le j \le r). (^{\text{∗}})A binary grid is a grid where each cell contains (0) or (1). The cell on the (j)-th column of the (i)-th row is denoted as cell ((i,j)). (^{\text{†}})Note that these are the only rectangles in the grid; for example, ((1,1,1,5)) is not a rectangle as it does not satisfy (u<d). 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 two integers (n) and (m) ((2 \le n,m), (n\cdot m \le 250\,000)). Each of the (n) following lines contains a string of length (m) denoting the (i)-th row of (G) ((G_{i,j} \in \{0,1\})). It is guaranteed that the sum of (n\cdot m) over all test cases does not exceed (250\,000). For each test case, output a grid of (n) rows and (m) columns. On the (j)-th column of the (i)-th row, you should output: If there exists a rectangle ((u,d,l,r)) such that (u \le i \le d) and (l \le j \le r), output the minimum area of any