Sadly, Dora poured the paint when painting the class mural. Dora considers the mural as the matrix (b) of size (n \times n). Initially, (b_{i,j} = 0) for all (1 \le i, j \le n). Dora has only two brushes which have two different colors. In one operation, she can paint the matrix with one of two brushes: The first brush has color (1) on it and can paint one column of the matrix. That is, Dora chooses (1 \leq j \leq n) and makes (b_{i,j} := 1) for all (1 \leq i \leq n); The second brush has color (2) on it and can paint one row of the matrix. That is, Dora chooses (1 \leq i \leq n) and makes (b_{i,j} := 2) for all (1 \leq j \leq n). Dora paints the matrix so that the resulting matrix (b) contains only (1) and (2). For a matrix (b), let (f(b)) denote the minimum number of operations needed to turn the initial matrix (containing only (0)) into (b). The beauty of a matrix (b) is the number of ways to paint the initial matrix in exactly (f(b)) operations to turn it into (b). If there's no way to turn the initial matrix into (b), the beauty of (b) is (0). However, Dora made a uniformly random mistake; there's exactly one element different in the matrix (a) given to you from the real matrix (b). That is, there is exactly one pair ((i, j)) such that (a_{i, j} = 3 - b_{i, j}). Please help Dora compute the expected beauty of the real matrix (b) modulo (998\,244\,353) (all possible (n^2) mistakes have equal probability). Since the size of the matrix is too large, Dora will only tell you the positions of (m) elements of color (1), and the remaining (n^2-m) elements have color (2). Each test consists of multiple test cases. The first line contains a single integer (t) ((1 \leq t \leq 10^4)) — the number of test cases. The description of the test cases follows. The first line of each test case contains two integers $$$n$$