OpenJudge

We've known quite a lot about the determinant of an matrix from linear algebra course and we now take a review

in which is the set of permutations of , and

Now given an matrix , define as the remaining submatrix after deleting the row and the line of . For example, assume , then , , .

Your task is to compute the determinant of for any modulo .

The first line contains an integer $T$, indicating the number of matrices.

Then $T$ matrices follow. For each matrix $A$, the first line contains an integer $n$ indicating the size of $A$.

The following $n$ lines give the matrix. The $i^{th}$ line contains $n$ non-negative integers less than $p$ separated by a space, describing the $i^{th}$ row of the matrix.

The input guarantees that $1\leq T\leq 100$ and $2\leq n\leq 200$, and the number of matrices with $n>40$ is no more than 3.

For each input matrix, output an $n\times n$ matrix $B=(b_{i,j})$, in which $b_{i,j}=\operatorname{det}A(i,j)$ modulo $p$. Output an extra empty line at the end of each output matrix.

3
2
4 6
2 3
3
1 0 2
0 1 0
0 0 1
3
1 1 1
2 3 4
0 0 1

3 2
6 4

1 0 0
0 1 0
998244351 0 1

3 2 0
1 1 0
1 2 1