[Solution] Angled Flip CodeChef Solution

Problem

You are given two $N \times M$ integer matrices $A$ and $B$. You are allowed to perform the following operation on $A$ as many times as you like (possibly, zero):

• Pick any square submatrix of $A$ and flip it about either its main diagonal or its antidiagonal.

For example, suppose you choose the submatrix $\begin{bmatrix} 1 \;\;\;\; 2 \;\;\;\; 3 \\ 4 \;\;\;\; 5 \;\;\;\; 6 \\ 7 \;\;\;\; 8 \;\;\;\; 9 \end{bmatrix}$ .

It can be converted into either $\begin{bmatrix} 1 \;\;\;\; 4 \;\;\;\; 7 \\ 2 \;\;\;\; 5 \;\;\;\; 8 \\ 3 \;\;\;\; 6 \;\;\;\; 9 \end{bmatrix}$ by flipping about the main diagonal, or $\begin{bmatrix} 9 \;\;\;\; 6 \;\;\;\; 3 \\ 8 \;\;\;\; 5 \;\;\;\; 2 \\ 7 \;\;\;\; 4 \;\;\;\; 1 \end{bmatrix}$ by flipping about the antidiagonal.

Is it possible to convert $A$ to $B$ by performing this operation several (possibly, zero) times?

Note: For the purposes of this problem, a submatrix of a matrix is the intersection of a contiguous segment of rows

 with a contiguous segment of columns.

For example, if $A = \begin{bmatrix} 1 \;\;\;\; 2 \;\;\;\; 3 \\ 4 \;\;\;\; 5 \;\;\;\; 6 \\ 7 \;\;\;\; 8 \;\;\;\; 9 \end{bmatrix}$ then $\begin{bmatrix} 2 \end{bmatrix}$, $\begin{bmatrix} 5 \;\;\;\; 6 \\ 8 \;\;\;\; 9 \end{bmatrix}$, and $\begin{bmatrix}1 \\ 4\end{bmatrix}$ are submatrices of $A$, while $\begin{bmatrix}1 \;\;\;\; 3 \\ 7 \;\;\;\; 9\end{bmatrix}$ is not.

A square submatrix is a submatrix with the same number of rows and columns.

Input Format

• The first line of input will contain a single integer $T$, denoting the number of test cases.
• Each test case consists of multiple lines of input.
• The first line of each test case contains two space-separated integers $N$ and $M$ — the number of rows and columns of the matrices, respectively.
• The next $N$ lines describe the matrix $A$. The $i$-th of these lines contains $M$ space-separated integers ― the values $A_{i, 1}, A_{i, 2}, \ldots, A_{i, M}$.
• The next $N$ lines describe the matrix $B$. The $i$-th of these lines contains $M$ space-separated integers ― the values $B_{i, 1}, B_{i, 2}, \ldots, B_{i, M}$.

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Output Format

For each test case, print YES if its possible to convert $A$ to $B$, else print NO.

Each character of the output may be printed in either uppercase or lowercase. For example, the strings YES, yes, yeS, YeS will all be treated as identical.

Explanation:

Test case $1$: $A$ can be converted to $B$ as follows:

$$\begin{bmatrix} 1 \;\;\;\; 2 \;\;\;\; 3 \\ 4 \;\;\;\; 5 \;\;\;\; 6 \end{bmatrix} \to \begin{bmatrix} 1 \;\;\;\; \textcolor{red}{6} \;\;\;\; \textcolor{red}{3} \\ 4 \;\;\;\; \textcolor{red}{5} \;\;\;\; \textcolor{red}{2} \end{bmatrix} \to \begin{bmatrix} \textcolor{red}{1} \;\;\;\; \textcolor{red}{4} \;\;\;\; 3 \\ \textcolor{red}{6} \;\;\;\; \textcolor{red}{5} \;\;\;\; 2 \end{bmatrix}$$