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# [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):

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 YESyesyeSYeS will all be treated as identical.

### Explanation:

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

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