A13983 | Unusual Matrix

You are given two binary square matrices $a$ and $b$ of size $n \times n$ . A matrix is called binary if each of its elements is equal to $0$ or $1$ . You can do the following operations on the matrix $a$ arbitrary number of times (0 or more):

- vertical xor. You choose the number $j$ ( $1 \le j \le n$ ) and for all $i$ ( $1 \le i \le n$ ) do the following: $a_{i, j} := a_{i, j} \oplus 1$ ( $\oplus$ — is the operation [xor](https://en.wikipedia.org/wiki/Exclusive_or) (exclusive or)).
- horizontal xor. You choose the number $i$ ( $1 \le i \le n$ ) and for all $j$ ( $1 \le j \le n$ ) do the following: $a_{i, j} := a_{i, j} \oplus 1$ .

Note that the elements of the $a$ matrix change after each operation.

For example, if $n=3$ and the matrix $a$ is: $$$$ \begin{pmatrix} 1 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 1 & 0 \end{pmatrix} $$ Then the following sequence of operations shows an example of transformations: <ul> <li> vertical <span class="tex-font-style-tt">xor</span>, $j=1$ . $$ a= \begin{pmatrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 0 \end{pmatrix} $$ </li><li> horizontal <span class="tex-font-style-tt">xor</span>, $i=2$ . $$ a= \begin{pmatrix} 0 & 1 & 0 \\ 0 & 1 & 0 \\ 0 & 1 & 0 \end{pmatrix} $$ </li><li> vertical <span class="tex-font-style-tt">xor</span>, $j=2$ . $$ a= \begin{pmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{pmatrix} $$ </li></ul></p><p>Check if there is a sequence of operations such that the matrix $a$ becomes equal to the matrix $b$$$.

The first line contains one integer $t$ ( $1 \leq t \leq 1000$ ) — the number of test cases. Then $t$ test cases follow.

The first line of each test case contains one integer $n$ ( $1 \leq n \leq 1000$ ) — the size of the matrices.

The following $n$ lines contain strings of length $n$ , consisting of the characters '0' and '1' — the description of the matrix $a$ .

An empty line follows.

The following $n$ lines contain strings of length $n$ , consisting of the characters '0' and '1' — the description of the matrix $b$ .

It is guaranteed that the sum of $n$ over all test cases does not exceed $1000$ .

For each test case, output on a separate line:

- "YES", there is such a sequence of operations that the matrix $a$ becomes equal to the matrix $b$ ;
- "NO" otherwise.

You can output "YES" and "NO" in any case (for example, the strings yEs, yes, Yes and YES will be recognized as positive).