Description:
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 (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: $$$$$$ \begin{pmatrix} 1 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 1 & 0 \end{pmatrix} $$$$$$ Then the following sequence of operations shows an example of transformations:
- vertical xor, $$$j=1$$$. $$$$$$ a= \begin{pmatrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 0 \end{pmatrix} $$$$$$
- horizontal xor, $$$i=2$$$. $$$$$$ a= \begin{pmatrix} 0 & 1 & 0 \\ 0 & 1 & 0 \\ 0 & 1 & 0 \end{pmatrix} $$$$$$
- vertical xor, $$$j=2$$$. $$$$$$ a= \begin{pmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{pmatrix} $$$$$$
Check if there is a sequence of operations such that the matrix $$$a$$$ becomes equal to the matrix $$$b$$$.
Input Format:
The first line contains one integer $$$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$$$.
Output Format:
For each test case, output on a separate line:
- "YES", there is such a sequence of operations that the matrix $$$a$$$ becomes equal to the matrix $$$b$$$;
- "NO" otherwise.
You can output "YES" and "NO" in any case (for example, the strings yEs, yes, Yes and YES will be recognized as positive).
Note:
The first test case is explained in the statements.
In the second test case, the following sequence of operations is suitable:
- horizontal xor, $$$i=1$$$;
- horizontal xor, $$$i=2$$$;
- horizontal xor, $$$i=3$$$;
It can be proved that there is no sequence of operations in the third test case so that the matrix $$$a$$$ becomes equal to the matrix $$$b$$$.