Unusual Matrix
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 $b$.
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).
Input
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
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).
Samples
3
3
110
001
110
000
000
000
3
101
010
101
010
101
010
2
01
11
10
10
YES
YES
NO
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 $b$.