F. Unusual Matrix
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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

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).

Example
Input
3
3
110
001
110

000
000
000
3
101
010
101

010
101
010
2
01
11

10
10

Output
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 $b$.