← Home
write a go solution for Description:
You are given two binary square matrices a and b of size nxn. 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<=j<=n) and for all i (1<=i<=n) do the following: a_i,j:=a_i,joplus1 (oplus — is the operation xor (exclusive or)).
- horizontal xor. You choose the number i (1<=i<=n) and for all j (1<=j<=n) do the following: a_i,j:=a_i,joplus1.

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<=t<=1000) — the number of test cases. Then t test cases follow.

The first line of each test case contains one integer n (1<=n<=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.. Output only the code with no comments, explanation, or additional text.