F. Unusual Matrixtime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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.InputThe 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.OutputFor 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).ExampleInput
3
3
110
001
110

000
000
000
3
101
010
101

010
101
010
2
01
11

10
10
Output
YES
YES
NO
NoteThe 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.
3
3
110
001
110

000
000
000
3
101
010
101

010
101
010
2
01
11

10
10

YES YES NO 
['2-sat', 'brute force', 'constructive algorithms', '*1900']