Unusual Matrix

You are given two binary square matrices a and b of size n × 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 ≤ j ≤ n) and for all i (1 ≤ i ≤ n) do the following: a_{i, j} := a_{i, j} ⊕ 1 (⊕ — 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, j} ⊕ 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 ≤ 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

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.

inputFormat

Input

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.

outputFormat

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.

样例

3
3
110
001
110

000
000
000
3
101
010
101

010
101
010
2
01
11

10
10

YES
YES
NO

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