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](https://en.wikipedia.org/wiki/Exclusive_or) (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.
#include<bits/stdc++.h>
using namespace std;
const int mod= 1e9+7;
#define fastIO ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define what_is(x) cerr << #x << " = " << x << endl;
typedef long long ll;
char a[1009][1009],b[1009][1009];
int main()
{
    fastIO
    int t;
    cin>>t;

    while(t--)
    {
        int n;
        cin>>n;
        for (int i=1; i<=n; ++i)
            for (int j=1; j<=n; ++j)
                cin>>a[i][j];

        for (int i=1; i<=n; ++i)
            for (int j=1; j<=n; ++j)
                cin>>b[i][j];

        for (int i=1; i<=n; ++i)
        {
            if (a[1][i]!=b[1][i])
            {
                for (int j=1; j<=n; ++j)
                {
                    if (a[j][i]=='0')
                        a[j][i]='1';
                    else
                        a[j][i]='0';
                }
            }
        }
        for (int i=1; i<=n; ++i)
        {
            if (a[i][1]!=b[i][1])
            {
                for (int j=1; j<=n; ++j)
                {
                    if (a[i][j]=='0')
                        a[i][j]='1';
                    else
                        a[i][j]='0';
                }
            }
        }
        bool bo=1;
        for (int i=1; i<=n; ++i)
        {
            for (int j=1; j<=n; ++j)
            {
                if (a[i][j]!=b[i][j])
                {
                    bo=0;
                    break;
                }
            }
        }
        bo?cout<<"YES\n":cout<<"NO\n";



    }
}
