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.
import java.io.*;
import java.util.StringTokenizer;

public class F_UsualMatrix {
    private static final BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    private static final PrintWriter pw = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));

    private static int readIntLine() throws IOException {
        return Integer.parseInt(br.readLine());
    }

    public static void main(String[] args) throws IOException {
        int T = readIntLine();
        while (T-- > 0) {
            int n = readIntLine();
            char[][] a = new char[n][];
            for (int i = 0; i < n; i++) {
                a[i] = br.readLine().toCharArray();
            }
            br.readLine();
            boolean[][] diff = new boolean[n][n];
            for (int i = 0; i < n; i++) {
                char[] c = br.readLine().toCharArray();
                for (int j = 0; j < n; j++) {
                    diff[i][j] = a[i][j] == c[j];
                }
            }

            boolean possible = check(diff);

            pw.println(possible ? "YES" : "NO");
        }
        pw.close();
    }

    private static boolean check(boolean[][] b) {
        return consistentWithFirstRow(b) || consistentWithFirstRow(flipFirstRow(b));
    }

    private static boolean[][] flipFirstRow(boolean[][] b) {
        boolean[] firstRow = b[0];
        for (int i = 0; i < firstRow.length; i++) {
            firstRow[i] = !firstRow[i];
        }
        return b;
    }

    private static boolean consistentWithFirstRow(boolean[][] b) {
        boolean[] firstRow = b[0];
        for (int i = 1; i < b.length; i++) {
            boolean[] row = b[i];
            boolean consistent = true;
            for (int j = 0; j < row.length; j++) {
                if (firstRow[j] != row[j]) {
                    consistent = false;
                    break;
                }
            }
            if (consistent) continue;

            for (int j = 0; j < row.length; j++) {
                if (firstRow[j] == row[j]) {
                    return false;
                }
            }
        }
        return true;
    }
}
