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.*;
 
public class Main {
  static final FastReader FR = new FastReader();
  static final PrintWriter PW = new PrintWriter(new OutputStreamWriter(System.out));
 
  public static void main(String[] args) {
    StringBuilder solution = new StringBuilder();
    int tests = 1;
    tests = FR.nextInt();
    for (int t = 0; t < tests; ++t) {
      int matSize = FR.nextInt();
      char[][] given = new char[matSize][];
      for (int i = 0; i < matSize; i += 1) {
        given[i] = FR.next().toCharArray();
      }
      char[][] target = new char[matSize][];
      for (int i = 0; i < matSize; i += 1) {
        target[i] = FR.next().toCharArray();
      }
      
      boolean canTransform = checkTransformation(given, target);
      solution.append(canTransform ? "YES\n" : "NO\n");
    }
		PW.print(solution.toString());
    PW.close();
  }

  static boolean checkTransformation(char[][] given, char[][] target) {
    boolean[] swappedCol = new boolean[given.length];
    boolean[] swappedRow = new boolean[given.length];
    int maxSwappedCol = -1;
    for (int i = 0; i < given.length; i += 1) {
      for (int j = 0; j < given.length; j += 1) {
        boolean original = true;
        if (swappedRow[i]) original = !original;
        if (swappedCol[j]) original = !original;
        if (original == (given[i][j] == target[i][j])) continue;
        if (swappedRow[i] && swappedCol[j]) return false;
        if (j == 0) {
          swappedRow[i] = true;
        } else if (i == 0) {
          swappedCol[j] = true;
        } else {
          return false;
        }
      }
    }
    return true;
  }
 
  static class FastReader {
    BufferedReader br;
    StringTokenizer st;
  
    public FastReader() {
      br = new BufferedReader(new InputStreamReader(System.in));
    }
  
    String next() {
      while (st == null || !st.hasMoreElements()) {
        try {
          st = new StringTokenizer(br.readLine());
        } catch (IOException  e) {
          e.printStackTrace();
        }
      }
      return st.nextToken();
    }
  
    int nextInt() {
      return Integer.parseInt(next());
    }
  
    long nextLong() {
      return Long.parseLong(next());
    }
  
    double nextDouble() {
      return Double.parseDouble(next());
    }
 
    String nextLine() {
      String str = "";
      try {
        str = br.readLine();
      } catch (IOException e)  {
        e.printStackTrace();
      }
      return str;
    }
  }
}