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.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collection;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.Random;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.stream.Stream;

import java.util.Iterator;
import java.util.List;
import java.util.Map;
import java.util.PriorityQueue;


public class Main {
	

	


public static void main(String[] args){
 
   new Thread(null, null, "Anshum Gupta", 99999999) {
        public void run() {
            try {
                solve();
            } catch(Exception e) {
                e.printStackTrace();
                System.exit(1);
            }
        }
    }.start();
}
 

static final long INF_LONG = (long)(1e18 + 5), MOD = (long)1e9 + 7;//998244353; 
static final int MXN = (int)(1001), MXV = (int)(1e5 + 5), log = 18, INF = (int)1e9 + 500;
static ArrayList<ArrayList<Integer>> adj;
static boolean[][] vis;
static char[] S;
static int[][] A, B;
static long[][] dp;
static int N, M, K, Q, H, W;


public static void solve() throws Exception {
	   // solve the problem here
		s = new MyScanner();
   		out = new MyWriter(new BufferedOutputStream(System.out));
   		
        int T = s.nextInt();
        
        for(int i = 1; i <= T; i++) testcase();
          
        out.flush();
        out.close();
}




static void testcase() {
	
	N = s.nextInt();
	A = new int[N][N];
	B = new int[N][N];
	
	for(int i = 0; i < N; i++) {
		char[] line = s.next().toCharArray();
		for(int j = 0; j < N; j++)
			A[i][j] = line[j] - '0';
	}
	
	for(int i = 0; i < N; i++) {
		char[] line = s.next().toCharArray();
		for(int j = 0; j < N; j++)
			B[i][j] = line[j] - '0';
	}
	
	// for matrix A to be converted to B
	// check if both A and B can converge to a state ?
	
	/*
	 * 110
	 * 001
	 * 110
	 * 
	 * */
	
	// try making it work column wise
	// how many times will an element be xored
	
	for(int i = 0; i < N; i++) {
		
		if(A[i][0] != B[i][0]) {
			// flip ith row
			flipRow(i);
		}
		
	}
	
	for(int i = 1; i < N; i++) {
		
		if(A[0][i] != B[0][i]) {
			flipCol(i);
		}
		
	}
	
	for(int i = 0; i < N; i++) {
		for(int j = 0; j < N; j++) {
			if(A[i][j] != B[i][j]) {
				out.println("NO");
				return;
			}
		}
	}
	
	out.println("YES");
	
	
	
	
}








private static void flipCol(int col) {
	
	for(int i = 0; i < N; i++) {
		A[i][col] ^= 1;
	}
	
}




private static void flipRow(int row) {
	
	for(int i = 0; i < N; i++) {
		A[row][i] ^= 1;
	}
	
}


public static MyWriter out;
public static MyScanner s;
static void shuffleArray(int[] a) {
	Random random = new Random();
	for (int i = a.length-1; i > 0; i--) {
		int index = random.nextInt(i + 1);
		int tmp = a[index];
		a[index] = a[i];
		a[i] = tmp;
	}
}
static void shuffleSort(int[] a) {
	shuffleArray(a);
	Arrays.parallelSort(a);
}

static void shuffleArray(long[] a) {
	Random random = new Random();
	for (int i = a.length-1; i > 0; i--) {
		int index = random.nextInt(i + 1);
		long tmp = a[index];
		a[index] = a[i];
		a[i] = tmp;
	}
}
static void shuffleSort(long[] a) {
	shuffleArray(a);
	Arrays.parallelSort(a);
}

static void reverse(int[] a) {
	int[] copy = Arrays.copyOf(a, a.length);
	for(int i = 0; i < a.length; i++) {
		a[a.length - 1 - i] = copy[i];
	}
}

static class MyScanner {
 
    BufferedReader br;
    StringTokenizer st;
 
    public MyScanner() {
        br = new BufferedReader(new InputStreamReader(System.in));
    }
    public MyScanner(String fileName) {
    	try {
			br = new BufferedReader(new FileReader(fileName));
		} catch (FileNotFoundException e) {
			e.printStackTrace();
		}
    }
    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()); }
    int[] nextIntArray(int n){
    	int[] a = new int[n];
    	for(int i = 0; i < n; i++) {
    		a[i] = this.nextInt();
    	}
    	return a;
    }
    long[] nextlongArray(int n) {
    	long[] a = new long[n];
    	for(int i = 0; i < n; i++) {
    		a[i] = this.nextLong();
    	}
    	return a;
    }
    Integer[] nextIntegerArray(int n){
    	Integer[]a = new Integer[n];
    	for(int i=0; i<n; i++) {
    		a[i] = this.nextInt();
    	}
    	return a;
    }
    Long[] nextLongArray(int n) {
    	Long[]a = new Long[n];
    	for(int i=0; i<n; i++) {
    		a[i] = this.nextLong();
    	}
    	return a;
    }
    char[][] next2DCharArray(int n, int m){
    	char[][]arr = new char[n][m];
    	for(int i=0; i<n; i++) {
    		arr[i] = this.next().toCharArray();
    	}
    	return arr;
    }
    ArrayList<ArrayList<Integer>> readUndirectedUnweightedGraph(int n, int m) {
    	ArrayList<ArrayList<Integer>>adj = new ArrayList<ArrayList<Integer>>();
    	for(int i = 0; i < n; i++)adj.add(new ArrayList<Integer>());
    	for(int i = 0; i < m; i++) {
    		int u = s.nextInt();
    		int v = s.nextInt();
    		u--; v--;
    		adj.get(u).add(v);
    		adj.get(v).add(u);
    	}
    	return adj;
    }
    ArrayList<ArrayList<Integer>> readDirectedUnweightedGraph(int n, int m) {
    	ArrayList<ArrayList<Integer>>adj = new ArrayList<ArrayList<Integer>>();
    	for(int i = 0; i < n; i++)adj.add(new ArrayList<Integer>());
    	for(int i = 0; i < m; i++) {
    		int u = s.nextInt();
    		int v = s.nextInt();
    		u--; v--;
    		adj.get(u).add(v);
    	}
    	return adj;
    }
    String nextLine(){
        String str = "";
        try {
            str = br.readLine();
        } catch (IOException e) {
            e.printStackTrace();
        }
        return str;
    }
}
 
static class MyWriter extends PrintWriter {
    MyWriter(OutputStream out) {
        super(out);
    }
    void println(int[] x) {
        println(x, " ");
    }
    void println(int[] x, String delimiter) {
        if (x.length > 0) {
            print(x[0]);
            for (int i = 1; i < x.length; i++) {
                print(delimiter);
                print(x[i]);
            }
        }
        println();
    }
    void println(long[] x) {
        println(x, " ");
    }
    void println(long[] x, String delimiter) {
        if (x.length > 0) {
            print(x[0]);
            for (int i = 1; i < x.length; i++) {
                print(delimiter);
                print(x[i]);
            }
        }
        println();
    }
    void println(Iterable<?> iterable) {
        println(iterable, " ");
    }
    void println(Iterable<?> iterable, String delimiter) {
        Iterator<?> i = iterable.iterator();
        if (i.hasNext()) {
            print(i.next());
            while (i.hasNext()) {
                print(delimiter);
                print(i.next());
            }
        }
        println();
    }
    void printLines(int[] x) {
        println(x, System.lineSeparator());
    }
    void printLines(long[] x) {
        println(x, System.lineSeparator());
    }
    void printLines(Iterable<?> iterable) {
        println(iterable, System.lineSeparator());
    }
}
 
}