Monocarp is playing a computer game. Now he wants to complete the first level of this game.

A level is a rectangular grid of 2 rows and n columns. Monocarp controls a character, which starts in cell (1, 1) — at the intersection of the 1-st row and the 1-st column.

Monocarp's character can move from one cell to another in one step if the cells are adjacent by side and/or corner. Formally, it is possible to move from cell (x_1, y_1) to cell (x_2, y_2) in one step if |x_1 - x_2| ≤ 1 and |y_1 - y_2| ≤ 1. Obviously, it is prohibited to go outside the grid.

There are traps in some cells. If Monocarp's character finds himself in such a cell, he dies, and the game ends.

To complete a level, Monocarp's character should reach cell (2, n) — at the intersection of row 2 and column n.

Help Monocarp determine if it is possible to complete the level.

Input

The first line contains a single integer t (1 ≤ t ≤ 100) — the number of test cases. Then the test cases follow. Each test case consists of three lines.

The first line contains a single integer n (3 ≤ n ≤ 100) — the number of columns.

The next two lines describe the level. The i-th of these lines describes the i-th line of the level — the line consists of the characters '0' and '1'. The character '0' corresponds to a safe cell, the character '1' corresponds to a trap cell.

Additional constraint on the input: cells (1, 1) and (2, n) are safe.

Output

For each test case, output YES if it is possible to complete the level, and NO otherwise.

Example

Input


4
3
000
000
4
0011
1100
4
0111
1110
6
010101
101010


Output


YES
YES
NO
YES

Note

Consider the example from the statement.

In the first test case, one of the possible paths is (1, 1) → (2, 2) → (2, 3).

In the second test case, one of the possible paths is (1, 1) → (1, 2) → (2, 3) → (2, 4).

In the fourth test case, one of the possible paths is (1, 1) → (2, 2) → (1, 3) → (2, 4) → (1, 5) → (2, 6).
1
9
000000010
000000000
 1
9
000000010
000100000
 1
60
000000000000000000000000000000000000000000000000000000000010
000000000000000000000000000000000000000000000000000000000010

YES
 YES
 NO

//---#ON_MY_WAY---
import static java.lang.Math.*;
import java.io.*;
import java.math.*;
import java.util.*;

public class apples {
	static class pair {
		int x, y;

		public pair(int a, int b) {
			x = a;
			y = b;
		}
	}

	static FastReader x = new FastReader();
	static OutputStream outputStream = System.out;
	static PrintWriter out = new PrintWriter(outputStream);

	/*---------------------------------------CODE STARTS HERE-------------------------*/
	public static void main(String[] args) throws NumberFormatException, IOException {
		long startTime = System.nanoTime();
		int mod = 1000000007;
		int t = x.nextInt();
		StringBuilder str = new StringBuilder();
		ArrayList<Integer> al = primes(100000);
		TreeSet<Integer> ts = new TreeSet<>(al);
		while (t > 0) {
			int n = x.nextInt();
			char ch = x.next().charAt(0);
			String s = x.next();
			int f = 0, ind = -1;
			for (int i = 0; i < n; i++) {
				if(s.charAt(i)!=ch) {
					f = 1;
					break;
				}
			}
			if(f==0) {
				str.append(0);
			}
			else {
				for (int i = 0; i < n; i++) {
					if(s.charAt(i)==ch&&(i+1)*2>n) {
						ind = i+1;
						break;
					}
				}
				if(ind==-1) {
					str.append(2+"\n"+n+" "+(n-1));
				}
				else {
					str.append(1+"\n"+ind);
				}
			}
			str.append("\n");
			t--;
		}
		out.println(str);
		out.flush();
		long endTime = System.nanoTime();
		//System.out.println((endTime-startTime)/1000000000.0);
	}

	/*--------------------------------------------FAST I/O--------------------------------*/
	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;
		}

		char nextchar() {
			char ch = ' ';
			try {
				ch = (char) br.read();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return ch;
		}
	}

	/*--------------------------------------------BOILER PLATE---------------------------*/
	static int[] readarr(int n) {
		int arr[] = new int[n];
		for (int i = 0; i < n; i++) {
			arr[i] = x.nextInt();
		}
		return arr;
	}

	static int[] sortint(int a[]) {
		ArrayList<Integer> al = new ArrayList<>();
		for (int i : a) {
			al.add(i);
		}
		Collections.sort(al);
		for (int i = 0; i < a.length; i++) {
			a[i] = al.get(i);
		}
		return a;
	}

	static long[] sortlong(long a[]) {
		ArrayList<Long> al = new ArrayList<>();
		for (long i : a) {
			al.add(i);
		}
		Collections.sort(al);
		for (int i = 0; i < al.size(); i++) {
			a[i] = al.get(i);
		}
		return a;
	}

	static long pow(long x, long y) {
		long result = 1;
		while (y > 0) {
			if (y % 2 == 0) {
				x = x * x;
				y = y / 2;
			} else {
				result = result * x;
				y = y - 1;
			}
		}
		return result;
	}

	static int[] revsort(int a[]) {
		ArrayList<Integer> al = new ArrayList<>();
		for (int i : a) {
			al.add(i);
		}
		Collections.sort(al, Comparator.reverseOrder());
		for (int i = 0; i < a.length; i++) {
			a[i] = al.get(i);
		}
		return a;
	}

	static int[] gcd(int a, int b, int ar[]) {
		if (b == 0) {
			ar[0] = a;
			ar[1] = 1;
			ar[2] = 0;
			return ar;
		}
		ar = gcd(b, a % b, ar);
		int t = ar[1];
		ar[1] = ar[2];
		ar[2] = t - (a / b) * ar[2];
		return ar;
	}

	static boolean[] esieve(int n) {
		boolean p[] = new boolean[n + 1];
		Arrays.fill(p, true);
		for (int i = 2; i * i <= n; i++) {
			if (p[i] == true) {
				for (int j = i * i; j <= n; j += i) {
					p[j] = false;
				}
			}
		}
		return p;
	}

	static ArrayList<Integer> primes(int n) {
		boolean p[] = new boolean[n + 1];
		ArrayList<Integer> al = new ArrayList<>();
		Arrays.fill(p, true);
		int i = 0;
		for (i = 2; i * i <= n; i++) {
			if (p[i] == true) {
				al.add(i);
				for (int j = i * i; j <= n; j += i) {
					p[j] = false;
				}
			}
		}
		for (i = i; i <= n; i++) {
			if (p[i] == true) {
				al.add(i);
			}
		}
		return al;
	}

	static int etf(int n) {
		int res = n;
		for (int i = 2; i * i <= n; i++) {
			if (n % i == 0) {
				res /= i;
				res *= (i - 1);
				while (n % i == 0) {
					n /= i;
				}
			}
		}
		if (n > 1) {
			res /= n;
			res *= (n - 1);
		}
		return res;
	}

	static int gcd(int a, int b) {
		if (a == 0) {
			return b;
		}
		return gcd(b % a, a);
	}

	static long gcd(long a, long b) {
		if (a == 0) {
			return b;
		}
		return gcd(b % a, a);
	}
}