Problem: Ashish has n elements arranged in a line. 

These elements are represented by two integers a_i — the value of the element and b_i — the type of the element (there are only two possible types: 0 and 1). He wants to sort the elements in non-decreasing values of a_i.

He can perform the following operation any number of times: 

  * Select any two elements i and j such that b_i ≠ b_j and swap them. That is, he can only swap two elements of different types in one move. 



Tell him if he can sort the elements in non-decreasing values of a_i after performing any number of operations.

Input

The first line contains one integer t (1 ≤ t ≤ 100) — the number of test cases. The description of the test cases follows.

The first line of each test case contains one integer n (1 ≤ n ≤ 500) — the size of the arrays.

The second line contains n integers a_i (1 ≤ a_i ≤ 10^5) — the value of the i-th element.

The third line containts n integers b_i (b_i ∈ \{0, 1\}) — the type of the i-th element.

Output

For each test case, print "Yes" or "No" (without quotes) depending on whether it is possible to sort elements in non-decreasing order of their value.

You may print each letter in any case (upper or lower).

Example

Input


5
4
10 20 20 30
0 1 0 1
3
3 1 2
0 1 1
4
2 2 4 8
1 1 1 1
3
5 15 4
0 0 0
4
20 10 100 50
1 0 0 1


Output


Yes
Yes
Yes
No
Yes

Note

For the first case: The elements are already in sorted order.

For the second case: Ashish may first swap elements at positions 1 and 2, then swap elements at positions 2 and 3.

For the third case: The elements are already in sorted order.

For the fourth case: No swap operations may be performed as there is no pair of elements i and j such that b_i ≠ b_j. The elements cannot be sorted.

For the fifth case: Ashish may swap elements at positions 3 and 4, then elements at positions 1 and 2.

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;

public class aaaaaaaaaaaaaaaa {
	public void run() throws Exception {
		FastReader file = new FastReader();
		int times = file.nextInt();
		for (int asdf = 0; asdf < times; asdf++) {
//			int r = file.nextInt(), c = file.nextInt();
//			int[][] mat = new int[r][c];
//			for (int i = 0; i  < r; i++) {
//				for (int j = 0; j < c; j++) {
//					mat[i][j] = file.nextInt();
//				}
//			}
//			int cnt = 0;
//			for (int i= 0; i < r; i++) {
//				boolean b = true;
//				for (int j = 0; j < c; j++) {
//					if (mat[i][j] == 1)
//				}
//			}
			int n = file.nextInt();
			ArrayList<Integer> x = new ArrayList(), y = new ArrayList();
			HashSet<Integer>a = new HashSet();
			for (int i = 0; i < n; i++) x.add(file.nextInt());
			for (int i = 0; i < n; i++) y.add(file.nextInt());
			for (int i : y) a.add(i);
			if (a.size() == 1 && !isSorted(x)) System.out.println("No");
			else System.out.println("Yes");
		}
	}
	public static boolean isSorted(ArrayList<Integer> t ) {
		for (int i = 1; i < t.size(); i++) {
			if (t.get(i) < t.get(i -1)) return false;
		}
		return true;
	}

	public static void main(String[] args) throws Exception {
		new aaaaaaaaaaaaaaaa().run();
	}

	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;
		}
	}
}