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.io.*;
import java.util.*;
public class Test {

	static boolean isSorted(int arr[] , int n) {

		if (n == 0 || n == 1) return true;

		for (int i = 1; i < n; i++) {
			if (arr[i] < arr[i - 1]) {
				return false;
			}
		}
		return true;
	}

	static boolean check01(int arr[], int n) {

		int zeros = 0;
		int ones = 0;
		for (int i = 0; i < n; i++) {
			if (arr[i] == 0) {
				zeros++;
			} else {
				ones++;
			}
		}

		if (zeros != 0 && ones != 0) {
			return true;
		} else return false;
	}


	public static void main(String[] args) throws IOException {
		Scanner sc = new Scanner(System.in);

		int t = sc.nextInt();
		int n = 0;

		for (int k = 0; k < t; k++) {
			n = sc.nextInt();
			int ar[][] = new int[2][n];
			for (int i = 0 ; i < 2 ; i++) {
				for (int j = 0; j < n; j++) {
					ar[i][j] = sc.nextInt();
				}
			}

			if (isSorted(ar[0] , n)) {
				System.out.println("Yes");
			} else {
				if (check01(ar[1] , n)) {
					System.out.println("Yes");
				} else {
					System.out.println("No");
				}
			}

		}
	}
}