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 Code {

	public static void swap(int[] a, int[] b, int i, int j) {
		int tmp = a[i];
		a[i] = a[j];
		a[j] = tmp;

		tmp = b[i];
		b[i] = b[j];
		b[j] = tmp;
	}

	public static boolean TroubleSort(int[] a, int[] b, int n) {
		boolean isSorted = true;
		for (int i=0; i<n-1; i++) {
			if (a[i] > a[i+1]) {
				isSorted = false;
				break;
			}
		}
		if (isSorted == true) {return true;}
		
		int zero = 0;
		int ones = 0;
		for (int i=0; i<n; i++) {
			if (b[i] == 1) {
				ones++;
			}else {
				zero++;
			}
		}
		return ((zero > 0) && (ones > 0));
	}
	
	public static void main(String[] args) throws IOException
	{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int t = Integer.parseInt(br.readLine());
		while (t > 0) {
			int n = Integer.parseInt(br.readLine());
			int[] a = new int[n];
			int[] b = new int[n];
			String[] lines = br.readLine().trim().split(" ");
			for (int i=0; i<n; i++) {
				a[i] = Integer.parseInt(lines[i]);
			}
			lines = br.readLine().trim().split(" ");
			for (int i=0; i<n; i++) {
				b[i] = Integer.parseInt(lines[i]);
			}
			System.out.println((TroubleSort(a,b,n)==false) ? "No" : "Yes");
			t -= 1;
		}
	}
}