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.Arrays;
import java.util.Collections;
import java.util.Scanner;

public class Problem1365b {
	
	private static Scanner sc;

	public static void main(String[] args) {
		// TODO Auto-generated method stub

		sc = new Scanner (System.in);
		
		int t = sc.nextInt();
		
		while(t-- > 0)
		{
			int n = sc.nextInt();
			int[] a = new int[n];
			int[] b = new int[n];
			
			for(int i = 0; i < n; i++)
				a[i] = sc.nextInt();
			
			for(int i = 0; i < n; i++)
				b[i] = sc.nextInt();
			
			
			System.out.println(solve(a, b, n));
		}
	}
	
	private static String solve(int[] a, int[] b, int n)
	{
		int[] x = Arrays.copyOf(a, n);
		Arrays.sort(x);
		
		if(Arrays.equals(a, x))
			return ("Yes");
		
		else if(areSame(b))
				if(Arrays.equals(a, x))
					return ("Yes");
				else
					return ("No");
		
		else
		    return ("Yes");
	}
	
	public static boolean areSame(int arr[]) 
    { 
       int first = arr[0]; 
       for (int i=1; i<arr.length; i++) 
           if (arr[i] != first) 
                return false; 
       return true; 
    } 

}