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.lang.*;
import java.io.*;

public class pb2
{
	static boolean sort(int a[], int n)
	{
		for(int i=1;i<n;i++)
		{
			if(a[i-1]<=a[i])
				continue;
			else
				return false;
		}
		return true;
	} 
	public static void main (String[] args)
	{
		Scanner in = new Scanner(System.in);

		int t;
		t = in.nextInt();

		for(int y=0; y<t; y++)
		{
			int n;
			n = in.nextInt();

			int a[] = new int[n];
			int b[] = new int[n];
			int sort[] = new int[n];

			for(int i=0; i<n; i++)
				a[i] = in.nextInt();

			int zero = 0, one = 0;
			for(int i=0; i<n; i++)
			{
				b[i] = in.nextInt();
				if(b[i] == 0)
					zero++;
				else
					one++;
			}

			if(zero > 0 && one > 0)
				System.out.println("Yes");
			else
			{
				if(sort(a,n))
					System.out.println("Yes");
				else
					System.out.println("No");
			}
		}
	}
}