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.BufferedReader;
import java.io.FileWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;
import java.util.Vector;

import javax.swing.text.StyledEditorKit.ForegroundAction;


public class main {
	
	public static void main(String[] args) throws NumberFormatException, IOException
	{
		BufferedReader br= new BufferedReader(new InputStreamReader(System.in));
		PrintWriter pw= new PrintWriter(System.out);
		int T= Integer.parseInt(br.readLine());
		for (int i = 0; i < T; i++) {
			int n= Integer.parseInt(br.readLine());
			StringTokenizer st= new StringTokenizer(br.readLine());
			int[] a = new int[n];
			int[] b= new int[n];
			int zero=0;
			int one=0;
			Integer[] order = new Integer[n];
			for (int j = 0; j < a.length; j++) {
				a[j]= Integer.parseInt(st.nextToken());
				order[j]=a[j];
			}
			st= new StringTokenizer(br.readLine());
			for (int j = 0; j < b.length; j++) {
				b[j]= Integer.parseInt(st.nextToken());
				if(b[j]==0)
				{
					zero++;
				}
				else if(b[j]==1)
				{
					one++;
				}
			}
			Arrays.sort(order);
			boolean ordered=true;
			for (int j = 0; j < order.length; j++) {
				if(a[j]!=order[j])
				{
					ordered=false;break;
				}
			}
			if(ordered||!((zero==n&&one==0)||(zero==0&&one==n)))
			{
				pw.println("Yes");
			}
			else
			{
				pw.println("No");
			}
		}
		
		pw.close();
	}
	static class pair implements Comparable<pair>
	{
		int value;
		int type;
		public pair(int value, int type) {
			this.value=value;
			this.type=type;
		}
		@Override
		public int compareTo(pair p) {
			// TODO Auto-generated method stub
			return this.value-p.value;
		}
		public String toString()
		{
			return "("+value+","+type+")";
		}
	}
}