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.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.io.ObjectInputStream.GetField;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.Set;
import java.util.StringTokenizer;
import java.util.TreeMap;
 
public class Main {
	public static boolean check(int[]arr,int sort[])
	{
		Arrays.sort(sort);
		for(int i=0;i<arr.length;i++)
		{
			if(arr[i]!=sort[i])
				return false;
			
		}
		return true;
	}
	public static void main(String[] args) {
		FastReader in = new FastReader();
		PrintWriter out = new PrintWriter(System.out);
		int current = 0,prev,t=in.nextInt(),nOne,n;
		int arr[];
		while(t-->0)
		{
			n=in.nextInt();
			arr=new int[n];
			for(int i=0;i<n;i++)
				arr[i]=in.nextInt();
			nOne=0;

		for(int i=0;i<n;i++) {
			int val=in.nextInt();
			if(val==1)
				nOne++;
		}
		
	if(nOne==0||nOne==n) {
		
		if(check(arr,Arrays.copyOf(arr, n)))
		out.println("Yes");
		else 
			out.println("No");

	
	
	}
	else 
		out.println("Yes");

		
		
			
		}
		
		
		
		
		
 
		out.close();
	}
 
}
 
class FastReader {
	BufferedReader br;
	StringTokenizer st;
 
	public FastReader() {
		br = new BufferedReader(new InputStreamReader(System.in));
 
	}
 
	String next() {
		while (st == null || !st.hasMoreElements()) {
			try {
				st = new StringTokenizer(br.readLine());
 
			} catch (IOException e) {
				e.printStackTrace();
			}
 
		}
 
		return st.nextToken();
 
	}
 
	int nextInt() {
 
		return Integer.parseInt(next());
	}
 
	double nextDouble() {
 
		return Double.parseDouble(next());
	}
 
	long nextLong() {
 
		return Long.parseLong(next());
	}
 
	String nextLine() {
		String str = "";
		try {
			str = br.readLine();
 
		} catch (IOException e) {
 
			e.printStackTrace();
		}
		return str;
 
	}
}