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 B {

	public static void main(String[] args) {
		
		FastReader f = new FastReader();
		StringBuffer sb=new StringBuffer();
		int test=f.nextInt();
		out:
		while(test-->0)
		{		
			int n=f.nextInt();
			List<Integer> a=new ArrayList<>(),b=new ArrayList<>(),list=new ArrayList<>();
			for(int i=0;i<n;i++)
			{
				int var=f.nextInt();
				a.add(var);
				list.add(var);
			}
			for(int i=0;i<n;i++)
				b.add(f.nextInt());
			
			Collections.sort(list);
			boolean poss=true;
			for(int i=0;i<n;i++)
			{	
				int val1=a.get(i);
				int val2=list.get(i);
				if(val1!=val2)
				{
					poss=false;
					break;
				}
			}
//			System.out.println(a);
//			System.out.println(list);
//			System.out.println(poss);
			if(poss)
			{
				sb.append("Yes\n");
				continue;
			}
			boolean allSame=true;
			for(int i=0;i<n-1;i++)
				if(b.get(i)!=b.get(i+1))
				{
					allSame=false;
					break;
				}
			if(allSame)
				sb.append("No\n");
			else
				sb.append("Yes\n");
		}
		System.out.println(sb);
	}
	
	static 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()); 
	    } 
	    long nextLong() { 
	        return Long.parseLong(next()); 
	    } 
	    double nextDouble() { 
	        return Double.parseDouble(next()); 
	    } 
	    String nextLine() { 
	        String str = ""; 
	        try{ 
	            str = br.readLine(); 
	        } 
	        catch (IOException e) { 
	            e.printStackTrace(); 
	        } 
	        return str; 
	    } 
	} 
}