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.io.*;
public class cf645 {

	public static void main(String[] args) throws NumberFormatException, IOException {
	   BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
	   int t=Integer.parseInt(br.readLine().trim());
	   while(t-->0) {
		   int n=Integer.parseInt(br.readLine().trim());
		   String str[]=br.readLine().trim().split(" ");
		   int a[]=new int[n];
		   int b[]=new int[n];
		   boolean f=false;
		   for(int i=0;i<n;i++) {
			   a[i]=Integer.parseInt(str[i]);
			   
		   }
		   
		   
		    str=br.readLine().trim().split(" ");
		    int c0=0,c1=0;
		    for(int i=0;i<n;i++)
		    {  	
		    	b[i]=Integer.parseInt(str[i]);
		    	if(b[i]==0)c0++;
		    	else c1++;
		    }
		    if(c0==n || c1==n) {
		    	  for(int i=1;i<n;i++) {
		    		  if(a[i-1]>a[i]) {
		    			  System.out.println("no");
		    			  f=true;
		    			  break;
		    		  }
		    	  }
		    	  if(!f) {
		    		  System.out.println("yes");
		    	  }
		    }else {
		    	System.out.println("yes");
		    }
				   
	   }
	}
}