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 DemoC{
    static  ArrayList<Integer>[] graph;
       static int[] vis;
	public static void main(String[] args) {
	Scanner sc=new Scanner(System.in);
           int t=sc.nextInt();
           StringBuilder sb=new StringBuilder();
           while(t-->0){
               
          
	         int n=sc.nextInt();
	        
	         
	        int[] a=new int[n];
	        int[] b=new int[n];
	          int[] c=new int[n];
 HashSet<Integer> al=new HashSet<>();
	        
	        for(int i=0;i<n;i++) {a[i]=sc.nextInt(); c[i]=a[i];}
	        
	        for(int i=0;i<n;i++){
	            
	         b[i]=sc.nextInt();
	         al.add(b[i]);
	        }
	        
	        if(n==1){
	           // System.out.println("yes");
	            sb.append("yes");
	            sb.append(System.getProperty("line.separator"));
	            
	        }
	        else{
	            boolean ok=true;
	            for(int i=1;i<n;i++){
	               if( a[i-1]>a[i]) ok=false;
	            }
	            
	            if(ok==true){ //System.out.println("yes");
	                    sb.append("yes");
	            sb.append(System.getProperty("line.separator"));
	            }
	            
	            else{
	                  if(al.size()==1 &&( b[0]==0|| b[0]==1)){
	                      //System.out.println("NO");
	                      sb.append("no");
	            sb.append(System.getProperty("line.separator"));
	                  }
	                  else{
	                     
	                         // System.out.println("YES");
	                         sb.append("yes");
	            sb.append(System.getProperty("line.separator"));
	                      }
	                  }
	                
	            }
	        
	       
	     
   }
   System.out.println(sb);
   
	}
}