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 Main
{
       public static void main(String[] args) {
        Scanner scn = new Scanner(System.in);
        int t = scn.nextInt();
        for(int p=0;p<t;p++){
            
            // System.out.println(t+" t");
            
            int n = scn.nextInt();
            
            int a[] = new int[n];
            int b[] = new int[n];
            
            for(int i=0;i<n;i++)
                a[i]=scn.nextInt();
    
              // ArrayList<ArrayList<Integer> > aList = new ArrayList<ArrayList<Integer>>(n);            
           int a0=0;
            boolean flg0=true,flg1=true;
            for(int i=0;i<n;i++){
                b[i]=scn.nextInt();
                a0+=b[i];
            }
            
          boolean flg=true;
          int prev=-1;
          for(int i=1;i<n;i++){
              if(a[i-1]<=a[i])
                continue;
             else{
                 flg=false;
                 break;
             }
          }
            
        if(flg)
            System.out.println("Yes");
        else{
            if(a0!=0 && a0!=n)
                System.out.println("Yes");
            else
                System.out.println("No");
        }    
            
              
            
        }
    }
}