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.Scanner;
import java.util.*;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

import static java.lang.Math.*;

public class Main {

    static class FastScanner {
        StringTokenizer tok = new StringTokenizer("");
        BufferedReader in;

        FastScanner()  {
            in = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() throws IOException {
            while (!tok.hasMoreElements())
                tok = new StringTokenizer(in.readLine());
            return tok.nextToken();
        }

        int nextInt() throws IOException {
            return Integer.parseInt(next());
        }


    }
    static int a[] = new int[500];
    static int b[] = new int[500];
    public static void main(String[] args) throws IOException {

        FastScanner input = new FastScanner();
        Scanner in = new Scanner(System.in);
        int t;
        t = input.nextInt();
        for( int tc = 0 ; tc < t ; tc ++ ){
           int n;
           n = input.nextInt();
           for( int i = 0 ; i < n ; i++ ){
               a[i] = input.nextInt();
           }
           boolean ZeroPresent = false , OnePresent = false;
           for( int i = 0 ; i < n ; i++ ){
               b[i] = input.nextInt();
               if(b[i]==0)ZeroPresent = true;
               else OnePresent = true;
           }

           int flag = 0 ;
           for( int i = 1 ; i < n  ; i++ ){
               if(a[i] < a[i-1]){
                   flag = 1;
                   break;
               }
           }

           if(flag == 0){
               System.out.println("Yes");
               continue;
           }
           else if( ZeroPresent == true && OnePresent == true ){
               System.out.println("Yes");

           }
           else{
               System.out.println("No");
           }


        }




    }
}