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 static java.lang.Math.*;
import java.io.*;

public class S {
       
      public static void main(String args[])throws IOException{
              Scanner sc = new Scanner(System.in);
              int t = sc.nextInt();
              while(t > 0){
                     t--;
                     int n = sc.nextInt();
                     int a[] = new int[n];
                     int b[] = new int[n];
                     for(int i = 0; i < n; i++)
                            a[i] = sc.nextInt();
                     boolean type1 = false;
                     boolean type2 = false;
                     for(int i = 0; i < n; i++){
                            b[i] = sc.nextInt();
                            if(b[i] == 1)type1 = true;
                            if(b[i] == 0)type2 = true;
                     }
                     if(type1 == true && type2 == true){
                            System.out.println("Yes");
                     }else{
                            boolean sorted = true;
                            for(int i = 1; i < n; i++){
                                   if(a[i] < a[i-1]){
                                          sorted = false;
                                          break;
                                   }
                            }
                            String ans = sorted ? "Yes" : "No";
                            System.out.println(ans);
                     }
              }
      }
}