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:
/* package codechef; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{
	public static void main (String[] args) throws java.lang.Exception
	{
		Scanner sc = new Scanner(System.in);
		int t = sc.nextInt();
		while(t-- > 0) {
		  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();   
		  }
		  for(int i = 0; i < n; i++) {
		    b[i] = sc.nextInt();   
		  }
		  int prevA =  -1;
		  int prevB = -1;
		  int flagA = 0;
		  int flagB = 0;
		  int totalA = 0;
		  int totalB = 0;
		  for(int i = 0; i < n; i++) {
		      if(b[i] == 0) {
		          totalA++;
		          if(a[i] >= prevA) {
		              prevA = a[i];
		          }
		          else {
		              prevA = a[i];
		              flagA = 1;
		          }
		      }
		      else {
		          totalB++;
		          if (a[i] >= prevB) {
		              prevB = a[i];
		          }
		          else {
		              prevB = a[i];
		              flagB = 1;
		          }
		      }
		  }
		  if((totalA > 0 || (totalA == 0 && flagB == 0)) &&
		        (totalB > 0 || (totalB == 0 && flagA == 0))) {
		      System.out.println("Yes");
		  }
		  else System.out.println("No");
		}
	}
}