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;

public class trouble_sort {
	public static Scanner scn = new Scanner(System.in);

	public static void main(String[] args) {
		// TODO Auto-generated method stub
int t=scn.nextInt();
 for(int w=0;w<t;w++){
	 int n=scn.nextInt();
	 int zero=0;
	 int one=0;
	 boolean sorted=true;
	 int arr[]=new int[n];
	 int state[]=new int[n];
	 for(int i=0;i<n;i++){
		 arr[i]=scn.nextInt();
		 if(i!=0&&arr[i]<arr[i-1]){
			 sorted=false;
		 }
	 }
	 for(int i=0;i<n;i++){
		 arr[i]=scn.nextInt();
		 if(arr[i]==0) zero++;
		 else one++;
	 }
	 if(sorted){
		 System.out.println("Yes");
	 }
	 else if(one!=0&&zero!=0) System.out.println("Yes");
	 else System.out.println("No");
 }
	}

}