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.*;
public class solution{

	
    public static void main(String[] args){
    	
        Scanner s=new Scanner(System.in);
        int t=s.nextInt();
        while(t-->0) {
        	int n=s.nextInt();
        	int[] arr=new int[n];
        	int[] bin=new int[n];
        	
        	for(int i=0;i<n;i++) {
        		arr[i]=s.nextInt();
        	}
        	int one=0;
        	
        	for(int i=0;i<n;i++) {
        		bin[i]=s.nextInt();
        		if(bin[i]==1) {
        			one++;
        		}
        	}
        	
        	int zero=n-one;
        	boolean c=true;
        	
        	for(int i=0;i<n-1;i++) {
        		if(arr[i]>arr[i+1]) {
        			c=false;
        			break;
        		}
        	}
        	
        	if((zero==0||one==0)&&!c) {
        		System.out.println("No");
        	}else {
        		System.out.println("Yes");
        	}
		}
    }
}