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 java.lang.*;
import java.io.*;
 
/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{
    static ArrayList<pair>list;
    static HashMap<Integer,Integer>map;
    static int arr[];
    static int count[];
	public static void main (String[] args) throws java.lang.Exception
	{
		// your code goes here
		Scanner input = new Scanner(System.in);
		int test = input.nextInt();
		while(test-->0){
		    int n = input.nextInt();
		    int arr[] = new int[n];
		    for(int i =0;i<n;i++)arr[i] = input.nextInt();
		    boolean ok = true;
		    for(int i =0;i<n-1;i++){
		        if(arr[i]>arr[i+1]){
		            ok = false;
		        }
		    }
		    int b[] = new int[n];
		    boolean ok1 = false,ok2 = false;
		    for(int i =0;i<n;i++){
		        b[i] = input.nextInt();
		        if(b[i] == 0)ok1 = true;
		        if(b[i] == 1)ok2 = true;
		    }
		    if(ok){System.out.println("YES");continue;}
		    if(ok1&ok2){
		        System.out.println("YES");
		    }else{
		        System.out.println("NO");
		    }
		}
	}
	public static boolean solve(int gcd,int n){
	    list = new ArrayList<>();
	    int cache[] = new int[2001];
	    for(int i =0;i<1001;i++)cache[i] = count[i];
	    for(int j = gcd;j<=2000;j+=gcd){
    	    for(int i =0;i<2*n;i++){
    	        int req = Math.abs(j - arr[i]);
    	       if(req == arr[i] && cache[arr[i]]<2)continue;
    	        if(cache[arr[i]]>0 && cache[req]>0){
    	            list.add(new pair(req,arr[i]));
    	            cache[arr[i]]--;
    	            cache[req]--;
    	        }
    	        
    	    }
	    }
	  return true;
	    
	}
}
class pair{
    int a,b;
    public pair(int a,int b){
        this.a = a;
        this.b = b;
    }
}