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.io.*;

public class cp {

    public static void main(String args[]) {

    	Scanner sc = new Scanner();
    	int t = sc.nextInt();

    	

    	while(t-->0)
    	{
    		int n = sc.nextInt();

    		int ar[] = new int[n];

    		for(int i=0;i<n;i++){
    			ar[i] = sc.nextInt();
    		}
    		boolean one= false;
    		boolean zero = false;
    		for(int i=0;i<n;i++)
    		{
    			int x = sc.nextInt();
    			if(x==1)
    				one=true;
    			if(x==0)
    				zero=true;
    		}

int i=1;
    		for(i=1;i<n;i++)
    		{
    			if(ar[i]>=ar[i-1])
    			{

    			}else break;
    		}

    		
//1 3 2
    		if(one && zero || i==n)
    			out.println("Yes");
    		else out.println("No");
    	}

    	out.close();
    	
    }
    // static long find(long n,long k)
    // {
    // 	long ans = Math.sqrt(n);
    // 	if(ans*ans==n && k>=ans)
    // 		return ans;
    // 	return 
    // }


    static	PrintWriter out=new PrintWriter(System.out);
	static class Scanner {
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st=new StringTokenizer("");
		String nextLine() {
			while (!st.hasMoreTokens())
				try { 
                                        st=new StringTokenizer(br.readLine());				               
                                } catch (IOException e) {}
			return st.nextToken();
		}
		int nextInt() {
			return Integer.parseInt(nextLine());
		}
		float nextFloat() {
			return Float.parseFloat(nextLine());
		}
		double nextDouble() {
			return Double.parseDouble(nextLine());
		}
		long nextLong() {
			return Long.parseLong(nextLine());
		}
	}
}