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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;

/* 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
	{
		FastReader s = new FastReader();
		PrintWriter pw = new PrintWriter(System.out);
        int t=s.nextInt();
        while(t-->0){
            int n=s.nextInt();
            int[] arr=new int[n];
            for(int i=0;i<n;i++){
                arr[i]=s.nextInt();
            }
            int check=0;
            for(int i=1;i<n;i++){
                if(arr[i]<arr[i-1]){
                    check=1;
                    break;
                }
            }
            int a=0;
            int b=0;
            for(int i=0;i<n;i++){
                if(s.nextInt()==0)a++;
                else{b++;}
            }
            if(check==0){
                System.out.println("Yes");
            }
            else{
                if(a>=1&&b>=1){
                    System.out.println("Yes");
                }
                else{
                    System.out.println("No");
                }
            }
        }
	}
}
class FastReader {
	BufferedReader br;
	StringTokenizer st;
 
	public FastReader() {
		br = new BufferedReader(new
		                        InputStreamReader(System.in));
	}
 
	String next() {
		while (st == null || !st.hasMoreElements()) {
			try {
				st = new StringTokenizer(br.readLine());
			} catch (IOException  e) {
				e.printStackTrace();
			}
		}
		return st.nextToken();
	}
 
	int nextInt() {
		return Integer.parseInt(next());
	}
 
	long nextLong() {
		return Long.parseLong(next());
	}
 
	double nextDouble() {
		return Double.parseDouble(next());
	}
 
	String nextLine() {
		String str = "";
		try {
			str = br.readLine();
		} catch (IOException e) {
			e.printStackTrace();
		}
		return str;
	}
}