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 Main {
//        File file = new File("input.txt");
//        Scanner in = new Scanner(file);
//        PrintWriter out = new PrintWriter(new FileWriter("output.txt"));
    public static void main(String[] args) {
//        Scanner in = new Scanner(System.in);
        FastReader in = new FastReader();
        
        int t = in.nextInt();
        while(t-- > 0) {
        	int n = in.nextInt();
        	int[][] arr = new int[n][2];
        	for(int i = 0; i<n; i++)
        		arr[i][0] = in.nextInt();
        	for(int i = 0; i<n; i++)
        		arr[i][1] = in.nextInt();
        	
        	boolean ans = true;
        	for(int i = 0; i<n-1; i++) {
        		if(arr[i][0]>arr[i+1][0]) {
        			ans = false;
        			break;
        		}
        	}
        	if(ans) {
        		System.out.println("Yes");
        	}else {
        		int zero = 0, one = 0;
        		for(int i = 0; i<n; i++) {
        			if(arr[i][1]==0) zero++;
        			else one++;
        		}
        		if(zero>0 && one>0) {
        			System.out.println("Yes");
        		}else System.out.println("No");
        	}
        	
        }
        
    }
    
    private static int gcd(int a, int b) {
    	if(b==0) return a;
    	return gcd(b, a%b);
    }

	static 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;
        }
    }
}