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 javafx.util.Pair;

import java.io.*;
import java.util.ArrayList;
import java.util.StringTokenizer;

public class B_TroubleSort_1300 {
    public static void main(String[] args) {
        MyScanner sc = new MyScanner();
        out = new PrintWriter(new BufferedOutputStream(System.out));
        int t = sc.nextInt();
        while(t-->0) {
            int N = sc.nextInt();
            ArrayList<Pair<Integer, Integer>> numbers = new ArrayList<>();
            int[] temp1 = new int[N];
            int[] temp2 = new int[N];
            for(int i = 0; i < N; i++) {
                temp1[i] = Integer.parseInt(sc.next());
            }
            for(int i = 0; i < N; i++) {
                temp2[i] = Integer.parseInt(sc.next());
            }
            for(int i = 0; i < N; i++) {
                numbers.add(new Pair<>(temp1[i], temp2[i]));
            }

            int firstValue = numbers.get(0).getValue();
            int cur = numbers.get(0).getKey();
            int counter1 = 0;
            int counter2 = 0;
            for(int i = 0; i < N; i++) {
                if(numbers.get(i).getValue() == firstValue) {
                    counter1++;
                }
                if(numbers.get(i).getKey() >= cur) {
                    counter2++;
                }
                cur = numbers.get(i).getKey();
            }
            if(counter1 == N && counter2 != N) {
                System.out.println("No");
            } else {
                System.out.println("Yes");
            }
        }
        out.close();
    }

    public static PrintWriter out;

    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            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;
        }

    }
}