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.*;
import java.util.StringTokenizer;

public class B {
    public static void main(String[] args) throws  Exception{
        Reader sc = new Reader();
        /*--------------------------*/
        int tc = sc.nextInt() ;
        while(tc-- > 0) {
            boolean mark1, mark2, ok;
            mark1 = mark2 = false;
            ok = true;
            int n = sc.nextInt();
            int arr[] = new int[n];
            int brr[] = new int[n];

            for (int i = 0; i < n; i++) {
                arr[i] = sc.nextInt();
                if (i > 0) {
                    if (arr[i] < arr[i - 1]) {
                        ok = false;
                    }
                }
            }
            for (int i = 0; i < n; i++) {
                brr[i] = sc.nextInt();
                if (brr[i] == 0) {
                    mark1 = true;
                } else if (brr[i] == 1) {
                    mark2 = true;
                }
            }
            if (ok || (mark1 && mark2)) {
                pr.println("Yes");
            } else {
                pr.println("No");
            }
        }
        /*--------------------------*/
        pr.close();
    }

    static PrintWriter pr = new PrintWriter(System.out);
    static class Reader {
        BufferedReader br;
        StringTokenizer st;
        public Reader() {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }
        public Reader(String k) throws Exception {
            br = new BufferedReader(new FileReader(new File("input")));
        }
        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;
        }
    }
}