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 TroubleSort {
    static long mod = 1000000007;

    static void pnl(Object o) {
        System.out.println(o);
    }

    static void pn(Object o) {
        System.out.print(o + " ");
    }

    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;
        }
    }

    public static boolean isSorted(int a[]) {
        for (int i = 0; i < a.length - 1; i++) {
            if (a[i] > a[i + 1])
                return false;
        }
        return true;
    }

    public static void main(String args[]) {
        FastReader sc = new FastReader();
        int t = sc.nextInt();
        for (int p = 0; p < t; p++) {
            int n = sc.nextInt();
            int a[] = new int[n];
            int b[] = new int[n];
            int type1 = 0, type2 = 0;
            for (int i = 0; i < n; i++)
                a[i] = sc.nextInt();
            for (int i = 0; i < n; i++) {
                b[i] = sc.nextInt();
                type1 = b[i] == 0 ? (type1 + 1) : type1;
                type2 = b[i] == 1 ? (type2 + 1) : type2;
            }
            // System.out.println("type1 and type2 :" + type1 + " - " + type2);
            if (isSorted(a)) {
                System.out.println("Yes");
                continue;
            }
            if (type1 == 0 || type2 == 0)
                System.out.println("No");
            else
                System.out.println("Yes");

        }
    }
}