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.util.ArrayList;
import java.util.Collections;
import java.util.StringTokenizer;
import java.util.Arrays;
import java.util.Comparator;
public class TroubleSort {
    public static void main(String[] args) {
        handmadeInput.FastReader in = new handmadeInput.FastReader();
        int t = in.nextInt();
        while (t-- > 0) {
            int n = in.nextInt();
            Pair[] pairs = new Pair[n];
            int onec = 0, zeroc = 0;
            for (int i = 0; i < n; i++) {
                pairs[i] = new Pair(in.nextInt());
            }
            for (int i = 0; i < n; i++) {
                pairs[i].b = in.nextInt();
                if (pairs[i].b == 0) {
                    zeroc++;
                } else {
                    onec++;
                }
            }
            boolean ans = true;
            for (int i = 0; i < n - 1; i++) {
                if (pairs[i].a > pairs[i + 1].a) {
                    ans = false;
                    break;
                }
            }
            if (ans || (onec > 0 && zeroc > 0)) {
                System.out.println("YES");
            } else {
                System.out.println("NO");
            }


        }
    }

    static class Pair {
        int a, b;

        Pair(int a) {
            this.a = a;
        }
    }
}




// Additional Classes go here



// Fast inputOutput


class handmadeInput {
    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;
        }
    }
}

class UtilityFunctions {
    //! returns gcd of given numbers
    public int gcd(int a, int b) {
        // Everything divides 0
        if (a == 0)
            return b;
        if (b == 0)
            return a;
        // base case
        if (a == b)
            return a;
        // a is greater
        if (a > b)
            return gcd(a - b, b);
        return gcd(a, b - a);
    }


}