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:

//comment the next imports before submitting
import java.io.File;
import java.io.PrintStream;
//imports to be deleted ends here

import java.io.BufferedReader;
import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.Comparator;
import java.util.PriorityQueue;
import java.util.StringTokenizer;

//Problem URL here

public class TroubleSort1365B {

    public static void solve(Integer[] a, Integer[] b, int n) {
        boolean have0 = false;
        boolean have1 = false;

        for (int i = 0; i < n; i++) {
            if (b[i] == 0) {
                have0 = true;
            } else if (b[i] == 1) {
                have1 = true;
            }

            if (have0 && have1) {
                break;
            }
        }

        if (have1 && have0) {
            System.out.println("YES");
        } else if (isSorted(a, n)) {
            System.out.println("YES");
        } else {
            System.out.println("NO");
        }
    }

    private static boolean isSorted(Integer[] a, int n) {
        int prev = a[0];
        for (int i = 1; i < n; i++) {
            int curr = a[i];
            if (curr < prev) {
                return false;
            }
            prev = curr;
        }
        return true;
    }

    public static void main(String[] args) throws IOException {

        FastReader reader = new FastReader();

        int t = reader.nextInt();
        while (t-- > 0) {
            int n = reader.nextInt();

            Integer a[] = new Integer[n];
            Integer b[] = new Integer[n];

            for (int i = 0; i < n; i++) {
                a[i] = reader.nextInt();
            }

            for (int i = 0; i < n; i++) {
                b[i] = reader.nextInt();
            }

            // Arrays.sort(arr, new Comparator<Integer>() {
            // public int compare(Integer i1, Integer i2) {
            // return i1 - i2;
            // }
            // });

            // System.out.println(Arrays.toString(arr));

            solve(a, b, n);
        }

    }

    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;
        }
    }

}