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.*;

public class Main {

    static ArrayList<Integer>[] gr;
    static boolean[] was;
    static boolean[] want_h;
    static int to;
    static boolean ans;

    public static void main(String[] args) throws IOException {
        br = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
//        br = new BufferedReader(new FileReader(new File("input.txt")));
//        out = new PrintWriter(new File("output.txt"));
        int PUTEN = nextInt();
        for (int PUTIN_POMOGI = 0; PUTIN_POMOGI < PUTEN; PUTIN_POMOGI++) {
            int n = nextInt();
            boolean sorted = true;
            int z = -1;
            int o = -1;
            int []a = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextInt();
                if(i > 0 && a[i-1] > a[i])sorted = false;
            }
            for (int i = 0; i < n; i++) {
                int p = nextInt();
                if(p == 1)o = i;
                else z = i;
            }
            if(sorted)out.println("Yes");
            else if(z == -1 || o == -1)out.println("No");
            else out.println("Yes");
        }
        out.close();
    }


    static BufferedReader br;
    static PrintWriter out;
    static StringTokenizer in = new StringTokenizer("");

    static String next() throws IOException {
        while (!in.hasMoreTokens()) {
            in = new StringTokenizer(br.readLine());
        }
        return in.nextToken();
    }

    static int[] mix(int[] a) {
        Random rnd = new Random();
        for (int i = 1; i < a.length; i++) {
            int j = rnd.nextInt(i);
            int temp = a[i];
            a[i] = a[j];
            a[j] = temp;
        }
        return a;
    }

    static int nextInt() throws IOException {
        return Integer.parseInt(next());
    }

    static long nextLong() throws IOException {
        return Long.parseLong(next());
    }

    static Double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }

    static long gcd(long a, long b) {
        if (b == 0) return a;
        return gcd(b, a % b);
    }

    static class sort implements Comparator<point> {

        @Override
        public int compare(point o1, point o2) {
            return Integer.compare(o1.ind, o2.ind);
        }

    }

    static void dfs(int from, String want) {
        if (ans) return;
        was[from] = true;
        if (want_h[from] && want.equals("H")) ans = true;
        if (!want_h[from] && want.equals("G")) ans = true;
        for (int p : gr[from]) {
            if (!was[p]) dfs(p, want);
        }
        return;
    }

}

class point {
    int ind;
    int wight;
    int speed;

    public point(int ind, int wight, int speed) {
        this.ind = ind;
        this.wight = wight;
        this.speed = speed;
    }
}