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.IOException;
import java.io.InputStreamReader;
import java.io.BufferedReader;
import java.util.function.IntPredicate;

public class CF_B_1365
{
    public static void main(String[] args) throws IOException
    {
        int t = readInt();
        for (int __ = 0; __ < t; __++)
        {
            int n = readInt();
            int[] values = new int[n];
            boolean isGood = true;
            int lastEl = Integer.MIN_VALUE;
            for (int i = 0; i < n; i++)
            {
                int num = readInt();
                if (lastEl > num)
                {
                    isGood = false;
                }
                lastEl = num;
                values[i] = num;
            }
            boolean has0 = false;
            boolean has1 = false;
            int[] types = new int[n];
            for (int i = 0; i < n; i++)
            {
                int num = readInt();
                if (num == 1)
                {
                    has1 = true;
                }
                else
                {
                    has0 = true;
                }
                types[i] = num;
            }

            if (isGood || (has0 && has1))
            {
                System.out.println("Yes");
            }
            else
            {
                System.out.println("No");
            }
        }
    }

    static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    static StringTokenizer st;

    static int readInt() throws IOException
    {
        while (st == null || !st.hasMoreTokens())
        {
            st = new StringTokenizer(br.readLine());
        }
        return Integer.parseInt(st.nextToken());
    }
}