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.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class TroubleSort {
    static int n;
    static int[] a, b;
    public static void main(String[] args)throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        BufferedOutputStream out = new BufferedOutputStream(System.out);
        int t = Integer.parseInt(br.readLine());
        while(t-- > 0){
            n = Integer.parseInt(br.readLine());
            a = new int[n];
            b = new int[n];
            StringTokenizer st = new StringTokenizer(br.readLine());
            for(int i = 0; i < n; i++){
                a[i] = Integer.parseInt(st.nextToken());
            }
            st = new StringTokenizer(br.readLine());
            for(int i = 0; i < n; i++){
                b[i] = Integer.parseInt(st.nextToken());
            }
            out.write(((solve()? "Yes": "No") + "\n").getBytes());
        }
        out.close();
    }
    public static boolean solve()throws IOException{
        boolean hasOne, hasZero;
        hasOne = false;
        hasZero = false;
        for(int i : b){
            if(i == 1){
                hasOne = true;
            }
            if(i == 0){
                hasZero = true;
            }
        }
        if(hasOne && hasZero){
            return true;
        }else{
            for(int i = 1; i < n; i++){
                if(a[i] < a[i-1]){
                    return false;
                }
            }
        }
        return true;
    }

}