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.*;

public class B{
	private static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	private static BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
	
	public static void main (String[] args) throws IOException{
		int t = Integer.parseInt(br.readLine());
		while(t-- > 0){
		    int n = Integer.parseInt(br.readLine());
		    StringTokenizer st = new StringTokenizer(br.readLine());
            int a[] = new int[n];
            int sorted[] = new int[n];
            for(int i=0;i<n;i++){
                a[i] = Integer.parseInt(st.nextToken());
                sorted[i] = a[i];
            }
            st = new StringTokenizer(br.readLine());
            int type[] = new int[n];
            int zero = 0, one = 0;
            for(int i=0;i<n;i++){
                type[i] = Integer.parseInt(st.nextToken());
                if(type[i]==1){
                    one++;
                }else{
                    zero++;
                }
            }
            if(one>0 && zero>0){
                bw.write("Yes");
                bw.newLine();
                continue;
            }
            Arrays.sort(sorted);
            boolean sort = true;
            for(int i=0;i<n;i++){
                if(a[i] != sorted[i])
                    sort = false;
            }
            if(sort){
                bw.write("Yes");
                bw.newLine();
            }else{
                bw.write("No");
                bw.newLine();
            }
		}
		bw.flush();
	}
}