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.BufferedReader;
import java.io.InputStreamReader;

public class SolRound648B {
	public String possible(int[] a, int[] b){
		boolean countZer = false;
		boolean countOne = false;
		boolean violation = false;
		int len = a.length;
		for(int i = 0;i<len;i++){
			if(b[i] == 0)countZer = true;
			if(b[i] == 1)countOne = true;
		}
		for(int i = 0;i<len-1;i++){
			if(a[i] > a[i+1])violation  = true;
		}
		if((!countZer || !countOne) && violation)return "No";
		else return "Yes";
	}
	public static void main(String[] args)throws Exception{
		SolRound648B sd = new SolRound648B();
		BufferedReader obj = new BufferedReader(new InputStreamReader(System.in));
		String lineNo = obj.readLine();
		int lines = Integer.parseInt(lineNo);
		while(lines-- > 0 ){
			String line = obj.readLine();
			int n = Integer.parseInt(line);
			line = obj.readLine();
			String[] de = line.split(" ");
			line = obj.readLine();
			String[] de1 = line.split(" ");
			int len  = n ;//de.length;
			int[] inp = new int[len];
			int[] inpb = new int[len];
			
			for(int i = 0; i < len; i++){
				inp[i] = Integer.parseInt(de[i]);
				inpb[i] = Integer.parseInt(de1[i]);
			}
			System.out.println(sd.possible(inp, inpb));
		}
	}

}