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 Main
{
    private static String process(List<int[]> list) {
        List<Integer> a = new ArrayList<Integer>();
        List<Integer> b = new ArrayList<Integer>();
        
        for(int[] n : list) {
            if (n[1]==0) a.add(n[0]);
            else b.add(n[0]);
        }
        
        boolean isASorted = true && a.size() > 0;
        boolean isBSorted = true && b.size() > 0;
        
        for(int i = 1; i < a.size(); i++) {
            if (a.get(i)<a.get(i-1)) {
                isASorted = false;
                break;
            }
        }
        
        for(int i = 1; i < b.size(); i++) {
            if (b.get(i)<b.get(i-1)) {
                isBSorted = false;
                break;
            }
        }
        
        return isASorted || isBSorted || (a.size() > 0 && b.size() > 0)?"Yes":"No";
    }
	public static void main(String[] args) throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int t = Integer.parseInt(br.readLine());
		while(t-->0) {
		    int size = Integer.parseInt(br.readLine());
		    StringTokenizer tok = new StringTokenizer(br.readLine());
		    List<int[]> a = new ArrayList<int[]>();
		    for(int i = 0; i < size; i++) {
		        a.add(new int[]{Integer.parseInt(tok.nextToken()),0,i});
		    }
		    tok = new StringTokenizer(br.readLine());
		    for(int i = 0; i < size; i++) {
		        a.get(i)[1]=Integer.parseInt(tok.nextToken());
		    }
		    System.out.println(process(a));
		}
		br.close();
	}
}