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 cf_1365 {
	static int n,l,r;
	static pair arr[];
	static StringBuilder answer;
	static HashMap<Integer,Integer> map=new HashMap<>();
	public static void main(String[] args) throws IOException{
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		Integer t=Integer.parseInt(br.readLine().trim());
		answer=new StringBuilder();
		while(t-->0) {
			n=Integer.parseInt(br.readLine().trim());
			StringTokenizer tok=new StringTokenizer(br.readLine()," ");
			arr=new pair[n];
			for(int i=0;i<n;i++) {
				arr[i]=new pair(Integer.parseInt(tok.nextToken()),0);
				
			}
			tok=new StringTokenizer(br.readLine()," ");
			int one=0,zer=0;
			for(int i=0;i<n;i++) {
				arr[i].b=Integer.parseInt(tok.nextToken());
				if(arr[i].b==1) {
					one++;
				}
				else {
					zer++;
				}
				
			}
			boolean sorted=true;
			
			for(int i=1;i<n;i++) {
//			
				if(arr[i].a<arr[i-1].a) {
					sorted=false;
				}
				
			}
			if((!sorted && zer>0 && one>0)||sorted) {
				answer.append("YES\n");
			}
			else {
				answer.append("NO\n");
			}
//				addtoans(ans);
		}
		System.out.println(answer);
		
	}
	static class pair{
		int a,b;
		pair(int u,int v){
			a=u;
			b=v;
		}
	}
	static void addtoans(int a){
		answer.append(a+"\n");
	}	

	static class ss implements Comparator<pair>{
		public int compare(pair a,pair b) {
			if(a.b!=b.b)return a.a-b.a;
			return 0;
			
			
			
	}	
	}
}