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.*;
import java.util.*;
import java.math.*;

 
public class Main
{
	 /*static class Pair implements Comparable<Pair>{
       int index,value;
       Pair(int a,int b){
           index=a;value=b;
       }
       public int compareTo(Pair a){
           if(this.value==a.value)
           return this.index-a.index;
           return this.value-a.value;
       }
   }*/
	 /*static void seive(int p[]){
       for (int i = 2; i <100001;i++) { 
           if(p[i]==0){
            for(int j=i;j<100001;j=j+i){
                if(p[j]==0)
                p[j]=i;
            }}
        }
   }*/
  /* static long power(long x, long y, long m)  
    { 
        if (y == 0) 
            return 1; 
          
        long p = power(x, y / 2, m) % m; 
        p = (p * p) % m; 
      
        if (y % 2 == 0) 
            return p; 
        else
            return (x * p) % m; 
    } */
    public static void main(String[] args)
    {
        FastReader s=new FastReader();
		 int t=s.nextInt();
		 for(int f=0;f<t;f++){
		    int n=s.nextInt();
		    int a[]=new int[n];
		    for(int i=0;i<n;i++){
		        a[i]=s.nextInt();
		    }
		    int b[]=new int[n];
		    int count0=0,count1=0;
		    for(int i=0;i<n;i++){
		        b[i]=s.nextInt();
		        if(b[i]==0){
		            count0=1;
		        }
		        else count1=1;
		    }
		    if(count1==1 && count0==1){
		        System.out.println("Yes");
		    }
		    else{
		        int c=0;
		        for(int i=1;i<n;i++){
		            if(a[i]<a[i-1]){
		                c=1;
		                break;
		            }
		        }
		        if(c==0){
		            System.out.println("Yes");
		        }
		        else System.out.println("No");
		    }
		 }
    }
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
    static class FastReader
    {
        BufferedReader br;
        StringTokenizer st;
 
        public FastReader()
        {
            br = new BufferedReader(new
                     InputStreamReader(System.in));
        }
 
        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException  e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
 
        int nextInt()
        {
            return Integer.parseInt(next());
        }
 
        long nextLong()
        {
            return Long.parseLong(next());
        }
 
        double nextDouble()
        {
            return Double.parseDouble(next());
        }
 
        String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
    }
 
   
}