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{
    public static void main(String[] args) {
        FastScanner sc = new FastScanner();
        int t = sc.nextInt();
        while(t-->0){
            int n = sc.nextInt();
            int[] a = new int[n];
            int zero = 0, one = 0;
            for (int i = 0; i < n; i++){
                a[i] = sc.nextInt();
            }
            for (int i = 0; i < n; i++){
                int c = sc.nextInt();
                if(c == 0) zero++;
                else one++;
            }
            System.out.println(trsort(a, n, zero, one));
        }
    }

    public static String trsort(int[] a, int n, int one, int zero){
        if(n <= 1) return "YES";
        int d = Math.min(zero, one);
        if(d == 0){
            if(isSorted(a, n)) return "YES";
            else return "NO";
        }
        else return "YES";
    }

    public static boolean isSorted(int[] a, int n){
        for (int i = 1; i < n; i++){
            if(a[i] < a[i-1]){
                return false;
            }
        }
        return true;
    }

    public static class FastScanner{ 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastScanner(){ 
            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; 
        } 
    }
}