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;
import java.util.Arrays;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Map;
import java.util.Set;

public class CF{
  public static void main(String[] args) throws Exception{
    BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
    int cases = Integer.parseInt(reader.readLine());
    for(int c = 0; c < cases; c++){
    /*A
      Set<Integer> occRows = new HashSet<Integer>();
      Set<Integer> occCols = new HashSet<Integer>();
      String[] dimsS= reader.readLine().split(" ");
      int rows = Integer.parseInt(dimsS[0]);
      int cols = Integer.parseInt(dimsS[1]);
      for(int i = 0; i < rows; i++){
        String[] row = reader.readLine().split(" ");
        for(int j = 0; j < cols; j++){
          if(row[j].equals("1")){
            occRows.add(i);
            occCols.add(j);
          }
        }
      }
      problemA(occRows, occCols, dimsS);
    A*/
      reader.readLine();
      int[] values = Arrays.stream(reader.readLine()
                           .split("\\s"))
                           .mapToInt(Integer::parseInt)
                          .toArray();
      int[] types = Arrays.stream(reader.readLine()
                           .split("\\s"))
                           .mapToInt(Integer::parseInt)
                           .toArray();
      problemB(values, types);
    }
  }
  public static void problemA(Set<Integer> rows, Set<Integer> cols, String[] dimentions){
    int min = Math.min(Integer.parseInt(dimentions[0]) - rows.size(), Integer.parseInt(dimentions[1]) - cols.size());
    if(min % 2 == 1)
      System.out.println("Ashish");
    else
      System.out.println("Vivek");
    
  }
  public static void problemB(int[] values, int[] types){
    boolean zero = false;
    boolean one = false;
    for(int type: types){
      if(type == 0)
       zero = true;
      else
        one = true;
      if(zero && one)
        break;
    }
    if(!(zero && one)){
      for(int i = 0; i < values.length -1; i++){
        if(values[i] > values[i + 1]){
          System.out.println("No");
          return;
        }
      }
    }
    System.out.println("Yes");
  }
}