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.ByteArrayInputStream;
import java.io.PrintWriter;
import java.util.Scanner;


public class B {

  public static void main(String[] args) throws Exception {
    new B().go();
  }
  static boolean LOCAL = System.getProperty("ONLINE_JUDGE") == null;


  Scanner in;
  String INPUT = "5\r\n" +
      "4\r\n" +
      "10 20 20 30\r\n" +
      "0 1 0 1\r\n" +
      "3\r\n" +
      "3 1 2\r\n" +
      "0 1 1\r\n" +
      "4\r\n" +
      "2 2 4 8\r\n" +
      "1 1 1 1\r\n" +
      "3\r\n" +
      "5 15 4\r\n" +
      "0 0 0\r\n" +
      "4\r\n" +
      "20 10 100 50\r\n" +
      "1 0 0 1";


  void go() {
    if (LOCAL) {
      System.setIn(new ByteArrayInputStream(INPUT.getBytes()));
    }
    in = new Scanner(System.in);
    long startTime = System.currentTimeMillis();
    solve();
    if (LOCAL) {
      System.out.printf("[%dms]", System.currentTimeMillis()-startTime);
    }
    in.close();
  }


  PrintWriter out = new PrintWriter(System.out);
  StringBuffer sb = new StringBuffer();

  void solve() {


    int t = in.nextInt();
    for (int i=1; i<=t; i++) {
      solve2(i);
    }


    out.flush();
  } // end of solve



  void solve2(int caseNr) {


    int n = in.nextInt();
    int[] a = new int[n];
    int[] b = new int[n];

    for (int i=0; i<n; i++) {
      a[i] = in.nextInt();
    }
    for (int i=0; i<n; i++) {
      b[i] = in.nextInt();
    }

    //    ZZ.showIntegerArray(a);
    //    ZZ.showIntegerArray(b);
    //    System.out.println();

    boolean all_ones = true;
    boolean all_zeros = true;

    for (int i = 0; i < n; i++) {
      if (b[i] == 0) {
        all_ones = false;
      }
      if (b[i] == 1) {
        all_zeros = false;
      }
    }

    if (all_ones || all_zeros) {
      for (int i = 1; i < n; i++) {
        if (a[i-1]-a[i]>0) {
          System.out.println("No");
          return;
        }
      }
    }


    System.out.println("Yes");



  } // end of solve2


}