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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
long long int power(long long int x, unsigned long long int y) {
  long long int res = 1;
  while (y > 0) {
    if (y & 1) {
      res = res * x;
    }
    y = y >> 1;
    x = x * x;
  }
  return res;
}
long long int gcd(long long int a, long long int b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
long long int powermod(long long int x, unsigned long long int y,
                       long long int p) {
  long long int res = 1;
  x = x % p;
  while (y > 0) {
    if (y & 1) {
      res = (res * x) % p;
    }
    y = y >> 1;
    x = (x * x) % p;
  }
  return res;
}
int32_t main() {
  long long int T;
  cin >> T;
  while (T--) {
    long long int n;
    cin >> n;
    vector<long long int> v, b, u;
    long long int zc = 0, oc = 0;
    for (long long int i = (long long int)(0); i < (long long int)(n); i++) {
      long long int t;
      cin >> t;
      v.push_back(t);
    }
    for (long long int i = (long long int)(0); i < (long long int)(n); i++) {
      long long int t;
      cin >> t;
      if (t == 0)
        zc++;
      else
        oc++;
    }
    u.assign((v).begin(), (v).end());
    sort((u).begin(), (u).end());
    long long int ok = 1;
    for (long long int i = (long long int)(0); i < (long long int)(n); i++) {
      if (v[i] != u[i]) ok = 0;
    }
    if (zc != 0 && oc != 0)
      cout << "YES\n";
    else {
      if (ok)
        cout << "YES\n";
      else
        cout << "NO\n";
    }
  }
  return 0;
}