#include <bits/stdc++.h>
using namespace std;
long long mod = 1e9 + 7;
const long long N = 1e5 + 5;
long long n, m, t, u, v, k, l;
map<long long, long long> mp;
vector<long long> a;
vector<long long> sorted_a;
void place(long long j, long long i) {
  long long k;
  if (i + 1 != j) {
    k = i + 1;
  } else {
    k = i + 2;
  }
  long long temp = a[i];
  a[i] = a[j];
  mp[a[i]] = i;
  a[j] = a[k];
  mp[a[j]] = j;
  a[k] = temp;
  mp[a[k]] = k;
}
void solve(long long tc) {
  cin >> n;
  mp.clear();
  a = vector<long long>(n);
  for (int i = 0; i < (int)(n); ++i) {
    cin >> a[i];
    mp[a[i]] = i;
  }
  sorted_a = a;
  {
    sort((sorted_a).begin(), (sorted_a).end());
    sorted_a.erase(unique((sorted_a).begin(), (sorted_a).end()),
                   sorted_a.end());
  };
  if (int((sorted_a).size()) != int((a).size())) {
    cout << "YES\n";
    return;
  }
  for (int i = 0; i < (int)(n); ++i) {
    if (sorted_a[i] != a[i]) {
      if (i >= n - 2) {
        cout << "NO\n";
        return;
      }
      place(mp[sorted_a[i]], i);
    }
  }
  cout << "YES\n";
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  t = 1;
  cin >> t;
  for (int i = 0; i < (int)(t); ++i) {
    solve(t);
  }
}

### Prompt

Construct a CPP code solution to the problem outlined:

Petya has an array of integers a_1, a_2, …, a_n. He only likes sorted arrays. Unfortunately, the given array could be arbitrary, so Petya wants to sort it.

Petya likes to challenge himself, so he wants to sort array using only 3-cycles. More formally, in one operation he can pick 3 pairwise distinct indices i, j, and k (1 ≤ i, j, k ≤ n) and apply i → j → k → i cycle to the array a. It simultaneously places a_i on position j, a_j on position k, and a_k on position i, without changing any other element.

For example, if a is [10, 50, 20, 30, 40, 60] and he chooses i = 2, j = 1, k = 5, then the array becomes [\underline{50}, \underline{40}, 20, 30, \underline{10}, 60].

Petya can apply arbitrary number of 3-cycles (possibly, zero). You are to determine if Petya can sort his array a, i. e. make it non-decreasing.

Input

Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 5 ⋅ 10^5). Description of the test cases follows.

The first line of each test case contains a single integer n (1 ≤ n ≤ 5 ⋅ 10^5) — the length of the array a.

The second line of each test case contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ n).

It is guaranteed that the sum of n over all test cases does not exceed 5 ⋅ 10^5.

Output

For each test case, print "YES" (without quotes) if Petya can sort the array a using 3-cycles, and "NO" (without quotes) otherwise. You can print each letter in any case (upper or lower).

Example

Input


7
1
1
2
2 2
2
2 1
3
1 2 3
3
2 1 3
3
3 1 2
4
2 1 4 3


Output


YES
YES
NO
YES
NO
YES
YES

Note

In the 6-th test case Petya can use the 3-cycle 1 → 3 → 2 → 1 to sort the array.

In the 7-th test case Petya can apply 1 → 3 → 2 → 1 and make a = [1, 4, 2, 3]. Then he can apply 2 → 4 → 3 → 2 and finally sort the array.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
long long mod = 1e9 + 7;
const long long N = 1e5 + 5;
long long n, m, t, u, v, k, l;
map<long long, long long> mp;
vector<long long> a;
vector<long long> sorted_a;
void place(long long j, long long i) {
  long long k;
  if (i + 1 != j) {
    k = i + 1;
  } else {
    k = i + 2;
  }
  long long temp = a[i];
  a[i] = a[j];
  mp[a[i]] = i;
  a[j] = a[k];
  mp[a[j]] = j;
  a[k] = temp;
  mp[a[k]] = k;
}
void solve(long long tc) {
  cin >> n;
  mp.clear();
  a = vector<long long>(n);
  for (int i = 0; i < (int)(n); ++i) {
    cin >> a[i];
    mp[a[i]] = i;
  }
  sorted_a = a;
  {
    sort((sorted_a).begin(), (sorted_a).end());
    sorted_a.erase(unique((sorted_a).begin(), (sorted_a).end()),
                   sorted_a.end());
  };
  if (int((sorted_a).size()) != int((a).size())) {
    cout << "YES\n";
    return;
  }
  for (int i = 0; i < (int)(n); ++i) {
    if (sorted_a[i] != a[i]) {
      if (i >= n - 2) {
        cout << "NO\n";
        return;
      }
      place(mp[sorted_a[i]], i);
    }
  }
  cout << "YES\n";
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  t = 1;
  cin >> t;
  for (int i = 0; i < (int)(t); ++i) {
    solve(t);
  }
}

```