#include <bits/stdc++.h>
using namespace std;
void _print(bool t) { cerr << t; }
void _print(long long t) { cerr << t; }
void _print(string t) { cerr << t; }
void _print(char t) { cerr << t; }
void _print(double t) { cerr << t; }
template <class T>
void _print(vector<T> v) {
  cerr << "[  ";
  for (T i : v) {
    _print(i);
    cerr << "  ";
  }
  cerr << "]\n";
}
template <class T, class V>
void _print(pair<T, V> p) {
  cerr << "{";
  _print(p.first);
  cerr << ", ";
  _print(p.second);
  cerr << "}";
}
template <class T>
void _print(set<T> v) {
  cerr << "[  ";
  for (T i : v) {
    _print(i);
    cerr << "  ";
  }
  cerr << "]\n";
}
template <class T>
void _print(multiset<T> v) {
  cerr << "[  ";
  for (T i : v) {
    _print(i);
    cerr << "  ";
  }
  cerr << "]\n";
}
template <class T, class V>
void _print(map<T, V> v) {
  cerr << "[  ";
  for (auto i : v) {
    _print(i);
    cerr << "  ";
  }
  cerr << "]\n";
}
template <class T>
void _print(T v[], long long n) {
  cerr << "[  ";
  for (long long i = 0; i < n; i++) {
    _print(v[i]);
    cerr << "  ";
  }
  cerr << "]\n";
}
struct BIT {
  vector<long long> values;
  long long N, LOGN;
  void init(long long n) {
    N = n;
    LOGN = ceil(log2(N));
    values.assign(N + 1, 0);
  }
  void update(long long idx, long long val) {
    while (idx <= N) {
      values[idx] += val;
      idx += idx & -idx;
    }
  }
  long long sum(long long idx) {
    long long sum = 0;
    while (idx > 0) {
      sum += values[idx];
      idx -= idx & -idx;
    }
    return sum;
  }
  long long rangeSum(long long i, long long j) {
    return sum(j) - (i == 1 ? 0 : sum(i - 1));
  }
};
void run() {
  long long n;
  cin >> n;
  long long a[n];
  for (long long i = 0; i < n; i++) {
    cin >> a[i];
  }
  if (n == 1) {
    cout << "YES\n";
    return;
  }
  if (n == 2) {
    if (a[1] >= a[0])
      cout << "YES\n";
    else
      cout << "NO\n";
    return;
  }
  set<long long> s;
  for (long long i = 0; i < n; i++) s.insert(a[i]);
  if (s.size() != n) {
    cout << "YES\n";
    return;
  }
  BIT ds;
  ds.init(n + 10);
  long long ans = 0;
  for (long long i = n - 1; i >= 0; i--) {
    ans += ds.sum(a[i] - 1);
    ds.update(a[i], 1);
  }
  if (ans % 2 == 0)
    cout << "YES\n";
  else
    cout << "NO\n";
}
int32_t main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0), cout.tie();
  long long t;
  cin >> t;
  for (long long tc = 1; tc <= t; tc++) {
    run();
  }
}

### Prompt

Please provide a CPP coded solution to the problem described below:

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;
void _print(bool t) { cerr << t; }
void _print(long long t) { cerr << t; }
void _print(string t) { cerr << t; }
void _print(char t) { cerr << t; }
void _print(double t) { cerr << t; }
template <class T>
void _print(vector<T> v) {
  cerr << "[  ";
  for (T i : v) {
    _print(i);
    cerr << "  ";
  }
  cerr << "]\n";
}
template <class T, class V>
void _print(pair<T, V> p) {
  cerr << "{";
  _print(p.first);
  cerr << ", ";
  _print(p.second);
  cerr << "}";
}
template <class T>
void _print(set<T> v) {
  cerr << "[  ";
  for (T i : v) {
    _print(i);
    cerr << "  ";
  }
  cerr << "]\n";
}
template <class T>
void _print(multiset<T> v) {
  cerr << "[  ";
  for (T i : v) {
    _print(i);
    cerr << "  ";
  }
  cerr << "]\n";
}
template <class T, class V>
void _print(map<T, V> v) {
  cerr << "[  ";
  for (auto i : v) {
    _print(i);
    cerr << "  ";
  }
  cerr << "]\n";
}
template <class T>
void _print(T v[], long long n) {
  cerr << "[  ";
  for (long long i = 0; i < n; i++) {
    _print(v[i]);
    cerr << "  ";
  }
  cerr << "]\n";
}
struct BIT {
  vector<long long> values;
  long long N, LOGN;
  void init(long long n) {
    N = n;
    LOGN = ceil(log2(N));
    values.assign(N + 1, 0);
  }
  void update(long long idx, long long val) {
    while (idx <= N) {
      values[idx] += val;
      idx += idx & -idx;
    }
  }
  long long sum(long long idx) {
    long long sum = 0;
    while (idx > 0) {
      sum += values[idx];
      idx -= idx & -idx;
    }
    return sum;
  }
  long long rangeSum(long long i, long long j) {
    return sum(j) - (i == 1 ? 0 : sum(i - 1));
  }
};
void run() {
  long long n;
  cin >> n;
  long long a[n];
  for (long long i = 0; i < n; i++) {
    cin >> a[i];
  }
  if (n == 1) {
    cout << "YES\n";
    return;
  }
  if (n == 2) {
    if (a[1] >= a[0])
      cout << "YES\n";
    else
      cout << "NO\n";
    return;
  }
  set<long long> s;
  for (long long i = 0; i < n; i++) s.insert(a[i]);
  if (s.size() != n) {
    cout << "YES\n";
    return;
  }
  BIT ds;
  ds.init(n + 10);
  long long ans = 0;
  for (long long i = n - 1; i >= 0; i--) {
    ans += ds.sum(a[i] - 1);
    ds.update(a[i], 1);
  }
  if (ans % 2 == 0)
    cout << "YES\n";
  else
    cout << "NO\n";
}
int32_t main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0), cout.tie();
  long long t;
  cin >> t;
  for (long long tc = 1; tc <= t; tc++) {
    run();
  }
}

```