#include <bits/stdc++.h>
using namespace std;
const long long N = 2e5 + 5;
const long long mod = 1e9 + 7;
const long long M = 998244353;
const long long inf = 1e18 + 1;
void mistakes() {}
void purple() {
  long long n;
  cin >> n;
  vector<long long> v;
  v.push_back(0);
  set<long long> s;
  for (long long i = 0; i < n; i++) {
    long long x;
    cin >> x;
    s.insert(x);
    v.push_back(x);
  }
  if (((long long)(s).size()) != n or is_sorted(v.begin(), v.end())) {
    cout << "YES\n";
    return;
  }
  long long cnt = 0;
  map<long long, long long> m;
  for (long long i = 1; i <= n; i++) {
    if (!m[i]) {
      long long _cnt = 0, idx = i;
      while (!m[idx]) {
        _cnt++;
        m[idx] = 1;
        idx = v[idx];
      }
      if (not(_cnt & 1)) cnt++;
    }
  }
  if (cnt & 1)
    cout << "NO\n";
  else
    cout << "YES\n";
}
int32_t main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long long t = 1;
  cin >> t;
  while (t--) {
    purple();
  }
}

### Prompt

Please create a solution in CPP to the following problem:

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;
const long long N = 2e5 + 5;
const long long mod = 1e9 + 7;
const long long M = 998244353;
const long long inf = 1e18 + 1;
void mistakes() {}
void purple() {
  long long n;
  cin >> n;
  vector<long long> v;
  v.push_back(0);
  set<long long> s;
  for (long long i = 0; i < n; i++) {
    long long x;
    cin >> x;
    s.insert(x);
    v.push_back(x);
  }
  if (((long long)(s).size()) != n or is_sorted(v.begin(), v.end())) {
    cout << "YES\n";
    return;
  }
  long long cnt = 0;
  map<long long, long long> m;
  for (long long i = 1; i <= n; i++) {
    if (!m[i]) {
      long long _cnt = 0, idx = i;
      while (!m[idx]) {
        _cnt++;
        m[idx] = 1;
        idx = v[idx];
      }
      if (not(_cnt & 1)) cnt++;
    }
  }
  if (cnt & 1)
    cout << "NO\n";
  else
    cout << "YES\n";
}
int32_t main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long long t = 1;
  cin >> t;
  while (t--) {
    purple();
  }
}

```