description: 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.
solution: #include <bits/stdc++.h>
  using namespace std;
  const long long MOD = 1e9 + 7;
  const int maxn = 5e5 + 5;
  void File() {
    freopen(
        "j4f"
        ".inp",
        "r", stdin);
    freopen(
        "j4f"
        ".out",
        "w", stdout);
  }
  int n;
  pair<int, int> a[maxn];
  pair<int, int> p[maxn];
  int pos[maxn];
  void Swap(int u, int v) {
    swap(pos[a[u].second], pos[a[v].second]);
    swap(a[u], a[v]);
  }
  void solve() {
    cin >> n;
    for (int i = 1; i <= n; i++) {
      cin >> a[i].first;
      a[i].second = i;
      p[i] = a[i];
      pos[i] = i;
    }
    if (n == 1) {
      cout << "YES\n";
      return;
    }
    sort(p + 1, p + 1 + n);
    for (int i = 1; i < n; i++)
      if (p[i].first == p[i + 1].first) {
        cout << "YES\n";
        return;
      }
    for (int i = 1; i <= n - 2; i++) {
      if (a[i] == p[i]) continue;
      int u = pos[p[i].second], v = i + 1;
      if (v == u) v++;
      Swap(i, u);
      Swap(u, v);
    }
    if (a[n - 1].first <= a[n].first)
      cout << "YES\n";
    else
      cout << "NO\n";
  }
  int main() {
    ios::sync_with_stdio(0);
    cin.tie(0);
    int q;
    cin >> q;
    while (q--) solve();
    return 0;
  }
  