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;
  template <class c>
  struct rge {
    c b, e;
  };
  template <class c>
  rge<c> range(c i, c j) {
    return rge<c>{i, j};
  }
  template <class c>
  auto dud(c *x) -> decltype(cerr << *x, 0);
  template <class c>
  char dud(...);
  struct debug {
    template <class c>
    debug &operator<<(const c &) {
      return *this;
    }
  };
  template <typename T>
  void read(T &x) {
    cin >> x;
  }
  template <typename T, typename U>
  void read(T &x, U &y) {
    cin >> x >> y;
  }
  template <typename T>
  void read(vector<T> &a) {
    for (T &x : a) read(x);
  }
  template <typename T>
  T cd(T u, T v) {
    return (u + v - 1) / v;
  }
  void solve() {
    long long n;
    read(n);
    vector<long long> a(n);
    read(a);
    auto v = a;
    sort(v.begin(), v.end());
    if (n <= 2) {
      cout << (a == v ? "YES\n" : "NO\n");
      return;
    }
    map<long long, set<long long>> mp;
    for (long long i = 0; i < n; i++) mp[a[i]].insert(i);
    for (long long i = 0; i < n - 2; i++) {
      if (a[i] == v[i]) {
        mp[a[i]].erase(i);
      } else {
        long long j = *mp[v[i]].begin();
        long long k = (j == n - 1) ? n - 2 : n - 1;
        mp[a[i]].erase(i);
        mp[a[k]].erase(k);
        mp[a[j]].erase(j);
        long long temp = a[i];
        a[i] = a[j];
        a[j] = a[k];
        a[k] = temp;
        mp[a[k]].insert(k);
        mp[a[j]].insert(j);
        assert(set<long long>({i, j, k}).size() == 3);
      }
      debug() << " ["
              << "mp"
                 ": "
              << (mp) << "] ";
    }
    for (long long i = n - 2; i < n; i++) {
      if (a[i] != v[i]) {
        map<long long, long long> mpp;
        for (long long j = 0; j < n; j++) mpp[a[j]]++;
        for (auto &p : mpp) {
          if (p.second >= 2) {
            cout << "YES\n";
            return;
          }
        }
        cout << "NO\n";
        return;
      }
    }
    assert(is_sorted(a.begin(), a.end()));
    cout << "YES\n";
  }
  int32_t main() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    long long t = 1;
    read(t);
    for (long long testcase = 1; testcase <= t; testcase++) {
      solve();
    }
    return 0;
  }
  