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;
  using ll = long long;
  using db = double;
  using pii = pair<int, int>;
  using vec = vector<int>;
  using veg = vector<pii>;
  template <typename T>
  T read() {
    T x = 0;
    bool f = 0;
    char ch = getchar();
    while (!isdigit(ch)) f |= ch == '-', ch = getchar();
    while (isdigit(ch)) x = x * 10 + (ch ^ 48), ch = getchar();
    return f ? -x : x;
  }
  template <typename T>
  void chkmax(T &x, const T &y) {
    x = x > y ? x : y;
  }
  template <typename T>
  void chkmin(T &x, const T &y) {
    x = x < y ? x : y;
  }
  const int N = 1e6 + 10;
  int tr[N], a[N], n;
  bool vis[N];
  void add(int x, int v) {
    for (; x <= n; x += x & -x) tr[x] += v;
  }
  int query(int x) {
    int res = 0;
    for (; x; x -= x & -x) res += tr[x];
    return res;
  }
  void solve() {
    n = read<int>();
    for (int i = (1); i <= (n); i++) a[i] = read<int>(), vis[a[i]] = 0;
    for (int i = (1); i <= (n); i++) {
      if (vis[a[i]]) return puts("YES"), void();
      vis[a[i]] = true;
    }
    for (int i = (1); i <= (n); i++) tr[i] = 0;
    ll res = 0;
    for (int i = (1); i <= (n); i++) {
      res += i - 1 - query(a[i]);
      add(a[i], 1);
    }
    puts(res & 1 ? "NO" : "YES");
  }
  int main() {
    int T = read<int>();
    while (T--) solve();
    return 0;
  }
  