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;
  mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
  const int N = 5e5 + 5;
  const int M = 1e9 + 7;
  const int INF = 0x3f3f3f3f;
  const long long LINF = 0x3f3f3f3f3f3f3fll;
  const double pi = acos(-1.0);
  int read() {
    int a = 0;
    int d = 1;
    char c;
    while (c = getchar(), c < '0' || c > '9')
      if (c == '-') d = -1;
    a = a * 10 + c - 48;
    while (c = getchar(), c >= '0' && c <= '9') a = a * 10 + c - 48;
    a *= d;
    return a;
  }
  int a[N];
  int c[N];
  map<int, bool> mp;
  int ans;
  ;
  void msort(int l, int r) {
    if (l == r) return;
    int mid = (l + r) >> 1;
    msort(l, mid);
    msort(mid + 1, r);
    int i = l;
    int j = mid + 1;
    int idx = l;
    while (i <= mid && j <= r) {
      if (a[i] <= a[j])
        c[idx++] = a[i++];
      else {
        ans += mid - i + 1;
        c[idx++] = a[j++];
      }
    }
    while (i <= mid) c[idx++] = a[i++];
    while (j <= r) c[idx++] = a[j++];
    for (int k = l; k <= r; k++) a[k] = c[k];
  }
  signed main() {
    int t = read();
    while (t--) {
      mp.clear();
      int n = read();
      for (int i = 1; i <= n; i++) a[i] = read();
      bool f1 = false;
      bool f2 = false;
      for (int i = 1; i <= n; i++) {
        if (a[i] < a[i - 1]) f1 = true;
        if (mp[a[i]]) {
          f2 = true;
          break;
        }
        mp[a[i]] = true;
      }
      if (!f1 || f2) {
        puts("YES");
        continue;
      }
      if (n < 3) {
        puts("NO");
        continue;
      }
      ans = 0;
      msort(1, n);
      if (ans % 2 == 0)
        puts("YES");
      else
        puts("NO");
    }
    return 0;
  }
  