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 std::cerr;
  using std::cin;
  using std::cout;
  using std::endl;
  using std::greater;
  using std::less;
  using std::lower_bound;
  using std::make_pair;
  using std::map;
  using std::max;
  using std::min;
  using std::multiset;
  using std::pair;
  using std::priority_queue;
  using std::queue;
  using std::set;
  using std::sort;
  using std::string;
  using std::swap;
  using std::unique;
  using std::unordered_map;
  using std::upper_bound;
  using std::vector;
  template <typename T>
  void in(T &x) {
    x = 0;
    bool f = false;
    char ch = getchar();
    while (!isdigit(ch)) {
      if (ch == '-') f = true;
      ch = getchar();
    }
    while (isdigit(ch)) {
      x = x * 10 + ch - '0';
      ch = getchar();
    }
    if (f) x = -x;
  }
  template <typename T>
  void out(T x, char ch = '\n') {
    static int tp, sk[30];
    if (x < 0) {
      putchar('-');
      x = -x;
    }
    do {
      sk[++tp] = x % 10;
      x /= 10;
    } while (x);
    while (tp) {
      putchar(sk[tp--] + '0');
    }
    putchar(ch);
  }
  template <typename T>
  void Mx(T &x, T y) {
    x < y && (x = y);
  }
  template <typename T>
  void Mn(T &x, T y) {
    x > y && (x = y);
  }
  template <typename T>
  T sabs(T x) {
    return x < 0 ? -x : x;
  }
  namespace Mod {
  const int md = 998244353;
  inline int add(const int &a, const int &b) {
    int p = a + b;
    if (p >= md) p -= md;
    return p;
  }
  inline int sub(const int &a, const int &b) {
    int p = a - b;
    if (p < 0) p += md;
    return p;
  }
  inline int mul(const int &a, const int &b) { return 1ll * a * b % md; }
  inline int qpow(int a, int b) {
    int ret = 1;
    for (; b; b >>= 1, a = mul(a, a))
      if (b & 1) ret = mul(ret, a);
    return ret;
  }
  inline int inv(int x) { return qpow(x, md - 2); }
  }  // namespace Mod
  using Mod::add;
  using Mod::inv;
  using Mod::md;
  using Mod::mul;
  using Mod::qpow;
  using Mod::sub;
  const int N = 500010;
  int n;
  int a[N], c[N];
  void Insert(int x) {
    for (; x <= n; x += x & -x) ++c[x];
  }
  int query(int x) {
    int ret = 0;
    for (; x; x -= x & -x) ret += c[x];
    return ret;
  }
  namespace gvihvo {
  void main() {
    in(n);
    map<int, int> cnt;
    for (int i = 1; i <= n; ++i) {
      in(a[i]);
      ++cnt[a[i]];
    }
    for (auto i : cnt)
      if (i.second > 1) {
        puts("YES");
        return;
      }
    long long val = 0;
    for (int i = n; i >= 1; --i) {
      val += query(a[i]);
      Insert(a[i]);
    }
    val % 2 ? puts("NO") : puts("YES");
    memset(c, 0, sizeof(int) * (n + 10));
  }
  }  // namespace gvihvo
  int main() {
    int cza;
    scanf("%d", &cza);
    while (cza--) gvihvo::main();
    return 0;
  }
  