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: import java.util.*;
  import java.io.*;
  
  public class _1591_D {
      public static void main(String[] args) throws IOException {
          BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
          PrintWriter out = new PrintWriter(System.out);
          int t = Integer.parseInt(in.readLine());
          while(t-- > 0) {
              int n = Integer.parseInt(in.readLine());
              StringTokenizer line = new StringTokenizer(in.readLine());
              int[] a = new int[n];
              int[] ind = new int[n];
              HashSet<Integer> unique = new HashSet<Integer>();
              for(int i = 0; i < n; i++) {
                  a[i] = Integer.parseInt(line.nextToken()) - 1;
                  ind[a[i]] = i;
                  unique.add(a[i]);
              }
              if(unique.size() < n) {
                  out.println("YES");
              }else {
                  for(int i = n - 1; i >= 2; i--) {
                      int next_ind = ind[i];
                      if(next_ind == i) {
                          continue;
                      }else if(next_ind == i - 1) {
                          cycle(a, ind, i - 1, i, i - 2);
                      }else {
                          cycle(a, ind, next_ind, i, i - 1);
                      }
                  }
                  if(n == 1 || a[1] > a[0]) {
                      out.println("YES");
                  }else {
                      out.println("NO");
                  }
              }
          }
          in.close();
          out.close();
      }
      static void cycle(int[] a, int[] ind, int i, int j, int k) {
          int tempi = a[i];
          int tempj = a[j];
          int tempk = a[k];
  
          a[j] = a[i];
          a[k] = tempj;
          a[i] = tempk;
  
          ind[tempi] = j;
          ind[tempj] = k;
          ind[tempk] = i;
      }
  }
  