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.io.BufferedReader;
  import java.io.IOException;
  import java.io.InputStreamReader;
  import java.util.*;
  
  public class CF1 {
      public static void main(String[] args) {
          FastScanner sc=new FastScanner();
          int T=sc.nextInt();
          for (int tt=0; tt<T; tt++){
              int n= sc.nextInt();
              int arr[]= sc.readArray(n);
              int cycle=1;
              int even=0;
              int odd=0;
              boolean repeated=false;
              boolean visited[]= new boolean[n];
              int arr2[]= arr.clone();
              sort(arr2);
              HashMap<Integer, Integer> map = new HashMap<>();
              for (int i=0;i <n; i++){
                  if (map.containsKey(arr2[i])) {
                      repeated =true;
  
                  }
                  else {
                      map.put(arr2[i], i);
                  }
              }
              if (!repeated)
              for (int i=0; i<n; i++){
                  if (arr[i]!= arr2[i]){
  //                    int index=map.get(arr[i]);
                      while (true){
                          if (arr[i]== arr2[i]) {
                              if (cycle %2==0) even++;
                              else odd++;
                              cycle=1;
                              break;
                          }
                          int index=map.get(arr[i]);
                          arr[i]=arr[index];
                          arr[index]=arr2[index];
                          visited[index]=true;
                          cycle++;
                      }
  
                  }
              }
              if (repeated|| even%2==0) System.out.println("YES");
              else System.out.println("NO");
  
  
          }
      }
  
      static long mod =998244353L;
      static long power (long a, long b){
          long res=1;
          while (b>0){
              if ((b&1)== 1){
                  res= (res * a % mod)%mod;
              }
              a=(a%mod * a%mod)%mod;
              b=b>>1;
          }
          return res;
      }
      static void sort(int[] a) {
          ArrayList<Integer> l=new ArrayList<>();
          for (int i:a) l.add(i);
          Collections.sort(l);
          for (int i=0; i<a.length; i++) a[i]=l.get(i);
      }
      static void sortLong(long[] a) {
          ArrayList<Long> l=new ArrayList<>();
          for (long i:a) l.add(i);
          Collections.sort(l);
          for (int i=0; i<a.length; i++) a[i]=l.get(i);
      }
      static int gcd (int n, int m){
          if (m==0) return n;
          else return gcd(m, n%m);
      }
      static class Pair{
          int x,y;
          public Pair(int x, int y){
              this.x = x;
              this.y = y;
          }
      }
      static class FastScanner {
          BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
          StringTokenizer st=new StringTokenizer("");
          String next() {
              while (!st.hasMoreTokens())
                  try {
                      st=new StringTokenizer(br.readLine());
                  } catch (IOException e) {
                      e.printStackTrace();
                  }
              return st.nextToken();
          }
  
          int nextInt() {
              return Integer.parseInt(next());
          }
          int[] readArray(int n) {
              int[] a=new int[n];
              for (int i=0; i<n; i++) a[i]=nextInt();
              return a;
          }
          long nextLong() {
              return Long.parseLong(next());
          }
      }
  }