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: //https://www.codechef.com/problems/TRPLSRT
  //https://www.codechef.com/viewsolution/32812228
  import java.io.*;
  import java.util.*;
  
  public class Codeforces
  {
      public static void main(String args[])throws Exception
      {
          BufferedReader bu=new BufferedReader(new InputStreamReader(System.in));
          StringBuilder sb=new StringBuilder();
          int t=Integer.parseInt(bu.readLine());
          while(t-->0)
          {
              int n=Integer.parseInt(bu.readLine());
              String s[]=bu.readLine().split(" ");
              int i,a[]=new int[n];
              HashMap<Integer,Integer> hm=new HashMap<>();
              for(i=0;i<n;i++)
              {
                  a[i]=Integer.parseInt(s[i]);
                  hm.put(a[i],hm.getOrDefault(a[i],0)+1);
              }
  
              if(n<3)
              {
                  boolean sort=true;
                  for(i=1;i<n;i++) sort&=a[i]>=a[i-1];
                  if(sort) sb.append("YES\n");
                  else sb.append("NO\n");
                  continue;
              }
  
              PriorityQueue<int[]> pq=new PriorityQueue<>(new Comparator<int[]>() {
                  @Override
                  public int compare(int[] o1, int[] o2) {
                      if(o1[0]>o2[0]) return 1;
                      else if(o1[0]==o2[0]) return o1[1]>o2[1]?1:-1;
                      else return -1;
                  }});
              for(i=0;i<n;i++) pq.add(new int[]{a[i],i});
              int pos[]=new int[n];
              ArrayList<Integer> fir=new ArrayList<>();
              for(i=0;i<n;i++)
              a[pq.poll()[1]]=i;
              for(i=0;i<n;i++)
              {
                  pos[a[i]]=i;
                  if(a[i]!=i) fir.add(i);
              }
              if(fir.size()==0) {sb.append("YES\n"); continue;}
  
              ArrayList<Integer> sec=new ArrayList<>();
              for(i=0;i<fir.size();i++)
              {
                  int x=fir.get(i),v1=x,v2=a[x],v3=pos[x];
                  if(v1==v2) continue;
  
                  if(v2==v3)
                  {
                      sec.add(v1); sec.add(v2);
                      a[v3]=v3;
                      continue;
                  }
                  int va=a[v1],vb=a[v2],vc=a[v3];
                  //sw.add(v1); sw.add(v2); sw.add(v3);
                  a[i]=i; pos[a[i]]=i;
                  a[v2]=va; pos[a[v2]]=v2;
                  a[v3]=vb; pos[a[v3]]=v3;
              }
  
              if((sec.size()/2)%2==1)
              {
                  boolean two=false;
                  for(int x:hm.values()) two|=x>1;
                  if(two) sb.append("YES\n");
                  else sb.append("NO\n");
              }
              else sb.append("YES\n");
          }
          System.out.print(sb);
      }
  }