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.InputStreamReader;
  import java.util.StringTokenizer;
  import java.util.*;
  import java.io.*;
  public class Main {
      // Graph
      // prefix sums
      //inputs
      public static void main(String args[])throws Exception{
          Input sc=new Input();
          precalculates p=new precalculates();
          StringBuilder sb=new StringBuilder();
          int t=sc.readInt();
          for(int f=0;f<t;f++){
              int n=sc.readInt();
              int a[]=sc.readArray();
              int b[]=a.clone();
              Arrays.sort(b);
              boolean check=true;
              HashSet<Integer> set=new HashSet<>();
              for(int i=0;i<n;i++){
                  if(a[i]!=b[i]){
                      check=false;
                      break;
                  }
              }
              if(check){
                  sb.append("YES\n");
                  continue;
              }
              for(int i=0;i<n;i++){
                  if(!set.contains(a[i])){
                      set.add(a[i]);
                  }else{
                      check=true;
                      break;
                  }
              }
              if(check){
                  sb.append("YES\n");
                  continue;
              }
              union_find dd=new union_find(n+5);
              for(int i=0;i<n;i++){
                  dd.union(a[i],i+1);
              }
              int sum=0;
              for(int i=1;i<=n;i++){
                  if(dd.root(i)==i && dd.sz[i]%2==0){
                      sum++;
                  }
              }
  //            for(int i=0;i<n;i++){
  //                System.out.print(dd.size(i+1)+" ");
  //            }
  //            System.out.println();
              if(sum%2==0){
                  sb.append("YES\n");
              }else
                  sb.append("NO\n");
          }
          System.out.print(sb);
      }
  }
  class Input{
      BufferedReader br;
      StringTokenizer st;
      Input(){
          br=new BufferedReader(new InputStreamReader(System.in));
          st=new StringTokenizer("");
      }
      public int[] readArray() throws Exception{
          st=new StringTokenizer(br.readLine());
          int a[]=new int[st.countTokens()];
          for(int i=0;i<a.length;i++){
              a[i]=Integer.parseInt(st.nextToken());
          }
          return a;
      }
      public long[] readArrayLong() throws Exception{
          st=new StringTokenizer(br.readLine());
          long a[]=new long[st.countTokens()];
          for(int i=0;i<a.length;i++){
              a[i]=Long.parseLong(st.nextToken());
          }
          return a;
      }
      public int readInt() throws Exception{
          st=new StringTokenizer(br.readLine());
          return Integer.parseInt(st.nextToken());
      }
      public long readLong() throws Exception{
          st=new StringTokenizer(br.readLine());
          return Long.parseLong(st.nextToken());
      }
      public String readString() throws Exception{
          return br.readLine();
      }
      public int[][] read2dArray(int n,int m)throws Exception{
          int a[][]=new int[n][m];
          for(int i=0;i<n;i++){
              st=new StringTokenizer(br.readLine());
              for(int j=0;j<m;j++){
                  a[i][j]=Integer.parseInt(st.nextToken());
              }
          }
          return a;
      }
  }
  class precalculates{
      public int[] prefixSumOneDimentional(int a[]){
          int n=a.length;
          int dp[]=new int[n];
          for(int i=0;i<n;i++){
              if(i==0)
                  dp[i]=a[i];
              else
                  dp[i]=dp[i-1]+a[i];
          }
          return dp;
      }
      public int[] postSumOneDimentional(int a[]) {
          int n = a.length;
          int dp[] = new int[n];
          for (int i = n - 1; i >= 0; i--) {
              if (i == n - 1)
                  dp[i] = a[i];
              else
                  dp[i] = dp[i + 1] + a[i];
          }
          return dp;
      }
      public int[][] prefixSum2d(int a[][]){
          int n=a.length;int m=a[0].length;
          int dp[][]=new int[n+1][m+1];
          for(int i=1;i<=n;i++){
              for(int j=1;j<=m;j++){
                  dp[i][j]=a[i-1][j-1]+dp[i-1][j]+dp[i][j-1]-dp[i-1][j-1];
              }
          }
          return dp;
      }
      public long pow(long a,long b){
          long mod=1000000007;
          long ans=0;
          if(b<=0)
              return 1;
          if(b%2==0){
              ans=pow(a,b/2)%mod;
              return ((ans%mod)*(ans%mod))%mod;
          }else{
              return ((a%mod)*(ans%mod))%mod;
          }
      }
  
  }
  class GraphInteger{
      HashMap<Integer,vertex> vtces;
      class vertex{
          HashMap<Integer,Integer> children;
          public vertex(){
              children=new HashMap<>();
          }
      }
      public GraphInteger(){
          vtces=new HashMap<>();
      }
      public void addVertex(int a){
          vtces.put(a,new vertex());
      }
      public void addEdge(int a,int b,int cost){
          if(!vtces.containsKey(a)){
              vtces.put(a,new vertex());
          }
          if(!vtces.containsKey(b)){
              vtces.put(b,new vertex());
          }
          vtces.get(a).children.put(b,cost);
  //        vtces.get(b).children.put(a,cost);
      }
      public boolean isCyclicDirected(){
          boolean isdone[]=new boolean[vtces.size()+1];
          boolean check[]=new boolean[vtces.size()+1];
          for(int i=1;i<=vtces.size();i++) {
              if (!isdone[i] && isCyclicDirected(i,isdone, check)) {
                  return true;
              }
          }
          return false;
      }
      private boolean isCyclicDirected(int i,boolean isdone[],boolean check[]){
          if(check[i])
              return true;
          if(isdone[i])
              return false;
          check[i]=true;
          isdone[i]=true;
          Set<Integer> set=vtces.get(i).children.keySet();
          for(Integer ii:set){
              if(isCyclicDirected(ii,isdone,check))
                  return true;
          }
          check[i]=false;
          return false;
      }
  }
  class union_find {
      int n;
      int[] sz;
      int[] par;
  
      union_find(int nval) {
          n = nval;
          sz = new int[n + 1];
          par = new int[n + 1];
          for (int i = 0; i <= n; i++) {
              par[i] = i;
              sz[i] = 1;
          }
      }
  
      int root(int x) {
          if (par[x] == x)
              return x;
          return par[x] = root(par[x]);
      }
  
      boolean find(int a, int b) {
          return root(a) == root(b);
      }
  
      int union(int a, int b) {
          int ra = root(a);
          int rb = root(b);
          if (ra == rb)
              return 0;
          if(a==b)
              return 0;
          if (sz[a] > sz[b]) {
              int temp = ra;
              ra = rb;
              rb = temp;
          }
          par[ra] = rb;
          sz[rb] += sz[ra];
          return 1;
      }
  }
  
  
  
  
  