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://codeforces.com/contest/1591/problem/D
  
  import java.io.*;
  import java.util.*;
  
  public class D {
      public static void main(String[] args) {
          for (int t = IO.nextInt(), i = 0; i < t; i++)
              new SolD().solve();
          IO.close();
      }
  }
  
  class SolD {
  
      int n;
      int[] a;
  
      boolean[] visited;
  
      SolD() {
          n = IO.nextInt();
          a = new int[n];
          for (int i = 0; i < n; i++)
              a[i] = IO.nextInt();
      }
  
      void solve() {
          if (!distinct()) {
              IO.writer.println(Answer.YES);
              return;
          }
          visited = new boolean[n];
          boolean possible = true;
          for (int i = 0; i < n; i++)
              possible = !(possible ^ dfs(i));
          if (possible)
              IO.writer.println(Answer.YES);
          else
              IO.writer.println(Answer.NO);
      }
  
      boolean distinct() {
          visited = new boolean[n+1];
          for (int i = 0; i < n; i++) {
              if (visited[a[i]])
                  return false;
              visited[a[i]] = true;
          }
          return true;
      }
  
      boolean dfs(int x) {
          if (visited[x])
              return true;
          visited[x] = true;
  
          boolean evenT = true;
          for (int nxt = a[x]-1; !visited[nxt]; nxt = a[nxt]-1) {
              visited[nxt] = true;
              evenT = !evenT;
          }
          return evenT;
      }
  }
  
  enum Answer {
      YES,
      NO
  }
  
  class IO {
      static final BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
      static final PrintWriter writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
  
      static StringTokenizer tokens;
  
      static String readLine() {
          try {
              return reader.readLine();
          } catch (Exception e) {
              throw new RuntimeException(e);
          }
      }
  
      static void initializeTokens() {
          while (null == tokens || !tokens.hasMoreTokens())
              tokens = new StringTokenizer(readLine());
      }
  
      static String next() {
          initializeTokens();
          return tokens.nextToken();
      }
  
      static String next(String delim) {
          initializeTokens();
          return tokens.nextToken(delim);
      }
  
      static int nextInt() {
          return Integer.parseInt(next());
      }
  
      static long nextLong() {
          return Long.parseLong(next());
      }
  
      static void close() {
          try {
              reader.close();
              writer.close();
          } catch (Exception e) {
              throw new RuntimeException(e);
          }
      }
  }