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.BufferedOutputStream;
  import java.io.BufferedReader;
  import java.io.FileInputStream;
  import java.io.FileNotFoundException;
  import java.io.FileOutputStream;
  import java.io.IOException;
  import java.io.InputStream;
  import java.io.InputStreamReader;
  import java.io.PrintWriter;
  import java.util.InputMismatchException;
  import java.util.Random;
  import java.util.StringTokenizer;
  
  public class A4 {
  
      static MergeSort ms = new MergeSort(500_050);
      
      void solve() {
          int n = cint();
          int[] a = carr_int(n);
  
          if (n == 1) {
              cout("YES");
              return;
          }
          if (n == 2) {
              cout(a[0] <= a[1] ? "YES" : "NO");
              return;
          }
  
          ms.mergeSort(a);
          for (int i = 1; i < n; i++) {
              if (a[i] == a[i-1]) {
                  cout("YES");
                  return;
              }
          }
  
          if (ms.invariants % 2 == 1) {
              cout("NO");
          } else {
              cout("YES");
          }
      }
      
      static class MergeSort {
  
          final int[] b;
          long invariants; // сумма попарных инвариантов в изначальном массиве
  
          public MergeSort(int maxSize) { // доп память
              this.b = new int[maxSize];
          }
  
          void mergeSort(int[] a) {
              invariants = 0;
              mergeSort(a, 0, a.length-1);
          }
  
          void mergeSort(int[] a, int lo, int hi) {
              if (hi <= lo) {
                  return;
              }
              int mid = lo + (hi - lo) / 2;
              mergeSort(a, lo, mid);
              mergeSort(a, mid + 1, hi);
  
              System.arraycopy(a, lo, b, lo, hi-lo+1);
  
              int i = lo, j = mid + 1;
              for (int k = lo; k <= hi; k++) {
                  if (i > mid) {
                      a[k] = b[j++];
                  } else if (j > hi) {
                      a[k] = b[i++];
                  } else if (b[j] < b[i]) {
                      a[k] = b[j++];
                      invariants += (mid - i + 1);
                  } else {
                      a[k] = b[i++];
                  }
              }
          }
      }
  
      public static void main(String... args) throws Exception{
          int t = in.nextInt();
          for (int test = 0; test < t; test++) {
              new A4().solve();
          }
          out.flush();
      }
  
      static final QuickReader in = new QuickReader(System.in);
      static final PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out, 131_072));
  
      static int cint() {
          return in.nextInt();
      }
  
      static long clong() {
          return in.nextLong();
      }
  
      static String cstr() {
          return in.nextLine();
      }
  
      static int[] carr_int(int n) {
          return in.nextInts(n);
      }
  
      static long[] carr_long(int n) {
          return in.nextLongs(n);
      }
  
      static void cout(int... a) {
          StringBuilder buf = new StringBuilder();
          for (int i = 0; i < a.length; i++) {
              if (i != 0) {
                  buf.append(' ');
              }
              buf.append(a[i]);
          }
          out.println(buf);
      }
  
      static void cout(long... a) {
          StringBuilder buf = new StringBuilder();
          for (int i = 0; i < a.length; i++) {
              if (i != 0) {
                  buf.append(' ');
              }
              buf.append(a[i]);
          }
          out.println(buf);
      }
  
      static void cout(Object o) {
          out.println(o);
      }
  
      static class QuickReader {
          BufferedReader in;
          StringTokenizer token;
  
          public QuickReader(InputStream ins) {
              in = new BufferedReader(new InputStreamReader(ins));
              token = new StringTokenizer("");
          }
  
          public boolean hasNext() {
              while (!token.hasMoreTokens()) {
                  try {
                      String s = in.readLine();
                      if (s == null) {
                          return false;
                      }
                      token = new StringTokenizer(s);
                  } catch (IOException e) {
                      throw new InputMismatchException();
                  }
              }
              return true;
          }
  
          public String next() {
              hasNext();
              return token.nextToken();
          }
  
          public String nextLine() {
              try {
                  String s = in.readLine();
                  token = new StringTokenizer("");
                  return s;
              } catch (IOException e) {
                  throw new InputMismatchException();
              }
          }
  
          public int nextInt() {
              return Integer.parseInt(next());
          }
  
          public int[] nextInts(int n) {
              int[] res = new int[n];
              for (int i = 0; i < n; i++) {
                  res[i] = nextInt();
              }
              return res;
          }
  
          public long nextLong() {
              return Long.parseLong(next());
          }
  
          public long[] nextLongs(int n) {
              long[] res = new long[n];
              for (int i = 0; i < n; i++) {
                  res[i] = nextLong();
              }
              return res;
          }
      }
  }
  