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.IOException;
  import java.io.InputStream;
  import java.io.OutputStream;
  import java.io.PrintWriter;
  import java.math.BigInteger;
  import java.util.*;
  
  /**
   * @author Mubtasim Shahriar
   */
  
  public class YetAnotherSortingProblem {
  
      public static void main(String[] args) {
  
          InputStream inputStream = System.in;
          OutputStream outputStream = System.out;
          InputReader sc = new InputReader(inputStream);
          PrintWriter out = new PrintWriter(outputStream);
          Solver solver = new Solver();
          int t = sc.nextInt();
  //        int t = 1;
          while (t-- != 0) {
              solver.solve(sc, out);
          }
          out.close();
  
      }
  
      static class Solver {
          public void solve(InputReader sc, PrintWriter out) {
              int n = sc.nextInt();
              int[] arr = sc.nextIntArray(n);
              int[] tmp = new int[n];
              long inversions = mergeSortAndCount(arr,tmp,0,n-1);
              if(inversions%2==1) {
                  for(int i = 1; i<n; i++) if(arr[i]==arr[i-1]) {
                      out.println("YES");
                      return;
                  }
                  out.println("NO");
              } else {
                  out.println("YES");
              }
          }
  
          private long mergeSortAndCount(int[] arr, int[] tmp, int l, int r) {
              if(l>=r) return 0;
              long count = 0;
              int mid = (l+r)/2;
              count += mergeSortAndCount(arr,tmp,l,mid);
              count += mergeSortAndCount(arr,tmp,mid+1,r);
              count += mergeAndCount(arr,tmp,l,r);
              return count;
          }
  
          private long mergeAndCount(int[] arr, int[] tmp, int l, int r) {
              int mid = (l+r)/2;
              long swaps = 0;
              int left = l;
              int right = mid+1;
              int idx = l;
              while(left<=mid && right<=r) {
                  if(arr[left]<=arr[right]) {
                      tmp[idx] = arr[left++];
                  } else {
                      swaps += mid-left+1;
                      tmp[idx] = arr[right++];
                  }
                  idx++;
              }
              while(left<=mid) tmp[idx++] = arr[left++];
              while(right<=r) tmp[idx++] = arr[right++];
              for(int i = l; i <= r; i++) arr[i] = tmp[i];
              return swaps;
          }
      }
  
      static void sort(int[] arr) {
          ArrayList<Integer> al = new ArrayList();
          for (int i : arr) al.add(i);
          Collections.sort(al);
          int idx = 0;
          for (int i : al) arr[idx++] = i;
      }
  
      static void sort(long[] arr) {
          ArrayList<Long> al = new ArrayList();
          for (long i : arr) al.add(i);
          Collections.sort(al);
          int idx = 0;
          for (long i : al) arr[idx++] = i;
      }
  
      static void sortDec(int[] arr) {
          ArrayList<Integer> al = new ArrayList();
          for (int i : arr) al.add(i);
          Collections.sort(al, Collections.reverseOrder());
          int idx = 0;
          for (int i : al) arr[idx++] = i;
      }
  
      static void sortDec(long[] arr) {
          ArrayList<Long> al = new ArrayList();
          for (long i : arr) al.add(i);
          Collections.sort(al, Collections.reverseOrder());
          int idx = 0;
          for (long i : al) arr[idx++] = i;
      }
  
      static class InputReader {
          private boolean finished = false;
  
          private InputStream stream;
          private byte[] buf = new byte[1024];
          private int curChar;
          private int numChars;
          private SpaceCharFilter filter;
  
          public InputReader(InputStream stream) {
              this.stream = stream;
          }
  
          public int read() {
              if (numChars == -1) {
                  throw new InputMismatchException();
              }
              if (curChar >= numChars) {
                  curChar = 0;
                  try {
                      numChars = stream.read(buf);
                  } catch (IOException e) {
                      throw new InputMismatchException();
                  }
                  if (numChars <= 0) {
                      return -1;
                  }
              }
              return buf[curChar++];
          }
  
          public int peek() {
              if (numChars == -1) {
                  return -1;
              }
              if (curChar >= numChars) {
                  curChar = 0;
                  try {
                      numChars = stream.read(buf);
                  } catch (IOException e) {
                      return -1;
                  }
                  if (numChars <= 0) {
                      return -1;
                  }
              }
              return buf[curChar];
          }
  
          public int nextInt() {
              int c = read();
              while (isSpaceChar(c)) {
                  c = read();
              }
              int sgn = 1;
              if (c == '-') {
                  sgn = -1;
                  c = read();
              }
              int res = 0;
              do {
                  if (c < '0' || c > '9') {
                      throw new InputMismatchException();
                  }
                  res *= 10;
                  res += c - '0';
                  c = read();
              } while (!isSpaceChar(c));
              return res * sgn;
          }
  
          public long nextLong() {
              int c = read();
              while (isSpaceChar(c)) {
                  c = read();
              }
              int sgn = 1;
              if (c == '-') {
                  sgn = -1;
                  c = read();
              }
              long res = 0;
              do {
                  if (c < '0' || c > '9') {
                      throw new InputMismatchException();
                  }
                  res *= 10;
                  res += c - '0';
                  c = read();
              } while (!isSpaceChar(c));
              return res * sgn;
          }
  
          public String nextString() {
              int c = read();
              while (isSpaceChar(c)) {
                  c = read();
              }
              StringBuilder res = new StringBuilder();
              do {
                  if (Character.isValidCodePoint(c)) {
                      res.appendCodePoint(c);
                  }
                  c = read();
              } while (!isSpaceChar(c));
              return res.toString();
          }
  
          public boolean isSpaceChar(int c) {
              if (filter != null) {
                  return filter.isSpaceChar(c);
              }
              return isWhitespace(c);
          }
  
          public static boolean isWhitespace(int c) {
              return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
          }
  
          private String readLine0() {
              StringBuilder buf = new StringBuilder();
              int c = read();
              while (c != '\n' && c != -1) {
                  if (c != '\r') {
                      buf.appendCodePoint(c);
                  }
                  c = read();
              }
              return buf.toString();
          }
  
          public String readLine() {
              String s = readLine0();
              while (s.trim().length() == 0) {
                  s = readLine0();
              }
              return s;
          }
  
          public String readLine(boolean ignoreEmptyLines) {
              if (ignoreEmptyLines) {
                  return readLine();
              } else {
                  return readLine0();
              }
          }
  
          public BigInteger readBigInteger() {
              try {
                  return new BigInteger(nextString());
              } catch (NumberFormatException e) {
                  throw new InputMismatchException();
              }
          }
  
          public char nextCharacter() {
              int c = read();
              while (isSpaceChar(c)) {
                  c = read();
              }
              return (char) c;
          }
  
          public double nextDouble() {
              int c = read();
              while (isSpaceChar(c)) {
                  c = read();
              }
              int sgn = 1;
              if (c == '-') {
                  sgn = -1;
                  c = read();
              }
              double res = 0;
              while (!isSpaceChar(c) && c != '.') {
                  if (c == 'e' || c == 'E') {
                      return res * Math.pow(10, nextInt());
                  }
                  if (c < '0' || c > '9') {
                      throw new InputMismatchException();
                  }
                  res *= 10;
                  res += c - '0';
                  c = read();
              }
              if (c == '.') {
                  c = read();
                  double m = 1;
                  while (!isSpaceChar(c)) {
                      if (c == 'e' || c == 'E') {
                          return res * Math.pow(10, nextInt());
                      }
                      if (c < '0' || c > '9') {
                          throw new InputMismatchException();
                      }
                      m /= 10;
                      res += (c - '0') * m;
                      c = read();
                  }
              }
              return res * sgn;
          }
  
          public boolean isExhausted() {
              int value;
              while (isSpaceChar(value = peek()) && value != -1) {
                  read();
              }
              return value == -1;
          }
  
          public String next() {
              return nextString();
          }
  
          public SpaceCharFilter getFilter() {
              return filter;
          }
  
          public void setFilter(SpaceCharFilter filter) {
              this.filter = filter;
          }
  
          public interface SpaceCharFilter {
              public boolean isSpaceChar(int ch);
          }
  
          public int[] nextIntArray(int n) {
              int[] array = new int[n];
              for (int i = 0; i < n; ++i) array[i] = nextInt();
              return array;
          }
  
          public int[] nextSortedIntArray(int n) {
              int array[] = nextIntArray(n);
              Arrays.sort(array);
              return array;
          }
  
          public int[] nextSumIntArray(int n) {
              int[] array = new int[n];
              array[0] = nextInt();
              for (int i = 1; i < n; ++i) array[i] = array[i - 1] + nextInt();
              return array;
          }
  
          public long[] nextLongArray(int n) {
              long[] array = new long[n];
              for (int i = 0; i < n; ++i) array[i] = nextLong();
              return array;
          }
  
          public long[] nextSumLongArray(int n) {
              long[] array = new long[n];
              array[0] = nextInt();
              for (int i = 1; i < n; ++i) array[i] = array[i - 1] + nextInt();
              return array;
          }
  
          public long[] nextSortedLongArray(int n) {
              long array[] = nextLongArray(n);
              Arrays.sort(array);
              return array;
          }
      }
  
  
  }
  