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: //package Codeforces.Round759Div2;
  
  import java.io.*;
  import java.util.*;
  
  public class D {
      static int count(int[] arr, int ll, int mid, int ul){
          int n = mid - ll + 1;
          int[] L = new int[n];
          for(int i=0;i<n;i++){
              L[i] = arr[ll + i];
          }
  
          int m = ul - mid;
          int[] R = new int[m];
          for(int i=0;i<m;i++){
              R[i] = arr[mid + i + 1];
          }
  
          int p = 0, q = 0, k = ll;
          int count = 0;
          while(p<n && q<m){
              if(L[p]<R[q]){
                  arr[k] = L[p];
                  p++;
                  k++;
              }
              else{
                  arr[k] = R[q];
                  count += n - p;
                  q++;
                  k++;
              }
          }
  
          while(p<n){
              arr[k] = L[p];
              p++;
              k++;
          }
  
          while(q<m){
              arr[k] = R[q];
              q++;
              k++;
          }
  
          //System.out.println(count);
          return count;
      }
      static int countInversions(int[] arr, int ll, int ul){
          if(ll<ul){
              int mid = (ll + ul)/2;
              int lc = countInversions(arr, ll, mid);
              int rc = countInversions(arr, mid+1, ul);
              //System.out.println(lc+" "+rc);
              return lc + rc + count(arr, ll, mid, ul);
          }
          return 0;
      }
      public static void main(String[] args) throws IOException {
          Soumit sc = new Soumit();
  
          int t = sc.nextInt();
          StringBuilder sb = new StringBuilder();
          while (t-->0){
              int n = sc.nextInt();
              int[] arr = sc.nextIntArray(n);
  
              Set<Integer> set = new HashSet<>();
              for(int i: arr)
                  set.add(i);
  
              if(set.size()<n || countInversions(arr, 0, n-1)%2==0)
                  sb.append("YES\n");
              else sb.append("NO\n");
          }
  
          System.out.println(sb);
  
          sc.close();
      }
  
      static class Soumit {
          final private int BUFFER_SIZE = 1 << 18;
          final private DataInputStream din;
          final private byte[] buffer;
          private PrintWriter pw;
          private int bufferPointer, bytesRead;
          StringTokenizer st;
  
          public Soumit() {
              din = new DataInputStream(System.in);
              buffer = new byte[BUFFER_SIZE];
              bufferPointer = bytesRead = 0;
          }
  
          public Soumit(String file_name) throws IOException {
              din = new DataInputStream(new FileInputStream(file_name));
              buffer = new byte[BUFFER_SIZE];
              bufferPointer = bytesRead = 0;
          }
  
          public void streamOutput(String file) throws IOException {
              FileWriter fw = new FileWriter(file);
              BufferedWriter bw = new BufferedWriter(fw);
              pw = new PrintWriter(bw);
          }
  
          public void println(String a) {
              pw.println(a);
          }
  
          public void print(String a) {
              pw.print(a);
          }
  
          public String readLine() throws IOException {
              byte[] buf = new byte[3000064]; // line length
              int cnt = 0, c;
              while ((c = read()) != -1) {
                  if (c == '\n')
                      break;
                  buf[cnt++] = (byte) c;
              }
              return new String(buf, 0, cnt);
          }
  
          String next() {
              while (st == null || !st.hasMoreElements()) {
                  try {
                      st = new StringTokenizer(readLine());
                  } catch (IOException e) {
                      e.printStackTrace();
                  }
              }
              return st.nextToken();
          }
  
          public void sort(int[] arr) {
              ArrayList<Integer> arlist = new ArrayList<>();
              for (int i : arr)
                  arlist.add(i);
  
              Collections.sort(arlist);
              for (int i = 0; i < arr.length; i++)
                  arr[i] = arlist.get(i);
          }
  
          public void sort(long[] arr) {
              ArrayList<Long> arlist = new ArrayList<>();
              for (long i : arr)
                  arlist.add(i);
  
              Collections.sort(arlist);
              for (int i = 0; i < arr.length; i++)
                  arr[i] = arlist.get(i);
          }
  
          public int[] nextIntArray(int n) throws IOException {
              int[] arr = new int[n];
              for (int i = 0; i < n; i++) {
                  arr[i] = nextInt();
              }
  
              return arr;
          }
  
          public long[] nextLongArray(int n) throws IOException {
              long[] arr = new long[n];
              for (int i = 0; i < n; i++) {
                  arr[i] = nextLong();
              }
  
              return arr;
          }
  
          public double[] nextDoubleArray(int n) throws IOException {
              double[] arr = new double[n];
              for (int i = 0; i < n; i++) {
                  arr[i] = nextDouble();
              }
  
              return arr;
          }
  
          public int nextInt() throws IOException {
              int ret = 0;
              byte c = read();
              while (c <= ' ')
                  c = read();
              boolean neg = (c == '-');
              if (neg)
                  c = read();
              do {
                  ret = ret * 10 + c - '0';
              } while ((c = read()) >= '0' && c <= '9');
  
              if (neg)
                  return -ret;
              return ret;
          }
  
          public long nextLong() throws IOException {
              long ret = 0;
              byte c = read();
              while (c <= ' ')
                  c = read();
              boolean neg = (c == '-');
              if (neg)
                  c = read();
              do {
                  ret = ret * 10 + c - '0';
              }
              while ((c = read()) >= '0' && c <= '9');
              if (neg)
                  return -ret;
              return ret;
          }
  
          public double nextDouble() throws IOException {
              double ret = 0, div = 1;
              byte c = read();
              while (c <= ' ')
                  c = read();
              boolean neg = (c == '-');
              if (neg)
                  c = read();
  
              do {
                  ret = ret * 10 + c - '0';
              }
              while ((c = read()) >= '0' && c <= '9');
  
              if (c == '.') {
                  while ((c = read()) >= '0' && c <= '9') {
                      ret += (c - '0') / (div *= 10);
                  }
              }
  
              if (neg)
                  return -ret;
              return ret;
          }
  
          private void fillBuffer() throws IOException {
              bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
              if (bytesRead == -1)
                  buffer[0] = -1;
          }
  
          private byte read() throws IOException {
              if (bufferPointer == bytesRead)
                  fillBuffer();
              return buffer[bufferPointer++];
          }
  
          public void close() throws IOException {
              /*if (din == null)
                  return;*/
              if (din != null) din.close();
              if (pw != null) pw.close();
          }
      }
  }
  