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.util.*;
  
  import java.io.*;
  
  public class tr0 {
  	static PrintWriter out;
  	static StringBuilder sb;
  	static long mod = (long) 998244353;
  	static long inf = (long) 1e16;
  	static ArrayList<Integer>[] ad;
  	static int[][] remove, add;
  	static int[][][] memo;
  	static boolean vis[];
  	static long[] inv, f, ncr[];
  	static HashMap<Integer, Integer> hm;
  	static int[] pre, suf, Smax[], Smin[];
  	static int idmax, idmin;
  	static ArrayList<Integer> av;
  	static HashMap<Integer, Integer> mm;
  	static boolean[] msks;
  	static int[] lazy[], lazyCount;
  	static int[] dist;
  	static int[][] P;
  	static long N;
  	static ArrayList<Integer> gl;
  	static int[] a, b;
  	static String s;
  
  	public static void main(String[] args) throws Exception {
  		Scanner sc = new Scanner(System.in);
  		out = new PrintWriter(System.out);
  		int t = sc.nextInt();
  		while (t-- > 0) {
  			int n = sc.nextInt();
  			int[] a = sc.nextArrInt(n);
  			int ans = 0;
  			TreeSet<Integer> ts = new TreeSet<>();
  			FenwickTree ft = new FenwickTree(n + 5);
  			for (int i = 0; i < n; i++) {
  				ans += (ft.rsq(a[i] + 1) % 2);
  				ft.point_update(a[i], 1);
  				ts.add(a[i]);
  			}
  			ans %= 2;
  			if (ts.size() != n) {
  				out.println("YES");
  				continue;
  			}
  			if (ans == 0)
  				out.println("YES");
  			else
  				out.println("NO");
  		}
  		out.flush();
  	}
  
  	public static class FenwickTree { // one-based DS
  
  		int n;
  		int[] ft;
  
  		FenwickTree(int size) {
  			n = size;
  			ft = new int[n + 1];
  		}
  
  		int rsq(int b) // O(log n)
  		{
  			int sum = 0;
  			while (b <= n) {
  				sum += ft[b];
  				b += b & -b;
  			} // min?
  			return sum;
  		}
  
  		void point_update(int k, int val) // O(log n), update = increment
  		{
  			while (k > 0) {
  				ft[k] += val;
  				k -= k & -k;
  			} // min?
  		}
  
  	}
  
  	static class Scanner {
  		StringTokenizer st;
  		BufferedReader br;
  
  		public Scanner(InputStream system) {
  			br = new BufferedReader(new InputStreamReader(system));
  		}
  
  		public Scanner(String file) throws Exception {
  			br = new BufferedReader(new FileReader(file));
  		}
  
  		public String next() throws IOException {
  			while (st == null || !st.hasMoreTokens())
  				st = new StringTokenizer(br.readLine());
  			return st.nextToken();
  		}
  
  		public String nextLine() throws IOException {
  			return br.readLine();
  		}
  
  		public int nextInt() throws IOException {
  			return Integer.parseInt(next());
  		}
  
  		public double nextDouble() throws IOException {
  			return Double.parseDouble(next());
  		}
  
  		public char nextChar() throws IOException {
  			return next().charAt(0);
  		}
  
  		public Long nextLong() throws IOException {
  			return Long.parseLong(next());
  		}
  
  		public int[] nextArrInt(int n) throws IOException {
  			int[] a = new int[n];
  			for (int i = 0; i < n; i++)
  				a[i] = nextInt();
  			return a;
  		}
  
  		public long[] nextArrLong(int n) throws IOException {
  			long[] a = new long[n];
  			for (int i = 0; i < n; i++)
  				a[i] = nextLong();
  			return a;
  		}
  
  		public int[] nextArrIntSorted(int n) throws IOException {
  			int[] a = new int[n];
  			Integer[] a1 = new Integer[n];
  			for (int i = 0; i < n; i++)
  				a1[i] = nextInt();
  			Arrays.sort(a1);
  			for (int i = 0; i < n; i++)
  				a[i] = a1[i].intValue();
  			return a;
  		}
  
  		public long[] nextArrLongSorted(int n) throws IOException {
  			long[] a = new long[n];
  			Long[] a1 = new Long[n];
  			for (int i = 0; i < n; i++)
  				a1[i] = nextLong();
  			Arrays.sort(a1);
  			for (int i = 0; i < n; i++)
  				a[i] = a1[i].longValue();
  			return a;
  		}
  
  		public boolean ready() throws IOException {
  			return br.ready();
  		}
  
  		public void waitForInput() throws InterruptedException {
  			Thread.sleep(3000);
  		}
  	}
  }