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.*;
  import java.util.*;
  
  public class D {
  	
  	static class FenwickTree { // one-based DS
  
  		int n;
  		int[] ft;
  
  		FenwickTree(int size) {
  			n = size;
  			ft = new int[n + 1];
  		}
  
  		int query(int i) {
  			int sum = 0;
  			while (i > 0) {
  				sum += ft[i];
  				i -= i & -i;
  			}
  			return sum;
  		}
  
  		int query(int i, int j) {
  			return query(j) - query(i - 1);
  		}
  
  		void point_update(int i, int add) { // update = increment
  			while (i <= n) {
  				ft[i] += add;
  				i += i & -i;
  			}
  		}
  	}
  	
  	public static void main(String[] args)throws IOException {
  		
  		FastScanner scan = new FastScanner();
  		PrintWriter output = new PrintWriter(System.out);
  		int t = scan.nextInt();
  		for(int tt = 0;tt<t;tt++) {
  			
  			int n = scan.nextInt();
  			int arr[] = new int[n];
  			HashSet<Integer> hs = new HashSet<>();
  			for(int i = 0;i<n;i++) {
  				arr[i] = scan.nextInt();
  				hs.add(arr[i]);
  			}
  			if(hs.size()<n) {
  				output.println("YES");
  				continue;
  			}
  			long count = 0;
  			FenwickTree ft = new FenwickTree(n);
  			for(int i = 0;i<n;i++) {
  				count+= ft.query(arr[i], n);
  				ft.point_update(arr[i], 1);
  			}
  			if(count%2==0) output.println("YES");
  			else output.println("NO");
  		}
  		output.flush();
  	}
  	
  	public static int[] sort(int arr[]) {
  		List<Integer> list = new ArrayList<>();
  		for(int i:arr) list.add(i);
  		Collections.sort(list);
  		for(int i = 0;i<list.size();i++) arr[i] = list.get(i);
  		return arr;
  	}
  	
  	public static int gcd(int a, int b) {
  		if(a == 0) return b;
  		return gcd(b%a, a);
  	}
  	
  	public static void printArray(int arr[]) {
  		for(int i:arr) System.out.print(i+" ");
  		System.out.println();
  	}
  	
  	static class FastScanner {
  		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
  		StringTokenizer st=new StringTokenizer("");
  		String next() {
  			while (!st.hasMoreTokens())
  				try {
  					st=new StringTokenizer(br.readLine());
  				} catch (IOException e) {
  					e.printStackTrace();
  				}
  			return st.nextToken();
  		}
  
  		int nextInt() {
  			return Integer.parseInt(next());
  		}
  		int[] readArray(int n) {
  			int[] a=new int[n];
  			for (int i=0; i<n; i++) a[i]=nextInt();
  			return a;
  		}
  		long nextLong() {
  			return Long.parseLong(next());
  		}
  		
  		double nextDouble() {
  			return Double.parseDouble(next());
  		}
  	}
  
  }
  