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 Main {
  
  	public static void main(String[] args) throws Exception {
  		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
  		BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));
  		
  		int T = Integer.parseInt(in.readLine());
  		int[] A = new int[500500];
  		int[] location = new int[500500];
  		
  		for (int ts=1; ts<=T; ts++) {
  			int N = Integer.parseInt(in.readLine());
  			for (int i=1; i<=N; i++) {
  				location[i] = 0;
  			}
  			boolean duplicate = false;
  			{
  				int idx = 1;
  				for (final String str : in.readLine().split(" ")) {
  					A[idx] = Integer.parseInt(str);
  					if (location[A[idx]] != 0) {
  						duplicate = true;
  					}
  					location[A[idx]] = idx;
  					idx++;
  				}
  			}
  			
  			if (duplicate) {
  				out.write("YES\n");
  				continue;
  			}
  			
  			for (int i=1; i<=(N-2); i++) {
  				// move value i to ith position
  				if (location[i] == i) continue;
  				int x = i;
  				int y = location[i];
  				int z = N;
  				while ((z==x) || (z==y)) z--;
  				
  				int valx = A[x];
  				int valy = A[y];
  				int valz = A[z];
  				A[x] = valy;
  				A[y] = valz;
  				A[z] = valx;
  				
  				location[A[x]] = x;
  				location[A[y]] = y;
  				location[A[z]] = z;
  			}
  			
  			boolean sorted = true;
  			for (int i=1; i<N; i++) {
  				if (A[i] > A[i+1]) {
  					sorted = false;
  				}
  			}
  			out.write(sorted ? "YES\n" : "NO\n");
  			
  			//out.flush();
  		}
  		
  		in.close();
  		out.close();
  	}
  
  }
  
  
  /*public class Main {
  
  	private static TreeSet<String> states = new TreeSet<>();
  	
  	private static String stateToString(List<Integer> list) {
  		String result = "";
  		for (final Integer val : list) {
  			result += (" " + val);
  		}
  		return result;
  	}
  	
  	public static void main(String[] args) throws Exception {
  		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
  		BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));
  		
  		List<Integer> state = new ArrayList<>();
  		for (int i=1; i<=4; i++) {
  			state.add(i);
  		}
  		for (int i=3; i>=1; i--) {
  			state.add(i);
  		}
  		//state.add(3);
  		//state.add(5);
  		List<List<Integer>> bfs = new ArrayList<>();
  		bfs.add(state);
  		
  		states.add(stateToString(state));
  		
  		while (!bfs.isEmpty()) {
  			state = bfs.remove(bfs.size()-1);
  			for (int i=0; i<state.size(); i++) {
  				for (int j=0; j<state.size(); j++) {
  					for (int k=0; k<state.size(); k++) {
  						if (i==j || i==k || k==j) continue;
  						int vali = state.get(i);
  						int valj = state.get(j);
  						int valk = state.get(k);
  						
  						List<Integer> newState = new ArrayList<>(state);
  						newState.set(i, valj);
  						newState.set(j, valk);
  						newState.set(k, vali);
  						
  						if (!states.contains(stateToString(newState))) {
  							states.add(stateToString(newState));
  							bfs.add(newState);
  						}
  					}
  				}
  			}
  		}
  		
  		for (final String str : states) {
  			out.write(str + "\n");
  		}
  		out.write(states.size() + "\n");
  		
  		in.close();
  		out.close();
  	}
  
  }
  */