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 Main {
  	static class FastReader {
  		BufferedReader br;
  		StringTokenizer st;
  
  		public FastReader() {
  			br = new BufferedReader(new InputStreamReader(System.in));
  		}
  
  		String next() {
  			while (st == null || !st.hasMoreElements()) {
  				try {
  					st = new StringTokenizer(br.readLine());
  				} catch (IOException e) {
  					e.printStackTrace();
  				}
  			}
  			return st.nextToken();
  		}
  
  		int nextInt() {
  			return Integer.parseInt(next());
  		}
  
  		long nextLong() {
  			return Long.parseLong(next());
  		}
  
  		double nextDouble() {
  			return Double.parseDouble(next());
  		}
  
  		String nextLine() {
  			String str = "";
  			try {
  				str = br.readLine();
  			} catch (IOException e) {
  				e.printStackTrace();
  			}
  			return str;
  		}
  	}
  	public static class union_find {
  		int n;
  		int[] sz;
  		int[] par;
  
  		union_find(int nval) {
  			n = nval;
  			sz = new int[n + 1];
  			par = new int[n + 1];
  			for (int i = 0; i <= n; i++) {
  				par[i] = i;
  				sz[i] = 1;
  			}
  		}
  
  		int root(int x) {
  			if (par[x] == x)
  				return x;
  			return par[x] = root(par[x]);
  		}
  
  		boolean find(int a, int b) {
  			return root(a) == root(b);
  		}
  
  		int union(int a, int b) {
  			int ra = root(a);
  			int rb = root(b);
  			if (ra == rb)
  				return 0;
  			if (sz[a] > sz[b]) {				
  				int temp = ra;
  				ra = rb;
  				rb = temp;
  			}
  			par[ra] = rb;
  			sz[rb] += sz[ra];
  			return 1;
  		}
  	}
  	public static void main(String[] args) {
  		FastReader obj = new FastReader();
  		PrintWriter out = new PrintWriter(System.out);
  		int len = obj.nextInt();
  		while (len-- != 0) {
  			int n = obj.nextInt();
              int[] num=new int[n+1];
              HashSet<Integer> h=new HashSet<>();
              for(int i=1;i<=n;i++) {
              	num[i]=obj.nextInt();
              	h.add(num[i]);
              }
              if(h.size()==n)
              {
              	union_find dsu=new union_find(n+1);
              	for(int i=1;i<=n;i++) if(num[i]!=i) dsu.union(num[i],i);
              	int even=0;
              	for(int i=1;i<=n;i++)
              	{
              	  if(dsu.root(i)==i)if(dsu.sz[i]%2==0)even++;	
              	}
              	if(even%2==0)out.println("YES");
              	else out.println("NO");
              }
              else out.println("YES");
  		}
  		out.flush();
  	}
  	//Cover the small test cases like for n=1 .
  }