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.BufferedReader;
  import java.io.IOException;
  import java.io.InputStreamReader;
  import java.io.PrintWriter;
  import java.util.HashSet;
  import java.util.StringTokenizer;
  
  public class d {
  	public static void main(String[] args) {
  		FastScanner scan=new FastScanner();
  		PrintWriter out=new PrintWriter(System.out);
  		
  		int t=scan.nextInt();
  		t:for(int tt=0;tt<t;tt++) {
  			int n=scan.nextInt();
  			BIT b=new BIT(n+100);
  			int[] a=new int[n];
  			HashSet<Integer> set=new HashSet<>();
  			for(int i=0;i<n;i++) {
  				a[i]=scan.nextInt()+1;
  				set.add(a[i]);
  			}
  			if(set.size()!=n) out.println("YES");
  			else {
  				long inv=0;
  				for(int i=n-1;i>=0;i--) {
  					b.update(a[i],1);
  					inv+=b.sum(a[i]-1);
  				}
  				out.println(inv%2==0?"YES":"NO");
  			}
  		}
  		
  		out.close();
  	}
  	static class BIT {
  	    int n;
  	    long[] arr;
  	    BIT(int nn){
  	        n = nn;
  	        arr = new long[n + 1];
  	    }
  	    void update(int i, long v){
  	        if(i > n) return;
  	        arr[i] += v;
  	        update(i + (i & -i), v);
  	    }
  	    long sum(int i){
  	        if(i < 1) return 0;
  	        return arr[i] + sum(i - (i & -i));
  	    }
  	    int getKth(long k) {
  	        int pow = Integer.highestOneBit(n), idx = 0;
  	        while(pow > 0){
  	            if(idx + pow <= n && arr[idx + pow] <= k){
  	                idx += pow;
  	                k -= arr[idx];
  	            }
  	            pow /= 2;
  	        }
  	        return idx;
  	    }
  	}
  	static class FastScanner {
  		BufferedReader br;
  		StringTokenizer st;
  
  		public FastScanner() {
  			try	{
  				br = new BufferedReader(new InputStreamReader(System.in));
  				st = new StringTokenizer(br.readLine());
  			} catch (Exception e){e.printStackTrace();}
  		}
  
  		public String next() {
  			if (st.hasMoreTokens())	return st.nextToken();
  			try {st = new StringTokenizer(br.readLine());}
  			catch (Exception e) {e.printStackTrace();}
  			return st.nextToken();
  		}
  
  		public int nextInt() {return Integer.parseInt(next());}
  
  		public long nextLong() {return Long.parseLong(next());}
  
  		public double nextDouble() {return Double.parseDouble(next());}
  
  		public String nextLine() {
  			String line = "";
  			if(st.hasMoreTokens()) line = st.nextToken();
  			else try {return br.readLine();}catch(IOException e){e.printStackTrace();}
  			while(st.hasMoreTokens()) line += " "+st.nextToken();
  			return line;
  		}
  	}
  }