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 long mergeAndCount(int[] arr, int l, int m, int r) {
   
  		int[] left = Arrays.copyOfRange(arr, l, m + 1);
  		int[] right = Arrays.copyOfRange(arr, m + 1, r + 1);
   
  		int i = 0, j = 0, k = l;
  		long swaps = 0;
   
  		while (i < left.length && j < right.length) {
  			if (left[i] <= right[j])
  				arr[k++] = left[i++];
  			else {
  				arr[k++] = right[j++];
  				swaps += (m + 1) - (l + i);
  			}
  		}
  		while (i < left.length)
  			arr[k++] = left[i++];
  		while (j < right.length)
  			arr[k++] = right[j++];
  		return swaps;
  	}
  	private static long inv(int[] arr, int l, int r) {
  		long count = 0;
   
  		if (l < r) {
  			int m = (l + r) / 2;
  			count += inv(arr, l, m);
  			count += inv(arr, m + 1, r);
  			count += mergeAndCount(arr, l, m, r);
  		}
   
  		return count;
  	}
  	public static void main(String[] args) throws Exception {
  	
  	
  			
  		
   
  		
  			int t=sc.nextInt();
  			while(t-->0) {
  				int n=sc.nextInt();
  				int[]aa=sc.nextIntArray(n);
  				if(n==1) {
  					pw.println("YES");
  				}else if(n==2){
  					pw.println(aa[0]<=aa[1]?"YES":"NO");
  				}else {
  					long inversion = inv(aa,0,n-1);
  					HashSet<Integer>hs=new HashSet<Integer>();
  					for(int i=0;i<n;i++) {
  						if(hs.contains(aa[i]))inversion=0;
  						hs.add(aa[i]);
  					}
  		
  					pw.println(inversion%2==0?"YES":"NO");
  				}
  		}
  		pw.close();
  	}
   
  	static class Scanner {
  		StringTokenizer st;
  		BufferedReader br;
   
  		public Scanner(InputStream s) {
  			br = new BufferedReader(new InputStreamReader(s));
  		}
   
  		public Scanner(FileReader r) {
  			br = new BufferedReader(r);
  		}
   
  		public String next() throws IOException {
  			while (st == null || !st.hasMoreTokens())
  				st = new StringTokenizer(br.readLine());
  			return st.nextToken();
  		}
   
  		public int nextInt() throws IOException {
  			return Integer.parseInt(next());
  		}
   
  		public long nextLong() throws IOException {
  			return Long.parseLong(next());
  		}
   
  		public String nextLine() throws IOException {
  			return br.readLine();
  		}
   
  		public double nextDouble() throws IOException {
  			String x = next();
  			StringBuilder sb = new StringBuilder("0");
  			double res = 0, f = 1;
  			boolean dec = false, neg = false;
  			int start = 0;
  			if (x.charAt(0) == '-') {
  				neg = true;
  				start++;
  			}
  			for (int i = start; i < x.length(); i++)
  				if (x.charAt(i) == '.') {
  					res = Long.parseLong(sb.toString());
  					sb = new StringBuilder("0");
  					dec = true;
  				} else {
  					sb.append(x.charAt(i));
  					if (dec)
  						f *= 10;
  				}
  			res += Long.parseLong(sb.toString()) / f;
  			return res * (neg ? -1 : 1);
  		}
   
  		public long[] nextlongArray(int n) throws IOException {
  			long[] a = new long[n];
  			for (int i = 0; i < n; i++)
  				a[i] = nextLong();
  			return a;
  		}
   
  		public Long[] nextLongArray(int n) throws IOException {
  			Long[] a = new Long[n];
  			for (int i = 0; i < n; i++)
  				a[i] = nextLong();
  			return a;
  		}
   
  		public int[] nextIntArray(int n) throws IOException {
  			int[] a = new int[n];
  			for (int i = 0; i < n; i++)
  				a[i] = nextInt();
  			return a;
  		}
   
  		public Integer[] nextIntegerArray(int n) throws IOException {
  			Integer[] a = new Integer[n];
  			for (int i = 0; i < n; i++)
  				a[i] = nextInt();
  			return a;
  		}
   
  		public boolean ready() throws IOException {
  			return br.ready();
  		}
   
  	}
   
  	static class pair implements Comparable<pair> {
  		long x;
  		long y;
   
  		public pair(long x, long y) {
  			this.x = x;
  			this.y = y;
  		}
   
  		public String toString() {
  			return x + " " + y;
  		}
   
  		public boolean equals(Object o) {
  			if (o instanceof pair) {
  				pair p = (pair) o;
  				return p.x == x && p.y == y;
  			}
  			return false;
  		}
   
  		public int hashCode() {
  			return new Long(x).hashCode() * 31 + new Long(y).hashCode();
  		}
   
  		public int compareTo(pair other) {
  			if (this.x == other.x) {
  				return Long.compare(this.y, other.y);
  			}
  			return Long.compare(this.x, other.x);
  		}
  	}
   
  	static class tuble implements Comparable<tuble> {
  		int x;
  		int y;
  		int z;
   
  		public tuble(int x, int y, int z) {
  			this.x = x;
  			this.y = y;
  			this.z = z;
  		}
   
  		public String toString() {
  			return x + " " + y + " " + z;
  		}
   
  		public int compareTo(tuble other) {
  			if (this.x == other.x) {
  				if (this.y == other.y) {
  					return this.z - other.z;
  				}
  				return this.y - other.y;
  			} else {
  				return this.x - other.x;
  			}
  		}
  	}
  	static Scanner sc = new Scanner(System.in);
   
  	static long mod = 1000000007;
  	static Random rn = new Random();
  	static PrintWriter pw = new PrintWriter(System.out);
  }