description: YouKn0wWho has an integer sequence a_1, a_2, … a_n. Now he will split the sequence a into one or more consecutive subarrays so that each element of a belongs to exactly one subarray. Let k be the number of resulting subarrays, and h_1, h_2, …, h_k be the lengths of the longest increasing subsequences of corresponding subarrays.
  
  For example, if we split [2, 5, 3, 1, 4, 3, 2, 2, 5, 1] into [2, 5, 3, 1, 4], [3, 2, 2, 5], [1], then h = [3, 2, 1].
  
  YouKn0wWho wonders if it is possible to split the sequence a in such a way that the [bitwise XOR](https://en.wikipedia.org/wiki/Bitwise_operation#XOR) of h_1, h_2, …, h_k is equal to 0. You have to tell whether it is possible.
  
  The longest increasing subsequence (LIS) of a sequence b_1, b_2, …, b_m is the longest sequence of valid indices i_1, i_2, …, i_k such that i_1 < i_2 < … < i_k and b_{i_1} < b_{i_2} < … < b_{i_k}. For example, the LIS of [2, 5, 3, 3, 5] is [2, 3, 5], which has length 3.
  
  An array c is a subarray of an array b if c can be obtained from b by deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end.
  
  Input
  
  The first line contains a single integer t (1 ≤ t ≤ 10 000) — the number of test cases.
  
  The first line of each test case contains a single integer n (2 ≤ n ≤ 10^5).
  
  The second line of each test case contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^9).
  
  It is guaranteed that the sum of n over all test cases doesn't exceed 3 ⋅ 10^5.
  
  Output
  
  For each test case, print "YES" (without quotes) if it is possible to split into subarrays in the desired way, print "NO" (without quotes) otherwise. You can print each letter in any register (upper or lower).
  
  Example
  
  Input
  
  
  4
  7
  1 3 4 2 2 1 5
  3
  1 3 4
  5
  1 3 2 4 2
  4
  4 3 2 1
  
  
  Output
  
  
  YES
  NO
  YES
  YES
  
  Note
  
  In the first test case, YouKn0wWho can split the sequence in the following way: [1, 3, 4], [2, 2], [1, 5]. This way, the LIS lengths are h = [3, 1, 2], and the bitwise XOR of the LIS lengths is 3 ⊕ 1 ⊕ 2 = 0.
  
  In the second test case, it can be shown that it is impossible to split the sequence into subarrays that will satisfy the condition.
solution: import java.util.*;
  import java.lang.*;
  import java.io.*;
  
  public class Main
  {
      static long mod = (int)1e9 + 7;
      // static PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
  	public static void main (String[] args) throws java.lang.Exception
  	{
  		FastReader sc =new FastReader();
  		
  	    int t=sc.nextInt();
  	    
  	   // int t=1;
  	    
  	    while(t-->0)
  	    {
  	        int n = sc.nextInt();
  	        int arr[] = sc.readArray(n);
  	        
  	        if(n%2==0)
  	        {
  	            System.out.println("YES");
  	            continue;
  	        }
  	        int count = 0;
  	        
  	        for(int i=0;i<n-1;i++)
  	        {
  	            if(arr[i] >= arr[i+1])
  	            {
  	                count++;
  	                break;
  	            }
  	        }
  	        if(count == 1)
  	        {
  	            System.out.println("YES");
  	        }
  	        else
  	        {
  	            System.out.println("NO");
  	        }
  	    }
  	    
  	}
  	
  	
  	
  	
  	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());
          }
          
          float nextFloat()
          {
              return Float.parseFloat(next());
          }
   
          String nextLine()
          {
              String str = "";
              try {
                  str = br.readLine();
              }
              catch (IOException e) {
                  e.printStackTrace();
              }
              return str;
          }
          
          int[] readArray(int n) {
  			int[] a=new int[n];
  			for (int i=0; i<n; i++) a[i]=nextInt();
  			return a;
  		}
  		
  		long[] readArrayLong(int n) {
  			long[] a=new long[n];
  			for (int i=0; i<n; i++) a[i]=nextLong();
  			return a;
  		}
  		
      }
      
      
      
      public static int[] radixSort2(int[] a)
  	{
  		int n = a.length;
  		int[] c0 = new int[0x101];
  		int[] c1 = new int[0x101];
  		int[] c2 = new int[0x101];
  		int[] c3 = new int[0x101];
  		for(int v : a) {
  			c0[(v&0xff)+1]++;
  			c1[(v>>>8&0xff)+1]++;
  			c2[(v>>>16&0xff)+1]++;
  			c3[(v>>>24^0x80)+1]++;
  		}
  		for(int i = 0;i < 0xff;i++) {
  			c0[i+1] += c0[i];
  			c1[i+1] += c1[i];
  			c2[i+1] += c2[i];
  			c3[i+1] += c3[i];
  		}
  		int[] t = new int[n];
  		for(int v : a)t[c0[v&0xff]++] = v;
  		for(int v : t)a[c1[v>>>8&0xff]++] = v;
  		for(int v : a)t[c2[v>>>16&0xff]++] = v;
  		for(int v : t)a[c3[v>>>24^0x80]++] = v;
  		return a;
  	}
  	
  	static void reverse_sorted(int[] arr)
  	{
  	    ArrayList<Integer> list = new ArrayList<>();
  	    for(int i=0;i<arr.length;i++)
  	    {
  	        list.add(arr[i]);
  	    }
  	    Collections.sort(list , Collections.reverseOrder());
  	    for(int i=0;i<arr.length;i++)
  	    {
  	        arr[i] = list.get(i);
  	    }
  	}
  	
  	static int LowerBound(int a[], int x) { // x is the target value or key
          int l=-1,r=a.length;
          while(l+1<r) {
              int m=(l+r)>>>1;
              if(a[m]>=x) r=m;
              else l=m;
          }
          return r;
      }
      
      static int UpperBound(ArrayList<Integer> list, int x) {// x is the key or target value
          int l=-1,r=list.size();
          while(l+1<r) {
              int m=(l+r)>>>1;
              if(list.get(m)<=x) l=m;
              else r=m;
          }
          return l+1;
      }
      
      public static HashMap<String, Integer> sortByValue(HashMap<String, Integer> hm)
      {
          // Create a list from elements of HashMap
          List<Map.Entry<String, Integer> > list =
                 new LinkedList<Map.Entry<String, Integer> >(hm.entrySet());
   
          // Sort the list
          Collections.sort(list, new Comparator<Map.Entry<String, Integer> >() {
              public int compare(Map.Entry<String, Integer> o1,
                                 Map.Entry<String, Integer> o2)
              {
                  return (o1.getValue()).compareTo(o2.getValue());
              }
          });
           
          // put data from sorted list to hashmap
          HashMap<String, Integer> temp = new LinkedHashMap<String, Integer>();
          for (Map.Entry<String, Integer> aa : list) {
              temp.put(aa.getKey(), aa.getValue());
          }
          return temp;
      }
      
      static class Queue_Pair implements Comparable<Queue_Pair> {
  		int first , second;
  		public Queue_Pair(int first, int second) {
  			this.first=first;
  			this.second=second;
  		}
  		public int compareTo(Queue_Pair o) {
  			return Integer.compare(o.first, first);
  		}
  	}
      
      static void leftRotate(char arr[], int d, int n)
      {
          for (int i = 0; i < d; i++)
              leftRotatebyOne(arr, n);
      }
   
      static void leftRotatebyOne(char arr[], int n)
      {
          int i;
          char temp = arr[0];
          for (i = 0; i < n - 1; i++)
              arr[i] = arr[i + 1];
          arr[n-1] = temp;
          
      }
      
      static void rightRotate(char arr[], int d, int n)
      {
          for (int i = 0; i < d; i++)
              rightRotatebyOne(arr, n);
      }
   
      static void rightRotatebyOne(char arr[], int n)
      {
          int i;
          char temp = arr[n - 1];
          for (i = n - 1; i > 0; i--)
              arr[i] = arr[i - 1];
          arr[0] = temp;
          
      }
      
      static boolean isPalindrome(String str)
      {
   
          // Pointers pointing to the beginning
          // and the end of the string
          int i = 0, j = str.length() - 1;
   
          // While there are characters to compare
          while (i < j) {
   
              // If there is a mismatch
              if (str.charAt(i) != str.charAt(j))
                  return false;
   
              // Increment first pointer and
              // decrement the other
              i++;
              j--;
          }
   
          // Given string is a palindrome
          return true;
      }
      
      static boolean palindrome_array(char arr[], int n)
      {
          // Initialise flag to zero.
          int flag = 0;
   
          // Loop till array size n/2.
          for (int i = 0; i <= n / 2 && n != 0; i++) {
   
              // Check if first and last element are different
              // Then set flag to 1.
              if (arr[i] != arr[n - i - 1]) {
                  flag = 1;
                  break;
              }
          }
   
          // If flag is set then print Not Palindrome
          // else print Palindrome.
          if (flag == 1)
              return false;
          else
              return true;
      }
      
  	static boolean allElementsEqual(long[] arr,int n)
  	{
  	    int z=0;
  	        for(int i=0;i<n-1;i++)
  		    {
  		        if(arr[i]==arr[i+1])
  		        {
  		            z++;
  		        }
  		    }
  		    if(z==n-1)
  		    {
  		        return true;
  		    }
  		    else
  		    {
  		        return false;
  		    }
  		    
  	}
  	
  	static boolean allElementsDistinct(int[] arr,int n)
  	{
  	    int z=0;
  	        for(int i=0;i<n-1;i++)
  		    {
  		        if(arr[i]!=arr[i+1])
  		        {
  		            z++;
  		        }
  		    }
  		    if(z==n-1)
  		    {
  		        return true;
  		    }
  		    else
  		    {
  		        return false;
  		    }
  		    
  		    
  	}
  	
  	public static void reverse(int[] array)
      {
    
          // Length of the array
          int n = array.length;
    
          // Swaping the first half elements with last half
          // elements
          for (int i = 0; i < n / 2; i++) {
    
              // Storing the first half elements temporarily
              int temp = array[i];
    
              // Assigning the first half to the last half
              array[i] = array[n - i - 1];
    
              // Assigning the last half to the first half
              array[n - i - 1] = temp;
          }
      }
      
      public static void reverse_Long(long[] array)
      {
    
          // Length of the array
          int n = array.length;
    
          // Swaping the first half elements with last half
          // elements
          for (int i = 0; i < n / 2; i++) {
    
              // Storing the first half elements temporarily
              long temp = array[i];
    
              // Assigning the first half to the last half
              array[i] = array[n - i - 1];
    
              // Assigning the last half to the first half
              array[n - i - 1] = temp;
          }
      }
  	
  	static boolean isSorted(int[] a)
      {
          for (int i = 0; i < a.length - 1; i++)
          {
              if (a[i] > a[i + 1]) {
                  return false;
              }
          }
   
          return true;
      }
      
      
      
      static boolean isReverseSorted(int[] a)
      {
          for (int i = 0; i < a.length - 1; i++)
          {
              if (a[i] < a[i + 1]) {
                  return false;
              }
          }
   
          return true;
      }
      
      static int[] rearrangeEvenAndOdd(int arr[], int n)
      {
          ArrayList<Integer> list = new ArrayList<>();
  		    
  		    for(int i=0;i<n;i++)
  		    {
  		        if(arr[i]%2==0)
  		        {
  		            list.add(arr[i]);
  		        }
  		    }
  		    
  		    for(int i=0;i<n;i++)
  		    {
  		        if(arr[i]%2!=0)
  		        {
  		            list.add(arr[i]);
  		        }
  		    }
  		    int len = list.size();
  		    int[] array = list.stream().mapToInt(i->i).toArray();
  		    return array;
      }
      
      static long[] rearrangeEvenAndOddLong(long arr[], int n)
      {
          ArrayList<Long> list = new ArrayList<>();
  		    
  		    for(int i=0;i<n;i++)
  		    {
  		        if(arr[i]%2==0)
  		        {
  		            list.add(arr[i]);
  		        }
  		    }
  		    
  		    for(int i=0;i<n;i++)
  		    {
  		        if(arr[i]%2!=0)
  		        {
  		            list.add(arr[i]);
  		        }
  		    }
  		    int len = list.size();
  		    long[] array = list.stream().mapToLong(i->i).toArray();
  		    return array;
      }
  	
  	
      
      static boolean isPrime(long n)
      {
   
          // Check if number is less than
          // equal to 1
          if (n <= 1)
              return false;
   
          // Check if number is 2
          else if (n == 2)
              return true;
   
          // Check if n is a multiple of 2
          else if (n % 2 == 0)
              return false;
   
          // If not, then just check the odds
          for (long i = 3; i <= Math.sqrt(n); i += 2)
          {
              if (n % i == 0)
                  return false;
          }
          return true;
      }
      
      static long getSum(long n)
      {    
          long sum = 0;
            
          while (n != 0)
          {
              sum = sum + n % 10;
              n = n/10;
          }
        
      return sum;
      }
      
      static int gcd(int a, int b)
      {
        if (b == 0)
          return a;
        return gcd(b, a % b);
      }
       
      static long gcdLong(long a, long b)
      {
          if (b == 0)
          return a;
        return gcdLong(b, a % b);
      }
      
      static void swap(int i, int j)
      {
          int temp = i;
          i = j;
          j = temp;
      }
  	
  	static int countDigit(int n)
      {
          return (int)Math.floor(Math.log10(n) + 1);
      }
  	
  }
  
  class Pair
  {
      int first , second;
      Pair(int first , int second)
      {
          this.first = first;
          this.second = second;
      }
  }