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.io.*;
  import java.util.*;
  
  
  public class Practice
  {
  //	static final long mod=7420738134811L;
  	static int mod=998244353;
  	static final int size=501;
  	static FastReader sc=new FastReader(System.in);
  //	static Reader sc=new Reader();
  	static  PrintWriter out=new PrintWriter(System.out);
  	static long[] factorialNumInverse;
  	static long[] naturalNumInverse;	
  	static int[] sp;
  	static long[] fact;
  	static ArrayList<Integer> pr;
  	public static void main(String[] args) throws IOException
  	{
  //		System.setIn(new FileInputStream("input.txt"));
  //		System.setOut(new PrintStream("output.txt"));
  //		factorial(mod);
  //		InverseofNumber(mod);
  //		InverseofFactorial(mod);
  //		make_seive();
  		int t=1;
  		t=sc.nextInt();
  		while(t-->0)
  			solve();
  		out.close();
  		out.flush();
  	}
  	static void solve() throws IOException
  	{
  		int n=sc.nextInt();
  		int arr[]=new int[n];
  		for(int i=0;i<n;i++)
  			arr[i]=sc.nextInt();
  		if(n%2==0)
  		{
  			out.println("YES");
  			return;
  		}
  		boolean f=false;
  		for(int i=1;i<n && !f;i++)
  			if(arr[i-1]>=arr[i])
  				f=true;
  		if(f)
  			out.println("YES");
  		else
  			out.println("NO");
  	}
  	static class Pair implements Cloneable, Comparable<Pair>
  	{
  		int x,y;
  		Pair(int a,int b)
  		{
  			this.x=a;
  			this.y=b;
  		}
  		@Override
  		public boolean equals(Object obj) 
  		{
  			if(obj instanceof  Pair)
  			{
  				Pair p=(Pair)obj;
  				return p.x==this.x && p.y==this.y;
  			}
  			return false;
  		}
  		@Override
  		public int hashCode() 
  		{
  			return Math.abs(x)+101*Math.abs(y);
  		}
  		@Override
  		public String toString() 
  		{
  			return "("+x+" "+y+")";
  		}
  		@Override
  		protected Pair clone() throws CloneNotSupportedException {
  			return new Pair(this.x,this.y);
  		}
  		@Override
  		public int compareTo(Pair a) 
  		{
  			int t= this.x-a.x;
  			if(t!=0)
  				return t;
  			else
  				return this.y-a.y;
  		}
  		public void swap()
  		{
  			this.y=this.y+this.x;
  			this.x=this.y-this.x;
  			this.y=this.y-this.x;			
  		}
  	}
  	static class Tuple implements Cloneable, Comparable<Tuple>
  	{
  		int x,y,z;
  		Tuple(int a,int b,int c)
  		{
  			this.x=a;
  			this.y=b;
  			this.z=c;
  		}
  		public boolean equals(Object obj) 
  		{
  			if(obj instanceof  Tuple)
  			{
  				Tuple p=(Tuple)obj;
  				return p.x==this.x && p.y==this.y && p.z==this.z;
  			}
  			return false;
  		}
  		@Override
  		public String toString() 
  		{
  			return "("+x+","+y+","+z+")";
  		}
  		@Override
  		protected Tuple clone() throws CloneNotSupportedException {
  			return new Tuple(this.x,this.y,this.z);
  		}
  		@Override
  		public int compareTo(Tuple a) 
  		{
  			int x=this.x-a.x;
  			if(x!=0)
  				return x;
  			return this.y-a.y;
  		}
  	}
  	static void arraySort(int arr[])
  	{
  		ArrayList<Integer> a=new ArrayList<Integer>();
  		for (int i = 0; i < arr.length; i++) {
  			a.add(arr[i]);
  		}
  		Collections.sort(a);
  		for (int i = 0; i < arr.length; i++) {
  			arr[i]=a.get(i);
  		}
  	}
  	static void arraySort(long arr[])
  	{
  		ArrayList<Long> a=new ArrayList<Long>();
  		for (int i = 0; i < arr.length; i++) {
  			a.add(arr[i]);
  		}
  		Collections.sort(a);
  		for (int i = 0; i < arr.length; i++) {
  			arr[i]=a.get(i);
  		}
  	}
  	static HashSet<Integer> primeFactors(int n)
  	{
  		HashSet<Integer> ans=new HashSet<Integer>();
  		if(n%2==0)
  		{
  			ans.add(2);
  			while((n&1)==0)
  				n=n>>1;
  		}
  		for(int i=3;i*i<=n;i+=2)
  		{
  			if(n%i==0)
  			{
  				ans.add(i);
  				while(n%i==0)
  					n=n/i;
  			}
  		}
  		if(n!=1)
  			ans.add(n);
  		return ans;
  	}
  	static void make_seive()
  	{
  		sp=new int[size];
  		pr=new ArrayList<Integer>();
  		for (int i=2; i<size; ++i) {
  		    if (sp[i] == 0) {
  		        sp[i] = i;
  		        pr.add(i);
  		    }
  		    for (int j=0; j<(int)pr.size() && pr.get(j)<=sp[i] && i*pr.get(j)<size; ++j)
  		        sp[i * pr.get(j)] = pr.get(j);
  		}
  	}
  	public static void InverseofNumber(int p)
  	{
  		naturalNumInverse=new long[size];
  	    naturalNumInverse[0] = naturalNumInverse[1] = 1;
  	    for(int i = 2; i < size; i++)
  	        naturalNumInverse[i] = naturalNumInverse[p % i] * (long)(p - p / i) % p;
  	}
  	// Function to precompute inverse of factorials
  	public static void InverseofFactorial(int p)
  	{
  		factorialNumInverse=new long[size];
  	    factorialNumInverse[0] = factorialNumInverse[1] = 1;
  	    // pre-compute inverse of natural numbers
  	    for(int i = 2; i < size; i++)
  	        factorialNumInverse[i] = (naturalNumInverse[i] * factorialNumInverse[i - 1]) % p;
  	}
  	// Function to calculate factorial of 1 to 200001
  	public static void factorial(int p)
  	{
  		fact=new long[size];
  	    fact[0] = 1;
  	    for(int i = 1; i < size; i++)
  	        fact[i] = (fact[i - 1] * (long)i) % p;
  	}
  	 
  	// Function to return nCr % p in O(1) time
  	public static long Binomial(int N, int R)
  	{
  		if(R<0)
  			return 1;
  	    // n C r = n!*inverse(r!)*inverse((n-r)!)
  	    long ans = ((fact[N] * factorialNumInverse[R]) % mod * factorialNumInverse[N - R]) % mod;
  	    return ans;
  	}
  	static int findXOR(int x)	//from 0 to x
  	{
  		if(x<0)
  			return 0;
  		if(x%4==0)
  			return x;
  		if(x%4==1)
  			return 1;
  		if(x%4==2)
  			return x+1;
  		return 0;
  	}
  	static boolean isPrime(long x)
  	{
  		if(x==1)
  			return false;
  		if(x<=3)
  			return true;
  		if(x%2==0 || x%3==0)
  			return false;
  		for(int i=5;i<=Math.sqrt(x);i+=2)
  			if(x%i==0)
  				return false;
  		return true;
  	}
  	static long gcd(long a,long b)
  	{
  		return (b==0)?a:gcd(b,a%b);
  	}
  	static int gcd(int a,int b)
  	{
  		return (b==0)?a:gcd(b,a%b);
  	}
  	static class Node
  	{
  		int vertex,dis=0;
  		HashSet<Node> adj;
  		Node par;
  		Node(int ver)
  		{
  			vertex=ver;
  			dis=Integer.MAX_VALUE;
  			adj=new HashSet<Node>();
  			par=null;
  		}
  		@Override
  		public String toString() 
  		{
  			return vertex+" ";
  		}
  	}
  	static class Edge
  	{
  		Node to;
  		int cost;
  		Edge(Node t,int c)
  		{
  			this.to=t;
  			this.cost=c;
  		}
  		@Override
  		public String toString() {
  			return "("+to.vertex+","+cost+") ";
  		}
  	}
  	static long power(long x, long y)
  	  {
  		if(x<=0)
  			return 1;
  	    long res = 1; 
  	    x = x % mod; 
  	    if (x == 0)
  	      return 0; 
  	    while (y > 0)
  	    {
  	    	if ((y & 1) != 0)
  	    		res = (res * x) % mod;
  	    	
  	    	y = y >> 1; // y = y/2
  	    	x = (x * x) % mod;
  	    }
  	    return res;
  	  }
  	static long binomialCoeff(long n, long k)
      {
  		if(n<k)
  			return 0;
          long res = 1;
  //        if(k>n)
  //        	return 0;
          // Since C(n, k) = C(n, n-k)
          if (k > n - k)
              k = n - k;
   
          // Calculate value of
          // [n * (n-1) *---* (n-k+1)] / [k * (k-1) *----* 1]
          for (long i = 0; i < k; ++i) {
              res *= (n - i);
              res /= (i + 1);
          }
   
          return res;
      }
  	static class FastReader
  	{
          byte[] buf = new byte[2048];
          int index, total;
          InputStream in;
   
          FastReader(InputStream is) 
          {
              in = is;
          }
   
          int scan() throws IOException 
          {
              if (index >= total) {
                  index = 0;
                  total = in.read(buf);
                  if (total <= 0) {
                      return -1;
                  }
              }
              return buf[index++];
          }
   
          String next() throws IOException 
          {
              int c;
              for (c = scan(); c <= 32; c = scan());
              StringBuilder sb = new StringBuilder();
              for (; c > 32; c = scan()) {
                  sb.append((char) c);
              }
              return sb.toString();
          }
   
          int nextInt() throws IOException 
          {
              int c, val = 0;
              for (c = scan(); c <= 32; c = scan());
              boolean neg = c == '-';
              if (c == '-' || c == '+') {
                  c = scan();
              }
              for (; c >= '0' && c <= '9'; c = scan()) {
                  val = (val << 3) + (val << 1) + (c & 15);
              }
              return neg ? -val : val;
          }
   
          long nextLong() throws IOException 
          {
              int c;
              long val = 0;
              for (c = scan(); c <= 32; c = scan());
              boolean neg = c == '-';
              if (c == '-' || c == '+') {
                  c = scan();
              }
              for (; c >= '0' && c <= '9'; c = scan()) {
                  val = (val << 3) + (val << 1) + (c & 15);
              }
              return neg ? -val : val;
          }
      }
  	static class Reader 
  	{
          final private int BUFFER_SIZE = 1 << 16;
          private DataInputStream din;
          private byte[] buffer;
          private int bufferPointer, bytesRead;
   
          public Reader()
          {
              din = new DataInputStream(System.in);
              buffer = new byte[BUFFER_SIZE];
              bufferPointer = bytesRead = 0;
          }
   
          public Reader(String file_name) throws IOException
          {
              din = new DataInputStream(
                  new FileInputStream(file_name));
              buffer = new byte[BUFFER_SIZE];
              bufferPointer = bytesRead = 0;
          }
   
          public String readLine() throws IOException
          {
              byte[] buf = new byte[64]; // line length
              int cnt = 0, c;
              while ((c = read()) != -1) {
                  if (c == '\n') {
                      if (cnt != 0) {
                          break;
                      }
                      else {
                          continue;
                      }
                  }
                  buf[cnt++] = (byte)c;
              }
              return new String(buf, 0, cnt);
          }
   
          public int nextInt() throws IOException
          {
              int ret = 0;
              byte c = read();
              while (c <= ' ') {
                  c = read();
              }
              boolean neg = (c == '-');
              if (neg)
                  c = read();
              do {
                  ret = ret * 10 + c - '0';
              } while ((c = read()) >= '0' && c <= '9');
   
              if (neg)
                  return -ret;
              return ret;
          }
   
          public long nextLong() throws IOException
          {
              long ret = 0;
              byte c = read();
              while (c <= ' ')
                  c = read();
              boolean neg = (c == '-');
              if (neg)
                  c = read();
              do {
                  ret = ret * 10 + c - '0';
              } while ((c = read()) >= '0' && c <= '9');
              if (neg)
                  return -ret;
              return ret;
          }
   
          public double nextDouble() throws IOException
          {
              double ret = 0, div = 1;
              byte c = read();
              while (c <= ' ')
                  c = read();
              boolean neg = (c == '-');
              if (neg)
                  c = read();
   
              do {
                  ret = ret * 10 + c - '0';
              } while ((c = read()) >= '0' && c <= '9');
   
              if (c == '.') {
                  while ((c = read()) >= '0' && c <= '9') {
                      ret += (c - '0') / (div *= 10);
                  }
              }
   
              if (neg)
                  return -ret;
              return ret;
          }
   
          private void fillBuffer() throws IOException
          {
              bytesRead = din.read(buffer, bufferPointer = 0,
                                   BUFFER_SIZE);
              if (bytesRead == -1)
                  buffer[0] = -1;
          }
   
          private byte read() throws IOException
          {
              if (bufferPointer == bytesRead)
                  fillBuffer();
              return buffer[bufferPointer++];
          }
   
          public void close() throws IOException
          {
              if (din == null)
                  return;
              din.close();
          }
          public void printarray(int arr[])
          {
          	for (int i = 0; i < arr.length; i++)
  				System.out.print(arr[i]+" ");
          	System.out.println();
          }
      }
  }
  
  
  
  
  
  
  
  