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.io.*;
  // import java.lang.*;
  // import java.math.*;
  
  public class Codeforces {
      static FastReader sc=new FastReader();
  	static PrintWriter out=new PrintWriter(System.out);
  	static long mod=1000000007;
  	// static long mod=998244353;
  	static int MAX=Integer.MAX_VALUE;
  	static int MIN=Integer.MIN_VALUE;
  	static long MAXL=Long.MAX_VALUE;
  	static long MINL=Long.MIN_VALUE;
  	static ArrayList<Integer> graph[];
  	static long fact[];
  	static StringBuffer sb;
  	public static void main (String[] args) throws java.lang.Exception
  	{
  		// code goes here
  		int t=I();
  		outer:while(t-->0)
  		{
  			int n=I();
  			int a[]=new int[n];
  			for(int i=0;i<n;i++){
  				a[i]=I();
  			}
  			if(n%2==0){
  				out.println("YES");
  			}else{
  				int q=0;
  				for(int i=1;i<n;i++){
  					if(a[i]<=a[i-1]){
  						q=1;
  						break;
  					}
  				}
  				if(q==1)out.println("YES");
  				else out.println("NO");
  			}
  		}
  		out.close();
  	}
  	public static class pair
      {
      	long a;
      	long b;
      	public pair(long val,long index)
      	{
      	    a=val;
      	    b=index;
      	}
      }
  	public static class myComp implements Comparator<pair>
  	{
  		//sort in ascending order.
  		// public int compare(pair p1,pair p2)
  		// {
  		// 	if(p1.a==p2.a)
      	//     return 0;
      	//     else if(p1.a<p2.a)
      	//     return -1;
      	//     else
      	//     return 1;
  		// }
  		//sort in descending order.
  		public int compare(pair p1,pair p2)
      	{
      	    if(p1.a==p2.a)
      	    return 0;
      	    else if(p1.a<p2.a)
      	    return 1;
      	    else
      	    return -1;
      	}
  	}
  	public static long nPr(int n,int r)
  	{
  		long ans=divide(fact(n),fact(n-r),mod);
  		return ans;
  	}
  	public static long nCr(int n,int r)
  	{
  		long ans=divide(fact[n],mul(fact[n-r],fact[r]),mod);
  		return ans;
  	}
  	public static long kadane(long a[],int n)  //largest sum subarray
  	{
  		long max_sum=Long.MIN_VALUE,max_end=0;
  		for(int i=0;i<n;i++){
  			max_end+=a[i];
  			if(max_sum<max_end){max_sum=max_end;}
  			if(max_end<0){max_end=0;}
  		}
  		return max_sum;
  	}
  	public static void DFS(int s,boolean visited[])
  	{
  		visited[s]=true;
  		for(int i:graph[s]){
  			if(!visited[i]){
  				DFS(i,visited);
  			}
  		}
  	}
  	public static void setGraph(int n,int m)
  	{
  		graph=new ArrayList[n+1];
  		for(int i=0;i<=n;i++){
  			graph[i]=new ArrayList<>();
  		}
  		for(int i=0;i<m;i++){
  			int u=I(),v=I();
  			graph[u].add(v);
  			graph[v].add(u);
  		}
  	}
  	public static int BS(long a[],long x,int ii,int jj)
  	{
  		// int n=a.length;
  		int mid=0;
  		int i=ii,j=jj;
  		while(i<=j)
  		{
  			mid=(i+j)/2;
  			if(a[mid]<x){
  				i=mid+1;
  			}else if(a[mid]>x){
  				j=mid-1;
  			}else{
  				return mid;
  			}
  		}
  		return -1;
  	}
  
  	//LOWER_BOUND and UPPER_BOUND functions
  
  	public static int lower_bound(long arr[],int start, int end, long X)   //start=0,end=n-1
  	{
  		if(arr[arr.length-1]<X)return end;
  		if(arr[0]>X)return -1;
  		int left=start,right=end;
  		while(left<right){
  			int mid=(left+right)/2;
  			if(arr[mid]==X){                                      //Returns last index of lower bound value.
  				if(mid<end && arr[mid+1]==X){
  					left=mid+1;
  				}else{
  					return mid;
  				}
  			}
  			// if(arr[mid]==X){                                   //Returns first index of lower bound value.
  			// 	if(mid>start && arr[mid-1]==X){
  			// 		right=mid-1;
  			// 	}else{
  			// 		return mid;
  			// 	}
  			// }
  			else if(arr[mid]>X){
  				if(mid>start && arr[mid-1]<X){
  					return mid-1;
  				}else{
  					right=mid-1;
  				}
  			}else{
  				if(mid<end && arr[mid+1]>X){
  					return mid;
  				}else{
  					left=mid+1;
  				}
  			}
  		}
  		return left;
  	}
  	public static int upper_bound(long arr[],int start,int end,long X)			//start=0,end=n-1
  	{
  		if(arr[0]>=X)return start;
  		if(arr[arr.length-1]<X)return -1;
  		int left=start,right=end;
  		while(left<right){
  			int mid=(left+right)/2;
  			if(arr[mid]==X){                                   //returns first index of upper bound value.
  				if(mid>start && arr[mid-1]==X){
  					right=mid-1;
  				}else{
  					return mid;
  				}
  			}
  			// if(arr[mid]==X){									//returns last index of upper bound value.
  			// 	if(mid<end && arr[mid+1]==X){
  			// 		left=mid+1;
  			// 	}else{
  			// 		return mid;
  			// 	}
  			// }
  			else if(arr[mid]>X){
  				if(mid>start && arr[mid-1]<X){
  					return mid;
  				}else{
  					right=mid-1;
  				}
  			}else{
  				if(mid<end && arr[mid+1]>X){
  					return mid+1;
  				}else{
  					left=mid+1;
  				}
  			}
  		}
  		return left;
  	}
  
  	//END
  
  	public static boolean isSorted(int a[])
  	{
  		int n=a.length;
  		for(int i=0;i<n-1;i++){
  			if(a[i]>a[i+1])return false;
  		}
  		return true;
  	}
  	public static boolean isSorted(long a[])
  	{
  		int n=a.length;
  		for(int i=0;i<n-1;i++){
  			if(a[i]>a[i+1])return false;
  		}
  		return true;
  	}
  	public static int computeXOR(int n) //compute XOR of all numbers between 1 to n.
      {
          if (n % 4 == 0)
              return n;
          if (n % 4 == 1)
              return 1;
          if (n % 4 == 2)
              return n + 1;
          return 0;
      }
  	public static ArrayList<Integer> primeSieve(int n)
  	{
  	    ArrayList<Integer> arr=new ArrayList<>();
  	    boolean prime[] = new boolean[n + 1];
          for (int i = 0; i <= n; i++)
          prime[i] = true;
          for (int p = 2; p * p <= n; p++)
          {
              if (prime[p] == true)
              {
                  for (int i = p * p; i <= n; i += p)
                  prime[i] = false;
              }
          }
          for (int i = 2; i <= n; i++)
          {
              if (prime[i] == true)
              arr.add(i);
          }
          return arr;
  	}
  
  	// Fenwick / BinaryIndexed  Tree  USE IT - FenwickTree ft1=new FenwickTree(n);
  	public static class FenwickTree
  	{
  		int farr[];
  		int n;
  		public FenwickTree(int c)
  		{
  			n=c+1;
  			farr=new int[n];
  		}
  		// public void update_range(int l,int r,long p)
  		// {
  		// 	update(l,p);
  		// 	update(r+1,(-1)*p);
  		// }
  		public void update(int x,int p)
  		{
  			for(;x<n;x+=x&(-x))
  			{
  				farr[x]+=p;
  			}
  		}
  		public long get(int x)
  		{
  			long ans=0;
  			for(;x>0;x-=x&(-x))
  			{
  				ans=ans+farr[x];
  			}
  			return ans;
  		}
  	}
  	//Disjoint Set Union
  	public static class DSU
  	{
  	    int par[],rank[];
  	    public DSU(int c)
  	    {
  	        par=new int[c+1];
  	        rank=new int[c+1];
  	        for(int i=0;i<=c;i++)
  	        {
  	            par[i]=i;
  	            rank[i]=0;
  	        }
  	    }
  	    public int find(int a)
  	    {
  	        if(a==par[a])
  	        return a;
  	        return par[a]=find(par[a]);
  	    }
  	    public void union(int a,int b)
  	    {
  	        int a_rep=find(a),b_rep=find(b);
  	        if(a_rep==b_rep)
  	        return;
  	        if(rank[a_rep]<rank[b_rep])
  	        par[a_rep]=b_rep;
  	        else if(rank[a_rep]>rank[b_rep])
  	        par[b_rep]=a_rep;
  	        else
  	        {
  	            par[b_rep]=a_rep;
  	            rank[a_rep]++;
  	        }
  	    }
  	}
  	
      public static class myComp1 implements Comparator<pair1>
      {
  		//sort in ascending order.
      	public int compare(pair1 p1,pair1 p2)
      	{
      	    if(p1.a==p2.a)
      	    return 0;
      	    else if(p1.a<p2.a)
      	    return -1;
      	    else
      	    return 1;
      	}
  		//sort in descending order.
  		// public int compare(pair p1,pair p2)
      	// {
      	//     if(p1.a==p2.a)
      	//     return 0;
      	//     else if(p1.a<p2.a)
      	//     return 1;
      	//     else
      	//     return -1;
      	// }
      }
  	public static class pair1
      {
      	long a;
      	long b;
      	public pair1(long val,long index)
      	{
      	    a=val;
      	    b=index;
      	}
      }
      public static ArrayList<pair1> mergeIntervals(ArrayList<pair1> arr)
  	{
  	    //****************use this in main function-Collections.sort(arr,new myComp1());
  	    ArrayList<pair1> a1=new ArrayList<>();
  	    if(arr.size()<=1)
  	    return arr;
  	    a1.add(arr.get(0));
  	    int i=1,j=0;
  	    while(i<arr.size())
  	    {
  	        if(a1.get(j).b<arr.get(i).a)
  	        {
  	           a1.add(arr.get(i));
  	           i++;
  	           j++;
  	        }
  	        else if(a1.get(j).b>arr.get(i).a && a1.get(j).b>=arr.get(i).b)
  	        {
  	            i++;
  	        }
  	        else if(a1.get(j).b>=arr.get(i).a)
  	        {
  	            long a=a1.get(j).a;
  	            long b=arr.get(i).b;
  	            a1.remove(j);
  	            a1.add(new pair1(a,b));
  	            i++;
  	        }
  	    }
  	    return a1;
  	}
  	public static ArrayList<Long> primeFact(long a)
  	{
  	    ArrayList<Long> arr=new ArrayList<>();
  	    while(a%2==0){
  	        arr.add(2L);
  	        a=a/2;
  	    }
  	    for(long i=3;i*i<=a;i+=2){
  	        while(a%i==0){
  	            arr.add(i);
  	            a=a/i;
  	        }
  	    }
  	    if(a>2)arr.add(a);
  	    return arr;
  	}
  	public static boolean isInteger(double N)
  	{
  		int X = (int)N;
  		double temp2 = N - X;
  		if (temp2 > 0)
  		{
  			return false;
  		}
  		return true;
  	}
  	public static boolean isPalindrome(String s,int n)
  	{
  		for(int i=0;i<=n/2;i++){
  			if(s.charAt(i)!=s.charAt(n-i-1)){
  				return false;
  			}
  		}
  		return true;
  	}
  	public static int gcd(int a,int b)
  	{
  	    if(b==0)
  	    return a;
  	    else
  	    return gcd(b,a%b);
  	}
  	public static long gcd(long a,long b)
  	{
  	    if(b==0)
  	    return a;
  	    else
  	    return gcd(b,a%b);
  	}
  	public static long fact(long n)
  	{
  		long fact=1;
  		for(long i=2;i<=n;i++){
  			fact=((fact%mod)*(i%mod))%mod;
  		}
  		return fact;
  	}
  	public static long fact(int n)
  	{
  		long fact=1;
  		for(int i=2;i<=n;i++){
  			fact=((fact%mod)*(i%mod))%mod;
  		}
  		return fact;
  	} 
  	public static boolean isPrime(int n) 
  	{ 
  	    if (n <= 1) 
  	        return false; 
  	    if (n <= 3) 
  	        return true; 
  	    if (n % 2 == 0 || n % 3 == 0) 
  	        return false; 
  	    double sq=Math.sqrt(n);
  	  
  	    for (int i = 5; i <= sq; i = i + 6) 
  	        if (n % i == 0 || n % (i + 2) == 0) 
  	            return false; 
  	    return true; 
  	} 
      public static boolean isPrime(long n) 
  	{ 
  	    if (n <= 1) 
  	        return false; 
  	    if (n <= 3) 
  	        return true; 
  	    if (n % 2 == 0 || n % 3 == 0) 
  	        return false; 
  	    double sq=Math.sqrt(n);
  	
  	    for (int i = 5; i <= sq; i = i + 6) 
  	        if (n % i == 0 || n % (i + 2) == 0) 
  	            return false; 
  	    return true; 
  	}
  	public static void printArray(long a[])
  	{
  		for(int i=0;i<a.length;i++){
  			out.print(a[i]+" ");
  		}
  		out.println();
  	}
  	public static void printArray(int a[])
  	{
  		for(int i=0;i<a.length;i++){
  			out.print(a[i]+" ");
  		}
  		out.println();
  	}
  	public static void printArray(char a[])
  	{
  		for(int i=0;i<a.length;i++){
  			out.print(a[i]);
  		}
  		out.println();
  	}
  	public static void printArray(String a[])
  	{
  		for(int i=0;i<a.length;i++){
  			out.print(a[i]+" ");
  		}
  		out.println();
  	}
  	public static void printArray(boolean a[])
  	{
  		for(int i=0;i<a.length;i++){
  			out.print(a[i]+" ");
  		}
  		out.println();
  	}
  	public static void printArray(pair a[])
  	{
  		for(pair p:a){
  			out.println(p.a+"->"+p.b);
  		}
  	}
  	public static void printArray(int a[][])
  	{
  		for(int i=0;i<a.length;i++){
  			for(int j=0;j<a[i].length;j++){
  				out.print(a[i][j]+" ");
  			}out.println();
  		}
  	}
  	public static void printArray(long a[][])
  	{
  		for(int i=0;i<a.length;i++){
  			for(int j=0;j<a[i].length;j++){
  				out.print(a[i][j]+" ");
  			}out.println();
  		}
  	}
  	public static void printArray(char a[][])
  	{
  		for(int i=0;i<a.length;i++){
  			for(int j=0;j<a[i].length;j++){
  				out.print(a[i][j]+" ");
  			}out.println();
  		}
  	}
  	public static void printArrayL(ArrayList<Long> arr)
  	{
  		for(int i=0;i<arr.size();i++){
  			out.print(arr.get(i)+" ");
  		}
  		out.println();
  	}
  	public static void printArrayI(ArrayList<Integer> arr)
  	{
  		for(int i=0;i<arr.size();i++){
  			out.print(arr.get(i)+" ");
  		}
  		out.println();
  	}
  	public static void printArrayS(ArrayList<String> arr)
  	{
  		for(int i=0;i<arr.size();i++){
  			out.print(arr.get(i)+" ");
  		}
  		out.println();
  	}
  	public static void printMapInt(HashMap<Integer,Integer> hm){
  		for(Map.Entry<Integer,Integer> e:hm.entrySet()){
  			out.println(e.getKey()+"->"+e.getValue());
  		}out.println();
  	}
  	public static void printMapLong(HashMap<Long,Long> hm){
  		for(Map.Entry<Long,Long> e:hm.entrySet()){
  			out.println(e.getKey()+"->"+e.getValue());
  		}out.println();
  	}
  
  	//Modular Arithmetic
  
  	public static long add(long a,long b)
  	{
  		a+=b;
  		if(a>=mod)a-=mod;
  		return a;
  	}
  	public static long sub(long a,long b)
  	{
  		a-=b;
  		if(a<0)a+=mod;
  		return a;
  	}
  	public static long mul(long a,long b)
  	{
  		return ((a%mod)*(b%mod))%mod;
  	}
  	public static long divide(long a,long b,long m)
  	{
  		a=mul(a,modInverse(b,m));
  		return a;
  	}
  	public static long modInverse(long a,long m)
  	{
  		int x=0,y=0;
  		own p=new own(x,y);
  		long g=gcdExt(a,m,p);
  		if(g!=1){
  			out.println("inverse does not exists");
  			return -1;
  		}else{
  			long res=((p.a%m)+m)%m;
  			return res;
  		}
  	}
  	public static long gcdExt(long a,long b,own p)
  	{
  		if(b==0){
  			p.a=1;
  			p.b=0;
  			return a;
  		}
  		int x1=0,y1=0;
  		own p1=new own(x1,y1);
  		long gcd=gcdExt(b,a%b,p1);
  		p.b=p1.a - (a/b) * p1.b;
  		p.a=p1.b;
  		return gcd;
  	}
  	public static long pwr(long m,long n)
  	{
  		long res=1;
  		if(m==0)
  		return 0;
  		while(n>0)
  		{
  			if((n&1)!=0)
  			{
  				res=(res*m);
  			}
  			n=n>>1;
  			m=(m*m);
  		}
  		return res;
  	}
  	public static long modpwr(long m,long n)
  	{
  		long res=1;
  		m=m%mod;
  		if(m==0)
  		return 0;
  		while(n>0)
  		{
  			if((n&1)!=0)
  			{
  				res=(res*m)%mod;
  			}
  			n=n>>1;
  			m=(m*m)%mod;
  		}
  		return res;
  	}
  	public static class own
      {
      	long a;
      	long b;
      	public own(long val,long index)
      	{
      	    a=val;
      	    b=index;
      	}
      }
  
  	//Modular Airthmetic
  
  	public static void sort(int[] A)
  	{
          int n = A.length;
          Random rnd = new Random();
          for(int i=0; i<n; ++i)
  		{
              int tmp = A[i];
              int randomPos = i + rnd.nextInt(n-i);
              A[i] = A[randomPos];
              A[randomPos] = tmp;
          }
          Arrays.sort(A);
      }
  	public static void sort(char[] A)
  	{
          int n = A.length;
          Random rnd = new Random();
          for(int i=0; i<n; ++i)
  		{
              char tmp = A[i];
              int randomPos = i + rnd.nextInt(n-i);
              A[i] = A[randomPos];
              A[randomPos] = tmp;
          }
          Arrays.sort(A);
      }
      public static void sort(long[] A)
  	{
  	    int n = A.length;
          Random rnd = new Random();
          for(int i=0; i<n; ++i)
  		{
              long tmp = A[i];
              int randomPos = i + rnd.nextInt(n-i);
              A[i] = A[randomPos];
              A[randomPos] = tmp;
          }
  	    Arrays.sort(A);
  	}
  	public static int I(){return sc.I();}
      public static long L(){return sc.L();}
      public static String S(){return sc.S();}
      public static double D(){return sc.D();}
  }
  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 I(){ 
          return Integer.parseInt(next());
      }
      long L(){ 
          return Long.parseLong(next());
      }
      double D(){
           return Double.parseDouble(next());
      }
      String S(){
          String str = "";
          try 
          {
              str = br.readLine();
          }
          catch (IOException e)
          {
              e.printStackTrace();
          }
          return str;
      }
  }
  