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.*;
  
  
  import java.math.*;
  import java.math.BigInteger;
  
  
  public final class A
  {    
  	static PrintWriter out = new PrintWriter(System.out); 
  	static StringBuilder ans=new StringBuilder();
  	static FastReader in=new FastReader();
  	static ArrayList<Integer> g[];
  	static long mod=(long)998244353,INF=Long.MAX_VALUE;
  	static boolean set[]; 
  	static int par[],partial[];
  	static int Days[],P[][];
  	static int dp[][],sum=0,size[],D[];
  	static int seg[],col[];
  	static ArrayList<Long> A;
  	//	static HashSet<Integer> visited,imposters;
  	//	static HashSet<Integer> set;
  	//	static node1 seg[];
  	//static pair moves[]= {new pair(-1,0),new pair(1,0), new pair(0,-1), new pair(0,1)};
  	public static void main(String args[])throws IOException
  	{	
  		/*
  		 * star,rope
  		 */
  		int T=i();
  		outer:while(T-->0)
  		{
  			int N=i();
  			long A[]=inputLong(N);
  			boolean f=true;
  			if(N%2==0)
  			{
  				ans.append("YES\n");
  				continue outer;
  			}
  			for(int i=0; i<N-1; i++)
  			{
  				if(A[i]>=A[i+1])
  				{
  					f=false;
  					break;
  				}
  			}
  			if(f)ans.append("NO\n");//strict inc
  			else ans.append("YES\n");
  		}
  		out.println(ans);
  		out.close();
  	}
  	static long f(long a,long A[])
  	{
  		int l=-1,r=A.length;
  		while(r-l>1)
  		{
  			int m=(l+r)/2;
  			if(A[m]<=a)l=m;
  			else r=m;
  		}
  		return A[l];
  	}
  	static void build(int v,int tl,int tr,int A[])
  	{
  		if(tl==tr)
  		{
  			seg[v]=A[tl];
  			return;
  		}
  		int tm=(tl+tr)/2;
  		build(v*2,tl,tm,A);
  		build(v*2+1,tm+1,tr,A);
  		seg[v]=Math.min(seg[v*2], seg[v*2+1]);
  	}
  	static void update(int v,int tl,int tr,int index,int x)
  	{
  		if(tl==tr && tl==index)
  		{
  			seg[v]=x;
  			return;
  		}		
  		int tm=(tl+tr)/2;
  		if(index<=tm)update(v*2,tl,tm,index,x);
  		else update(v*2+1,tm+1,tr,index,x);
  		seg[v]=Math.min(seg[v*2], seg[v*2+1]);
  	}
  	static int ask(int v,int tl,int tr,int l,int r)
  	{
  		//		System.out.println(v);
  		//		if(v>100)return 0;
  		if(l>r)return Integer.MAX_VALUE;
  		if(tl==l && tr==r)return seg[v];
  		int tm=(tl+tr)/2;
  		int a=ask(v*2,tl,tm,l,Math.min(tm, r));
  		//		System.out.println("for--> "+(v)+" tm--> "+(tm+1)+" tr--> "+tr+" l--> "+Math.max(l, tm+1)+" r--> "+r);
  		int b=ask(v*2+1,tm+1,tr,Math.max(l, tm+1),r);
  		return Math.min(a, b);
  	}
  	static int find(int a)
  	{
  		if(par[a]<0)return a;
  		return par[a]=find(par[a]);
  	}
  	static void union(int a,int b)
  	{
  		a=find(a);
  		b=find(b);
  		if(a!=b)
  		{
  			par[a]+=par[b];
  			par[b]=a;
  		}
  	}
  	static int ask(int a,int b)
  	{
  		System.out.println("? "+a+" "+b);
  		return i();
  	}
  
  
  
  
  	static long and(int i,int j)
  	{
  		System.out.println("and "+i+" "+j);
  		return l();
  	}
  	static long or(int i,int j)
  	{
  		System.out.println("or "+i+" "+j);
  		return l();
  	}
  	static boolean is_Sorted(int A[])
  	{
  		int N=A.length;
  		for(int i=1; i<=N; i++)if(A[i-1]!=i)return false;
  		return true;
  	}
  	static boolean f(StringBuilder sb,String Y,String order)
  	{
  		StringBuilder res=new StringBuilder(sb.toString());
  		HashSet<Character> set=new HashSet<>();
  		for(char ch:order.toCharArray())
  		{
  			set.add(ch);
  			for(int i=0; i<sb.length(); i++)
  			{
  				char x=sb.charAt(i);
  				if(set.contains(x))continue;
  				res.append(x);
  			}
  		}
  
  		String str=res.toString();
  		return str.equals(Y);
  	}
  	static boolean all_Zero(int f[])
  	{
  		for(int a:f)if(a!=0)return false;
  		return true;
  	}
  	static long form(int a,int l)
  	{
  		long x=0;
  		while(l-->0)
  		{
  			x*=10;
  			x+=a;
  		}
  		return x;
  	}
  	static int count(String X)
  	{
  		HashSet<Integer> set=new HashSet<>();
  		for(char x:X.toCharArray())set.add(x-'0');
  		return set.size();
  	}
  
  
  	//	static void build(int v,int tl,int tr,long A[])
  	//	{
  	//		if(tl==tr)
  	//		{
  	//			seg[v]=A[tl];
  	//		}
  	//		else
  	//		{
  	//			int tm=(tl+tr)/2;
  	//			build(v*2,tl,tm,A);
  	//			build(v*2+1,tm+1,tr,A);
  	//			seg[v]=Math.min(seg[v*2], seg[v*2+1]);
  	//		}
  	//	}
  
  	static int [] sub(int A[],int B[])
  	{
  		int N=A.length;
  		int f[]=new int[N];
  		for(int i=N-1; i>=0; i--)
  		{
  			if(B[i]<A[i])
  			{
  				B[i]+=26;
  				B[i-1]-=1;
  			}
  			f[i]=B[i]-A[i];
  		}
  		for(int i=0; i<N; i++)
  		{
  			if(f[i]%2!=0)f[i+1]+=26;
  			f[i]/=2;
  		}
  		return f;
  	}
  
  
  
  
  
  	static int max(int a ,int b,int c,int d)
  	{
  		a=Math.max(a, b);
  		c=Math.max(c,d);
  		return Math.max(a, c);
  	}
  	static int min(int a ,int b,int c,int d)
  	{
  		a=Math.min(a, b);
  		c=Math.min(c,d);
  		return Math.min(a, c);
  	}
  
  
  
  	static HashMap<Integer,Integer> Hash(int A[])
  	{
  		HashMap<Integer,Integer> mp=new HashMap<>();
  		for(int a:A)
  		{
  			int f=mp.getOrDefault(a,0)+1;
  			mp.put(a, f);
  		}
  		return mp;
  	}
  	static long mul(long a, long b)
  	{
  		return ( a %mod * 1L * b%mod )%mod;
  	}
  	static void swap(int A[],int a,int b)
  	{
  		int t=A[a];
  		A[a]=A[b];
  		A[b]=t;
  	}
  
  
  
  	static boolean isSorted(int A[])
  	{
  		for(int i=1; i<A.length; i++)
  		{
  			if(A[i]<A[i-1])return false;
  		}
  		return true;
  	}
  
  	static boolean isDivisible(StringBuilder X,int i,long num)
  	{
  		long r=0;
  		for(; i<X.length(); i++)
  		{
  			r=r*10+(X.charAt(i)-'0');
  			r=r%num;
  		}
  		return r==0;
  	}    
  
  
  
  	static int lower_Bound(int A[],int low,int high, int x) 
  	{ 
  		if (low > high) 
  			if (x >= A[high]) 
  				return A[high]; 
  
  		int mid = (low + high) / 2; 
  
  		if (A[mid] == x) 
  			return A[mid]; 
  
  		if (mid > 0 && A[mid - 1] <= x && x < A[mid]) 
  			return A[mid - 1]; 
  
  		if (x < A[mid]) 
  			return lower_Bound( A, low, mid - 1, x); 
  
  		return lower_Bound(A, mid + 1, high, x); 
  	} 
  
  	static String f(String A)
  	{
  		String X="";
  		for(int i=A.length()-1; i>=0; i--)
  		{
  			int c=A.charAt(i)-'0';
  			X+=(c+1)%2;
  		}
  		return X;
  	}
  
  	static void sort(long[] a) //check for long
  	{
  		ArrayList<Long> l=new ArrayList<>();
  		for (long i:a) l.add(i);
  		Collections.sort(l);
  		for (int i=0; i<a.length; i++) a[i]=l.get(i);
  	}
  
  	static String swap(String X,int i,int j)
  	{
  		char ch[]=X.toCharArray();
  		char a=ch[i];
  		ch[i]=ch[j];
  		ch[j]=a;
  		return new String(ch);
  	}
  
  	static int sD(long n)  
  	{  
  
  		if (n % 2 == 0 )  
  			return 2;  
  
  		for (int i = 3; i * i <= n; i += 2) {  
  			if (n % i == 0 )  
  				return i;  
  		}  
  
  		return (int)n;  
  	}  
  
  	static void setGraph(int N)
  	{
  		//		tot=new int[N+1];
  		partial=new int[N+1];
  		Days=new int[N+1];
  		P=new int[N+1][(int)(Math.log(N)+10)];
  		set=new boolean[N+1];
  		g=new ArrayList[N+1];
  		D=new int[N+1];
  		for(int i=0; i<=N; i++)
  		{
  
  			g[i]=new ArrayList<>();		
  			Days[i]=-1;
  			D[i]=Integer.MAX_VALUE;
  			//D2[i]=INF;
  		}
  	}
  
  
  
  	static  long pow(long a,long b)
  	{
  		//long mod=1000000007;
  		long pow=1;
  		long x=a;
  		while(b!=0)
  		{
  			if((b&1)!=0)pow=(pow*x)%mod;
  			x=(x*x)%mod;
  			b/=2;
  		}
  		return pow;
  	}
  
  	static long toggleBits(long x)//one's complement || Toggle bits
  	{
  		int n=(int)(Math.floor(Math.log(x)/Math.log(2)))+1;
  
  		return ((1<<n)-1)^x;
  	}
  
  	static int countBits(long a)
  	{
  		return (int)(Math.log(a)/Math.log(2)+1);
  	}
  
  	static long fact(long N)
  	{ 
  		long n=2; 
  		if(N<=1)return 1;
  		else
  		{
  			for(int i=3; i<=N; i++)n=(n*i)%mod;
  		}
  		return n;
  	}
  
  	static int kadane(int A[])
  	{
  		int lsum=A[0],gsum=A[0];
  		for(int i=1; i<A.length; i++)
  		{
  			lsum=Math.max(lsum+A[i],A[i]);
  			gsum=Math.max(gsum,lsum);
  		}
  		return gsum;
  	}
  
  	static void sort(int[] a) {
  		ArrayList<Integer> l=new ArrayList<>();
  		for (int i:a) l.add(i);
  		Collections.sort(l);
  		for (int i=0; i<a.length; i++) a[i]=l.get(i);
  	}
  
  	static boolean isPrime(long N)
  	{
  		if (N<=1)  return false; 
  		if (N<=3)  return true; 
  		if (N%2 == 0 || N%3 == 0) return false; 
  		for (int i=5; i*i<=N; i=i+6) 
  			if (N%i == 0 || N%(i+2) == 0) 
  				return false; 
  		return true; 
  	}
  	static void print(char A[])
  	{
  		for(char c:A)System.out.print(c+" ");
  		System.out.println();
  	}
  	static void print(boolean A[])
  	{
  		for(boolean c:A)System.out.print(c+" ");
  		System.out.println();
  	}
  	static void print(int A[])
  	{
  		for(int a:A)System.out.print(a+" ");
  		System.out.println();	
  	}
  	static void print(long A[])
  	{
  		for(long i:A)System.out.print(i+ " ");
  		System.out.println();
  
  	}
  	static void print(boolean A[][])
  	{
  		for(boolean a[]:A)print(a);
  	}
  	static void print(long A[][])
  	{
  		for(long a[]:A)print(a);
  	}
  	static void print(int A[][])
  	{
  		for(int a[]:A)print(a);
  	}
  	static void print(ArrayList<Integer> A)
  	{
  		for(int a:A)System.out.print(a+" ");
  		System.out.println();
  	}
  
  	static int i()
  	{
  		return in.nextInt();
  	}
  
  	static long l()
  	{
  		return in.nextLong();
  	}
  
  	static int[] input(int N){
  		int A[]=new int[N];
  		for(int i=0; i<N; i++)
  		{
  			A[i]=in.nextInt();
  		}
  		return A;
  	}
  
  	static long[] inputLong(int N)     {
  		long A[]=new long[N];
  		for(int i=0; i<A.length; i++)A[i]=in.nextLong();
  		return A;
  	}
  
  	static long GCD(long a,long b) 
  	{
  		if(b==0)
  		{
  			return a;
  		}
  		else return GCD(b,a%b );
  	}
  
  }
  class Edge
  {
  	int a,cnt;
  	//	boolean said;
  	Edge(int a,int cnt)
  	{
  		this.a=a;
  		//		this.said=said;
  		this.cnt=cnt;
  	}
  
  }
  
  
  //Code For FastReader
  //Code For FastReader
  //Code For FastReader
  //Code For FastReader
  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());
  	}
  
  	String nextLine()
  	{
  		String str="";
  		try
  		{
  			str=br.readLine();
  		}
  		catch (IOException e)
  		{
  			e.printStackTrace();
  		}
  		return str;
  	}
  
  }