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.BigInteger;
  
  /**
   __                  __
   ( _)                ( _)
   / / \\              / /\_\_
   / /   \\            / / | \ \
   / /     \\          / /  |\ \ \
   /  /   ,  \ ,       / /   /|  \ \
   /  /    |\_ /|      / /   / \   \_\
   /  /  |\/ _ '_| \   / /   /   \    \\
   |  /   |/  0 \0\    / |    |    \    \\
   |    |\|      \_\_ /  /    |     \    \\
   |  | |/    \.\ o\o)  /      \     |    \\
   \    |     /\\`v-v  /        |    |     \\
   | \/    /_| \\_|  /         |    | \    \\
   | |    /__/_ `-` /   _____  |    |  \    \\
   \|    [__]  \_/  |_________  \   |   \    ()
   /    [___] (    \         \  |\ |   |   //
   |    [___]                  |\| \|   /  |/
   /|    [____]                  \  |/\ / / ||
   (  \   [____ /     ) _\      \  \    \| | ||
   \  \  [_____|    / /     __/    \   / / //
   |   \ [_____/   / /        \    |   \/ //
   |   /  '----|   /=\____   _/    |   / //
   __ /  /        |  /   ___/  _/\    \  | ||
   (/-(/-\)       /   \  (/\/\)/  |    /  | /
   (/\/\)           /   /   //
   _________/   /    /
   \____________/    (
  
  
   @author NTUDragons-Reborn
   */
  
  public class Solution{
      public static void main(String[] args) {
          InputStream inputStream = System.in;
          OutputStream outputStream = System.out;
          InputReader in = new InputReader(inputStream);
          PrintWriter out = new PrintWriter(outputStream);
          Task solver = new Task();
          solver.solve(in, out);
          out.close();
      }
      // main solver
      static class Task{
  
          double eps= 0.00000001;
          static final int MAXN = 200015;
          static final int MOD= 998244353;
  
          // stores smallest prime factor for every number
          static int spf[] = new int[MAXN];
  
          static boolean[] prime;
  
          Map<Integer,Set<Integer>> dp= new HashMap<>();
  
          // Calculating SPF (Smallest Prime Factor) for every
          // number till MAXN.
          // Time Complexity : O(nloglogn)
          public void sieve()
          {
              spf[1] = 1;
              for (int i=2; i<MAXN; i++)
  
                  // marking smallest prime factor for every
                  // number to be itself.
                  spf[i] = i;
  
              // separately marking spf for every even
              // number as 2
              for (int i=4; i<MAXN; i+=2)
                  spf[i] = 2;
  
              for (int i=3; i*i<MAXN; i++)
              {
                  // checking if i is prime
                  if (spf[i] == i)
                  {
                      // marking SPF for all numbers divisible by i
                      for (int j=i*i; j<MAXN; j+=i)
  
                          // marking spf[j] if it is not
                          // previously marked
                          if (spf[j]==j)
                              spf[j] = i;
                  }
              }
          }
  
          void sieveOfEratosthenes(int n)
          {
              // Create a boolean array
              // "prime[0..n]" and
              // initialize all entries
              // it as true. A value in
              // prime[i] will finally be
              // false if i is Not a
              // prime, else true.
              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] is not changed, then it is a
                  // prime
                  if (prime[p] == true)
                  {
                      // Update all multiples of p
                      for (int i = p * p; i <= n; i += p)
                          prime[i] = false;
                  }
              }
          }
  
          // A O(log n) function returning primefactorization
          // by dividing by smallest prime factor at every step
          public Set<Integer> getFactorization(int x)
          {
              if(dp.containsKey(x)) return dp.get(x);
              Set<Integer> ret = new HashSet<>();
              while (x != 1)
              {
                  if(spf[x]!=2) ret.add(spf[x]);
                  x = x / spf[x];
              }
              dp.put(x,ret);
              return ret;
          }
          // function to find first index >= x
          public int lowerIndex(List<Integer> arr, int n, int x)
          {
              int l = 0, h = n - 1;
              while (l <= h)
              {
                  int mid = (l + h) / 2;
                  if (arr.get(mid) >= x)
                      h = mid - 1;
                  else
                      l = mid + 1;
              }
              return l;
          }
          public int lowerIndex(int[] arr, int n, int x)
          {
              int l = 0, h = n - 1;
              while (l <= h)
              {
                  int mid = (l + h) / 2;
                  if (arr[mid] >= x)
                      h = mid - 1;
                  else
                      l = mid + 1;
              }
              return l;
          }
  
          // function to find last index <= y
          public int upperIndex(List<Integer> arr, int n, int y)
          {
              int l = 0, h = n - 1;
              while (l <= h)
              {
                  int mid = (l + h) / 2;
                  if (arr.get(mid) <= y)
                      l = mid + 1;
                  else
                      h = mid - 1;
              }
              return h;
          }
          public int upperIndex(int[] arr, int n, int y)
          {
              int l = 0, h = n - 1;
              while (l <= h)
              {
                  int mid = (l + h) / 2;
                  if (arr[mid] <= y)
                      l = mid + 1;
                  else
                      h = mid - 1;
              }
              return h;
          }
  
          // function to count elements within given range
          public int countInRange(List<Integer> arr, int n, int x, int y)
          {
              // initialize result
              int count = 0;
              count = upperIndex(arr, n, y) -
                      lowerIndex(arr, n, x) + 1;
              return count;
          }
  
          public int add(int a, int b){
              a+=b;
              while(a>=MOD) a-=MOD;
              while(a<0) a+=MOD;
              return a;
          }
  
          public int mul(int a, int b){
              long res= (long)a*(long)b;
              return (int)(res%MOD);
          }
  
          public int power(int a, int b) {
              int ans=1;
              while(b>0){
                  if((b&1)!=0) ans= mul(ans,a);
                  b>>=1;
                  a= mul(a,a);
              }
              return ans;
          }
  
          int[] fact= new int[MAXN];
          int[] inv= new int[MAXN];
  
          public int Ckn(int n, int k){
              if(k<0 || n<0) return 0;
              return mul(mul(fact[n],inv[k]),inv[n-k]);
          }
  
          public int inverse(int a){
              return power(a,MOD-2);
          }
  
          public void preprocess() {
              fact[0]=1;
              for(int i=1;i<MAXN;i++) fact[i]= mul(fact[i-1],i);
              inv[MAXN-1]= inverse(fact[MAXN-1]);
              for(int i=MAXN-2;i>=0;i--){
                  inv[i]= mul(inv[i+1],i+1);
              }
          }
  
          /**
           * return VALUE of lower bound for unsorted array
           */
          public int lowerBoundNormalArray(int[] arr, int x){
              TreeSet<Integer> set= new TreeSet<>();
              for(int num: arr) set.add(num);
              return set.lower(x);
          }
          /**
           * return VALUE of upper bound for unsorted array
           */
          public int upperBoundNormalArray(int[] arr, int x){
              TreeSet<Integer> set= new TreeSet<>();
              for(int num: arr) set.add(num);
              return set.higher(x);
          }
  
          public void debugArr(int[] arr){
              for(int i: arr) out.print(i+" ");
              out.println();
          }
  
          public int rand(){
              int min=0, max= MAXN;
              int random_int = (int)Math.floor(Math.random()*(max-min+1)+min);
              return random_int;
          }
          
          InputReader in; PrintWriter out;
          CustomFileReader cin;
          int[] xor= new int[3*100000+5];
          int[] pow2= new int[1000000+1];
          public void solve(InputReader in, PrintWriter out) {
              this.in=in; this.out=out;
              // sieve();
              // pow2[0]=1;
              // for(int i=1;i<pow2.length;i++){
              //     pow2[i]= mul(pow2[i-1],2);
              // }
              int t= in.nextInt();;
              // preprocess();
              // int t=in.nextInt();
              // int t= cin.nextIntArrLine()[0];
              for(int i=1;i<=t;i++) solveA(i);
          }
          int[]a,b;
          
          public void solveA(int t){
              int n= in.nextInt();
              int[] a= new int[n];
              for(int i=0;i<n;i++) a[i]= in.nextInt();
              if(n%2==0) {
                  out.println("YES"); return;
              }
              boolean exist= false;
              for(int i=1;i<n;i++){
                  if(a[i]<=a[i-1]) exist= true;
              }
              if(exist) out.println("YES");
              else out.println("NO");
          }
  
          private int f(int i){
              return i+b[i]-a[i+b[i]];
          }
          
          public int _gcd(int a,  int b)
          {
  
              if(b == 0) {
                  return a;
              }
              else {
                  return _gcd(b, a % b);
              }
          }
          public int _lcm(int a, int b){
              return (a*b)/_gcd(a,b);
          }
  
      }
  
  
      static class SEG {
  
          Pair[] segtree;
          
          public SEG(int n){
              
              segtree= new Pair[4*n];
              Arrays.fill(segtree, new Pair(-1,Long.MAX_VALUE));
          }
          // void buildTree(int l, int r, int index) {
          //     if (l == r) {
          //         segtree[index].y = a[l];
          //         return;
          //     }
          //     int mid = (l + r) / 2;
          //     buildTree(l, mid, 2 * index + 1);
          //     buildTree(mid + 1, r, 2 * index + 2);
          //     segtree[index].y = Math.min(segtree[2 * index + 1].y, segtree[2 * index + 2].y);
          // }
          
          void update(int l, int r, int index, int pos, Pair val) {
              if (l == r) {
                  segtree[index] = val;
                  return;
              }
              int mid = (l + r) / 2;
              if (pos <= mid) update(l, mid, 2 * index + 1, pos, val);
              else update(mid + 1, r, 2 * index + 2, pos, val);
              if(segtree[2 * index + 1].y < segtree[2 * index + 2].y){
                  segtree[index]= segtree[2 * index + 1];
              }
              else {
                  segtree[index]= segtree[2 * index + 2];
              }
          }
          
          // Pair query(int l, int r, int from, int to, int index) {
          //     if (from <= l && r <= to)
          //         return segtree[index];
          //     if (r < from | to < l)
          //         return 0;
          //     int mid = (l + r) / 2;
          //     Pair left= query(l, mid, from, to, 2 * index + 1);
          //     Pair right= query(mid + 1, r, from, to, 2 * index + 2);
          //     if(left.y < right.y) return left;
          //     else return right;
              
          // }
          
          
      }
  
      static class Venice{
          public Map<Long,Long> m= new HashMap<>();
          public long base=0;
          public long totalValue=0;
          private int M= 1000000007;
  
          private long addMod(long a, long b){
              a+=b;
              if(a>=M) a-=M;
              return a;
          }
  
          public void reset(){
              m= new HashMap<>();
              base=0;
              totalValue=0;
          }
          public void update(long add){
              base= base+ add;
          }
          public void add(long key, long val){
              long newKey= key-base;
              m.put(newKey, addMod(m.getOrDefault(newKey,(long)0),val));
          }
      }
  
  
  
      static class Tuple implements Comparable<Tuple>{
          int x, y, z;
          public Tuple(int x, int y, int z){
              this.x= x;
              this.y= y;
              this.z=z;
          }
          @Override
          public int compareTo(Tuple o){
              return this.z-o.z;
          }
      }
  
      static class Pair implements Comparable<Pair>{
          public int x;
          public long y;
          public Pair(int x, long y){
              this.x= x;
              this.y= y;
          }
  
          @Override
          public int compareTo(Pair o) {
              if(this.x!=o.x) return this.x-o.x;
              return (int)(this.y-o.y);
          }
      }
  
      // public static class compareL implements Comparator<Tuple>{
      //     @Override
      //     public int compare(Tuple t1, Tuple t2) {
      //         return t2.l - t1.l;
      //     }
      // }
  
      // fast input reader class;
      static class InputReader {
          BufferedReader br;
          StringTokenizer st;
  
          public InputReader(InputStream stream) {
              br = new BufferedReader(new InputStreamReader(stream));
          }
  
          public String nextToken() {
              while (st == null || !st.hasMoreTokens()) {
                  String line = null;
                  try {
                      line = br.readLine();
                  } catch (IOException e) {
                      throw new RuntimeException(e);
                  }
                  if (line == null) {
                      return null;
                  }
                  st = new StringTokenizer(line);
              }
              return st.nextToken();
          }
  
          public int nextInt() {
              return Integer.parseInt(nextToken());
          }
          public double nextDouble(){
              return Double.parseDouble(nextToken());
          }
          public long nextLong(){
              return Long.parseLong(nextToken());
          }
          public int[] nextIntArr(int n){
              int[] arr= new int[n];
              for(int i=0;i<n;i++) arr[i]= nextInt();
              return arr;
          }
          public long[] nextLongArr(int n){
              long[] arr= new long[n];
              for(int i=0;i<n;i++) arr[i]= nextLong();
              return arr;
          }
          public List<Integer> nextIntList(int n){
              List<Integer> arr= new ArrayList<>();
              for(int i=0;i<n;i++) arr.add(nextInt());
              return arr;
          }
          public int[][] nextIntMatArr(int n, int m){
              int[][] mat= new int[n][m];
              for(int i=0;i<n;i++) for(int j=0;j<m;j++) mat[i][j]= nextInt();
              return mat;
          }
          public List<List<Integer>> nextIntMatList(int n, int m){
              List<List<Integer>> mat= new ArrayList<>();
              for(int i=0;i<n;i++){
                  List<Integer> temp= new ArrayList<>();
                  for(int j=0;j<m;j++) temp.add(nextInt());
                  mat.add(temp);
              }
              return mat;
          }
          public char[] nextStringCharArr(){
              return nextToken().toCharArray();
          }
      }
  
      static class CustomFileReader{
          String path="";
          Scanner sc;
          public CustomFileReader(String path){
              this.path=path;
              try{
                  sc= new Scanner(new File(path));
              }
              catch(Exception e){}
          }
          public String nextLine(){
              return sc.nextLine();
          }
          public int[] nextIntArrLine(){
              String line= sc.nextLine();
              String[] part= line.split("[\\s+]");
              int[] res= new int[part.length];
              for(int i=0;i<res.length;i++) res[i]= Integer.parseInt(part[i]);
              return res;
          }
      }
  }