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.BufferedReader;
  import java.io.IOException;
  import java.io.InputStreamReader;
  import java.util.ArrayList;
  import java.util.Arrays;
  import java.util.StringTokenizer;
  
  import static java.lang.Math.max;
  import static java.lang.System.currentTimeMillis;
  import static java.lang.System.out;
  import static java.util.Arrays.sort;
  import static java.util.Collections.reverseOrder;
  
  public class B {
      public static final boolean LOCAL = System.getProperty("ONLINE_JUDGE") == null;
      // public static final boolean LOCAL = System.getProperty("LOCAL")!=null;
      public static final String ANSI_RED = "\u001B[31m";
      public static final String ANSI_RESET = "\u001B[0m";
      static final int M = (int) 1e9 + 7;
      static final long MM = (long) M * M;
      static final int MAX = Integer.MAX_VALUE;
      static final int MIN = Integer.MIN_VALUE;
      static final int SIZE = (int) 1e9 * 2;
      static ArrayList<Integer> primes = new ArrayList<>();
      //static Scanner sc = new Scanner(System.in);
      static FastReader sc = new FastReader();
      static long startTime;
      static long endTime;
      static boolean[] prime;
      static int[] visited;
      static ArrayList<ArrayList<Integer>> graph;
      static ArrayList<Integer> dfs;
      static boolean isCyclic = false;
  
      public static int swap(int... args) {
          return args[0];
      }
  
      public static void main(String[] args) throws IOException {
          do {
              startTime = currentTimeMillis();
              //setOut(new PrintStream("output"));
              //setIn(new FileInputStream("input"));
              int T = sc.nextInt();
              while (T-- != 0) {
                  solve();
  
              }
              endTime = currentTimeMillis();
              long duration = endTime - startTime;
              //out.println(duration);
              if (false) {
                  out.println(max(3, 2));
                  Integer[] ARRAY = new Integer[2];
                  ArrayList<Integer> LIST = new ArrayList<>();
                  LIST.add(2);
                  // sort(LIST, reverseOrder());
                  LIST.sort(reverseOrder());
                  sort(ARRAY, reverseOrder());
                  out.println(LIST + " " + Arrays.toString(ARRAY));
              }
          } while (LOCAL);
      }
  
      public static void solve() {
  /////////////////////////////////////////////////////////////////////
          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");
          }
          else {
              for (int i = 0; i < n-1; i++) {
                  if(arr[i]>=arr[i+1]){
                      out.println("YES");
                      return;
                  }
              }
              out.println("NO");
          }
  
  ///////////////////////////////////////////////////////////////////////
  
      }
  
      static void dfs(int src) {
          visited[src] = 1;
          for (Integer integer : graph.get(src)) {
              if (visited[integer] != 1) {
                  dfs(integer);
              }
          }
          dfs.add(src);
  
      }
  
      static void detectCycle(int src) {
          visited[src] = 2;
          for (Integer integer : graph.get(src)) {
              if (visited[integer] == 0) {
                  detectCycle(integer);
              } else if (visited[integer] == 2) {
                  isCyclic = true;
                  return;
              }
  
          }
          visited[src] = 1;
      }
  
      static <Array, Target> int count(Array[] array, Target target) {
          int cn = 0;
          for (Array value : array) {
              if (value.equals(target)) cn++;
          }
          return cn;
      }
  
      static int count(String string, char target) {
          int cn = 0;
          for (int i = 0; i < string.length(); i++) {
              if (string.charAt(i) == target) cn++;
          }
          return cn;
      }
  
      static <Array> void revArray(Array[] arr) {
          int n = arr.length;
          for (int i = 0; i < n / 2; i++) {
              Array temp = arr[i];
              arr[i] = arr[n - i - 1];
              arr[n - i - 1] = temp;
          }
  
      }
  
      static <Array> void printArray(Array[] arr) {
          int n = arr.length;
          for (Array array : arr) out.print(array + " ");
          out.println();
      }
  
      static void yes() {
          out.println("YES");
      }
  
      static void no() {
          out.println("NO");
      }
  
      public static boolean isPal(String s) {
          StringBuilder stringBuilder = new StringBuilder(s);
          return s.equals(stringBuilder.reverse().toString());
      }
  
      public static int lowerBound(Integer[] array, int length, int value) {
          int low = -1;
          int hi = length;
          while (low + 1 < hi) {
              int mid = (low + hi) / 2;
              if (array[mid] <= value) {
                  low = mid;
              } else {
                  hi = mid;
              }
          }
          return low;
      }
  
      public static int upperBound(Integer[] array, int length, int value) {
          int low = -1;
          int hi = length;
          while (low + 1 < hi) {
              int mid = (low + hi) >> 1;
              if (array[mid] >= value) {
                  hi = mid;
              } else low = mid;
          }
          return hi;
      }
  
      public static int binarySearch(Integer[] arr, int length, int value) {
          int low = 0;
          int hi = length - 1;
          int ans = -1;
          while (low <= hi) {
              int mid = (low + hi) >> 1;
              if (arr[mid] > value) {
                  hi = mid - 1;
              } else if (arr[mid] < value) {
                  low = mid + 1;
              } else {
                  ans = mid;
                  break;
              }
          }
          return ans;
      }
  
      public static int gcd(int a, int b) {
          return b == 0 ? a : gcd(b, a % b);
      }
  
      public static int lcm(int a, int b) {
          return a / gcd(a, b) * b;
      }
  
      public static int countDivs(int n) {
          int cn = 0;
          int sqr = (int) Math.sqrt(n);
          for (int i = 1; i <= sqr; ++i) {
              if (n % i == 0) {
                  ++cn;
              }
          }
          cn *= 2;
          if (sqr * sqr == n) cn--;
          return cn;
      }
  
      static void prime(int x) {
          //sieve algorithm. nlog(log(n)).
          prime = new boolean[(x + 1)];
          Arrays.fill(prime, true);
          prime[0] = prime[1] = false;
          for (int i = 2; i * i <= x; i++)
              if (prime[i])
                  for (int j = i * i; j <= x; j += i)
                      prime[j] = false;
      }
  
      static boolean isEven(long x) {
          return x % 2 == 0;
      }
  
      static boolean isPrime(long x) {
          boolean flag = true;
          int sqr = (int) Math.sqrt(x);
          if (x < 2) return false;
          for (int i = 2; i <= sqr; i++) {
              if (x % i == 0) {
                  flag = false;
                  break;
              }
          }
          return flag;
      }
  
      static long factorial(long x) {
          long total = 1;
          for (int i = 2; i <= x; i++)
              total = (total * i) % M;
          return total;
      }
  
      static long power1(long x, long y, long p) {
          long res = 1; // Initialize result
  
          x = x % p; // Update x if it is more than or
          // equal to p
  
          if (x == 0)
              return 0; // In case x is divisible by p;
  
          while (y > 0) {
  
              // If y is odd, multiply x with result
              if ((y & 1) != 0)
                  res = (res * x) % p;
  
              // y must be even now
              y = y >> 1; // y = y/2
              x = (x * x) % p;
          }
          return res;
      }
  
      static long power(long x, long n) {
          if (n == 0) {
              return 1;
          }
          long pow = power(x, n / 2L);
          if ((n & 1) == 1) {
              return (x % MM * (pow % MM) * (pow % MM)) % MM;
          }
          return (pow % MM * pow % MM) % MM;
      }
  
      private static <T> String ts(T t) {
          if (t == null) {
              return "null";
          }
          try {
              return ts((Iterable) t);
          } catch (ClassCastException e) {
              if (t instanceof int[]) {
                  String s = Arrays.toString((int[]) t);
                  return "{" + s.substring(1, s.length() - 1) + "}";
              } else if (t instanceof long[]) {
                  String s = Arrays.toString((long[]) t);
                  return "{" + s.substring(1, s.length() - 1) + "}";
              } else if (t instanceof char[]) {
                  String s = Arrays.toString((char[]) t);
                  return "{" + s.substring(1, s.length() - 1) + "}";
              } else if (t instanceof double[]) {
                  String s = Arrays.toString((double[]) t);
                  return "{" + s.substring(1, s.length() - 1) + "}";
              } else if (t instanceof boolean[]) {
                  String s = Arrays.toString((boolean[]) t);
                  return "{" + s.substring(1, s.length() - 1) + "}";
              }
              try {
                  return ts((Object[]) t);
              } catch (ClassCastException e1) {
                  return t.toString();
              }
          }
      }
  
      private static <T> String ts(T[] arr) {
          StringBuilder ret = new StringBuilder();
          ret.append("{");
          boolean first = true;
          for (T t : arr) {
              if (!first) {
                  ret.append(", ");
              }
              first = false;
              ret.append(ts(t));
          }
          ret.append("}");
          return ret.toString();
      }
  
      private static <T> String ts(Iterable<T> iter) {
          StringBuilder ret = new StringBuilder();
          ret.append("{");
          boolean first = true;
          for (T t : iter) {
              if (!first) {
                  ret.append(", ");
              }
              first = false;
              ret.append(ts(t));
          }
          ret.append("}");
          return ret.toString();
      }
  
      public static void dbg(Object... o) {
          if (LOCAL) {
              System.err.print("Line #" + Thread.currentThread().getStackTrace()[2].getLineNumber() + ": [");
              for (int i = 0; i < o.length; i++) {
                  if (i != 0) {
                      System.err.print(", ");
                  }
                  System.err.print(ts(o[i]));
              }
              System.err.println("]");
          }
      }
  
      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());
          }
  
          String nextLine() {
              String str = "";
              try {
                  str = br.readLine();
              } catch (IOException e) {
                  e.printStackTrace();
              }
              return str;
          }
      }
  
      static class Pair implements Comparable<Pair> {
          private int ID;
          private int wins;
  
          public Pair(int ID, int value) {
              this.ID = ID;
              this.wins = value;
          }
  
          public void setID(int ID) {
              this.ID = ID;
          }
  
          public void setWins(int wins) {
              this.wins = wins;
          }
  
          public int second() {
              return wins;
          }
  
          @Override
          public int compareTo(Pair o) {
              //   out.println(o.wins +" " + wins);
              int winVal = Integer.compare(o.wins, wins);
              //  dbg(winVal);
              if (winVal == 0) {
                  return -Integer.compare(o.ID, ID);
              }
              return winVal;
          }
  
          @Override
          public String toString() {
              return "Pair{" + "x=" + ID + ", y=" + wins + '}';
          }
      }
  
  }
  