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.BufferedWriter;
  import java.io.File;
  import java.io.FileReader;
  import java.io.FileWriter;
  import java.io.IOException;
  import java.io.InputStreamReader;
  import java.io.OutputStreamWriter;
  import java.io.PrintWriter;
  import java.lang.reflect.Array;
  import java.util.ArrayDeque;
  import java.util.ArrayList;
  import java.util.Arrays;
  import java.util.Collections;
  import java.util.Comparator;
  import java.util.Deque;
  import java.util.HashMap;
  import java.util.HashSet;
  import java.util.LinkedHashMap;
  import java.util.LinkedList;
  import java.util.List;
  import java.util.Map;
  import java.util.PriorityQueue;
  import java.util.Queue;
  import java.util.Random;
  import java.util.Set;
  import java.util.Stack;
  import java.util.StringTokenizer;
  import java.util.TreeSet;
  import java.util.stream.Collectors;
  
  public class Main {
      static int mod = (int) (1e9) + 7;
  
      /* ======================DSU===================== */
      static class dsu {
          static int parent[], n;// min[],value[];
          static long size[];
  
          dsu(int n) {
              parent = new int[n + 1];
              size = new long[n + 1];
              // min=new int[n+1];
              // value=new int[n+1];
              Main.dsu.n = n;
              makeSet();
          }
  
          static void makeSet() {
              for (int i = 1; i <= n; i++) {
                  parent[i] = i;
                  size[i] = 1;
                  // min[i]=i;
              }
          }
  
          static int find(int a) {
              if (parent[a] == a)
                  return a;
              else {
                  return parent[a] = find(parent[a]);// Path Compression
              }
          }
  
          static void union(int a, int b) {
              int setA = find(a);
              int setB = find(b);
              if (setA == setB)
                  return;
              if (size[setA] >= size[setB]) {
                  parent[setB] = setA;
                  size[setA] += size[setB];
              } else {
                  parent[setA] = setB;
                  size[setB] += size[setA];
              }
          }
      }
  
      /* ======================================================== */
      static class Pair<X extends Number, Y extends Number> implements Comparator<Pair> {
          X x;
          Y y;
  
          // Constructor
          public Pair(X x, Y y) {
              this.x = x;
              this.y = y;
          }
  
          public Pair() {
  
          }
  
          @Override
          public int compare(Main.Pair o1, Main.Pair o2) {
              return ((int) (o1.y.intValue() - o2.y.intValue()));// Ascending Order based on 'y'
          }
      }
  
      /* ===============================Tries================================= */
      static class TrieNode {
          private HashMap<Character, TrieNode> children = new HashMap<>();
          public int size;
          boolean endOfWord;
  
          public void putChildIfAbsent(char ch) {
              children.putIfAbsent(ch, new TrieNode());
          }
  
          public TrieNode getChild(char ch) {
              return children.get(ch);
          }
      }
  
      static private TrieNode root;
  
      public static void insert(String str) {
          TrieNode curr = root;
          for (char ch : str.toCharArray()) {
              curr.putChildIfAbsent(ch);
              curr = curr.getChild(ch);
              curr.size++;
          }
          // mark the current nodes endOfWord as true
          curr.endOfWord = true;
      }
  
      public static int search(String word) {
          TrieNode curr = root;
  
          for (char ch : word.toCharArray()) {
              curr = curr.getChild(ch);
              if (curr == null) {
                  return 0;
              }
          }
          // size contains words starting with prefix- word
          return curr.size;
      }
  
      public boolean delete(TrieNode current, String word, int index) {
          if (index == word.length()) {
              // when end of word is reached only delete if currrent.endOfWord is true.
              if (!current.endOfWord) {
                  return false;
              }
              current.endOfWord = false;
              // if current has no other mapping then return true
              return current.children.size() == 0;
          }
          char ch = word.charAt(index);
          TrieNode node = current.children.get(ch);
          if (node == null) {
              return false;
          }
          boolean shouldDeleteCurrentNode = delete(node, word, index + 1);
  
          // if true is returned then delete the mapping of character and trienode
          // reference from map.
          if (shouldDeleteCurrentNode) {
              current.children.remove(ch);
              // return true if no mappings are left in the map.
              return current.children.size() == 0;
          }
          return false;
      }
  
      /* ================================================================= */
  
      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 (long i = 5; i * i <= n; i = i + 6)
              if (n % i == 0 || n % (i + 2) == 0)
                  return false;
          return true;
      }
  
      static Pair<Integer, Integer> lowerBound(long[] a, long x) { // x is the target, returns lowerBound. If not found
                                                                   // return -1
          int l = -1, r = a.length;
          while (l + 1 < r) {
              int m = (l + r) >>> 1;
              if (a[m] == x) {
                  return new Pair<>(m, 1);
              }
              if (a[m] >= x)
                  r = m;
              else
                  l = m;
          }
          return new Pair<>(r, 0);
      }
  
      static Pair<Integer, Integer> upperBound(long[] a, long x) {// x is the target, returns upperBound. If not found
          int l = -1, r = a.length;
          while (l + 1 < r) {
              int m = (l + r) >>> 1;
              if (a[m] == x) {
                  return new Pair<>(m, 1);
              }
              if (a[m] <= x)
                  l = m;
              else
                  r = m;
          }
          return new Pair<>(l + 1, 0);
      }
  
      static long gcd(long a, long b) {
          if (a == 0)
              return b;
          return gcd(b % a, a);
      }
  
      static long lcm(long a, long b) {
          return (a * b) / gcd(a, b);
      }
  
      static long power(long x, long y) {
          long res = 1;
          while (y > 0) {
              if (y % 2 == 1)
                  res = (res * x);
              y >>= 1;
              x = (x * x);
          }
          return res;
      }
  
      public double binPow(double x, int n) {// binary exponentiation with negative power as well
          if (n == 0)
              return 1.0;
          double binPow = binPow(x, n / 2);
          if (n % 2 == 0) {
              return binPow * binPow;
          } else {
              return n > 0 ? (binPow * binPow * x) : (binPow * binPow / x);
          }
      }
  
      static long ceil(long x, long y) {
          return (x % y == 0 ? x / y : (x / y + 1));
      }
  
      /*
       * ===========Modular Operations==================
       */
      static long modPower(long x, long y, long p) {
          long res = 1;
          x = x % p;
          while (y > 0) {
              if (y % 2 == 1)
                  res = (res * x) % p;
              y = y >> 1; // y = y/2
              x = (x * x) % p;
          }
          return res;
      }
  
      static long modInverse(long n, long p) {
          return modPower(n, p - 2, p);
      }
  
      static long modAdd(long a, long b) {
          return ((a + b + mod) % mod);
      }
  
      static long modMul(long a, long b) {
          return ((a % mod) * (b % mod)) % mod;
      }
  
      static long[] fac = new long[200000 + 5];
      static long[] invFac = new long[200000 + 5];
  
      static long nCrModPFermat(int n, int r) {
          if (r == 0)
              return 1;
          // return (fac[n] * modInverse(fac[r], mod) % mod * modInverse(fac[n - r], mod)
          // % mod) % mod;
          return (fac[n] * invFac[r] % mod * invFac[n - r] % mod) % mod;
      }
  
      /*
       * ===============================================
       */
  
      static void ruffleSort(long[] a) {
          int n = a.length;
          Random r = new Random();
          for (int i = 0; i < a.length; i++) {
              int oi = r.nextInt(n);
              long temp = a[i];
              a[i] = a[oi];
              a[oi] = temp;
          }
          Arrays.sort(a);
      }
  
      static void ruffleSort(int[] a) {
          int n = a.length;
          Random r = new Random();
          for (int i = 0; i < a.length; i++) {
              int oi = r.nextInt(n);
              int temp = a[i];
              a[i] = a[oi];
              a[oi] = temp;
          }
          Arrays.sort(a);
      }
  
      static String binString32(int n) {
          StringBuilder str = new StringBuilder("");
          String bin = Integer.toBinaryString(n);
          if (bin.length() != 32) {
              for (int k = 0; k < 32 - bin.length(); k++) {
                  str.append("0");
              }
              str.append(bin);
          }
          return str.toString();
      }
  
      static class sparseTable {
          public static int st[][];
          public static int log = 4;
  
          static int func(int a, int b) {// make func as per question(here min range query)
              return (int) gcd(a, b);
          }
  
          void makeTable(int n, int a[]) {
  
              st = new int[n][log];
              for (int i = 0; i < n; i++) {
                  st[i][0] = a[i];
              }
              for (int j = 1; j < log; j++) {
                  for (int i = 0; i + (1 << j) <= n; i++) {
                      st[i][j] = func(st[i][j - 1], st[i + (1 << (j - 1))][j - 1]);
                  }
              }
          }
  
          static int query(int l, int r) {
              int length = r - l + 1;
              int k = 0;
              while ((1 << (k + 1)) <= length) {
                  k++;
              }
              return func(st[l][k], st[r - (1 << k) + 1][k]);
          }
  
          static void printTable(int n) {
              for (int j = 0; j < log; j++) {
                  for (int i = 0; i < n; i++) {
                      System.out.print(st[i][j] + " ");
                  }
                  System.out.println();
              }
          }
      }
  
      /*
       * ====================================Main=================================
       */
  
      // static int st[], a[];
  
      // static void buildTree(int treeIndex, int lo, int hi) {
      // if (hi == lo) {
      // st[treeIndex] = a[lo];
      // return;
      // }
      // int mid = (lo + hi) / 2;
      // buildTree(treeIndex * 2 + 1, lo, mid);
      // buildTree(treeIndex * 2 + 2, mid + 1, hi);
      // st[treeIndex] = merge(st[treeIndex * 2 + 1], st[treeIndex * 2 + 2]);
      // }
  
      // static void update(int treeIndex, int lo, int hi, int arrIndex, int val) {
      // if (hi == lo) {
      // st[treeIndex] = val;
      // a[arrIndex] = val;
      // return;
      // }
      // int mid = (hi + lo) / 2;
      // if (mid < arrIndex) {
      // update(treeIndex * 2 + 2, mid + 1, hi, arrIndex, val);
      // } else {
      // update(treeIndex * 2 + 1, lo, mid, arrIndex, val);
      // }
      // st[treeIndex] = merge(st[treeIndex * 2 + 1], st[treeIndex * 2 + 2]);
      // }
  
      // static int query(int treeIndex, int lo, int hi, int l, int r) {
      // if (l <= lo && r >= hi) {
      // return st[treeIndex];
      // }
      // if (l > hi || r < lo) {
      // return 0;
      // }
      // int mid = (hi + lo) / 2;
      // return query(treeIndex * 2 + 1, lo, mid, l, Math.min(mid, r));
      // }
  
      // static int merge(int a, int b) {
      // return a + b;
      // }
  
      public static long findKthPositive(long[] A, long k) {
          int l = 0, r = A.length, m;
          while (l < r) {
              m = (l + r) / 2;
              if (A[m] - 1 - m < k)
                  l = m + 1;
              else
                  r = m;
          }
          return l + k;
      }
  
      static int[] z_function(char ar[]) {
          int[] z = new int[ar.length];
          z[0] = ar.length;
          int l = 0;
          int r = 0;
          for (int i = 1; i < ar.length; i++) {
              if (r < i) {
                  l = i;
                  r = i;
                  while (r < ar.length && ar[r - l] == ar[r])
                      r++;
                  z[i] = r - l;
                  r--;
              } else {
                  int k = i - l;
                  if (z[k] < r - i + 1) {
                      z[i] = z[k];
                  } else {
                      l = i;
                      while (r < ar.length && ar[r - l] == ar[r])
                          r++;
                      z[i] = r - l;
                      r--;
                  }
              }
          }
          return z;
      }
  
      static void mergeSort(int a[]) {
          int n = a.length;
          if (n >= 2) {
              int mid = n / 2;
              int left[] = new int[mid];
              int right[] = new int[n - mid];
              for (int i = 0; i < mid; i++) {
                  left[i] = a[i];
              }
              for (int i = mid; i < n; i++) {
                  right[i - mid] = a[i];
              }
              mergeSort(left);
              mergeSort(right);
              mergeSortedArray(left, right, a);
          }
      }
  
      static void mergeSortedArray(int left[], int right[], int a[]) {
          int i = 0, j = 0, k = 0, n = left.length, m = right.length;
          while (i != n && j != m) {
              if (left[i] < right[j]) {
                  a[k++] = left[i++];
              } else {
                  a[k++] = right[j++];
              }
          }
          while (i != n) {
              a[k++] = left[i++];
          }
          while (j != m) {
              a[k++] = right[j++];
          }
      }
  
      // BINARY SEARCH
      // count of set bits in a particular position
      // suffix max array/ suffix sum array/ prefix
      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;
          }
  
          int[] intArr(int n) {
              int res[] = new int[n];
              for (int i = 0; i < n; i++)
                  res[i] = nextInt();
              return res;
          }
  
          long[] longArr(int n) {
              long res[] = new long[n];
              for (int i = 0; i < n; i++)
                  res[i] = nextLong();
              return res;
          }
      }
  
      static FastReader f = new FastReader();
      static BufferedWriter w = new BufferedWriter(new OutputStreamWriter(System.out));
  
      public static void main(String args[]) throws Exception {
          int t = 1;
          t = f.nextInt();
          int tc = 1;
          // fac[0] = 1;
          // for (int i = 1; i <= 200000; i++) {
          // fac[i] = fac[i - 1] * i % mod;
          // invFac[i] = modInverse(fac[i], mod);
          // }
          while (t-- != 0) {
              int n = f.nextInt();
              int a[] = new int[n];
  
              a = f.intArr(n);
              if (n % 2 == 0) {
                  w.write("YES\n");
              } else {
                  int flag=0;
                  for(int i=1;i<n;i++){
                      if(a[i]<=a[i-1]){
                          flag=1;
                          break;
                      }
                  }
                  // w.write(evenStart + " " + oddStart + " " + oddEnd + "\n");
                  if (flag==1) {
                      w.write("YES\n");
                  } else {
                      w.write("NO\n");
                  }
              }
          }
          w.flush();
      }
  }
  /*
  
   */