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: /*
  ⠀⠀⠀⠀⣠⣶⡾⠏⠉⠙⠳⢦⡀⠀⠀⠀⢠⠞⠉⠙⠲⡀⠀
  ⠀⠀⠀⣴⠿⠏⠀⠀⠀⠀⠀⠀⢳⡀⠀⡏⠀⠀Y⠀⠀⢷
  ⠀⠀⢠⣟⣋⡀⢀⣀⣀⡀⠀⣀⡀⣧⠀⢸⠀⠀A⠀⠀ ⡇
  ⠀⠀⢸⣯⡭⠁⠸⣛⣟⠆⡴⣻⡲⣿⠀⣸⠀⠀S⠀  ⡇
  ⠀⠀⣟⣿⡭⠀⠀⠀⠀⠀⢱⠀⠀⣿⠀⢹⠀⠀H⠀⠀ ⡇
  ⠀⠀⠙⢿⣯⠄⠀⠀⠀⢀⡀⠀⠀⡿⠀⠀⡇⠀⠀⠀⠀⡼
  ⠀⠀⠀⠀⠹⣶⠆⠀⠀⠀⠀⠀⡴⠃⠀⠀⠘⠤⣄⣠⠞⠀
  ⠀⠀⠀⠀⠀⢸⣷⡦⢤⡤⢤⣞⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
  ⠀⠀⢀⣤⣴⣿⣏⠁⠀⠀⠸⣏⢯⣷⣖⣦⡀⠀⠀⠀⠀⠀⠀
  ⢀⣾⣽⣿⣿⣿⣿⠛⢲⣶⣾⢉⡷⣿⣿⠵⣿⠀⠀⠀⠀⠀⠀
  ⣼⣿⠍⠉⣿⡭⠉⠙⢺⣇⣼⡏⠀⠀⠀⣄⢸⠀⠀⠀⠀⠀⠀
  ⣿⣿⣧⣀⣿………⣀⣰⣏⣘⣆⣀⠀⠀
   */
  
  import java.io.IOException;
  import java.io.InputStream;
  import java.io.PrintWriter; // System.out is a PrintStream
  import java.util.InputMismatchException;
  
  
  public class B1604 {
      private static int MOD = (int)1e9 + 7, mod = 99_82_44_353;
      private static double PI = 3.14159265358979323846;
  
      public static void main(String[] args) throws IOException {
          FasterScanner scn = new FasterScanner();
          PrintWriter out = new PrintWriter(System.out);
          for (int tc = scn.nextInt(); tc > 0; tc--) {
              int N = scn.nextInt();
              int[] arr = new int[N];
              for (int i = 0; i < N; i++) {
                  arr[i] = scn.nextInt();
              }
              boolean flag = (N & 1) == 0;
              if (!flag) {
                  for (int i = 1; i < N && !flag; i++) {
                      if (arr[i - 1] >= arr[i]) {
                          flag = true;
                      }
                  }
              }
              out.println(flag ? "YES" : "NO");
          }
          out.close();
      }
  
      /* ------------------- Sorting ------------------- */
      private static void ruffleSort(int[] arr) {
          // int N = arr.length;
          // Random rand = new Random();
          // for (int i = 0; i < N; i++) {
          //     int oi = rand.nextInt(N), temp = arr[i];
          //     arr[i] = arr[oi];
          //     arr[oi] = temp;
          // }
          // Arrays.sort(arr);
      }
          
      /* ------------------- Sorting ------------------- */
      
      private static boolean isPalindrome(String str) {
          for (int i = 0, j = str.length() - 1; i < j; i++, j--) {
              if (str.charAt(i) != str.charAt(j)) {
                  return false;
              }
          }
          return true;
      }
      
      private static boolean isPalindrome(char[] str) {
          for (int i = 0, j = str.length - 1; i < j; i++, j--) {
              if (str[i] != str[j]) {
                  return false;
              }
          }
          return true;
      }
      
      /* ------------------- Pair class ------------------- */
      private static class Pair implements Comparable<Pair> {
  		int x, y;
  		Pair(int x, int y) {
  			this.x = x;
  			this.y = y;
  		}
  		public int compareTo(Pair o) {
  			return this.x == o.x ? this.y - o.y : this.x - o.x;
  		}
  	}
  
      /* ------------------- HCF and LCM ------------------- */
      private static int gcd(int num1, int num2) {
          int temp = 0;
          while (num2 != 0) {
              temp = num1;
              num1 = num2;
              num2 = temp % num2;
          }
          return num1;
      }
      
      private static int lcm(int num1, int num2) {
          return (int)((1L * num1 * num2) / gcd(num1, num2));
      }
      
      /* ------------------- primes and prime factorization ------------------- */
      private static boolean[] seive(int N) {
          // true means not prime, false means is a prime number :)
          boolean[] notPrimes = new boolean[N + 1];
          notPrimes[0] = notPrimes[1] = true;
          for (int i = 2; i * i <= N; i++) {
              if (notPrimes[i]) continue;
              for (int j = i * i; j <= N; j += i) {
                  notPrimes[j] = true;
              }
          }
          return notPrimes;
      }
  
  	/*
      private static TreeMap<Integer, Integer> primeFactors(long N) {
  		TreeMap<Integer, Integer> primeFact = new TreeMap<>();
  		for (int i = 2; i <= Math.sqrt(N); i++) {
              int count = 0;
              while (N % i == 0) {
                  N /= i;
                  count++;
              }
              if (count != 0) {
                  primeFact.put(i, count);
              }
  		}
  		if (N != 1) {
              primeFact.put((int)N, 1);
          }
  		return primeFact;
  	}
      */
  
      /* ------------------- Binary Search ------------------- */
      private static long factorial(int N) {
          long ans = 1L;
          for (int i = 2; i <= N; i++) {
              ans *= i;
          }
          return ans;
      }
  
      private static long[] factorialDP(int N) {
          long[] factDP = new long[N + 1];
          factDP[0] = factDP[1] = 1;
          for (int i = 2; i <= N; i++) {
              factDP[i] = factDP[i - 1] * i;
          }
          return factDP;
      }
  
      private static long factorialMod(int N, int mod) {
          long ans = 1L;
          for (int i = 2; i <= N; i++) {
              ans = ((ans % mod) * (i % mod)) % mod;
          }
          return ans;
      }
  
      /* ------------------- Binary Search ------------------- */
      private static int floorSearch(int[] arr, int st, int ed, int tar) {
          int ans = -1;
          while (st <= ed) {
              int mid = ((ed - st) >> 1) + st;
              if (arr[mid] <= tar) {
                  ans = mid;
                  st = mid + 1;
              } else {
                  ed = mid - 1;
              }
          }
          return ans;
      }
      
      private static int ceilingSearch(int[] arr, int st, int ed, int tar) {
          int ans = -1;
          while (st <= ed) {
              int mid = ((ed - st) >> 1) + st;
              if (arr[mid] < tar) {
                  st = mid + 1;
              } else {
                  ans = mid;
                  ed = mid - 1;
              }
          }
          return ans;
      }
      
      /* ------------------- Power Function ------------------- */
      public static long pow(long x, long y) {
          long res = 1;
  		while (y > 0) {
              if ((y & 1) != 0) {
                  res = (res * x);
  				y--;
  			}
  			x = (x * x);
  			y >>= 1;
  		}
  		return res;
  	}
      
  	public static long powMod(long x, long y, int mod) {
          long res = 1;
  		while (y > 0) {
              if ((y & 1) != 0) {
                  res = (res * x) % mod;
  				y--;
  			}
  			x = (x * x) % mod;
  			y >>= 1;
  		}
  		return res % mod;
  	}
  
      /* ------------------- Disjoint Set(Union and Find) ------------------- */
      private static class DSU {
  		public int[] parent, rank;
  		DSU(int N) {
  			parent = new int[N];
  			rank = new int[N];
  			for (int i = 0; i < N; i++) {
  				parent[i] = i;
                  rank[i] = 1;
              }
  		}
  		public int find(int a) {
  			if (parent[a] == a) {
  				return a;
              }
              return parent[a] = find(parent[a]);
  		}
  		public boolean union(int a, int b) {
  			int parA = find(a), parB = find(b);
  			if (parA == parB) return false;
  			if (rank[parA] > rank[parB]) {
                  parent[parB] = parA;
              } else if (rank[parA] < rank[parB]) {
                  parent[parA] = parB;
              } else {
                  parent[parA] = parB;
                  rank[parB]++;
              }
              return true;
  		}
  	}
      
      /* ------------------- Scanner class for input ------------------- */
      
      private static class FasterScanner {
  		private InputStream stream;
  		private byte[] buffer = new byte[1024];
  		private int curChar, numChars;
  		private SpaceCharFilter filter;
  
  		public FasterScanner() {
              // default
  			this.stream = System.in;
  		}
  
  		public FasterScanner(InputStream stream) {
  			this.stream = stream;
  		}
  
  		private int readChar() {
  			if (numChars == -1) {
  				throw new InputMismatchException();
              }
  			if (curChar >= numChars) {
  				curChar = 0;
  				try {
  					numChars = stream.read(buffer);
  				} catch (IOException e) {
  					throw new InputMismatchException(e.getMessage());
  				}
  				if (numChars <= 0) {
  					return -1;
                  }
  			}
  			return buffer[curChar++];
  		}
  
  		private boolean isWhiteSpace(int c) {
  			if (filter != null) {
  				return filter.isWhiteSpace(c);
              }
  			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
  		}
  
  		private boolean isNewLine(int ch) {
  			if (filter != null) {
  				return filter.isNewLine(ch);
              }
  			return ch == '\r' || ch == '\n' || ch == -1;
  		}
  
          public char nextChar() {
              int ch = readChar();
              char res = '\0';
              while (isWhiteSpace(ch)) {
                  ch = readChar();
              }
              do {
                  res = (char)ch;
                  ch = readChar();
              } while (!isWhiteSpace(ch));
              return res;
          }
  
  		public String next() {
  			int ch = readChar();
              StringBuilder res = new StringBuilder();
  			while (isWhiteSpace(ch)) {
  				ch = readChar();
              }
  			do {
  				res.appendCodePoint(ch);
  				ch = readChar();
  			} while (!isWhiteSpace(ch));
  			return res.toString();
  		}
  
  		public String nextLine() {
  			int ch = readChar();
              StringBuilder res = new StringBuilder();
  			do {
  				res.appendCodePoint(ch);
  				ch = readChar();
  			} while (!isNewLine(ch));
  			return res.toString();
  		}
  
  		public int nextInt() {
  			int ch = -1, sgn = 1, res = 0;
              do {
                  ch = readChar();
              } while (isWhiteSpace(ch));
  			if (ch == '-') {
  				sgn = -1;
  				ch = readChar();
  			}
  			do {
  				if (ch < '0' || ch > '9') {
  					throw new InputMismatchException("not a number");
                  }
  				res = (res * 10) + (ch - '0');
  				ch = readChar();
  			} while (!isWhiteSpace(ch));
              
  			return res * sgn;
  		}
  
  		public long nextLong() {
  			int ch = -1, sgn = 1;
              long res = 0L;
              do {
                  ch = readChar();
              } while (isWhiteSpace(ch));
  			if (ch == '-') {
  				sgn = -1;
  				ch = readChar();
  			}
  			do {
  				if (ch < '0' || ch > '9') {
  					throw new InputMismatchException("not a number");
                  }
  				res = (10L * res) + (ch - '0');
  				ch = readChar();
  			} while (!isWhiteSpace(ch));
  
  			return 1L * res * sgn;
  		}
  
          public double nextDouble() {
              return Double.parseDouble(next());
          }
  
          /* for custom delimiters */
  		public interface SpaceCharFilter {
  			public boolean isWhiteSpace(int ch);
  			public boolean isNewLine(int ch);
  		}
  	}
  }
  