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: //package contest.CodeforcesRound752;
  
  import java.io.*;
  import java.util.*;
  
  /***********************
   @oj: codeforces
   @id: hitwanyang
   @email: 296866643@qq.com
   @date: 2021/10/31 0:20
   @url: https://codeforc.es/contest/1604/problem/B
   ***********************/
  public class B1604 {
  
      InputStream is;
      FastWriter out;
      String INPUT = "";
  
      //提交时注意需要注释掉首行package
      //基础类型数组例如long[]使用Arrays排序容易TLE,可以替换成Long[]
      //int 最大值2**31-1,2147483647;
      //尽量使用long类型,避免int计算的数据溢出
      //String尽量不要用+号来,可能会出现TLE,推荐用StringBuffer
      //注意对象类型Long,Integer相等使用equals代替== !!!
      void solve() {
          int t = ni();
          for (; t > 0; t--) {
              go();
          }
      }
  
      void go() {
          int n = ni();
          int[] a = new int[n];
          for (int i = 0; i < n; i++) {
              a[i] = ni();
          }
          if (n == 1) {
              out.println("NO");
              return;
          }
          if (n % 2 == 0) {
              out.println("YES");
          } else {
              for (int i = 1; i < n; i++) {
                  if (a[i] <= a[i - 1]) {
                      out.println("YES");
                      return;
                  }
              }
              out.println("NO");
          }
      }
  
      void run() throws Exception {
          is = System.in;
          out = new FastWriter(System.out);
  
          long s = System.currentTimeMillis();
          solve();
          out.flush();
          //debug log
          //tr(System.currentTimeMillis() - s + "ms");
      }
  
      public static void main(String[] args) throws Exception {
          new B1604().run();
      }
  
      private byte[] inbuf = new byte[1024];
      public int lenbuf = 0, ptrbuf = 0;
  
      private int readByte() {
          if (lenbuf == -1) {
              throw new InputMismatchException();
          }
          if (ptrbuf >= lenbuf) {
              ptrbuf = 0;
              try {
                  lenbuf = is.read(inbuf);
              } catch (IOException e) {
                  throw new InputMismatchException();
              }
              if (lenbuf <= 0) {
                  return -1;
              }
          }
          return inbuf[ptrbuf++];
      }
  
      private boolean isSpaceChar(int c) {
          return !(c >= 33 && c <= 126);
      }
  
      private int skip() {
          int b;
          while ((b = readByte()) != -1 && isSpaceChar(b))
              ;
          return b;
      }
  
      private double nd() {
          return Double.parseDouble(ns());
      }
  
      private char nc() {
          return (char) skip();
      }
  
      private String ns() {
          int b = skip();
          StringBuilder sb = new StringBuilder();
          while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != ' ')
              sb.appendCodePoint(b);
              b = readByte();
          }
          return sb.toString();
      }
  
      private char[] ns(int n) {
          char[] buf = new char[n];
          int b = skip(), p = 0;
          while (p < n && !(isSpaceChar(b))) {
              buf[p++] = (char) b;
              b = readByte();
          }
          return n == p ? buf : Arrays.copyOf(buf, p);
      }
  
      private Integer[] na(int n) {
          Integer[] a = new Integer[n];
          for (int i = 0; i < n; i++) {
              a[i] = ni();
          }
          return a;
      }
  
      private Long[] nal(int n) {
          Long[] a = new Long[n];
          for (int i = 0; i < n; i++) {
              a[i] = nl();
          }
          return a;
      }
  
      private char[][] nm(int n, int m) {
          char[][] map = new char[n][];
          for (int i = 0; i < n; i++) {
              map[i] = ns(m);
          }
          return map;
      }
  
      private Integer[][] nmi(int n, int m) {
          Integer[][] map = new Integer[n][];
          for (int i = 0; i < n; i++) {
              map[i] = na(m);
          }
          return map;
      }
  
      private int ni() {
          return (int) nl();
      }
  
      private long nl() {
          long num = 0;
          int b;
          boolean minus = false;
          while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
              ;
          if (b == '-') {
              minus = true;
              b = readByte();
          }
  
          while (true) {
              if (b >= '0' && b <= '9') {
                  num = num * 10 + (b - '0');
              } else {
                  return minus ? -num : num;
              }
              b = readByte();
          }
      }
  
      public static class FastWriter {
  
          private static final int BUF_SIZE = 1 << 13;
          private final byte[] buf = new byte[BUF_SIZE];
          private final OutputStream out;
          private int ptr = 0;
  
          private FastWriter() {
              out = null;
          }
  
          public FastWriter(OutputStream os) {
              this.out = os;
          }
  
          public FastWriter(String path) {
              try {
                  this.out = new FileOutputStream(path);
              } catch (FileNotFoundException e) {
                  throw new RuntimeException("FastWriter");
              }
          }
  
          public FastWriter write(byte b) {
              buf[ptr++] = b;
              if (ptr == BUF_SIZE) {
                  innerflush();
              }
              return this;
          }
  
          public FastWriter write(char c) {
              return write((byte) c);
          }
  
          public FastWriter write(char[] s) {
              for (char c : s) {
                  buf[ptr++] = (byte) c;
                  if (ptr == BUF_SIZE) {
                      innerflush();
                  }
              }
              return this;
          }
  
          public FastWriter write(String s) {
              s.chars().forEach(c -> {
                  buf[ptr++] = (byte) c;
                  if (ptr == BUF_SIZE) {
                      innerflush();
                  }
              });
              return this;
          }
  
          private static int countDigits(int l) {
              if (l >= 1000000000) {
                  return 10;
              }
              if (l >= 100000000) {
                  return 9;
              }
              if (l >= 10000000) {
                  return 8;
              }
              if (l >= 1000000) {
                  return 7;
              }
              if (l >= 100000) {
                  return 6;
              }
              if (l >= 10000) {
                  return 5;
              }
              if (l >= 1000) {
                  return 4;
              }
              if (l >= 100) {
                  return 3;
              }
              if (l >= 10) {
                  return 2;
              }
              return 1;
          }
  
          public FastWriter write(int x) {
              if (x == Integer.MIN_VALUE) {
                  return write((long) x);
              }
              if (ptr + 12 >= BUF_SIZE) {
                  innerflush();
              }
              if (x < 0) {
                  write((byte) '-');
                  x = -x;
              }
              int d = countDigits(x);
              for (int i = ptr + d - 1; i >= ptr; i--) {
                  buf[i] = (byte) ('0' + x % 10);
                  x /= 10;
              }
              ptr += d;
              return this;
          }
  
          private static int countDigits(long l) {
              if (l >= 1000000000000000000L) {
                  return 19;
              }
              if (l >= 100000000000000000L) {
                  return 18;
              }
              if (l >= 10000000000000000L) {
                  return 17;
              }
              if (l >= 1000000000000000L) {
                  return 16;
              }
              if (l >= 100000000000000L) {
                  return 15;
              }
              if (l >= 10000000000000L) {
                  return 14;
              }
              if (l >= 1000000000000L) {
                  return 13;
              }
              if (l >= 100000000000L) {
                  return 12;
              }
              if (l >= 10000000000L) {
                  return 11;
              }
              if (l >= 1000000000L) {
                  return 10;
              }
              if (l >= 100000000L) {
                  return 9;
              }
              if (l >= 10000000L) {
                  return 8;
              }
              if (l >= 1000000L) {
                  return 7;
              }
              if (l >= 100000L) {
                  return 6;
              }
              if (l >= 10000L) {
                  return 5;
              }
              if (l >= 1000L) {
                  return 4;
              }
              if (l >= 100L) {
                  return 3;
              }
              if (l >= 10L) {
                  return 2;
              }
              return 1;
          }
  
          public FastWriter write(long x) {
              if (x == Long.MIN_VALUE) {
                  return write("" + x);
              }
              if (ptr + 21 >= BUF_SIZE) {
                  innerflush();
              }
              if (x < 0) {
                  write((byte) '-');
                  x = -x;
              }
              int d = countDigits(x);
              for (int i = ptr + d - 1; i >= ptr; i--) {
                  buf[i] = (byte) ('0' + x % 10);
                  x /= 10;
              }
              ptr += d;
              return this;
          }
  
          public FastWriter write(double x, int precision) {
              if (x < 0) {
                  write('-');
                  x = -x;
              }
              x += Math.pow(10, -precision) / 2;
              //		if(x < 0){ x = 0; }
              write((long) x).write(".");
              x -= (long) x;
              for (int i = 0; i < precision; i++) {
                  x *= 10;
                  write((char) ('0' + (int) x));
                  x -= (int) x;
              }
              return this;
          }
  
          public FastWriter writeln(char c) {
              return write(c).writeln();
          }
  
          public FastWriter writeln(int x) {
              return write(x).writeln();
          }
  
          public FastWriter writeln(long x) {
              return write(x).writeln();
          }
  
          public FastWriter writeln(double x, int precision) {
              return write(x, precision).writeln();
          }
  
          public FastWriter write(int... xs) {
              boolean first = true;
              for (int x : xs) {
                  if (!first) {
                      write(' ');
                  }
                  first = false;
                  write(x);
              }
              return this;
          }
  
          public FastWriter write(long... xs) {
              boolean first = true;
              for (long x : xs) {
                  if (!first) {
                      write(' ');
                  }
                  first = false;
                  write(x);
              }
              return this;
          }
  
          public FastWriter writeln() {
              return write((byte) '\n');
          }
  
          public FastWriter writeln(int... xs) {
              return write(xs).writeln();
          }
  
          public FastWriter writeln(long... xs) {
              return write(xs).writeln();
          }
  
          public FastWriter writeln(char[] line) {
              return write(line).writeln();
          }
  
          public FastWriter writeln(char[]... map) {
              for (char[] line : map) {
                  write(line).writeln();
              }
              return this;
          }
  
          public FastWriter writeln(String s) {
              return write(s).writeln();
          }
  
          private void innerflush() {
              try {
                  out.write(buf, 0, ptr);
                  ptr = 0;
              } catch (IOException e) {
                  throw new RuntimeException("innerflush");
              }
          }
  
          public void flush() {
              innerflush();
              try {
                  out.flush();
              } catch (IOException e) {
                  throw new RuntimeException("flush");
              }
          }
  
          public FastWriter print(byte b) {
              return write(b);
          }
  
          public FastWriter print(char c) {
              return write(c);
          }
  
          public FastWriter print(char[] s) {
              return write(s);
          }
  
          public FastWriter print(String s) {
              return write(s);
          }
  
          public FastWriter print(int x) {
              return write(x);
          }
  
          public FastWriter print(long x) {
              return write(x);
          }
  
          public FastWriter print(double x, int precision) {
              return write(x, precision);
          }
  
          public FastWriter println(char c) {
              return writeln(c);
          }
  
          public FastWriter println(int x) {
              return writeln(x);
          }
  
          public FastWriter println(long x) {
              return writeln(x);
          }
  
          public FastWriter println(double x, int precision) {
              return writeln(x, precision);
          }
  
          public FastWriter print(int... xs) {
              return write(xs);
          }
  
          public FastWriter print(long... xs) {
              return write(xs);
          }
  
          public FastWriter println(int... xs) {
              return writeln(xs);
          }
  
          public FastWriter println(long... xs) {
              return writeln(xs);
          }
  
          public FastWriter println(char[] line) {
              return writeln(line);
          }
  
          public FastWriter println(char[]... map) {
              return writeln(map);
          }
  
          public FastWriter println(String s) {
              return writeln(s);
          }
  
          public FastWriter println() {
              return writeln();
          }
      }
  
      public void trnz(int... o) {
          for (int i = 0; i < o.length; i++) {
              if (o[i] != 0) {
                  System.out.print(i + ":" + o[i] + " ");
              }
          }
          System.out.println();
      }
  
      // print ids which are 1
      public void trt(long... o) {
          Queue<Integer> stands = new ArrayDeque<>();
          for (int i = 0; i < o.length; i++) {
              for (long x = o[i]; x != 0; x &= x - 1) {
                  stands.add(i << 6 | Long.numberOfTrailingZeros(x));
              }
          }
          System.out.println(stands);
      }
  
      public void tf(boolean... r) {
          for (boolean x : r) {
              System.out.print(x ? '#' : '.');
          }
          System.out.println();
      }
  
      public void tf(boolean[]... b) {
          for (boolean[] r : b) {
              for (boolean x : r) {
                  System.out.print(x ? '#' : '.');
              }
              System.out.println();
          }
          System.out.println();
      }
  
      public void tf(long[]... b) {
          if (INPUT.length() != 0) {
              for (long[] r : b) {
                  for (long x : r) {
                      for (int i = 0; i < 64; i++) {
                          System.out.print(x << ~i < 0 ? '#' : '.');
                      }
                  }
                  System.out.println();
              }
              System.out.println();
          }
      }
  
      public void tf(long... b) {
          if (INPUT.length() != 0) {
              for (long x : b) {
                  for (int i = 0; i < 64; i++) {
                      System.out.print(x << ~i < 0 ? '#' : '.');
                  }
              }
              System.out.println();
          }
      }
  
      private void tr(Object... o) {
          System.out.println(Arrays.deepToString(o));
      }
  }
  