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.OutputStream;
  import java.io.IOException;
  import java.io.InputStream;
  import java.io.PrintWriter;
  import java.io.BufferedReader;
  import java.io.InputStreamReader;
  import java.util.*;
  
  public class Main {
      public static void main(String[] args){
          InputStream inputStream = System.in;
          OutputStream outputStream = System.out;
          InputReader in = new InputReader(inputStream);
          PrintWriter out = new PrintWriter(outputStream);
          solve(in, out);
          out.close();
      }
  
      static String reverse(String s) {
          return (new StringBuilder(s)).reverse().toString();
      }
  
      static void sieveOfEratosthenes(int n, int factors[], ArrayList<Integer> ar) 
      { 
          factors[1]=1;
          int p;
          for(p = 2; p*p <=n; p++) 
          { 
              if(factors[p] == 0) 
              { 
                  ar.add(p);
                  factors[p]=p;
                  for(int i = p*p; i <= n; i += p) 
                      if(factors[i]==0)
                          factors[i] = p; 
              } 
          } 
          for(;p<=n;p++){
              if(factors[p] == 0) 
              { 
                  factors[p] = p;
                  ar.add(p);
              } 
          }
      }
  
      static void sort(int ar[]) {
          int n = ar.length;
          ArrayList<Integer> a = new ArrayList<>();
          for (int i = 0; i < n; i++)
              a.add(ar[i]);
          Collections.sort(a);
          for (int i = 0; i < n; i++)
              ar[i] = a.get(i);
      }
  
      static void sort1(long ar[]) {
          int n = ar.length;
          ArrayList<Long> a = new ArrayList<>();
          for (int i = 0; i < n; i++)
              a.add(ar[i]);
          Collections.sort(a);
          for (int i = 0; i < n; i++)
              ar[i] = a.get(i);
      }
  
      static void sort2(char ar[]) {
          int n = ar.length;
          ArrayList<Character> a = new ArrayList<>();
          for (int i = 0; i < n; i++)
              a.add(ar[i]);
          Collections.sort(a);
          for (int i = 0; i < n; i++)
              ar[i] = a.get(i);
      }
  
      static long ncr(long n, long r, long mod) {
          if (r == 0)
              return 1;
          long val = ncr(n - 1, r - 1, mod);
          val = (n * val) % mod;
          val = (val * modInverse(r, mod)) % mod;
          return val;
      }
  
      static long min[];
      static long lz[];
      
      // static void build(long a[], int v, int tl, int tr) {
      //     if (tl == tr) {
      //         min[v] = a[tl];
              
      //     } else {
      //         int tm = (tl + tr) / 2;
      //         build(a, v*2, tl, tm);
      //         build(a, v*2+1, tm+1, tr);
      //         min[v] = min[v*2] + min[v*2+1];
      //     }
      // }
  
      // static void push(int v, int tl, int tr){
      //     if(tl==tr){
      //         lz[v] = 0;
      //         return;
      //     }
      //     min[2*v] += lz[v];
      //     // min[2*v] %= m;
      //     min[2*v+1] += lz[v];
      //     // min[2*v+1] %= m;
      //     lz[2*v] += lz[v];
      //     lz[2*v] %= m;
      //     lz[2*v+1] += lz[v];
      //     lz[2*v+1] %= m;
      //     lz[v] = 0;
      // }
  
      static void update(int v, int tl, int tr, int l, int r, long val) {
          // push(v,tl,tr);
          if(tl>r||tr<l)
              return;
          if(tl>=l&&tr<=r){
              min[v] = Math.min(val, min[v]);
              return;
          }
          int tm = ((tl + tr) >> 1);
          update(v*2, tl, tm, l, r, val);
          update(v*2+1, tm+1, tr, l, r, val);
          min[v] = Math.min(min[2*v],min[2*v+1]);
      }
  
      static long get(int v, int tl, int tr, int l, int r) {
          // push(v,tl,tr);
          if(l>r)
              return Long.MAX_VALUE;
          if (tl >= l && tr <= r) {
              return min[v];
          }
          int tm = ((tl + tr) >> 1);
          if(l>tm){
              return get(2*v+1, tm+1, tr, l, r);
          }
          if(r<tm+1){
              return get(2*v, tl, tm, l, r);
          }
          return Math.min(get(2*v, tl, tm, l, r), get(2*v+1, tm+1, tr, l, r));
      }
  
      // static int y = 0;
  
      static int parent[];
      static int rank[];
  
      static long m = 0;
  
      static int find_set(int v) {
          if (v == parent[v])
              return v;
          return find_set(parent[v]);
      }
      
      static void make_set(int v) {
          parent[v] = v;
          rank[v] = 1;
      }
      
      static void union_sets(int a, int b) {
          a = find_set(a);
          b = find_set(b);
          if (a != b) {
              if (rank[a] < rank[b]){
                  int tmp = a;
                  a = b;
                  b = tmp;
              }
              parent[b] = a;
              // if (rank[a] == rank[b])
              //     rank[a]++;
              rank[a] += rank[b];
          }
      }
  
      static int parent1[];
      static int rank1[];
  
      static int find_set1(int v) {
          if (v == parent1[v])
              return v;
          return find_set1(parent1[v]);
      }
      
      static void make_set1(int v) {
          parent1[v] = v;
          rank1[v] = 1;
      }
      
      static void union_sets1(int a, int b) {
          a = find_set1(a);
          b = find_set1(b);
          if (a != b) {
              if (rank1[a] < rank1[b]){
                  int tmp = a;
                  a = b;
                  b = tmp;
              }
              parent1[b] = a;
              // if (rank1[a] == rank1[b])
              //     rank1[a]++;
              rank1[a] += rank1[b];
          }
      }
  
      static int count = 0;
      static int count1 = 0;
  
      public static void solve(InputReader sc, PrintWriter pw){
          int i, j = 0;
          // int t = 1; 
          long mod = 1000000007;
          int t = sc.nextInt();
          u: while (t-- > 0) {
              int n = sc.nextInt();
              int a[] = new int[n];
              for(i=0;i<n;i++){
                  a[i] = sc.nextInt();
              }
              int f = 0;
              for(i=0;i<n-1;i++){
                  if(a[i]>=a[i+1]){
                      f = 1;
                  }
              }
              if(n%2==0||f==1){
                  pw.println("YES");
              }
              else{
                  pw.println("NO");
              }
          }
      }
  
      static void KMPSearch(char pat[], char txt[], int pres[]){
          int M = pat.length;
          int N = txt.length;
          int lps[] = new int[M];
          int j = 0; 
          computeLPSArray(pat, M, lps);
          int i = 0;
          while (i < N) {
              if (pat[j] == txt[i]) {
                  j++;
                  i++;
              }
              if (j == M) {
                  pres[i-1] = 1;
                  j = lps[j - 1];
              }
              else if (i < N && pat[j] != txt[i]) {
                  if (j != 0)
                      j = lps[j - 1];
                  else
                      i = i + 1;
              }
          }
      }
    
      static void computeLPSArray(char pat[], int M, int lps[])
      {
          int len = 0;
          int i = 1;
          lps[0] = 0; 
          while (i < M) {
              if (pat[i] == pat[len]) {
                  len++;
                  lps[i] = len;
                  i++;
              }
              else 
              {
                  if (len != 0) {
                      len = lps[len - 1];
                  }
                  else
                  {
                      lps[i] = len;
                      i++;
                  }
              }
          }
      }
  
      static long[][] matrixMult(long a[][], long b[][], long mod){
          int n = a.length;
          int m = a[0].length;
          int p = b[0].length;
          long c[][] = new long[n][p];
          for(int i=0;i<n;i++){
              for(int j=0;j<m;j++){
                  for(int k=0;k<p;k++){
                      c[i][k] += a[i][j]*b[j][k];
                      c[i][k] %= mod;
                  }
              }
          }
          return c;
      }
  
      static long[][] exp(long mat[][], long b, long mod){
          if(b==0){
              int n = mat.length;
              long res[][] = new long[n][n];
              for(int i=0;i<n;i++){
                  res[i][i] = 1;
              }
              return res;
          }
          long half[][] = exp(mat, b/2, mod);
          long res[][] = matrixMult(half, half, mod);
          if(b%2==1){
              res = matrixMult(res, mat, mod);
          }
          return res;
      }
  
      static void countPrimeFactors(int num, int a[], HashMap<Integer,Integer> pos){
          for(int i=2;i*i<num;i++){
              if(num%i==0){
                  int y = pos.get(i);
                  while(num%i==0){
                      a[y]++;
                      num/=i;
                  }
              }
          }
          if(num>1){
              int y = pos.get(num);
              a[y]++;
          }
      }
  
      static void assignAnc(ArrayList<Integer> ar[], int depth[], int sz[], int par[][] ,int curr, int parent, int d){
          depth[curr] = d;
          sz[curr] = 1;
          par[curr][0] = parent;
          for(int v:ar[curr]){
              if(parent==v)
                  continue;
              assignAnc(ar, depth, sz, par, v, curr, d+1);
              sz[curr] += sz[v];
          }
      }
  
      static int findLCA(int a, int b, int par[][], int depth[]){
          if(depth[a]>depth[b]){
              a = a^b;
              b = a^b;
              a = a^b;
          }
          int diff = depth[b] - depth[a];
          for(int i=19;i>=0;i--){
              if((diff&(1<<i))>0){
                  b = par[b][i];
              }
          }
          if(a==b)
              return a;
          for(int i=19;i>=0;i--){
              if(par[b][i]!=par[a][i]){
                  b = par[b][i];
                  a = par[a][i];
              }
          }
          return par[a][0];
      }
  
      static void formArrayForBinaryLifting(int n, int par[][]){
          for(int j=1;j<20;j++){
              for(int i=0;i<n;i++){
                  if(par[i][j-1]==-1)
                      continue;
                  par[i][j] = par[par[i][j-1]][j-1];
              }
          }
      }
  
      static long lcm(int a, int b){
          return a*b/gcd(a,b);
      }
  
      static class Pair1 {
          long a;
          long b;
          
          Pair1(long a, long b) {
              this.a = a;
              this.b = b;
          }
      }
  
      static class Pair implements Comparable<Pair> {
          int a;
          int b;
          // int c;
          
          Pair(int a, int b) {
              this.a = a;
              this.b = b;
              // this.c = c;
          }
   
          public int compareTo(Pair p) {
              if(a!=p.a)
                  return a-p.a;
              return b-p.b;
          }
      }
  
      static class Pair2 implements Comparable<Pair2> {
          int a;
          int b;
          int c;
          
          Pair2(int a, int b, int c) {
              this.a = a;
              this.b = b;
              this.c = c;
          }
   
          public int compareTo(Pair2 p) {
              return a-p.a;
          }
      }
  
      static boolean isPrime(int n) { 
          if (n <= 1) 
              return false; 
          if (n <= 3) 
              return true; 
          if (n % 2 == 0 ||  n % 3 == 0) 
              return false; 
          for (int i = 5; i * i <= n; i = i + 6) 
              if (n % i == 0 || n % (i + 2) == 0) 
                  return false; 
          return true; 
      } 
  
      static long gcd(long a, long b) {
          if (b == 0)
              return a;
          return gcd(b, a % b);
      }
  
      static long fast_pow(long base, long n, long M) {
          if (n == 0)
              return 1;
          if (n == 1)
              return base % M;
          long halfn = fast_pow(base, n / 2, M);
          if (n % 2 == 0)
              return (halfn * halfn) % M;
          else
              return (((halfn * halfn) % M) * base) % M;
      }
  
      static long modInverse(long n, long M) {
          return fast_pow(n, M - 2, M);
      }
  
      static class InputReader {
          public BufferedReader reader;
          public StringTokenizer tokenizer;
  
          public InputReader(InputStream stream) {
              reader = new BufferedReader(new InputStreamReader(stream), 9992768);
              tokenizer = null;
          }
  
          public String next() {
              while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                  try {
                      tokenizer = new StringTokenizer(reader.readLine());
                  } catch (IOException e) {
                      throw new RuntimeException(e);
                  }
              }
              return tokenizer.nextToken();
          }
  
          public int nextInt() {
              return Integer.parseInt(next());
          }
  
          public long nextLong() {
              return Long.parseLong(next());
          }
      }
  }