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.

import java.io.*;
import java.util.*;
import java.math.BigDecimal;
import java.math.*;

public class Main{
	
	public static void main(String[] args) {
	    
	      TaskA solver = new TaskA();
//	      boolean[]prime=seive(3*100001);
	      
	      int t = in.nextInt();
	      for (int i = 1; i <= t ; i++) {
	          solver.solve(i, in, out);
	      }
	     
	      
//	      solver.solve(1, in, out);
	      
	      
	      out.flush();
	    out.close();
	  }
	
	 static class TaskA {
	      public void solve(int testNumber, InputReader in, PrintWriter out) {
	    	  int n= in.nextInt();
	    	  int[]arr=new int[n];
	    	  int inc=0;
	    	  int dec=0;
	    	  int eq=0;
	    	  for(int i=0;i<n;i++) {
	    		  arr[i]=in.nextInt();
	    	  }
	    	  for(int i=1;i<n;i++) {
	    		  if((arr[i]>arr[i-1])) {
	    			  inc++;
	    		  }
	    		  if((arr[i]<arr[i-1])) {
	    			  dec++;
	    		  }
	    		  if(arr[i]==arr[i-1]) {
	    			  eq++;
	    		  }
	    	  }
	    	  if(n%2==0||dec>0||eq>0) {
	    		  println("YES");
	    	  }
	    	 
	    	  else {
	    		  println("NO");
	    	  }
	      }
	 }
	 
	 
	 static long pow(long b, long e) {
	        long ans = 1;
	        while (e > 0) {
	            if (e % 2 == 1)
	                ans = ans * b % mod;
	            e >>= 1;
	            b = b * b % mod;
	        }
	        return ans;
	    }
	 static int[]dp;  //global variable 
	 static int minStep(int n) {
		 if(n<0) {
			 return Integer.MAX_VALUE;       //this is never possible should be handled bcz n-1,n-5 can be negative
		 }
		 if(n==0) {return 0;}
		 if(dp[n]!=0) {
			 return dp[n];  //if solution we have already calculated
		 }
		 else {
			 int x=1+Math.min(minStep(n-1),Math.min(minStep(n-3),minStep(n-5)));
			 dp[n]=x;        //update the array after calculation
			 return x;
		 }
		 
	 }
	 
	 
	 
	 static void sortF(Pair arr[])
	    {
	        // Comparator to sort the pair according to second element
	        Arrays.sort(arr, new Comparator<Pair>() {
	            @Override public int compare(Pair p1, Pair p2)
	            {	if(p1.first==p2.first) {
	            	return p1.second-p2.second;
	            }
	                return p1.first - p2.first;
	            }
	        });
	    }
	 
	 static int[] shift (int[]inp,int i,int j){
		 int[]arr=new int[j-i+1];
		 int n=j-i+1;
		 for(int k=i;k<=j;k++) {
			 arr[(k-i+1)%n]=inp[k];
		 }
		 for(int k=0;k<n;k++ ) {
			 inp[k+i]=arr[k];
		 }
		 return inp;
	 }
	 static int sumDigits(long n) {
		 int total=0;
		 while(n!=0) {
			 total+=n%10;
			 n=n/10;
		 }
		 return total;
	 }
	 
	 static long[] fac;
	    static long mod = (long) 1000000007;
	 
	    static void initFac(long n) {
	        fac = new long[(int)n + 1];
	        fac[0] = 1;
	        for (int i = 1; i <= n; i++) {
	            fac[i] = (fac[i - 1]  * i) % mod;
	        }
	    }
	 
	 
	 
	    static long nck(int n, int k) {
	        if (n < k)
	            return 0;
	        long den = inv((int) (fac[k] * fac[n - k] % mod));
	        return fac[n] * den % mod;
	    }
	 
	    static int[]MakeArr(int n){
			int[]arr=new int[n];
			for(int i=0;i<n;i++) {
				arr[i]=in.nextInt();
			}
			return arr;
		}
	static int[]arr(){
		int n= in.nextInt();
		int[]arr=new int[n];
		for(int i=0;i<n;i++) {
			arr[i]=in.nextInt();
		}
		return arr;
	}
	 
	    static long inv(long x) {
	        return pow(x, mod - 2);
	    }
	 
	 
	    static void sort(int[] a) {
	        ArrayList<Integer> q = new ArrayList<>();
	        for (int i : a) q.add(i);
	        Collections.sort(q);
	        for (int i = 0; i < a.length; i++) a[i] = q.get(i);
	    }
	 
	    static void sort(long[] a) {
	        ArrayList<Long> q = new ArrayList<>();
	        for (long i : a) q.add(i);
	        Collections.sort(q);
	        for (int i = 0; i < a.length; i++) a[i] = q.get(i);
	    }
	    
	 public static int bfsSize(int source,LinkedList<Integer>[]a,boolean[]visited) {
			Queue<Integer>q=new LinkedList<>();
			q.add(source);
			visited[source]=true;
			int distance=0;
			while(!q.isEmpty()) {
				int curr=q.poll();
				distance++;
				for(int neighbour:a[curr]) {
					if(!visited[neighbour]) {
						visited[neighbour]=true;
						q.add(neighbour);
					}
				}
			}
			return distance;
		}
	 public static Set<Integer>factors(int n){
		 Set<Integer>ans=new HashSet<>();
		 ans.add(1);
		 for(int i=2;i*i<=n;i++) {
			 if(n%i==0) {
				 ans.add(i);
				 ans.add(n/i);
			 }
		 }
		 return ans;
	 }
	public static int bfsSp(int source,int destination,ArrayList<Integer>[]a) {
		boolean[]visited=new boolean[a.length];
		int[]parent=new int[a.length];
		Queue<Integer>q=new LinkedList<>();
		int distance=0;
		q.add(source);
		visited[source]=true;
		parent[source]=-1;
		while(!q.isEmpty()) {
			int curr=q.poll();
			if(curr==destination) {
				break;
			}
			for(int neighbour:a[curr]) {
				if(neighbour!=-1&&!visited[neighbour]) {
					visited[neighbour]=true;
					q.add(neighbour);
					parent[neighbour]=curr;
				}
			}
		}
		int cur=destination;
		while(parent[cur]!=-1) {
			distance++;
			cur=parent[cur];
		}
		return distance;
	}
	 static int bs(int size,int[]arr) {
		 int x = -1;
    	 for (int b = size/2; b >= 1; b /= 2) {
        	 while (!ok(arr));
        	 }
    	 int k = x+1;
    	 return k;
	 }
	 
	 static boolean ok(int[]x) {
		 return false;
	 }
	 
	 public static int solve1(ArrayList<Integer> A) {
		 long[]arr =new long[A.size()+1];
		 int n=A.size();
		 for(int i=1;i<=A.size();i++) {
			 arr[i]=((i%2)*((n-i+1)%2))%2;
			 arr[i]%=2;
		 }
		 int ans=0;
		 for(int i=0;i<A.size();i++) {
			 if(arr[i+1]==1) {
				 ans^=A.get(i);
			 }
		 }
		 return ans;
	   }
	 
	     public static String printBinary(long a) {
	    	 String str="";
	    	 for(int i=31;i>=0;i--) {
	    		 if((a&(1<<i))!=0) {
	    			 str+=1;
	    		 }
	    		 
	    		 if((a&(1<<i))==0 && !str.isEmpty()) {
	    			 str+=0;
	    		 }
	    		 
	    	 }
	    	 return str;
	     }
	     
		 public static String reverse(long a) {
		        long rev=0;
		        String str="";
		        int x=(int)(Math.log(a)/Math.log(2))+1;
		        for(int i=0;i<32;i++) {
		        	rev<<=1;
		        	if((a&(1<<i))!=0) {
		        		rev|=1;
		        		str+=1;
		        	}
		        	else {
		        		str+=0;
		        	}
		        }
		        return str;
			}
		
	 
	 ////////////////////////////////////////////////////////
	 
	 static void sortS(Pair arr[])
	    {
	        // Comparator to sort the pair according to second element
	        Arrays.sort(arr, new Comparator<Pair>() {
	            @Override public int compare(Pair p1, Pair p2)
	            {
	                return p1.second - p2.second;
	            }
	        });
	    }
	 
	 static class Pair implements Comparable<Pair>
	 {
	   int first ;int second  ;
	  
	   public  Pair(int x, int y)
	   {
	       this.first = x ;this.second = y ;
	   }
	   
	   @Override
	  public boolean equals(Object obj)
	  {
	      if(obj == this)return true  ;
	      
	      if(obj == null)return false  ;
	      
	      if(this.getClass() != obj.getClass()) return false ;
	      
	      Pair other  = (Pair)(obj) ;
	      
	      if(this.first != other.first)return false  ;
	      if(this.second != other.second)return false  ;
	      
	      return true  ;
	      
	  }
	     
	     @Override
	     
	     public int hashCode()
	     {
	         return this.first^this.second  ;
	     }
	       
	 @Override
	 	public String toString() {
	 	
	 	String ans = "" ;ans  += this.first ;	ans += " ";	ans += this.second ;
	 	return ans  ;
	 	}

	

	@Override
	public int compareTo(Main.Pair o) {
		{	if(this.first==o.first) {
        	return this.second-o.second;
        }
            return this.first - o.first;
        }
	}
	 	

	 }
	 //////////////////////////////////////////////////////////////////////////
	
	    
	 
	
	 static int nD(long num) {
		 String s=String.valueOf(num);
		 return s.length();
	 }
	 
	 
	 static int CommonDigits(int x,int y) {
		 String s=String.valueOf(x);
		 String s2=String.valueOf(y);
		 return 0;
	 }
	 
	 
	 
	 static int lcs(String str1, String str2, int m, int n)
	    {
	        int L[][] = new int[m + 1][n + 1];
	        int i, j;
	 
	        // Following steps build L[m+1][n+1] in
	        // bottom up fashion. Note that L[i][j]
	        // contains length of LCS of str1[0..i-1]
	        // and str2[0..j-1]
	        for (i = 0; i <= m; i++) {
	            for (j = 0; j <= n; j++) {
	                if (i == 0 || j == 0)
	                    L[i][j] = 0;
	 
	                else if (str1.charAt(i - 1)
	                         == str2.charAt(j - 1))
	                    L[i][j] = L[i - 1][j - 1] + 1;
	 
	                else
	                    L[i][j] = Math.max(L[i - 1][j],
	                                       L[i][j - 1]);
	            }
	        }
	 
	        // L[m][n] contains length of LCS
	        // for X[0..n-1] and Y[0..m-1]
	        return L[m][n];
	    }
	 
	 /////////////////////////////////
	 boolean IsPowerOfTwo(int x)
	 {
	     return (x != 0) && ((x & (x - 1)) == 0);
	 }
	 ////////////////////////////////
	 
	 static long power(long a,long b,long m ) {
		 long ans=1;
		 while(b>0) {
			 if(b%2==1) {
				 ans=((ans%m)*(a%m))%m; b--;
			 }
			 else {
				 a=(a*a)%m;b/=2;
			 }
			 
		 }
		 return ans%m;
	 }
	 ///////////////////////////////
	 public static boolean repeatedSubString(String string) {
		    return ((string + string).indexOf(string, 1) != string.length());
		}
	 static int search(char[]c,int start,int end,char x) {
		 for(int i=start;i<end;i++) {
			 if(c[i]==x) {return i;}
		 }
		 return -2;
	 }
	 ////////////////////////////////
	 
	
	 
	 static int gcd(int a, int b) {
	        while (b != 0) {
	            int t = b;
	            b = a % b;
	            a = t;
	        }
	        return a;
	    }
	
	 
	
	 
	 static long fac(long a)
	 {
	     if(a== 0L || a==1L)return 1L ;
	     
	     return a*fac(a-1L) ;
	 }
	 
	 
	 
	 static ArrayList al() {
		 ArrayList<Integer>a =new ArrayList<>();
			return a;
		}
	 
	static HashSet h() {
			return new HashSet<Integer>();
		}
	static void debug(int[][]a) {
		int n= a.length;
		for(int i=1;i<=n;i++) {
	  		for(int j=1;j<=n;j++) {
	  			out.print(a[i][j]+" ");
	  		}
	  		out.print("\n");
	  	}
	}
	static void debug(int[]a) {
			out.println(Arrays.toString(a));
		}
	
	static void debug(ArrayList<Integer>a) {
				out.println(a.toString());
		}
	
	static boolean[]seive(int n){
		boolean[]b=new boolean[n+1];
		 for (int i = 2; i <= n; i++)
	            b[i] = true;
		 
		for(int i=2;i*i<=n;i++) {
			if(b[i]) {
				for(int j=i*i;j<=n;j+=i) {
					b[j]=false;
				}
			}
			
		}
		return b;
	}
	
	 static int longestIncreasingSubseq(int[]arr) {
		  int[]sizes=new int[arr.length];
		  Arrays.fill(sizes, 1);
		  int max=1;
		  for(int i=1;i<arr.length;i++) {
			  for(int j=0;j<i;j++) {
				  if(arr[j]<arr[i]) {
					  sizes[i]=Math.max(sizes[i],sizes[j]+1);
					  max=Math.max(max, sizes[i]);
				  }
			  }
		  }
		  return max;
	 }
	 
	 public static ArrayList primeFactors(long n)
	    {
		    ArrayList<Long>h= new ArrayList<>();
	        // Print the number of 2s that divide n
	        if(n%2 ==0) {h.add(2L);}
	 
	        // n must be odd at this point.  So we can
	        // skip one element (Note i = i +2)
	        for (long i = 3; i <= Math.sqrt(n); i+= 2)
	        {
	            if(n%i==0) {h.add(i);}
	        }
	        if (n > 2)
	            h.add(n);
	        return h;
	    }
	 
	 static boolean Divisors(long n){
		 if(n%2==1) {
			 return true;
		 }
	     for (long i=2; i<=Math.sqrt(n); i++){
	            if (n%i==0 && i%2==1){
	                   return true;
	            } 
	        }
	     return false;
	    }
	
	static InputStream inputStream = System.in;
    static OutputStream outputStream = System.out;
    static InputReader in = new InputReader(inputStream);
    static PrintWriter out = new PrintWriter(outputStream);
    
    public static void superSet(int[]a,ArrayList<String>al,int i,String s) {
    	if(i==a.length) {
    		al.add(s);
    		return;
    	}
    	superSet(a,al,i+1,s);
    	superSet(a,al,i+1,s+a[i]+" ");
    }
    
	public static long[] makeArr() {
		long size=in.nextInt();
		long []arr=new long[(int)size];
		for(int i=0;i<size;i++) {
			arr[i]=in.nextInt();
		}
		return arr;
	}
	
	public static long[] arr(int n) {
		long []arr=new long[n+1];
		for(int i=1;i<n+1;i++) {
			arr[i]=in.nextLong();
		}
		return arr;
	}
	
  public static void sort(long arr[], int l, int r)
  {
      if (l < r)
      {
          // Find the middle point
          int m = (l+r)/2;

          // Sort first and second halves
          sort(arr, l, m);
          sort(arr , m+1, r);

          // Merge the sorted halves
          merge(arr, l, m, r);
      }
  }
  static void println(long x) {
		 out.println(x);
	 }
  static void print(long c) {
		 out.print(c);
	 }
  static void print(int c) {
		 out.print(c);
	 }
	 static void println(int x) {
		 out.println(x);
	 }
	 static void print(String s) {
		 out.print(s);
	 }
	 static void println(String s) {
		 out.println(s);
	 }
public static void merge(long arr[], int l, int m, int r)
  {
      // Find sizes of two subarrays to be merged
      int n1 = m - l + 1;
      int n2 = r - m;

      /* Create temp arrays */
      long L[] = new long[n1];
      long R[] = new long[n2];

      //Copy data to temp arrays
      for (int i=0; i<n1; ++i)
          L[i] = arr[l + i];
      for (int j=0; j<n2; ++j)
          R[j] = arr[m + 1+ j];


      /* Merge the temp arrays */

      // Initial indexes of first and second subarrays
      int i = 0, j = 0;

      // Initial index of merged subarry array
      int k = l;
      while (i < n1 && j < n2)
      {
          if (L[i] <= R[j])
          {
              arr[k] = L[i];
              i++;
          }
          else
          {
              arr[k] = R[j];
              j++;
          }
          k++;
      }

      /* Copy remaining elements of L[] if any */
      while (i < n1)
      {
          arr[k] = L[i];
          i++;
          k++;
      }

      /* Copy remaining elements of R[] if any */
      while (j < n2)
      {
          arr[k] = R[j];
          j++;
          k++;
      }
  }

public static void reverse(int[] array)
{
    int n = array.length;
    for (int i = 0; i < n / 2; i++) {
        int temp = array[i];
        array[i] = array[n - i - 1];
        array[n - i - 1] = temp;
    }
}

  public static long nCr(int n,int k)
  {
      long ans=1L;
      k=k>n-k?n-k:k;
     
      for( int j=1;j<=k;j++,n--)
      {
          if(n%j==0)
          {
              ans*=n/j;
          }else
          if(ans%j==0)
          {
              ans=ans/j*n;
          }else
          {
              ans=(ans*n)/j;
          }
      }
      return ans;
  }

  static int searchMax(int index,long[]inp) {
	  while(index+1<inp.length &&inp[index+1]>inp[index]) {
		  index+=1;
	  }
	  return index;
  }
  static int searchMin(int index,long[]inp) {
	  while(index+1<inp.length &&inp[index+1]<inp[index]) {
		  index+=1;
	  }
	  return index;
  }
  public class ListNode {
	       int val;
	       ListNode next;
	       ListNode() {}
	       ListNode(int val) { this.val = val; }
	       ListNode(int val, ListNode next) { this.val = val; this.next = next; }
	   }
  static class Pairr implements Comparable<Pairr>{
		 private int index;
		 private int cumsum;
		 private ArrayList<Integer>indices;
		 public Pairr(int index,int cumsum) {
			 this.index=index;
			 this.cumsum=cumsum;
			 indices=new ArrayList<Integer>();
		 }
		 public int compareTo(Pairr other) {
			 return Integer.compare(cumsum, other.cumsum);
		 }
	 }
	 
  
  static class InputReader {
      public BufferedReader reader;
      public StringTokenizer tokenizer;

      public InputReader(InputStream stream) {
          reader = new BufferedReader(new InputStreamReader(stream), 32768);
          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());
      }
  }
}