Taro and Jiro will play the following game against each other.

Initially, they are given a sequence a = (a_1, a_2, \ldots, a_N). Until a becomes empty, the two players perform the following operation alternately, starting from Taro:

* Remove the element at the beginning or the end of a. The player earns x points, where x is the removed element.



Let X and Y be Taro's and Jiro's total score at the end of the game, respectively. Taro tries to maximize X - Y, while Jiro tries to minimize X - Y.

Assuming that the two players play optimally, find the resulting value of X - Y.

Constraints

* All values in input are integers.
* 1 \leq N \leq 3000
* 1 \leq a_i \leq 10^9

Input

Input is given from Standard Input in the following format:


N
a_1 a_2 \ldots a_N


Output

Print the resulting value of X - Y, assuming that the two players play optimally.

Examples

Input

4
10 80 90 30


Output

10


Input

3
10 100 10


Output

-80


Input

1
10


Output

10


Input

10
1000000000 1 1000000000 1 1000000000 1 1000000000 1 1000000000 1


Output

4999999995


Input

6
4 2 9 7 1 5


Output

2
import java.io.*; 
import java.util.*; 
//import javafx.util.*; 
import java.math.*;
//import java.lang.*;
public class Main 
{ 
  //  static int n;static ArrayList<Integer> arr[];
   // int ans[];
 
    public static void main(String[] args) throws IOException { 
    //    Scanner sc=new Scanner(System.in);
        PrintWriter pw = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
        br = new BufferedReader(new InputStreamReader(System.in));
        int n=nextInt();
        long dp[][]=new long[n][n];
        long a[]=new long[n];
        for(int i=0;i<n;i++){
            a[i]=nextLong();
        }

        
        for(int gap=0;gap<n;gap++){
            for(int l=0;l<n;l++){
                int r=l+gap;
                if(r<n){
                    if(l==r){
                        dp[l][r]=a[l];
                    }        
                    else{
                        dp[l][r]=Math.max(a[l]-dp[l+1][r],a[r]-dp[l][r-1]);
                    }
                }
            }
        }   
        pw.println(dp[0][n-1]);
      //  printf("%lld\n", dp[0][n-1]);
        pw.close();

    }
    
    static long maxSubArraySum(long a[],int size)  
{  
      
    long max_so_far = 0, max_ending_here = 0;  
  
    for (int i = 0; i < size; i++)  
    {  
        max_ending_here = max_ending_here + a[i]; 
        if (max_ending_here < 0)  
            max_ending_here = 0;  
          
        /* Do not compare for all 
           elements. Compare only  
           when max_ending_here > 0 */
        else if (max_so_far < max_ending_here)  
            max_so_far = max_ending_here;  
          
    }  
    return max_so_far;  
}  
    public static BufferedReader br;
    public static StringTokenizer st;
    public static String next() {
        while (st == null || !st.hasMoreTokens()) {
       try {
                st = new StringTokenizer(br.readLine());
            } catch (Exception e) {
                throw new RuntimeException(e);
            }
        }
        return st.nextToken();
    }
 
    public static Integer nextInt() {
        return Integer.parseInt(next());
    }
 
    public static Long nextLong() {
        return Long.parseLong(next());
    }
 
    public static Double nextDouble() {
        return Double.parseDouble(next());
    }
    static class Pair{
        int x;int y;int z;
        Pair(int x,int y,int z){
            this.x=x;
            this.y=y;
            this.z=z;
          //  this.i=i;
        }
    }
    static class sorting implements Comparator<Pair>{
        public int compare(Pair a,Pair b){
            //return (a.y)-(b.y);
            return (a.x-b.x);
        }
    }
    public static int[] na(int n)throws IOException{
        int[] a = new int[n];
        for(int i = 0;i < n;i++)a[i] = nextInt();
        return a;
    }
    static class query implements Comparable<query>{
        int l,r,idx,block;
        static int len;
        query(int l,int r,int i){
            this.l=l;
            this.r=r;
            this.idx=i;
            this.block=l/len;
        }   
        public int compareTo(query a){
            return block==a.block?r-a.r:block-a.block;
        }
    }
    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 modInverse(long a, long m) { 
        long g = gcd(a, m); 
        if (g != 1) 
            return -1; 
        else{ 
            // If a and m are relatively prime, then modulo inverse 
            // is a^(m-2) mode m 
            return (power(a, m - 2, m)); 
        } 
    } 
      
    // To compute x^y under modulo m 
    static long power(long x, long y, long m){ 
        if (y == 0) 
            return 1;      
        long p = power(x, y / 2, m) % m; 
        p = (p * p) % m; 
      
        if (y % 2 == 0) 
            return p; 
        else
            return (x * p) % m; 
    }
    static long fast_pow(long base,long n,long M){
        if(n==0)
           return 1;
        if(n==1)
        return base;
        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,int M){
        return fast_pow(n,M-2,M);
    }
    
} 