Problem:
Score : 100 points

Problem Statement

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.

Sample Input 1

4
10 80 90 30

Sample Output 1

10

The game proceeds as follows when the two players play optimally (the element being removed is written bold):

Taro: (10, 80, 90, 30) → (10, 80, 90)

Jiro: (10, 80, 90) → (10, 80)

Taro: (10, 80) → (10)

Jiro: (10) → ()

Here, X = 30 + 80 = 110 and Y = 90 + 10 = 100.

Sample Input 2

3
10 100 10

Sample Output 2

-80

The game proceeds, for example, as follows when the two players play optimally:

Taro: (10, 100, 10) → (100, 10)

Jiro: (100, 10) → (10)

Taro: (10) → ()

Here, X = 10 + 10 = 20 and Y = 100.

Sample Input 3

1
10

Sample Output 3

10

Sample Input 4

10
1000000000 1 1000000000 1 1000000000 1 1000000000 1 1000000000 1

Sample Output 4

4999999995

The answer may not fit into a 32-bit integer type.

Sample Input 5

6
4 2 9 7 1 5

Sample Output 5

2

The game proceeds, for example, as follows when the two players play optimally:

Taro: (4, 2, 9, 7, 1, 5) → (4, 2, 9, 7, 1)

Jiro: (4, 2, 9, 7, 1) → (2, 9, 7, 1)

Taro: (2, 9, 7, 1) → (2, 9, 7)

Jiro: (2, 9, 7) → (2, 9)

Taro: (2, 9) → (2)

Jiro: (2) → ()

Here, X = 5 + 1 + 9 = 15 and Y = 4 + 7 + 2 = 13.

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Runtime Error)

import java.util.*;
import java.lang.*;
import java.io.*;
 public class Main{
	static long[][][]dp=new long[31][31][2];
	static long solve(int i,int j,int[]arr,int turn){
		if(i>j)
			return 0;
		if(dp[i][j][turn]!=0)
			return dp[i][j][turn];
		if(turn==1)
			return dp[i][j][turn]=Math.max(arr[i]+solve(i+1,j,arr,0),arr[j]+solve(i,j-1,arr,0));
		else
			return dp[i][j][turn]=Math.min(solve(i+1,j,arr,1),solve(i,j-1,arr,1));
	}
	public static void main(String[] args)throws IOException{
		//Scanner in=new Scanner(System.in);
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		int n=Integer.parseInt(br.readLine());
		int []arr=new int[n+1];
		long sum=0;
		String s=br.readLine();
		String[]s1=s.split(" ");
		long y=0;
		for(int i=0;i<n;i++){
			arr[i]=Integer.parseInt(s1[i]);
			sum+=arr[i];
		}
		long x=solve(0,n-1,arr,1);
		 y=sum-x;
		System.out.println(x-y);
	}
}