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: Accepted)

import java.io.BufferedReader;
import java.io.InputStreamReader;

public class Main {


	static int MAXN= 3005;

	static long dp[][];
	static long as [];
	static long min(long a, long b) {
		return Math.min(a, b);
	}
	static long max(long a, long b) {
		return Math.max(a, b);
	}
	static long calc(int inicio, int fin, int p){
	    if(dp[inicio][fin]!=-1){
	        return dp[inicio][fin];
	    }
	    if(p==0){
	        return dp[inicio][fin]=max(as[inicio]+calc(inicio+1,fin,1),as[fin]+calc(inicio,fin-1,1));
	    }
	    return dp[inicio][fin]=min(calc(inicio+1,fin,0),calc(inicio,fin-1,0));
	}

	public static void main(String[] args) throws Exception{
	    int n;
	    long suma =0,X,rta;
	    dp = new long[MAXN][MAXN];
	    as  = new long [MAXN];
	    BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
	    n = Integer.parseInt(bf.readLine());
	    String[] data = bf.readLine().split(" ");
	    for(int i =0; i<MAXN; i++){
	        for(int j =0; j<MAXN; j++){
	            dp[i][j]=-1;
	        }
	    }
	    for(int i=0; i<n; i++){
	        as[i] = Long.parseLong(data[i]);
	        suma+=as[i];
	        if(n%2==1){
	            dp[i][i]  = as[i];
	        }
	        else{
	            dp[i][i] = 0;
	        }
	    }
	    X = calc(0,n-1,0);
	    rta = 2*X-suma;
	    System.out.println(rta);
	}
	
}