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.util.*;
import java.io.*;

public class Main
{
    public static void main(String[] args) throws IOException
    {
        Scanner scan = new Scanner(System.in);
        int n = scan.nextInt();
        
        int[] arr = new int[n];
        for (int i = 0; i < n; i++)
            arr[i] = scan.nextInt();
        
        long[][] dp = new long[n + 1][n + 1];
        for (int i = n - 1; i >= 0; i--)
        {
            for (int j = i; j < n; j++)
            {
                if (j == i)
                    dp[i][j] = arr[i];
                else
                    dp[i][j] = Math.max(arr[j] - dp[i][j - 1], arr[i] - dp[i + 1][j]);
            }
        }
        System.out.println(dp[0][n - 1]);
    }
}