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.Scanner;

public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        int[] A = new int[N+1];
        for(int i = 1; i <= N; i++) A[i] = sc.nextInt();
        // dp[i][j]：先頭がｉ番目、末尾がｊ番目から始まる時のＸ－Ｙ（後手の時はＹ－Ｘ）
        long[][] dp = new long[N+1][N+1];
        // len：のこりの要素数
        for(int len = 1; len <= N; len++){
            // i：残り要素の先頭位置
            for(int i = 1; len +i -1 <= N; i++){
                int j = len +i -1;
                if(len == 1){
                    dp[i][j] = A[i];
                }else{
                    // 現在取れる要素から、それ以降の相手の得点
                    // （厳密には先手視点ではＹ－Ｘ，後手視点ではＸ－Ｙ）を引いた結果のうち、
                    // より大きくなるほうを選択する
                    dp[i][j] = Math.max(A[i] - dp[i+1][j], A[j] - dp[i][j-1]);
                }
            }
        }
        System.out.println(dp[1][N]);
        sc.close();

    }

}
