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 scanner = new Scanner(System.in);
        int N = scanner.nextInt();
        long S = 0;
        int[] a = new int[N];
        for (int i = 0; i < N; ++i) {
            a[i] = scanner.nextInt();
            S += a[i];
        }

        long[][] dp = new long[N + 1][N + 1];
        for (int i = 0; i < N; i++) {
            for (int j = 0; j < N-i; j++) {
                if ((N - i) % 2 == 1) {
                    if (i==0) {
                        dp[j][j] = a[j];
                    } else {
                        dp[j][j+i] = Math.max(dp[j][j+i-1] + a[j+i], dp[j+1][j+i]+ a[j]);
                    }
                } else {
                    if (i==0) {
                        dp[j][j] = 0;
                    } else {
                        dp[j][j + i] = Math.min(dp[j][j+i-1], dp[j+1][j+i]);
                    }
                }
            }
        }

        long X = dp[0][N-1];
        long Y = S-X;

        System.out.println(X-Y);
    }
}