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;

/**
 * Deque
 */
public class Main {

    public static void main(String[] args) throws Exception {
        try (Scanner sc = new Scanner(System.in)) {
            int N = sc.nextInt();
            long[] A = new long[N];
            for (int i = 0; i < N; i++) {
                A[i] = sc.nextLong();
            }

            long[][] dp = new long[N][N];
            for (int i = 0; i < N; i++) {
                dp[i][i] = A[i] * (N % 2 == 1 ? 1 : -1);
            }

            for (int k = 1; k < N; k++) {
                for (int i = 0; i < N; i++) {
                    if (i + k >= N) {
                        break;
                    }

                    if ((N - k) % 2 == 1) {
                        dp[i][i + k] = Math.max(dp[i][i + k - 1] + A[i + k], dp[i + 1][i + k] + A[i]);
                    } else {
                        dp[i][i + k] = Math.min(dp[i][i + k - 1] - A[i + k], dp[i + 1][i + k] - A[i]);
                    }
                }
            }

            System.out.println(dp[0][N - 1]);
        }
    }

}
