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.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Scanner;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskL solver = new TaskL();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskL {
        public void solve(int testNumber, Scanner in, PrintWriter out) {
            int n = in.nextInt();
            int[] arr = new int[n];
            for (int i = 0; i < n; i++)
                arr[i] = in.nextInt();
            long[][] dp = new long[n + 1][n + 1];
            long[] sum = new long[n + 1];
            sum[0] = 0;
            for (int i = 0; i < n; i++)
                sum[i + 1] = sum[i] + arr[i];
            for (int j = 0; j < n; j++) {
                for (int i = j; i >= 0; i--) {
                    if (i == j) {
                        dp[i][j] = arr[i];
                    } else {
                        dp[i][j] = Math.max(sum[j + 1] - sum[i + 1] - dp[i + 1][j] + arr[i], sum[j] - sum[i] - dp[i][j - 1] + arr[j]);
                    }
                }
            }
            out.println(2 * dp[0][n - 1] - sum[n]);
        }

    }
}

