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.Arrays;
import java.util.Scanner;

public class Main {
    void run() {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        long[] arr = new long[n];
        for (int i = 0; i < n; i++) {
            arr[i] = sc.nextLong();
        }

        // dp[i][j] ... 区間[i, j)における、X-Yの値
        long[][] dp = new long[n + 1][n + 1];

        for (int len = 1; len <= n; len++) {
            for (int i = 0; i <= n - len; i++) {
                int j = i + len;
                boolean isFirst = (n - len) % 2 == 0;
                if (isFirst) {
                    dp[i][j] = Math.max(dp[i + 1][j] + arr[i], dp[i][j - 1] + arr[j - 1]);
                } else {
                    dp[i][j] = Math.min(dp[i + 1][j] - arr[i], dp[i][j - 1] - arr[j - 1]);
                }
            }
        }

//        debug(dp);

        System.out.println(dp[0][n]);
    }

    void debug(Object... os) {
        System.err.println(Arrays.deepToString(os));
    }

    public static void main(String[] args) {
        new Main().run();
    }
}
