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;
import java.util.stream.IntStream;

public class Main {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();

        int []a = IntStream.range(0, n).map(x -> in.nextInt()).toArray();
        long [][]dp = new long[n][n];

        for(int i = 0; i < n; i++) {
            dp[i][i] = a[i];
        }
        for (int i = 0; i < n - 1; i++) {
            dp[i][i + 1] = Math.max(a[i], a[i + 1]) - Math.min(a[i], a[i + 1]);
        }

        for(int len = 2; len < n; len++) {
            for(int start = 0; start + len < n; start++) {
                int end = start + len;
                dp[start][end] = Math.max(a[start] - dp[start + 1][end], a[end] - dp[start][end - 1]);
            }
        }
        System.out.println(dp[0][n - 1]);
    }
}
