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.*;
import java.util.*;

class Main {

	public static void main(String[] args) throws Exception {
		final Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int[] a = new int[n];
		for (int i = 0; i < n; i++) {
			a[i] = sc.nextInt();
		}

		long[][] dp = new long[n + 1][n + 1];

		for (int d = 1; d <= n; d++) {
			for (int l = 0; l <= n; l++) {
				int r = l + d;
				if (r > n) break;
				if ((n - d) % 2 == 0) {
					// maximize
					dp[l][r] = Math.max(dp[l + 1][r] + a[l], dp[l][r - 1] + a[r - 1]);
				} else {
					// minimize
					dp[l][r] = Math.min(dp[l + 1][r] - a[l], dp[l][r - 1] - a[r - 1]);
				}
			}
		}

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