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;

class Main{
	static int N;
	static int[] a;

	static long[][][] memo;
	static boolean[][][] flag;

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		N = sc.nextInt();

		a = new int[N];
		memo = new long[2][N][N];
		flag = new boolean[2][N][N];
		for(int i = 0; i < N; i++) {
			a[i] = sc.nextInt();
			Arrays.fill(flag[0][i], false);
			Arrays.fill(flag[1][i], false);
		}

		System.out.println(dp(0, 0, 0));
		sc.close();
	}

	static long dp(int i, int x, int y) {
		if(x + y == N) {
			return 0;
		}
		if(flag[i][x][y]) {
			return memo[i][x][y];
		}
		flag[i][x][y] = true;

		long r;
		if(i == 0) {
			memo[i][x][y] = dp(1, x + 1, y) + a[x];
			r = dp(1, x, y + 1) + a[N - y - 1];
			if(memo[i][x][y] < r)
				memo[i][x][y] = r;
		}
		else {
			memo[i][x][y] = dp(0, x + 1, y) - a[x];
			r = dp(0, x, y + 1) - a[N - y - 1];
			if(memo[i][x][y] > r)
				memo[i][x][y] = r;
		}

		return memo[i][x][y];
	}
}