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.Vector;

public class Main {
	static int a[];
	static long dp[][];
	static int g[][];
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		dp = new long [n][n];
		g = new int[n][n];
		a = new int[n];
		for (int i=0;i<n;i++) 
			a[i]=sc.nextInt();
			f(0,n-1);
		System.out.println(dp[0][n-1]);
	}
	private static long f(int l, int r) {
		if (l==r) {
			g[l][r] = 1;
			dp[l][r] = a[l];
			return a[l];
		}
		if (g[l][r]>0) return dp[l][r];
		long ans = a[r] - f(l,r-1);
		long ans1 = a[l] - f(l+1,r);
		if (ans<ans1) ans = ans1;
		
		g[l][r] = 1;
		dp[l][r] = ans;
		return ans;
	}
}
