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;

public class Main{
	 public static  long stoneGame(int[] piles) {
		 long[][] dp = new long[piles.length + 1][piles.length];
			

			for (int gap = 0; gap < piles.length; gap++) {
				for (int i = 0, j = i + gap; j < piles.length; j++, i++) {
					if (gap == 0) {
						dp[i][j] = piles[i];
					} else {
						dp[i][j] = Math.max(piles[i] - dp[i + 1][j], piles[j] - dp[i][j - 1]);
					}

				}

			}
		
			return dp[0][piles.length - 1];
		}

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner scn=new Scanner(System.in);
		int n=scn.nextInt();
		int piles[]=new int[n];
		for(int i=0;i<n;i++){
			piles[i]=scn.nextInt();
		}
		System.out.println(stoneGame(piles));
		

	}

}
