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.*;
public class Main {
	static int n;
	static long[] a=new long[3005];
	static boolean[][] vis=new boolean[3005][3005];
	static long[][] dp=new long[3005][3005];
	static long DP(int x,int y) {
		if (x+y>=n) return 0;
		if (vis[x][y]) return dp[x][y];
		vis[x][y]=true;
		if ((x+y)%2==0) dp[x][y]=Math.max(DP(x+1,y)+a[x],DP(x,y+1)+a[n-1-y]);
		else dp[x][y]=Math.min(DP(x+1,y)-a[x],DP(x,y+1)-a[n-1-y]);
		return dp[x][y];
	}
	public static void main(String[] args) {
		Scanner in=new Scanner(System.in);
		n=in.nextInt();
		for (int i=0;i<n;++i) a[i]=in.nextLong();
		System.out.println(DP(0,0));
	}
}