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;

public class Main{
	static int N;
	static long[] a;
	static long[][] dp;
	static long f(int i, int j) {
		if(i == j) return ((N + i - j - 1) % 2 == 0) ? a[i] : -a[i];
		if(dp[i][j] != Long.MIN_VALUE) return dp[i][j];
		if((N + i - j - 1) % 2 == 0) {
			return dp[i][j] = Math.max(f(i + 1, j) + a[i], f(i, j - 1) + a[j]);
		}else {
			return dp[i][j] = Math.min(f(i + 1, j) - a[i], f(i, j - 1) - a[j]);
		}
	}
	public static void main(String[] args){
		Scanner sc=new Scanner(System.in);
		while(sc.hasNext()) {
			N = sc.nextInt();
			a = new long[N];
			dp = new long[N][N];
			for(int i = 0; i < N; i++) {
				a[i] = sc.nextInt();
			}
			for(int i = 0; i < N; i++)  Arrays.fill(dp[i], Long.MIN_VALUE);
			System.out.println(f(0, N - 1));
		}
	}
}