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 {
	private static long max(long dp[][], int i, int j,int n, int arr[]) {
		if(i==j) {
			dp[i][j] = arr[i];
			return dp[i][j];
		}
		if( dp[i][j]!=-1)
			return dp[i][j];
		dp[i][j]= Math.max(arr[i]-max( dp, i+1,j,n, arr), arr[j]- max(dp, i, j-1,n,arr));
		return dp[i][j];
	}

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner in= new Scanner(System.in);
		int n = in.nextInt();
		long dp[][] = new long[n][n];
		int [] arr = new int[n];
		for(int i=0; i<n; i++) {
			arr[i]= in.nextInt();
			Arrays.fill(dp[i], -1);
		}
		max(dp, 0,n-1, n, arr);
		System.out.println(dp[0][n-1]);
	}

}
