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.Arrays;

public class Main {
    public static void main(String[] args) {
        Scanner scan = new Scanner(System.in);
        int n = scan.nextInt();
        int[] deque = new int[n];
        for(int i = 0 ; i < n ; i++) {
            deque[i] = scan.nextInt();
        }
        
        long[][] dp = new long[n][n];
        // We would have to get the 2d loop for getting the answer.
        for(int left = n-1 ; left >= 0 ; left--) {
            for(int right = left ; right < n ; right++) {
                if(left == right) {
                    dp[left][right] = deque[left];
                } else {
                    dp[left][right] = Math.max(deque[left] - dp[left+1][right] , deque[right]-dp[left][right-1]);
                }
            }
        }
        System.out.println(dp[0][n-1]); // last column in the first row will give the max gain for the entire range for the first player.
    }
}