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 {

  static long[][] sol;
  static boolean[][] flag;

  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    int N = sc.nextInt();
    sol = new long[N][N];
    flag = new boolean[N][N];
    int[] arr = new int[N];
    for (int i = 0; i < N; i++) {
      arr[i] = sc.nextInt();
    }
    if (N == 1) {
      System.out.println(arr[0]);
    } else {
      System.out.println(solve(arr, 0, N - 1));
    }
  }


  private static long solve(int[] arr, int i, int length) {
    if (i == length) {
      return arr[i];
    } else {
      if (!flag[i + 1][length]) {
        sol[i + 1][length] = solve(arr, i + 1, length);
        flag[i + 1][length] = true;
      }
      if (!flag[i][length - 1]) {
        sol[i][length - 1] = solve(arr, i, length - 1);
        flag[i][length - 1] = true;
      }
      return Math.max((arr[i] - sol[i + 1][length]), (arr[length] - sol[i][length - 1]));
    }
  }

}
