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;
  static Long[][][] memo;
  public static void main(String[]  args)
  {
	Scanner in = new Scanner(System.in);
 	n = in.nextInt();
    a = new long[n];
    for (int i = 0; i < n; i++)
      a[i] = in.nextLong();
    memo = new Long[2][n][n];
    System.out.println(dp(0, 0, n-1));
    in.close();
  }
  
  public static long dp(int who, int l, int r)
  {
    if (l == r)
      return a[l];
    if (memo[who][l][r] != null)
      return memo[who][l][r];
    long ans = -(long)1e18;
    ans = Math.max(ans, a[l]-dp(1-who, l+1, r));
    ans = Math.max(ans, a[r]-dp(1-who, l, r-1));
    return memo[who][l][r] = ans;
  }
}