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.*;
import java.math.*;

public class Main {
  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    int N = sc.nextInt();
    int[] a = new int[N];
    for (int i = 0; i < N; i++)
      a[i] = sc.nextInt();
    sc.close();

    long[][] dp = new long[N][N];
    long ans = l(dp, a, 0, N - 1);
    System.out.println(ans);
  }

  private static long l(long[][] dp, int[] a, int head, int tail) {
    if (dp[head][tail] != 0) return dp[head][tail];
    if (head == tail) return a[head];
    long res = Math.max(
        a[head] - l(dp, a, head + 1, tail),
        a[tail] - l(dp, a, head, tail - 1));
    dp[head][tail] = res;
    return res;
  }
}