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];
    for (int head = N - 1; 0 <= head; head--) {
      for (int tail = 0; tail < N; tail++) {
        if (dp[head][tail] != 0) continue;
        if (head == tail) {
          dp[head][tail] = a[head];
        } else {
          if (tail == 0) {
            dp[head][tail] = a[tail];
          } else if (head == N - 1) {
            dp[head][tail] = a[head];
          } else {
            dp[head][tail] = Math.max(
                a[head] - dp[head + 1][tail],
                a[tail] - dp[head][tail - 1]);
          }
        }
      }
    }

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