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.io.*;

class Main {

  

  public static void main(String[] args) {
    Scanner in = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
    
    int N = in.nextInt();
    long[] a = new long[N];
    for (int i = 0; i < N; i++) {
      a[i] = in.nextInt();
    }

    

    long[][] dp = new long[N][N];
    for (int i = 0; i < N; i++) {
      dp[i][i] = a[i];
    }

    for (int i = 1; i < N; i++) {
      a[i] += a[i - 1];
    }

    for (int len = 2; len <= N; len++) {
      for (int i = 0; i < N; i++) {
        int j = i + len - 1; 
        if (j >= N) {break;}
        dp[i][j] = a[j] - (i == 0 ? 0 : a[i - 1]) - Math.min(dp[i + 1][j], dp[i][j - 1]);
      }
    }




    System.out.println(2 * dp[0][N - 1] - a[N - 1]);
  }

}
