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.text.*;

public class Main {
    static long MOD = (long)1e9+7;
    public static void main(String args[]) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        long[] a = new long[n];
        for(int i = 0; i< n; i++)a[i] = in.nextLong();
        
        long[][] res = new long[n][n];
        for(int i = 0; i< n; i++)Arrays.fill(res[i], Long.MAX_VALUE);
        for(int i = 0; i< n; i++){
            if(n%2 == 1)res[i][i] = a[i];
            else res[i][i] = -a[i];
        }
        for(int sz = 2; sz<= n; sz++){
            int turn = (n-sz)%2;
            for(int l = 0, r = sz-1; r < n; l++, r++){
                if(turn == 0)res[l][r] = Math.max(a[l]+res[l+1][r], res[l][r-1]+a[r]);
                else res[l][r] = Math.min(-a[l]+res[l+1][r], res[l][r-1]-a[r]);
            }
        }
        System.out.println(res[0][n-1]);
    }
}