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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class Main {
    /**
     * Consider small intervals and evaluate them before larger intervals
     * @param a
     * @return max difference when the game is played optimally
     */
    public static long maxDiff(long[] a){
        long[][] dp = new long[a.length+1][a.length+1];
        for (int L = a.length-1; L >= 0; L--) {
            for (int R = L; R < a.length; R++) {
                if (L==R){
                    dp[L][R] = a[L];
                } else {
                    dp[L][R] = Math.max(a[L] - dp[L+1][R], a[R] - dp[L][R-1]);
                }
            }
        }
        return dp[0][a.length - 1];
    }

    public static void main(String[] args) throws IOException {
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(reader.readLine());
        StringTokenizer st = new StringTokenizer(reader.readLine());
        long[] a = new long[n];
        for (int i = 0; i < n; i++) {
            a[i] = Long.parseLong(st.nextToken());
        }
        System.out.println(maxDiff(a));
    }
}
