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 javax.swing.*;
import java.io.*;
import java.sql.Struct;
import java.text.DecimalFormat;
import java.util.*;

public class Main {


    public static void main(String[] args) throws IOException {
        BufferedReader rd = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(rd.readLine());
        int[] arr = new int[n];
        StringTokenizer s = new StringTokenizer(rd.readLine());
        for (int i = 0; i < n; i++) {
            arr[i] = Integer.parseInt(s.nextToken());
        }
        long[][] dp = new long[n + 1][n + 1];

        for (int i = 0; i < n; i++) {
            dp[i][i] = arr[i];
        }

        for (int i = 2; i < n + 1; i++) {
            for (int j = 0; j <= n - i; j++) {
                int start = j;
                int end = start + i - 1;
                dp[start][end] = Math.max(-dp[start + 1][end] + arr[start], -dp[start][end -1]+arr[end]);

            }
        }

        System.out.println(dp[0][n - 1]);
    }
}