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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Washoum
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        inputClass in = new inputClass(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        LDeque solver = new LDeque();
        solver.solve(1, in, out);
        out.close();
    }

    static class LDeque {
        public void solve(int testNumber, inputClass sc, PrintWriter out) {
            int n = sc.nextInt();
            int[] tab = new int[n];
            for (int i = 0; i < n; i++) {
                tab[i] = sc.nextInt();
            }
            long[][] dp = new long[n][n];

            if (n % 2 == 0) {
                for (int i = 0; i < n; i++) {
                    dp[i][i] = -tab[i];
                }
                for (int len = 2; len <= n; len++) {
                    if (len % 2 == 0) {
                        for (int i = 0; len + i - 1 < n; i++) {
                            dp[i][i + len - 1] = Math.max(dp[i + 1][i + len - 1] + tab[i], dp[i][i + len - 2] + tab[i + len - 1]);
                        }
                    } else {
                        for (int i = 0; len + i - 1 < n; i++) {
                            dp[i][i + len - 1] = Math.min(dp[i + 1][i + len - 1] - tab[i], dp[i][i + len - 2] - tab[i + len - 1]);
                        }
                    }
                }
            } else {
                for (int i = 0; i < n; i++) {
                    dp[i][i] = tab[i];
                }
                for (int len = 2; len <= n; len++) {
                    if (len % 2 == 1) {
                        for (int i = 0; len + i - 1 < n; i++) {
                            dp[i][i + len - 1] = Math.max(dp[i + 1][i + len - 1] + tab[i], dp[i][i + len - 2] + tab[i + len - 1]);
                        }
                    } else {
                        for (int i = 0; len + i - 1 < n; i++) {
                            dp[i][i + len - 1] = Math.min(dp[i + 1][i + len - 1] - tab[i], dp[i][i + len - 2] - tab[i + len - 1]);
                        }
                    }
                }
            }
            out.println(dp[0][n - 1]);
        }

    }

    static class inputClass {
        BufferedReader br;
        StringTokenizer st;

        public inputClass(InputStream in) {

            br = new BufferedReader(new InputStreamReader(in));
        }

        public String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

    }
}

