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.InputStreamReader;
import java.io.IOException;
import java.io.Reader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.ArrayList;
import java.util.Collections;
import java.util.ArrayDeque;
import java.util.List;
import java.util.Queue;
import java.util.StringTokenizer;

/**
 * The Java template file for AtCoder online judge.
 */
public class Main {

  private static FastScanner scanner;
  private static PrintWriter printer;

  public static void solve() {
    int n = scanner.nextInt();
    int[] values = new int[n];
    for (int i = 0; i < n; i++) {
      values[i] = scanner.nextInt();
    }
    Long[][] cache = new Long[n][n];
    long result = recur(values, 0, n - 1, cache);
    printer.println(result);
  }

  private static long recur(int[] values, int low, int high, Long[][] cache) {
    if (low > high) {
      return 0;
    }
    if (low == high) {
      return values[low];
    }
    if (cache[low][high] != null) {
      return cache[low][high];
    }
    cache[low][high] = Math.max(
        values[low] - recur(values, low + 1, high, cache),
        values[high] - recur(values, low, high - 1, cache)
    );
    return cache[low][high];
  }

  public static void main(String[] args) {
    scanner = new FastScanner();
    printer = new PrintWriter(System.out);
    solve();
    printer.flush();
  }

  private static class FastScanner {
    BufferedReader br;
    StringTokenizer st;

    public FastScanner(Reader in) {
      br = new BufferedReader(in);
    }

    public FastScanner() {
      this(new InputStreamReader(System.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());
    }

    public long nextLong() {
      return Long.parseLong(next());
    }

    public double nextDouble() {
      return Double.parseDouble(next());
    }

    public String nextLine() {
      String str = "";
      try {
        str = br.readLine();
      } catch (IOException e) {
        e.printStackTrace();
      }
      return str;
    }

    public int[] readIntArray(int size) {
      int[] ret = new int[size];
      for (int i = 0; i < size; i++) {
        ret[i] = nextInt();
      }
      return ret;
    }
  }
}
