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.*;

public class Main {
    public long getBalance(int[] A, int L, int R, long[][] memo) {
        // System.out.println(String.format("L: %d, R: %d", L, R));
        if (L == R) {
            return A[L];
        }
        if (memo[L][R] != Long.MIN_VALUE) {
            return memo[L][R];
        }
        long left = A[L] - getBalance(A, L + 1, R, memo);
        long right = A[R] - getBalance(A, L, R - 1, memo);
        long maxHere = Math.max(left, right);
        if (maxHere > memo[L][R]) {
            memo[L][R] = maxHere;
        }
        return memo[L][R];
    }
    public static void main(String[] args)  {
        try (BufferedReader br = new BufferedReader(new InputStreamReader(System.in))) {
            br.readLine();
          	Main app = new Main();
            String[] split = br.readLine().split(" ");
            int n = split.length;
            int[] A = new int[n];
            for (int i = 0; i < n; i++) {
               A[i] = Integer.parseInt(split[i]); 
            }
            long[][] memo = new long[n + 1][n + 1];
            for (long[] row: memo) {
                Arrays.fill(row, Long.MIN_VALUE);
            }
            long result = app.getBalance(A, 0, n - 1, memo);
            System.out.println(result);
        } catch (IOException e) {
            e.printStackTrace();
        }
    }
}
