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.util.*;

public class Main {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int size = scanner.nextInt();
        int arr[] = new int[size];
        for (int i = 0; i < size; i++) {
            arr[i] = scanner.nextInt();

        }
        long ans[][][] = new long[arr.length][arr.length][2];
        for (int i = 0; i < ans.length; i++) {
            for (int j = 0; j < arr.length; j++) {
                for (int k = 0; k < 2; k++) {
                    ans[i][j][k] = Long.MIN_VALUE;
                }
            }
        }
        // System.out.println(getXY(arr, 0, arr.length - 1, 0));
        System.out.println(getXY2(arr, 0, arr.length - 1, 0, ans));
        // System.out.println(visited);

    }

   
   
    public static int visited = 0;

    public static long getXY2(int arr[], int start, int end, int p, long ans[][][]) {
        if (ans[start][end][p] != Long.MIN_VALUE) {
            visited++;
            return ans[start][end][p];
        }
        if (start == end) {
            if (p == 0) {
                ans[start][end][p] = arr[start];
                return arr[start];
            } else
                ans[start][end][p] = -arr[start];
            return -arr[start];
        }

        int o = (p == 1) ? 0 : 1;
        long op1 = getXY2(arr, start + 1, end, o, ans);
        long op2 = getXY2(arr, start, end - 1, o, ans);
        if (p == 0) {
            op1 += arr[start];
            op2 += arr[end];
            ans[start][end][p] = Math.max(op1, op2);
            return ans[start][end][p];
        } else {
            op1 -= arr[start];
            op2 -= arr[end];
            ans[start][end][p] = Math.min(op1, op2);

            return ans[start][end][p];
        }

    }
}
