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 {

    static int N;
    static long[] a;
    static long[][] dp;
    static long INF = Long.MAX_VALUE;

    static long dp(int left, int right) {
        if (dp[left][right]!=INF) return dp[left][right];
        int flag = 1;
        if ((N-left-right)%2==0) flag*=-1;

        if (left==right) {
            dp[left][right] = flag*a[left];
            return flag*a[left];
        }

        long tmp = -INF;
        if (flag==1) {
            tmp = Math.max(a[left]+dp(left+1, right), a[right]+dp(left, right-1));
        } else { // flag=-1
            tmp = Math.min(-a[left]+dp(left+1, right), -a[right]+dp(left, right-1));
        }
        dp[left][right] = tmp;
        return tmp;
    }

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        N = Integer.parseInt(sc.next());
        a = new long[N];
        dp = new long[N][N];
        for (int i=0;i<N;i++) {
            for (int j=0;j<N;j++) {
                dp[i][j] = INF;
            }
        }
        for (int i=0;i<N;i++) {
            a[i] = Integer.parseInt(sc.next());
        }
        System.out.println(dp(0, N-1));
    }
}