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.*;
import java.io.*;

public class Main {

    public static void main(String[] args) throws Exception {
        // Your code here!
        Scanner in = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
        
        int N = in.nextInt();
        long[] a = new long[N];
        long[][] dp = new long[3005][3005];
        for(int i = 0; i < N; i++) {
            a[i] = in.nextLong();
        }
        
        for(int L = N-1; L >= 0; --L) {
            for(int R = L; R < N; ++R) {
                if(L == R) {
                    dp[L][R] = a[L];
                }
                else {
                    dp[L][R] = Math.max(a[L] - dp[L+1][R], a[R]-dp[L][R-1]);
                }
            }
        }
        
        System.out.println(dp[0][N-1]);
    }
    

        
}
