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 long dp[][][];
    public static long solve(long arr[] , int i , int j , int turn){
        if(i > j){
            return 0;
        }
        if(dp[i][j][turn] != -1){
            return dp[i][j][turn];
        }

        if(turn == 1){
            long ans = arr[i] + solve(arr , i+1 , j , 2);
            ans = Math.max(ans , arr[j] + solve(arr , i , j-1 , 2));
            return dp[i][j][turn] = ans;
        }else {
            long ans = solve(arr , i+1 , j , 1);
            ans = Math.min(ans , solve(arr , i , j-1 , 1));
            return dp[i][j][turn] = ans;
        }
    }
    public static void main(String args[]) {
        Scanner s = new Scanner(System.in);
        int n = s.nextInt();
        long arr[] = new long[n+1];
        dp = new long[n+1][n+1][3];
        for(int i = 0 ; i <= n ; i++){
            for(int j = 0 ; j <= n ; j++){
                for(int k = 0 ; k <= 2 ; k++){
                    dp[i][j][k] = -1;
                }
            }
        }
        long sum = 0;
        for(int i = 1 ; i <= n ; i++){
            arr[i] = s.nextLong();
            sum += arr[i];
        }
        long first = solve(arr , 1 , n , 1);
        long second = sum - first;
        System.out.println(first - second);
    }
}