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.BufferedInputStream;
import java.util.Scanner;

/**
 * Created by Harry on 4/6/20.
 */

public class Main {
    public static void main(String[] args){
        Scanner scanner = new Scanner(new BufferedInputStream(System.in));
        int n = scanner.nextInt();
        long[] A = new long[n];
        for(int i=0; i<n; i++){
            A[i] = scanner.nextLong();
        }
        long[] preSum = new long[n+1];
        long[][] dp = new long[n][n];
        long sum = 0;
        for(int i=0; i<n; i++){
            preSum[i+1] = preSum[i]+A[i];
        }

        for(int j=0; j<n; j++){
            for(int i=j; i>=0; i--){
                if(i==j){
                    dp[i][j] = A[i];
                }
                else{
                    dp[i][j] = Math.max(preSum[j+1]-preSum[i]-dp[i+1][j], preSum[j+1]-preSum[i]-dp[i][j-1]);
                }
            }
        }
        long x = dp[0][n-1];
        long y = preSum[n]-x;
        System.out.print(x-y);
    }
}
