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.*;
import java.util.*;
public class Main {
    public static void main(String args[]) {
        int n = 0;
        int[] arr = null;
        try (Scanner scanner = new Scanner(System.in)) {
            n = scanner.nextInt();
            arr = new int[n];
            for(int i = 0; i < n ;i++) {
                arr[i] = scanner.nextInt();
            }
        }
        
        long[][] dp = new long[n+1][n+1];
        for(int l = n - 1; l >= 0; l--) {
            for(int r = l; r < n; r++) {
                if(l == r)
                    dp[l][r] = arr[l];
                else
                    dp[l][r] = Math.max(arr[l] - dp[l+1][r]
                                    , arr[r] - dp[l][r-1]);
            }
        }
        
        
        // for(int[]d :dp) 
        //     System.out.println(Arrays.toString(d));
        
        System.out.println(dp[0][n- 1]);
        
    }
    
}