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.*;
class Main {
    static long[][] dp1;
    static long recurse1(long[] a, int i, int j) {
        if(i>j)
            return 0;
        if(i==j)
            return a[i];
        if(dp1[i][j]!=-1)
            return dp1[i][j];
        long max = Math.max(a[i]-recurse1(a, i+1, j), a[j]-recurse1(a, i, j-1));
        return dp1[i][j] = max;
    }
    public static void main (String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        long[] a = new long[n];
        for(int i = 0; i<n; i++)
            a[i] = sc.nextLong();
        dp1 = new long[n][n];
        for(long[] i: dp1)
            Arrays.fill(i, -1);
        System.out.println(recurse1(a, 0, n-1));
    }
}