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
#include <bits/stdc++.h>

using namespace std;

long long n,i,j,v[3010],d[3010][3010];
int main()
{
    cin>>n;
    for(i=1; i<=n; i++)
    {
        cin>>v[i];
        d[i][i]=v[i];
    }

    for(i=n; i>=1; i--)
    {
        for(j=i+1; j<=n; j++)
        {
            if(i+1<=n)d[i][j]=max(-d[i+1][j]+v[i],-d[i][j-1]+v[j]);
            else d[i][j]=-d[i][j-1]+v[j];
        }
    }

    cout<<d[1][n];
    return 0;
}
