Problem:
Score : 100 points

Problem Statement

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.

Sample Input 1

4
10 80 90 30

Sample Output 1

10

The game proceeds as follows when the two players play optimally (the element being removed is written bold):

Taro: (10, 80, 90, 30) → (10, 80, 90)

Jiro: (10, 80, 90) → (10, 80)

Taro: (10, 80) → (10)

Jiro: (10) → ()

Here, X = 30 + 80 = 110 and Y = 90 + 10 = 100.

Sample Input 2

3
10 100 10

Sample Output 2

-80

The game proceeds, for example, as follows when the two players play optimally:

Taro: (10, 100, 10) → (100, 10)

Jiro: (100, 10) → (10)

Taro: (10) → ()

Here, X = 10 + 10 = 20 and Y = 100.

Sample Input 3

1
10

Sample Output 3

10

Sample Input 4

10
1000000000 1 1000000000 1 1000000000 1 1000000000 1 1000000000 1

Sample Output 4

4999999995

The answer may not fit into a 32-bit integer type.

Sample Input 5

6
4 2 9 7 1 5

Sample Output 5

2

The game proceeds, for example, as follows when the two players play optimally:

Taro: (4, 2, 9, 7, 1, 5) → (4, 2, 9, 7, 1)

Jiro: (4, 2, 9, 7, 1) → (2, 9, 7, 1)

Taro: (2, 9, 7, 1) → (2, 9, 7)

Jiro: (2, 9, 7) → (2, 9)

Taro: (2, 9) → (2)

Jiro: (2) → ()

Here, X = 5 + 1 + 9 = 15 and Y = 4 + 7 + 2 = 13.

Solution in C++14 (GCC 5.4.1) (judge verdict: Runtime Error)

#include <bits/stdc++.h>

using namespace std;

#define ops cout<<"ops"<<endl;
#define freopens freopen("cowpatibility.in", "r", stdin);freopen("cowpatibility.out", "w", stdout);
#define fast ios::sync_with_stdio(0);cin.tie(0);cout.tie(0);

#define DIM 3007
#define DIMM 100007
#define INF 1000000000007.0
#define X (ll)(1<<32)
#define eps 0.0000001
#define PI 3.14159265358979323846
#define MAX 25
#define MODULO (long long)1000000007

const long double gr=(1+sqrt(5))/2;

typedef int I;
typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;

typedef pair<I,I> pII;
typedef pair<ll,ll> pllll;
typedef pair<ld,ld> pldld;

typedef vector<I> vI;
typedef vector<ll> vll;
typedef vector<pllll> vpllll;

typedef char cr;
typedef string str;

ll n;
ll a[DIM],dp[DIM][DIM];

int main()
{
    //ops;
    //freopens;
    fast;
    //ll x1,y1,xs,ys,x2,y2,x3,x4,y3,y4;

    cin>>n;
    for(int i=1;i<=n;i++)cin>>a[i];

    for(int l=1;l<=n;l++){
     for(int s=1;s<=(n-s+1);s++){
      dp[s][l]=max((a[s+l-1]-dp[s][l-1]),(a[s]-dp[s+1][l-1]));
     }
    }
    cout<<dp[1][n]<<endl;
    return 0;
}