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: Accepted)

#include <bits/stdc++.h>
using namespace std;
#define __ <<" "<<
#define ___ <<" "
#define bash push_back
#define ALL(x) x.begin(),x.end()
#define int long long

struct IoSetup {
    IoSetup() {
        cin.tie(0);
        ios::sync_with_stdio(false);
        cout <<fixed<<setprecision(12);
        cerr <<fixed<<setprecision(12);
    }
}IoSetup;

typedef long long ll;
typedef pair < int , int >  pii;
static constexpr const signed int INF = 0x3f3f3f3f;
static constexpr const signed long long LINF = 0x3f3f3f3f3f3f3f3fLL;
static constexpr const signed int SMOD = 1000000007;
static constexpr const signed int NMOD = 998244353;
static constexpr const signed int dx[]={1,0,-1,0,1,1,-1,-1};
static constexpr const signed int dy[]={0,-1,0,1,-1,1,-1,1};

inline bool inside(int x,int y,int w,int h){return (x>=0 && y>=0 && x<w && y<h);}
template<class T>bool chmax(T &a, const T &b){return(a=max(a,b))==b;}
template<class T>bool chmin(T &a, const T &b){return(a=min(a,b))==b;}
inline int qp(int a,ll b,int mo){int ans=1;do{if(b&1)ans=1ll*ans*a%mo;a=1ll*a*a%mo;}while(b>>=1);return ans;}

int n;
int a[3030];
int mem[3030][3030];

int dp(int l, int r) {
    if(l==r) return a[l];
    if(~mem[l][r]) return mem[l][r];
    return mem[l][r] = max(a[l] - dp(l+1, r), a[r] - dp(l, r-1));
}

signed main() {

    cin >> n;
    for(int i = 0; i < n; i++) 
        cin >> a[i];
    
    memset(mem, -1, sizeof(mem));

    cout << dp(0, n-1) << endl;
  
    return 0;
}