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;

typedef unsigned int ui;
typedef long long ll;
typedef unsigned long long ull;

constexpr int MAXN = 3000;

ll dp[MAXN + 2][MAXN + 2];

int main() {
	int N;
	cin >> N;
	for(int i = 0; i < N; i++)
		cin >> dp[1][i];
	for(int i = 2; i <= N; i++)
		for(int j = 0; i + j <= N; j++)
			dp[i][j] = max(dp[1][i + j - 1] - dp[i - 1][j], dp[1][j] - dp[i - 1][j + 1]);
	cout << dp[N][0] << endl;
}
