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;

int main(){
	int n;
	cin >> n;
	vector<long long> a(n);
	vector<vector<long long> > dp(n,vector<long long>(n));
	for(int i = 0; i < n; i++){
		cin >> a[i];
		dp[i][i] = a[i];
	}
	for(int i = 1; i < n; i++){
		for(int j = 0; j < n-i; j++){
			int l = j, r = j + i;
			dp[l][r] = max(-dp[l+1][r] + a[l] , -dp[l][r-1] + a[r]);  
		}
	}
	cout << dp[0][n-1] << "\n";
	return 0;
}
