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>
#define re register
#define SIZE 3005
#define LL long long
using namespace std;
int n;
LL a[SIZE],dp[SIZE][SIZE];
int main()
{
	cin>>n;
	for(re int i=1;i<=n;++i)
		cin>>a[i],dp[i][i]=a[i];
	for(re int len=1;len<=n;++len)
		for(re int l=1;l<n;++l)
		{
			int r=l+len-1;
			if(r>n)
				break;
			dp[l][r]=max(a[l]-dp[l+1][r],a[r]-dp[l][r-1]);
		}
	cout<<dp[1][n]<<endl;
	return 0;
} 