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;

const int N = 3e3 + 3;

int n,a[N];

long long dp[N][N];

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