Description

Bessie and Bonnie have found a treasure chest full of marvelous gold coins! Being cows, though, they can't just walk into a store and buy stuff, so instead they decide to have some fun with the coins.

The N (1 <= N <= 5,000) coins, each with some value C_i (1 <= C_i <= 5,000) are placed in a straight line. Bessie and Bonnie take turns, and for each cow's turn, she takes exactly one coin off of either the left end or the right end of the line. The game ends when there are no coins left.

Bessie and Bonnie are each trying to get as much wealth as possible for themselves. Bessie goes first. Help her figure out the maximum value she can win, assuming that both cows play optimally.

Consider a game in which four coins are lined up with these values:

        30  25  10  35

Consider this game sequence:

Player Side CoinValue BessieTotal BonnieTotal NewCoinLine

Bessie Right 35 35 0 30 25 10

Bonnie Left 30 35 30 25 10

Bessie Left 25 60 30 10

Bonnie Right 10 60 40 --

This is the best game Bessie can play.

Input

（多组数据）

• Line 1: A single integer: N

• Lines 2..N+1: Line i+1 contains a single integer: C_i

Output

• Line 1: A single integer, which is the greatest total value Bessie

    can win if both cows play optimally.

Sample

Input

4
30
25
10
35

Output

60