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Points: 10
Time limit: 1.0s
Memory limit: 16M

Problem types

There are a bunch of coins on a table, laid out in a straight line.
Each coin has a (positive) value from 1 to 1\,000. Now, you're going to play a game with a friend.

At every turn, you must remove a coin from one end of the line.
Turns alternate, so your friend goes immediately after you're done.
The game ends when there are no coins remaining.

An example game:
The coins start like this:
4, 4, 9, 4
You always go first, so you take the 4 from the left side:
4, 9, 4
Your friend takes any of the 4s (it doesn't matter)
9, 4
Now you can take the 9, and your friend takes the remaining 4.

Your score, in this case, is 4+9 = 13.
(In this case, you can always beat your friend.)
Find the maximum possible score you can achieve.

Input Specification

N \le 1\,000, the number of coins.
N lines, each with the value of a coin.

Output Specification

Your maximum possible score, provided that you go first and your friend plays perfectly.


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