There are a bunch of coins on a table, laid out in a straight line.
Each coin has a (positive) value from to . 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:
You always go first, so you take the from the left side:
Your friend takes any of the s (it doesn't matter)
Now you can take the , and your friend takes the remaining .
Your score, in this case, is .
(In this case, you can always beat your friend.)
Find the maximum possible score you can achieve.
, the number of coins.
lines, each with the value of a coin.
Your maximum possible score, provided that you go first and your friend plays perfectly.