You and your friend are playing a game. There is a number of treasure chests hidden under piles of stones. That is, the *i-th* chest has **stones[i]** stones piled on top of it. You take turns taking exactly one stone from the top of one of the chests. Whoever takes the last stone from the top of a chest takes the chest and the treasure inside. The inside of the *i-th* chest is worth **treasure[i]**. The game objective is to gather as much treasure as possible.
Unfortunately, your friend is a cyborg and always makes the best possible move (maximizing his final win). Given **stones** and **treasure**, return the maximum total amount you can get from the chests given that you move first. |