Oipotato loves his girlfriend very much. Since Valentine's Day is coming, he decides to buy some presents for her.
There are $n$ presents in the shop, and Oipotato can choose to buy some of them. We know that his girlfriend will possibly feel extremely happy if she receives a present. Therefore, if Oipotato gives $k$ presents to his girlfriend, she has $k$ chances to feel extremely happy. However, Oipotato doesn't want his girlfriend to feel extremely happy too many times for the gifts.
Formally, for each present $i$, it has a possibility of $P_i$ to make Oipotato's girlfriend feel extremely happy. Please help Oipotato decide what to buy and maximize the possibility that his girlfriend feels extremely happy for exactly one time.