|Taro and Hanako are playing a game called Nisoku, which is played as follows. Initially, there is a pile of cards. Each card contains a real number between 1.5 and 10.0, inclusive. You are given a double cards, the i-th element of which is the number written on the i-th card.
Repeat the following step until there is only one card left in the pile: Remove any two cards from the pile, and add one new card to the pile. Write either a+b or a*b on the new card, where a and b are the numbers written on the two cards that were removed.
Return the maximal possible number written on the final card in the pile.
|-||Your return value must have an absolute or relative error less than 1e-9.|
|-||cards will contain between 2 and 50 elements, inclusive.|
|-||Each element of cards will be between 1.5 and 10.0, inclusive.|