### Problem Statement

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.

### Definition

 Class: Nisoku Method: theMax Parameters: double[] Returns: double Method signature: double theMax(double[] cards) (be sure your method is public)

### Notes

-Your return value must have an absolute or relative error less than 1e-9.

### Constraints

-cards will contain between 2 and 50 elements, inclusive.
-Each element of cards will be between 1.5 and 10.0, inclusive.

### Examples

0)

 `{5, 8}`
`Returns: 40.0`
 5 * 8 = 40.
1)

 `{1.5, 1.8}`
`Returns: 3.3`
 1.5 + 1.8 = 3.3.
2)

 `{8.26, 7.54, 3.2567}`
`Returns: 202.82857868`
3)

 `{1.5, 1.7, 1.6, 1.5}`
`Returns: 9.920000000000002`
4)

 ```{10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10}```
`Returns: 1.0E50`
 The answer can be extremely big.

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=10760

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=14148&pm=10760

rng_58

#### Testers:

PabloGilberto , misof , ivan_metelsky

Greedy, Math