URI Online Judge | 2348
# Dating On-Line

**Timelimit: 1**

By Rafael Garcia Gomes Colombia

Alex registered in an online dating system to search for the perfect partner. The system requires each of its members to fill a form specifying how much they enjoy **N** different activities, grading them on a scale from 0 to 100. To present this information to potential dates, the system creates a profile featuring a special kind of polygon called “radial diagram”.

A radial diagram for **N** activities is drawn by marking **N** points on the plane. Starting from the vertical direction, the **i**-th point in clockwise order represents the **i**-th activity specified by the member, and is a distance **S _{i}** away from the center of the diagram, where

For example, if **N** = 6 Alex might specify the following activities: singing with score **S _{1}** = 10, running with score

The area of a radial diagram depends on the order in which the different activities are specified, and Alex suspects that a profile depicting a radial diagram with greater area might be more successful. For example, the radial diagram in the following figure features the same activities and scores as the example above, but has a greater area.

Alex has asked you to write a program to find the maximum possible area of a radial diagram given a list of activities graded with scores between 0 and 100.

The first line contains an integer **N** representing the number of activities (3 ≤ **N** ≤ 10^{5}). The second line contains **N** integers **S _{1}**,

Output a line with a rational number representing the maximum possible area of a radial diagram featuring the scores given in the input. The result must be output as a rational number with exactly 3 digits after the decimal point, rounded if necessary.

Input Samples | Output Samples |

6 |
10002.593 |

3 |
12990.381 |

7 |
2772.765 |