Ultimate Weapon

Time Limit: 2000MS

Memory Limit: 131072K

Description

In year 2008 of the Cosmic Calendar, the Aliens send a huge armada towards the Earth seeking after conquest. The humans now depend on their ultimate weapon to retain their last hope of survival. The weapon, while capable of creating a continuous, closed and convex lethal region in the space and annihilating everything enclosed within, unfortunately exhausts upon each launch a tremendous amount of energy which is proportional to the surface area of the lethal region. Given the positions of all battleships in the Aliens' armada, your task is to calculate the minimum amount of energy required to destroy the armada with a single launch of the ultimate weapon. You need to report the surface area of the lethal region only.

Input

The first line contains one number N -- the number of battleships.(1 ≤ N ≤ 500) Following N lines each contains three integers presenting the position of one battleship.

Output

The minimal area rounded to three decimal places.

Sample Input

4
0 0 0
4 0 0
2 3 0
1 1 2


Sample Output

19.137

Hint

There are no four coplaner battleships.

Source

POJ Founder Monthly Contest – 2008.03.16, Jia