Faqiang Company produces a metal product made of straight metal bars, which are welded together at their intersection points. For aesthetic reasons, the product needs to be wrapped in a special material. To save costs, the company wants to minimize the amount of material used (ignoring any waste from cutting).

Write a program that takes the number of vertices of the product and the coordinates of all vertices as input, and calculates the minimum surface area of the material required to wrap the product. The result should be rounded to six decimal places.

Input

The input consists of several lines: the first line contains an integer $n$ ($4 \le n \le 100$), representing the number of vertices. The next $n$ lines each contain three real numbers $x_i, y_i, z_i$, representing the coordinates of the $i$-th vertex. All vertex positions are distinct.

Output

The output contains a single real number, representing the minimum surface area of the material required to wrap the product.

Examples

Input 1

4
0 0 0
1 0 0
0 1 0
0 0 1

Output 1

2.366025

Note

The input example contains 4 points.