Convex hull

Description

There are M circles (0 ≤ M ≤ 100) on a plane. Some circles can have zero radius. The task is to calculate the area of minimum convex domain containing all the circles.

Input

The input contains the description of one test including:

a line with value M;
M lines; every line contains coordinates of the center and the radius for one circle. These are real numbers separated by spaces.
Output

The output contains a single line with the result given with accuracy 10-4.

Sample Input

4
0 0 1
0 4 1
4 4 1
4 0 1
Sample Output

35.1416