Convex hull

Time Limit: 2000ms
Memory Limit: Unknown KB
This problem will be judged on PKU. Original ID: 3405
64-bit integer IO format: %lld      Java class name: Main
Special Judge

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

Source

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