Three Circles

Given up to N ≤ 3 circles on a plane, your task is to calculate the area of their union.

This problem is straightforward, so please avoid overly complex solutions.

Input

The first line contains the integer N (1 ≤ N ≤ 3).

Each of the next N lines contains 3 integers, representing the coordinates of the center and the radius of each circle.

All circles are entirely contained within the square defined by 0×0 to 100×100.

The radius of each circle is positive.

Output

Output a single real number representing the area of the union of the circles.

The result should have a relative error no greater than 10^{-6}.

Examples