Area of union of circles X17161

We want to calculate the area of the union of a set of circles. This is a problem that has some non-trivial algorithm for the exact computation. Instead, we would be satisfied by finding an approximation using a Montecarlo method. The ideas is as follows:

• Calculate a bounding box around the circles.

• Generate random points within the bounding box.

• Count how many points are inside some circle.

Input

The input contains a set of cases. Each case specifies the number of circles, $n\geq 0$, and the number of random points generated for the Montecarlo approximation. After that, a list of $n$ circles is specified, each one with the coordinates of the center, $(x,y)$, and the radius. The coordinates and the radius are real numbers.

Output

For every case print the estimated area as a real number in free format.

Observation

There is no need to compute the exact area. The output will be considered correct if it is a good approximation of the area.