Circles and Segments#4900
Alexei has a sheet of paper where he has drawn both a circle and an -gon. He is interested in finding the shortest possible segment that can connect the circle to the -gon, as well as determining how many such shortest segments exist.
Note: If the shortest distance between the circle and the -gon is , then the number of "minimal" segments corresponds to the number of tangent points and intersections between the -gon and the circle.
The first line of the input specifies , the number of vertices of the -gon, where 3 \leq n \leq 100. The -gon is neither degenerate nor self-intersecting. The next lines provide the coordinates of the vertices of the -gon, listed in the order they are traversed (the direction of traversal is arbitrary). The final line contains three integers , , , representing the coordinates and radius of the circle, with absolute values not exceeding .
The output should be a single line containing two numbers separated by a space. The first number is the shortest distance from the circle to the -gon, expressed as a real number with precision up to three decimal places. The second number is the count of "minimal" segments.
Example 1