Wild Dogs Wild Dogs
Moderate
RU JA English
The dust from the blast has shraded away and you entered the grounds of the estate. But what is that piercing howl you’re hearing from afar? By taking a closer look you’ve realized that a small pack of huge black shaggy dogs, looking more like wolves, are headed your way. These are probably the wild offsprings of the guard dogs who’ve used to protect the castle from the unwanted visitors. The good news is that you have a rifle. The bad news is that you don’t have a lot of bullets. Therefore, your survival depends on finding the best vantage point for shooting. Choose your location wisely and try to make each shot count.

As input you’ll be given the coordinates of the dogs. Your task is to find the distance to the nearest point from which you can kill the maximum number of animals with one shot (any number of dogs on the same line can be killed with one shot). Your starting position is the point (0, 0).

If the calculated distance is an integer, return it as int, otherwise round it to 2 decimal places.
Don't worry about the situation when a few dogs on the line is behind your back (dog dog you dog) - there no such situation in the tests.

Input: coordinates of the dogs.

Output: distance to the best spot.

Example:

wild_dogs([(7, 122), (8, 139), (9, 156), 
           (10, 173), (11, 190), (-100, 1)]) == 0.18

How it is used: For the tactical analisys and troops placement.

Precondition:
2 <= amount of the dogs <= 15
0 <= distance to the right place <= 20