Mushroom Rain#502
At the edge of the forest, a friendly family of mushrooms grows. The position of each mushroom is given by coordinates , , and the mushroom cap has a radius . When it rains, the radius of each mushroom's cap increases at a rate of centimeter per minute. When the rain stops (and it does not last more than minutes), the caps stop growing. If, during the rain, the caps of two mushrooms come into contact, they immediately stop growing to avoid harming each other. Mushrooms are very friendly: if two mushrooms stop growing, all the others also stop growing.
Your task is to calculate by how many centimeters the radius of each mushroom's cap will increase after the rain ends.
The first line contains the number — the number of test cases. The first line of each test contains two integers: the number of mushrooms (K \le 10) and the duration of the rain (T \le 100). The next lines contain descriptions of the mushrooms: the coordinates and (X \le 100, Y \le 100) and the initial cap radius (R \le 10). Coordinates and radius are given in centimeters.
For each test case, print one number — the value by which the radius of all mushrooms increases. The answer should not contain insignificant zeros and should be given to two decimal places.
Example 1