Solarium for mushrooms

And again Michael does his experiments. This time he decided to clone the mushrooms. For this, he prepared $n$ spores, which he will soon plant in the ground and grow. So that spores, as they develop and increase in size, won't touch each other, Michael decided to plant them only at integer coordinates. And also to speed up the growth process, he is going to build a large round lamp which will warm the spores up. The center of the lamp he wants to place at a point with integer coordinates, and let the radius of the lamp be integer too. But what should the radius be? Of course, you can build a lamp under which the whole forest can fit, but it will take a lot of extra time. So, the radius of the lamp must be as small as possible.