Chocolate Chip Cookies

Making chocolate chip cookies means mixing flour, salt, oil, baking soda, and chocolate chips into a dough, then rolling that dough out into a flat sheet about 50 cm square. Circles are cut from the sheet, placed on a baking tray, and baked for about twenty minutes.

Here we care only about cutting the first cookie once the dough has been rolled out. Every chip is visible on the flat dough, so the task is simply to position the circular cutter so that it encloses as many chocolate chips as possible.

The input consists of several lines. Each line contains two floating-point numbers giving the $(x, y)$ coordinates of one chip on the square surface of the dough. Each coordinate is between $0.0$ and $50.0$ (in centimeters). Each chip is treated as a single point, and no two chips share the same position. There are at most $200$ chips.

Output a single integer: the maximum number of chocolate chips that can lie within one circular cookie whose diameter is $5$ cm. A chip lying exactly on the cutting circle counts as contained. The cutter does not have to fit entirely inside the $50$ cm square of dough — it may hang over an edge (so a cookie may end up with a flat side).