Making chocolate chip cookies involves mixing flour, salt, oil, baking soda, and chocolate chips to form dough, which is then rolled into a plane about 50 cm square. Circles are cut from this plane, placed on a cookie sheet, and baked in an oven for about 20 minutes. When the cookies are done, they are removed from the oven and allowed to cool before being eaten.
We are concerned here with the process of cutting the first cookie after the dough has been rolled. Each chip is visible in the planar dough, so we simply need to place the cutter so as to maximize the number of chocolate chips contained in its perimeter.
The input begins with a single positive integer on a line by itself indicating the number of test cases. This line is followed by a blank line, and there is also a blank line between two consecutive test cases.
Each input case consists of a number of lines, each containing two floating point numbers indicating the (x, y) coordinates of a chip in the square surface of cookie dough. Each coordinate is between 0.0 and 50.0 (cm). Each chip may be considered a point; i.e., these are not President's Choice cookies. All of the at most 200 chocolate chips are at different positions.
For each test case, the output consists of a single integer: the maximum number of chocolate chips that can be contained in a single cookie whose diameter is 5 cm. The cookie need not be fully contained in the 50-cm square dough (i.e., it may have a flat side).
The output of two consecutive cases must be separated by a blank line.
1 4.0 4.0 4.0 5.0 5.0 6.0 1.0 20.0 1.0 21.0 1.0 22.0 1.0 25.0 1.0 26.0