Chocolate Chip Cookies

Time Limit: 2 Seconds
Memory Limit: 65536 KB

Making chocolate chip cookies involves mixing flour, salt, oil, baking soda and
chocolate chips to form dough which is rolled into a plane about 50 cm square.
Circles are cut from the plane, placed on a cookie sheet, and baked in an oven
for about twenty 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 need simply to
place the cutter so as to maximize the number of chocolate chips contained in
its perimeter.

**Input**

Standard input 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). Each chip
is at a different position. There are at most 200 chocolate chips.

Subsequent test cases are separated with a single blank line.

**Output**

Standard output consists of a single integer: the 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).

**Sample Input**

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

**Sample Output**

4

Source:

**University of Waterloo Local Contest 1998.10.17**
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