Circle and Points

Time Limit: 5 Seconds
Memory Limit: 32768 KB

You are given *N* points in the *xy*-plane. You have a
circle of radius one and move it on the *xy*-plane, so as to
enclose as many of the points as possible. Find how many points can be
simultaneously enclosed at the maximum. A point is considered
*enclosed* by a circle when it is inside or on the circle.

Fig 1. Circle and Points

**Input**

The input consists of a series of data sets, followed by a single line
only containing a single character '0', which indicates the end of the
input. Each data set begins with a line containing an integer *N*,
which indicates the number of points in the data set. It is
followed by *N* lines describing the coordinates of the
points. Each of the *N* lines has two decimal fractions *X*
and *Y*, describing the *x*- and *y*-coordinates of a
point, respectively. They are given with five digits after the decimal
point.

You may assume 1 <= *N* <= 300, 0.0 <= *X* <= 10.0, and 0.0
<= *Y* <= 10.0. No two points are closer than 0.0001. No two
points in a data set are approximately at a distance of 2.0. More
precisely, for any two points in a data set, the distance *d*
between the two never satisfies 1.9999 <= *d* <= 2.0001. Finally,
no three points in a data set are simultaneously very close to a
single circle of radius one. More precisely,
let P_{1}, P_{2}, and P_{3} be any three points in a
data set, and *d*_{1}, *d*_{2}, and *d*_{3}
the distances from an arbitrarily selected point in the *xy*-plane to each of them
respectively. Then it never simultaneously holds that 0.9999 <=
*d*_{i} <= 1.0001 (*i* = 1, 2, 3).

**Output**

For each data set, print a single line containing the maximum number
of points in the data set that can be simultaneously enclosed by a
circle of radius one. No other characters including leading and
trailing spaces should be printed.

**Sample Input**

3

6.47634 7.69628

5.16828 4.79915

6.69533 6.20378

6

7.15296 4.08328

6.50827 2.69466

5.91219 3.86661

5.29853 4.16097

6.10838 3.46039

6.34060 2.41599

8

7.90650 4.01746

4.10998 4.18354

4.67289 4.01887

6.33885 4.28388

4.98106 3.82728

5.12379 5.16473

7.84664 4.67693

4.02776 3.87990

20

6.65128 5.47490

6.42743 6.26189

6.35864 4.61611

6.59020 4.54228

4.43967 5.70059

4.38226 5.70536

5.50755 6.18163

7.41971 6.13668

6.71936 3.04496

5.61832 4.23857

5.99424 4.29328

5.60961 4.32998

6.82242 5.79683

5.44693 3.82724

6.70906 3.65736

7.89087 5.68000

6.23300 4.59530

5.92401 4.92329

6.24168 3.81389

6.22671 3.62210

0

Sample Output

2

5

5

11

Source:

**Asia 2004, Ehime (Japan), Japan Domestic**
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