题目描述

平面上 $N$ 个点，用一个半径 $R$ 的圆去覆盖，最多能覆盖多少个点？

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.

输入格式

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 $1 \leq N \leq 300$, $0.0 \leq X \leq 10.0$, and $0.0 \leq Y \leq 10.0$. 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 $1.9999 \leq d \leq 2.0001$. Finally, no three points in a data set are simultaneously very close to a single circle of radius one. More precisely, let $P_1,\ P_2,\ P_3$ be any three points in a data set, and $d_1,\ d_2,\ d_3$ the distances from an arbitrarily selected point in the xy-plane to each of them respectively. Then it never simultaneously holds that $0.9999 \leq di \leq 1.0001$ ($i = 1,\ 2,\ 3$).

输出格式

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.

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

2
5
5
11