Problem: 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.

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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 P1, P2, and P3 be any three points in a data set, and d1, d2, and d3 the distances from an arbitrarily selected point in the xy-plane to each of them respectively. Then it never simultaneously holds that 0.9999 <= di <= 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.

Example

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


Output

2
5
5
11

Solution (in JAVA):

Solution:
import java.io.IOException;
import java.util.LinkedList;
import java.util.Scanner;

public class Main{
	public static double EPS = 1e-6;
	public static void main(String[] args) throws IOException{
		Scanner in = new Scanner(System.in);
		while(true){
			int n = in.nextInt();
			if(n == 0) break;
			Circle[] c = new Circle[n];
			LinkedList<Point> p = new LinkedList<Point>();
			for(int i=0; i<n; i++){
				c[i] = new Circle(in.nextDouble(), in.nextDouble(), 1);
				for(int j=i-1; j>=0; j--){
					Point[] pos = c[i].crossPoint(c[j]);
					if(pos == null) continue;
					p.add(pos[0]);
					p.add(pos[1]);
				}
			}
			int res = 1;
			for(Point pos: p){
				int count = 0;
				for(int i=0; i<n; i++){
					if(pos.dist2(c[i].p) <= 1+EPS) count++;
				}
				res = Math.max(res, count);
			}
			System.out.println(res);
		}
	}
}

class Circle{
	final static double EPS = 1e-6;
	
	Point p;
	double r;
	public Circle(double x, double y, double r){
		p = new Point(x, y);
		this.r = r;
	}
	
	public Point[] crossPoint(Circle c){
		if(!cross(c)) return null;
		double x1 = c.p.x - p.x;
		double y1 = c.p.y - p.y;
		double a = (x1*x1+y1*y1+r*r-c.r*c.r)/2.0;
		Point[] res = {
				new Point(culc(x1, y1, r, a, true)+p.x, culc(y1, x1, r, a, false)+p.y),
				new Point(culc(x1, y1, r, a, false)+p.x, culc(y1, x1, r, a, true)+p.y),
		};
		return res;
	}
	
	private static double culc(double x, double y, double r, double a, boolean sign){
		return (a*x + (sign?1:-1)*y*Math.sqrt((x*x+y*y)*r*r-a*a)+EPS)/(x*x+y*y);
	}
	
	public boolean cross(Circle c){
		return p.dist2(c.p) <= (r+c.r)*(r+c.r) + EPS;
	}
}

class Point{
	double x, y;
	public Point(double x, double y){
		this.x = x;
		this.y = y;
	}
	
	public double dist2(Point p){
		return (x-p.x)*(x-p.x) + (y-p.y)*(y-p.y);
	}
}