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.awt.geom.*;
import java.util.*;

public class Main {
	final double EPS = 1.0e-08;
	Point2D [] plist;

	private void doit(){
		Scanner sc = new Scanner(System.in);
		while(sc.hasNext()){
			int n = sc.nextInt();
			if(n == 0) break;
			plist = new Point2D[n];
			for(int i=0; i < n; i++){
				double x = sc.nextDouble(), y = sc.nextDouble();
				plist[i] = new Point2D.Double(x, y);
			}
			int ans = 1;
			for(int i=0; i < n; i++){
				for(int j=i+1; j < n; j++){					
					Point2D [] cpList = centerPoint(plist[i], plist[j]);
					if(cpList == null) continue;
					int res1 = distanceWithin1Radius(cpList[0]);
					int res2 = distanceWithin1Radius(cpList[1]);
					ans = Math.max(ans, Math.max(res1, res2));
				}
			}
			System.out.println(ans);
		}
	}

	private Point2D[] centerPoint(Point2D p1, Point2D p2) {
		double r = 1.0;
		double midx = (p1.getX() + p2.getX()) / 2.0;
		double midy = (p1.getY() + p2.getY()) / 2.0;
		Point2D midP = new Point2D.Double(midx, midy);
		Point2D p2p1 = sub(p2,p1);
		Point2D normalV1 = normalVector1(p2p1);
		Point2D normalV2 = normalVector2(p2p1);
		double halfdis = p1.distance(p2) / 2.0;
		if(halfdis > r + EPS) return null;
		double tocenterDis = Math.sqrt(r - halfdis * halfdis);
		Point2D [] res = new Point2D[2];
		res[0] = add(mul(normalV1, tocenterDis / norm(normalV1)), midP);
		res[1] = add(mul(normalV2, tocenterDis / norm(normalV1)), midP);
		return res;
	}
	private Point2D add(Point2D p1, Point2D p2) {
		double x = p2.getX() + p1.getX();
		double y = p2.getY() + p1.getY();
		return new Point2D.Double(x, y);
	}
	
	private Point2D sub(Point2D p2, Point2D p1) {
		double x = p2.getX() - p1.getX();
		double y = p2.getY() - p1.getY();
		return new Point2D.Double(x, y);
	}
	
	private Point2D mul(Point2D p,double value) {
		return new Point2D.Double(p.getX() * value, p.getY() * value);
	}
	
	private double norm(Point2D p){
		return Math.sqrt(p.getX() * p.getX() + p.getY() * p.getY());
	}
	
	private Point2D normalVector1(Point2D p) {
		return new Point2D.Double(-p.getY(), p.getX());
	}
	
	private Point2D normalVector2(Point2D p) {
		return new Point2D.Double(p.getY(), -p.getX());
	}

	private int distanceWithin1Radius(Point2D p) {
		int count = 0;
		for(int i=0; i < plist.length;i++){
			double res = p.distance(plist[i]);
			if(res<= 1.0 + EPS) count++;
		}
		return count;
	}

	public static void main(String[] args) {
		Main obj = new Main();
		obj.doit();
	}
}