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.util.*;

public class Main{
    static double[] x,y;
    static int n;
    static int max;

    public static void main(String[] args){
	Scanner sc = new Scanner(System.in);

	n = sc.nextInt();

	while(n!=0){
	    max = 1;
	    x = new double[n];
	    y = new double[n];

	    for(int i=0; i<n; i++){
		x[i] = sc.nextDouble();
		y[i] = sc.nextDouble();
	    }

	    solve();
	    System.out.println(max);

	    n = sc.nextInt();
	}
    }

   public static void solve(){
	for(int i=0; i<n; i++){
	    for(int j=i+1; j<n; j++){
		double ab = getDist(x[i],y[i],x[j],y[j]);
		if(ab<=2){
		    double mx = (x[i]+x[j])/2;//点aと点bの中点m
		    double my = (y[i]+y[j])/2;
		    double mc = Math.sqrt(1-(ab*ab)/4);//中点mから中心cまでの距離
		    double[][] nv = getNormalVector(x[i]-x[j],y[i]-y[j]);

		    int count = 0;
		    for(int l=0; l<2; l++){
			double cx = mx + nv[l][0]*mc;//中点cの座標
			double cy = my + nv[l][1]*mc;
			for(int k=0; k<n; k++){
			    if(getDist2(cx,cy,x[k],y[k])<1.0+(1e-6)){count++;}
			}
			if(count>max){max = count;}
			count = 0;
		    }
		}
	    }
	}
    }
    //a-bの絶対値（ab間の距離）
    public static double getDist(double x1,double y1,double x2,double y2){
	return Math.sqrt((x1-x2)*(x1-x2)+(y1-y2)*(y1-y2));
    }

    //絶対値なしの比較用　絶対値取る処理は重いため
    public static double getDist2(double x1,double y1,double x2,double y2){
	return (x1-x2)*(x1-x2)+(y1-y2)*(y1-y2);
    }

    //単位法線ベクトルを求める
    public static double[][] getNormalVector(double x, double y){
	
	double d = Math.sqrt(x*x+y*y);//|a|
	
	double[][] nv = new double[2][2];
	
	nv[0][0] = -y/d;
	nv[0][1] = x/d;
	nv[1][0] = y/d;
	nv[1][1] = -x/d;
	
	return nv;
    }
}