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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;

double Dis(double x1, double y1, double x2, double y2);
int main(void){
	while(1){
		int n;
		int ans = 1;
		vector< pair<double, double> > p;

		cin >> n;
		if(n == 0) break;

		for(int i=0; i<n; i++){
			pair<double, double> t;
			cin >> t.first >> t.second;
			p.push_back(t);
		}

		for(int i=0; i<n; i++){
			for(int j=i+1; j<n; j++){
				//中点
				double mpx = (p[i].first + p[j].first) / 2.0;
				double mpy = (p[i].second + p[j].second) / 2.0;
				//2点間の距離
				double d1 = Dis(p[i].first, p[i].second, p[j].first, p[j].second);
				if(d1 > 2.0) continue;
				//p[i]からp[j]へ向かうベクトル
				double v1x = (p[j].first - p[i].first) / d1;
				double v1y = (p[j].second - p[i].second) / d1;
				//中点から円の中心へ向かう単位ベクトル
				double v2x = -v1y;
				double v2y = v1x;
				//中心から円の中心へ向かうベクトルの長さ
				double d2 = sqrt(1.0 - (d1*d1/4.0));

				//円の中心の座標
				double cx = mpx + v2x * d2;
				double cy = mpy + v2y * d2;

				int cnt = 0;
				for(int k=0; k<n; k++){
					if(k == i || k == j || (cx-p[k].first)*(cx-p[k].first) + (cy-p[k].second)*(cy-p[k].second) <= 1.0)	cnt++;
				}
				if(cnt > ans){
					ans = cnt;
				}

				cx = mpx - v2x * d2;
				cy = mpy - v2y * d2;

				cnt = 0;
				for(int k=0; k<n; k++){
					if(k == i || k == j || (cx-p[k].first)*(cx-p[k].first) + (cy-p[k].second)*(cy-p[k].second) <= 1.0)	cnt++;
				}
				if(cnt > ans){
					ans = cnt;
				}
			}
		}

		cout << ans << endl;


	}
	
	return 0;
}

double Dis(double x1, double y1, double x2, double y2){
	return sqrt((x1 - x2)*(x1 - x2) + (y1 - y2)*(y1 - y2));
}