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.io.InputStream;
import java.util.ArrayList;
import java.util.NoSuchElementException;
import java.util.Collections;
import java.util.Arrays;

public class Main {
	public static void main(String[] args) {
		FS fs = new FS();
		while(true) {
			int n = fs.nextInt();
			if(n==0) break;
			if(n==1) {
				double x = fs.nextDouble();
				double y = fs.nextDouble();
				System.out.println(1);
				continue;
			}
			double[] px = new double[n];
			double[] py = new double[n];
			for(int i=0; i<n; i++) {
				px[i] = fs.nextDouble();
				py[i] = fs.nextDouble();
			}
			ArrayList<Double> csx = new ArrayList<Double>();
			ArrayList<Double> csy = new ArrayList<Double>();
			for(int i=0; i<n-1; i++) {
				for(int j=i+1; j<n; j++) {
					double vx = px[j]-px[i];
					double vy = py[j]-py[i];
					double l = Math.sqrt(Math.pow(vx,2.0)+Math.pow(vy,2.0));
					if(l > 2.0) continue;
					double r = Math.sqrt(1.0 - Math.pow(l/2.0, 2.0));
					vx = vx/l*r;
					vy = vy/l*r;
					double mx = (px[i]+px[j])/2.0;
					double my = (py[i]+py[j])/2.0;
					csx.add(mx-vy);
					csy.add(my+vx);
					csx.add(mx+vy);
					csy.add(my-vx);
				}
			}
			int maxCount = 1;
			for(int i=0; i<csx.size(); i++) {
				int count = 0;
				for(int j=0; j<n; j++) {
					if(Math.pow(csx.get(i)-px[j],2.0)+Math.pow(csy.get(i)-py[j],2.0) <= 1.0000000001) {
						count++;
					}
				}
				maxCount = Math.max(maxCount, count);
			}
			System.out.println(maxCount);
		}
	}

	// Read Class
	static class FS {
		private final InputStream in = System.in;
		private final byte[] buffer = new byte[1024];
		private int ptr = 0;
		private int buflen = 0;
		private boolean hasNextByte() {
			if (ptr < buflen) {
				return true;
			} else {
				ptr = 0;
				try {
					buflen = in.read(buffer);
				} catch (IOException e) {
					e.printStackTrace();
				}
				if (buflen <= 0) {
					return false;
				}
			}
			return true;
		}

		private int readByte() { return hasNextByte() ? buffer[ptr++] : -1;}
		private boolean isPrintableChar(int c) {return 33 <= c && c <= 126;}
		private void skipUnprintable() {while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;}

		public boolean hasNext() { skipUnprintable(); return hasNextByte();}
		public String next() {
			if (!hasNext()) throw new NoSuchElementException();
			StringBuilder sb = new StringBuilder();
			int b = readByte();
			while(isPrintableChar(b)) {
				sb.appendCodePoint(b);
				b = readByte();
			}
			return sb.toString();
		}
		public int nextInt() {
			return (int)nextLong();
		}
		public double nextDouble() {
			return Double.parseDouble(next());
		}
		public long nextLong() {
			if (!hasNext()) throw new NoSuchElementException();
			long n = 0;
			boolean minus = false;
			int b = readByte();
			if (b == '-') {
				minus = true;
				b = readByte();
			}
			if (b < '0' || '9' < b) {
				throw new NumberFormatException();
			}
			while(true) {
				if ('0' <= b && b <= '9') {
					n *= 10;
					n += b - '0';
				} else if(b == -1 || !isPrintableChar(b)) {
					return minus ? -n : n;
				} else {
					throw new NumberFormatException();
				}
				b = readByte();
			}
		}
	}
}