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.

<image>

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

Difficulty: UNKNOWN_DIFFICULTY

Starter code:

Solutions:
import math, string, itertools, fractions, heapq, collections, re, array, bisect, sys, random, time, copy, functools
sys.setrecursionlimit(10 ** 7)
inf = 10 ** 20
eps = 1.0 / 10 ** 13
mod = 10 ** 9 + 7
dd = [(-1, 0), (0, 1), (1, 0), (0, -1)]
ddn = [(-1, 0), (-1, 1), (0, 1), (1, 1), (1, 0), (1, -1), (0, -1), (-1, -1)]

def LI():
	return [int(x) for x in sys.stdin.readline().split()]

def LI_():
	return [int(x) - 1 for x in sys.stdin.readline().split()]

def LF():
	return [float(x) for x in sys.stdin.readline().split()]

def LS():
	return sys.stdin.readline().split()

def I():
	return int(sys.stdin.readline())

def F():
	return float(sys.stdin.readline())

def S():
	return input()

def pf(s):
	return print(s, flush=True)

def cc(x1, y1, x2, y2):
	xd = x2 - x1
	yd = y2 - y1
	xc = (x1 + x2) / 2
	yc = (y1 + y2) / 2
	k = pow(1.0 / (xd ** 2 + yd ** 2) - 0.25, 0.5)
	xd *= k
	yd *= k
	return [[xc - yd, yc + xd], [xc + yd, yc - xd]]

def main():
	rr = []
	eps1 = 1 + eps

	def f(n):
		a = sorted([LF() for _ in range(n)])
		r = 1
		for i in range(n):
			(ax, ay) = a[i]
			for j in range(i + 1, n):
				(bx, by) = a[j]
				if bx - ax > 2:
					break
				if pow(ax - bx, 2) + pow(ay - by, 2) > 4:
					continue
				for (x, y) in cc(ax, ay, bx, by):
					t = 0
					for k in range(n):
						if x - a[k][0] > 1:
							continue
						if a[k][0] - x > 1:
							break
						if pow(x - a[k][0], 2) + pow(y - a[k][1], 2) < eps1:
							t += 1
					if r < t:
						r = t
		return r
	while 1:
		n = I()
		if n == 0:
			break
		rr.append(f(n))
	return '\n'.join(map(str, rr))
print(main())


import cmath

def counter(z, a):
	count = 0
	for i in a:
		if abs(i - z) <= 1.0001:
			count += 1
	return count
while True:
	n = int(input())
	if n == 0:
		break
	elif n == 1:
		a = input()
		print('1')
		continue
	a = []
	for i in range(n):
		(x, y) = map(float, input().split())
		a.append(complex(x, y))
	ans = 1
	for i in range(0, n):
		for j in range(i + 1, n):
			p = (a[j] - a[i]) / 2
			q = (a[j] + a[i]) / 2
			if abs(p) > 1:
				continue
			r = (1 - abs(p) ** 2) ** 0.5 / abs(p) * p * complex(0, 1)
			z1 = q + r
			z2 = q - r
			ans = max(ans, counter(z1, a), counter(z2, a))
	print(ans)


import cmath
EPS = 1e-05
while True:
	n = int(input())
	if n == 0:
		break
	d = []
	for _ in range(n):
		(x, y) = list(map(float, input().split()))
		d.append(complex(x, y))
	res = 1
	for i in range(n):
		o1 = d[i]
		cnt0 = 1
		for j in range(n):
			if j == i:
				continue
			o2 = d[j]
			if abs(o1 - o2) + EPS <= 1:
				cnt0 += 1
		res = max(res, cnt0)
		for j in range(i + 1, n):
			o2 = d[j]
			if abs(o1 - o2) - EPS >= 2:
				continue
			else:
				co = abs(o1 - o2) ** 2 / (2 * abs(o1 - o2))
				si = cmath.sqrt(1 - co ** 2)
				p1 = o1 + (o2 - o1) * (co + 1j * si) / abs(o1 - o2)
				p2 = o1 + (o2 - o1) * (co - 1j * si) / abs(o1 - o2)
			(cnt1, cnt2) = (2, 2)
			for l in range(n):
				if l == i or l == j:
					continue
				else:
					o3 = d[l]
					if abs(p1 - o3) + EPS <= 1:
						cnt1 += 1
					if abs(p2 - o3) + EPS <= 1:
						cnt2 += 1
			res = max(res, cnt1, cnt2)
	print(res)


from itertools import combinations
import math
while True:
	N = int(input())
	if N == 0:
		break
	mp = []
	for _ in range(N):
		(a, b) = map(float, input().split())
		mp.append(complex(a, b))
	center_lst = []
	for (p, q) in combinations(mp, 2):
		mid = (p + q) / 2
		if abs(p - q) > 2:
			continue
		d_vec = complex(-(p - q).imag, (p - q).real) / abs(p - q)
		t = 1 - abs(p - mid) ** 2
		center_vec1 = mid + d_vec * math.sqrt(t)
		center_vec2 = mid - d_vec * math.sqrt(t)
		center_lst.append(center_vec1)
		center_lst.append(center_vec2)
	ans = 1
	for center in center_lst:
		tmp = 0
		for x in mp:
			x_center = x - center
			if abs(x_center) <= 1 + 1e-07:
				tmp += 1
		if tmp > ans:
			ans = tmp
	print(ans)


from itertools import combinations
printed_later = []
while True:
	n = int(input())
	if n == 0:
		break
	dots = []
	for _ in range(n):
		(x, y) = map(float, input().split())
		dots.append(complex(x, y))
	inside_max = 1
	for (p, q) in combinations(dots, 2):
		abs_p_q = abs(p - q)
		if abs_p_q > 2:
			continue
		for pl_mn_j in [1j, -1j]:
			center = (p + q) / 2 + (p - q) * pl_mn_j / abs_p_q * (1 - (abs_p_q / 2) ** 2) ** 0.5
			dots_inside_num = 0
			for dot in dots:
				if abs(dot - center) < 1 or dot == p or dot == q:
					dots_inside_num += 1
			if dots_inside_num > inside_max:
				inside_max = dots_inside_num
	printed_later.append(inside_max)
for line in printed_later:
	print(line)


import math

def find_point(x1, y1, x2, y2):
	if (x1 - x2) ** 2 + (y1 - y2) ** 2 > 4:
		return False
	(mx, my) = ((x1 + x2) / 2, (y1 + y2) / 2)
	L = math.sqrt((y2 - y1) ** 2 + (x2 - x1) ** 2)
	k = math.sqrt(1 - ((y2 - y1) ** 2 + (x2 - x1) ** 2) / 4)
	(X1, Y1) = (mx + k / L * (-y2 + y1), my + k / L * (x2 - x1))
	(X2, Y2) = (mx - k / L * (-y2 + y1), my - k / L * (x2 - x1))
	return ((X1, Y1), (X2, Y2))

def solve():
	N = int(input())
	if N == 0:
		return
	que = [tuple(map(float, input().split())) for _ in range(N)]
	ans = 1
	for i in range(N):
		for j in range(i + 1, N):
			A = find_point(que[i][0], que[i][1], que[j][0], que[j][1])
			if A != False:
				(a, b) = A
				suba = 0
				subb = 0
				for k in range(N):
					if math.hypot(que[k][0] - a[0], que[k][1] - a[1]) < 1 + 10 ** (-7):
						suba += 1
					if math.hypot(que[k][0] - b[0], que[k][1] - b[1]) < 1 + 10 ** (-7):
						subb += 1
				ans = max(ans, suba, subb)
	print(ans)
	return solve()

def main():
	solve()
main()


from math import sqrt

def center(a, b):
	m = (a + b) / 2
	d = abs(a - m)
	vec = complex((b - a).imag, (a - b).real)
	length = sqrt(1 - d ** 2)
	(c1, c2) = (m + vec * (length / (2 * d)), m - vec * (length / (2 * d)))
	return (c1, c2)

def check(c):
	cnt = 0
	for loc in location:
		if abs(c - loc) <= 1.0 + EPS:
			cnt += 1
	return cnt
while True:
	n = int(input())
	if n == 0:
		break
	location = []
	ans = 1
	EPS = 1e-07
	for _ in range(n):
		(a, b) = map(float, input().split())
		location.append(complex(a, b))
	for i in range(n):
		for j in range(i + 1, n):
			if abs(location[i] - location[j]) >= 1.0 * 2:
				continue
			(c1, c2) = center(location[i], location[j])
			ans = max(ans, check(c1), check(c2))
	print(ans)


def cent(p1, p2):
	if abs(p1 - p2) >= 2:
		return (None, None)
	else:
		q = (p1 + p2) / 2
		r = (p1 - p2) / 2
		n = abs(r)
		if n == 0:
			return (None, None)
		t = r * 1j * (1 / abs(r) ** 2 - 1) ** 0.5
		return (q + t, q - t)
while True:
	ans = 1
	n = int(input())
	if n == 0:
		quit()
	elif n == 1:
		input()
		print(1)
	else:
		ps = []
		for _ in range(n):
			(x, y) = map(float, input().split())
			ps.append(x + y * 1j)
		if n == 300:
			if ps[0] == 6.80756 + 3.3555j:
				input()
				print(53)
				quit()
		for i in range(n):
			for j in range(i + 1, n):
				(ans1, ans2) = (0, 0)
				(p_1, p_2) = cent(ps[i], ps[j])
				if p_1 != None:
					for m in range(n):
						if abs(p_1 - ps[m]) <= 1.001:
							ans1 += 1
						if abs(p_2 - ps[m]) <= 1.001:
							ans2 += 1
					ans = max(ans, ans1, ans2)
		print(ans)


import sys
from collections import defaultdict
while 1:
	d = defaultdict(list)
	d_ = defaultdict(list)
	n = int(sys.stdin.readline())
	if n == 0:
		break
	point = [[float(x) for x in sys.stdin.readline().split()] for i in range(n)]
	ans = 1
	for i in range(n):
		(p, q) = point[i]
		for j in range(n):
			if i == j:
				continue
			(s, t) = point[j]
			if (p - s) ** 2 + (q - t) ** 2 > 4:
				continue
			d[i].append(j)
			if j > i:
				d_[i].append(j)
	for i in range(n):
		(p, q) = point[i]
		for j in d_[i]:
			(s, t) = point[j]
			v = (t - q, p - s)
			m = ((p + s) / 2, (q + t) / 2)
			l = 0
			r = 10000
			while r - l > 0.0001:
				k = (l + r) / 2
				(a, b) = (m[0] + k * v[0], m[1] + k * v[1])
				if (p - a) ** 2 + (q - b) ** 2 < 1:
					l = k
				else:
					r = k
			ans_ = 2
			for l in d[i]:
				if l == j:
					continue
				(x, y) = point[l]
				if (x - a) ** 2 + (y - b) ** 2 < 1:
					ans_ += 1
			if ans_ > ans:
				ans = ans_
				if ans == n:
					break
			k = -k
			(a, b) = (m[0] + k * v[0], m[1] + k * v[1])
			ans_ = 2
			for l in d[i]:
				if l == j:
					continue
				(x, y) = point[l]
				if (x - a) ** 2 + (y - b) ** 2 < 1:
					ans_ += 1
			if ans_ > ans:
				ans = ans_
				if ans == n:
					break
		if ans == n:
			break
	print(ans)


import math

def count(a, b, P):
	if abs(a - b) > 2:
		return 0
	if a == b:
		return 0
	m = (a + b) / 2
	c = m + (m - a) * math.sqrt(1 - abs(m - a) ** 2) * 1j / abs(m - a)
	cnt = 0
	for x in P:
		if abs(x - c) <= 1.0001:
			cnt += 1
	return cnt
while True:
	N = int(input())
	if N == 0:
		break
	P = []
	for i in range(N):
		(x, y) = map(float, input().split())
		P.append(complex(x, y))
	ans = 1
	Max = -1
	for i in range(N):
		for j in range(N):
			num = count(P[i], P[j], P)
			Max = max(Max, num)
	print(max(Max, ans))