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 PYTHON3):

Solution:
#import matplotlib.pyplot as plt
#import matplotlib.patches as patches
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:
                #plt.gca().add_patch(patches.Circle(xy=(center.real, center.imag), radius=1, fill=False, ec='r'))  # debug
                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)
    #plt.scatter([z.real for z in dots], [z.imag for z in dots])
    #plt.show()
for line in printed_later:
    print(line)