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.

<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

Solution (in PYTHON3):

Solution:
#2006_D
"""
import sys
from collections import defaultdict
def dfs(d,y,x,f):
    global ans
    if d >= 10:
        return
    f_ = defaultdict(int)
    for i in f.keys():
        f_[i] = f[i]
    for t,s in vr[(y,x)]:
        if a[t][s] == 3:
            ans = min(ans,d+1)
            break
        elif f[(t,s)]:
            if s == x+1:
                break
            f_[(t,s)] = 0
            dfs(d+1,t,s-1,f_)
            f_[(t,s)] = 1
            break

    for t,s in vl[(y,x)]:
        if a[t][s] == 3:
            ans = min(ans,d+1)
            break
        elif f[(t,s)]:
            if s == x-1:
                break
            f_[(t,s)] = 0
            dfs(d+1,t,s+1,f_)
            f_[(t,s)] = 1
            break

    for t,s in vd[(y,x)]:
        if a[t][s] == 3:
            ans = min(ans,d+1)
            break
        elif f[(t,s)]:
            if t == y+1:
                break
            f_[(t,s)] = 0
            dfs(d+1,t-1,s,f_)
            f_[(t,s)] = 1
            break

    for t,s in vu[(y,x)]:
        if a[t][s] == 3:
            ans = min(ans,d+1)
            break
        elif f[(t,s)]:
            if t == y-1:
                break
            f_[(t,s)] = 0
            dfs(d+1,t+1,s,f_)
            f_[(t,s)] = 1
            break
    return
while 1:
    w,h = map(int, sys.stdin.readline()[:-1].split())
    if w == h == 0:
        break
    a = [list(map(int, sys.stdin.readline()[:-1].split())) for i in range(h)]
    vr = defaultdict(list)
    vl = defaultdict(list)
    vd = defaultdict(list)
    vu = defaultdict(list)
    f = defaultdict(int)
    for y in range(h):
        for x in range(w):
            if a[y][x] == 1:
                f[(y,x)] = 1
            if a[y][x] in [1,3]:
                for x_ in range(x):
                    vr[(y,x_)].append((y,x))
            elif a[y][x] == 2:
                sy,sx = y,x
    for y in range(h):
        for x in range(w)[::-1]:
            if a[y][x] in (1,3):
                for x_ in range(x+1,w):
                    vl[(y,x_)].append((y,x))
    for x in range(w):
        for y in range(h):
            if a[y][x] in (1,3):
                for y_ in range(y):
                    vd[(y_,x)].append((y,x))
    for x in range(w):
        for y in range(h)[::-1]:
            if a[y][x] in (1,3):
                for y_ in range(y+1,h):
                    vu[(y_,x)].append((y,x))
    ind = [[[0]*4 for i in range(w)] for j in range(h)]
    ans = 11
    dfs(0,sy,sx,f)
    ans = ans if ans < 11 else -1
    print(ans)
"""

#2018_D
"""
import sys
from collections import defaultdict
sys.setrecursionlimit(1000000)

def dfs(d,s,l,v,dic):
    s_ = tuple(s)
    if dic[(d,s_)] != None:
        return dic[(d,s_)]
    if d == l:
        dic[(d,s_)] = 1
        for x in s:
            if x > (n>>1):
                dic[(d,s_)] = 0
                return 0
        return 1
    else:
        res = 0
        i,j = v[d]
        if s[i] < (n>>1):
            s[i] += 1
            res += dfs(d+1,s,l,v,dic)
            s[i] -= 1
        if s[j] < (n>>1):
            s[j] += 1
            res += dfs(d+1,s,l,v,dic)
            s[j] -= 1
        dic[(d,s_)] = res
        return res

def solve(n):
    dic = defaultdict(lambda : None)
    m = int(sys.stdin.readline())
    s = [0]*n
    f = [[1]*n for i in range(n)]
    for i in range(n):
        f[i][i] = 0
    for i in range(m):
        x,y = [int(x) for x in sys.stdin.readline().split()]
        x -= 1
        y -= 1
        s[x] += 1
        f[x][y] = 0
        f[y][x] = 0
    v = []
    for i in range(n):
        for j in range(i+1,n):
            if f[i][j]:
                v.append((i,j))
    l = len(v)
    print(dfs(0,s,l,v,dic))

while 1:
    n = int(sys.stdin.readline())
    if n == 0:
        break
    solve(n)
"""
#2011_D
"""
import sys
def dfs(s,d,f,v):
    global ans
    if ans == n-n%2:
        return
    if d > ans:
        ans = d
    for i in range(n):
        if s[i] == 0:
            for j in range(i+1,n):
                if s[j] == 0:
                    if f[i] == f[j]:
                        s[i] = -1
                        s[j] = -1
                        for k in v[i]:
                            s[k] -= 1
                        for k in v[j]:
                            s[k] -= 1
                        dfs(s,d+2,f,v)
                        s[i] = 0
                        s[j] = 0
                        for k in v[i]:
                            s[k] += 1
                        for k in v[j]:
                            s[k] += 1

def solve(n):
    p = [[int(x) for x in sys.stdin.readline().split()] for i in range(n)]
    v = [[] for i in range(n)]
    f = [0]*n
    s = [0]*n
    for i in range(n):
        x,y,r,f[i] = p[i]
        for j in range(i+1,n):
            xj,yj,rj,c = p[j]
            if (x-xj)**2+(y-yj)**2 < (r+rj)**2:
                v[i].append(j)
                s[j] += 1
    dfs(s,0,f,v)
    print(ans)
while 1:
    n = int(sys.stdin.readline())
    ans = 0
    if n == 0:
        break
    solve(n)
"""

#2003_D
"""
import sys
def root(x,par):
    if par[x] == x:
        return x
    par[x] = root(par[x],par)
    return par[x]

def unite(x,y,par,rank):
    x = root(x,par)
    y = root(y,par)
    if rank[x] < rank[y]:
        par[x] = y
    else:
        par[y] = x
        if rank[x] == rank[y]:
            rank[x] += 1

def solve(n):
    p = [[float(x) for x in sys.stdin.readline().split()] for i in range(n)]
    v = []
    for i in range(n):
        for j in range(i):
            xi,yi,zi,ri = p[i]
            xj,yj,zj,rj = p[j]
            d = max(0,((xi-xj)**2+(yi-yj)**2+(zi-zj)**2)**0.5-(ri+rj))
            v.append((i,j,d))
    par = [i for i in range(n)]
    rank = [0]*n
    v.sort(key = lambda x:x[2])
    ans = 0
    for x,y,d in v:
        if root(x,par) != root(y,par):
            unite(x,y,par,rank)
            ans += d
    print("{:.3f}".format(round(ans,3)))

while 1:
    n = int(sys.stdin.readline())
    if n == 0:
        break
    solve(n)
"""

#2009_D
"""
import sys
from heapq import heappop,heappush
from collections import defaultdict
def solve(n,m):
    s,g = [int(x) for x in sys.stdin.readline().split()]
    s -= 1
    g -= 1
    e = [[] for i in range(n)]
    for i in range(m):
        a,b,d,c = [int(x) for x in sys.stdin.readline().split()]
        a -= 1
        b -= 1
        e[a].append((b,d,c))
        e[b].append((a,d,c))
    dist = defaultdict(lambda : float("inf"))
    dist[(s,0,-1)] = 0
    q = [(0,s,0,-1)]
    while q:
        dx,x,v,p = heappop(q)
        if x == g and v == 1:
            print(dx)
            return
        for i in range(-1,2):
            v_ = v+i
            if v_ < 1 :continue
            for y,d,c in e[x]:
                if p == y:
                    continue
                if v_ > c:
                    continue
                z = d/v_
                if dx+z < dist[(y,v_,x)]:
                    dist[(y,v_,x)] = dx+z
                    heappush(q,(dist[(y,v_,x)],y,v_,x))
    print("unreachable")
    return

while 1:
    n,m = [int(x) for x in sys.stdin.readline().split()]
    if n == 0:
        break
    solve(n,m)
"""

#2016_D
"""
import sys
def solve(n):
    w = [int(x) for x in sys.stdin.readline().split()]
    dp = [[0]*(n+1) for i in range(n+1)]
    for le in range(n+1):
        for l in range(n):
            r = l+le
            if r > n:break
            if not (r-l)%2 and abs(w[l]-w[r-1]) < 2:
                if dp[l+1][r-1] == r-l-2:
                    dp[l][r] = r-l
                    continue
            for k in range(l+1,r):
                if dp[l][k] + dp[k][r] > dp[l][r]:
                    dp[l][r] = dp[l][k] + dp[k][r]
    print(dp[0][n])
while 1:
    n = int(sys.stdin.readline())
    if not n:
        break
    solve(n)
"""
#2009_D
"""
alp = list("abcdefghijklmnopqrstuvwxyz")
c = {}
key = {}
for i in range(25):
    c[alp[i]] = alp[i+1]
    key[alp[i]] = i
key["z"] = 25

def dfs(i,k,f,n):
    global ans
    if i == n:
        for j in k:
            if f[key[j]]:
                break
        else:
            ans.append(k)
    else:
        dfs(i+1,k+s[i],f,n)
        if s[i] != "z" and f[key[s[i]]+1]:
            f[key[s[i]]+1] = 0
            dfs(i+1,k+c[s[i]],f,n)
            f[key[s[i]]+1] = 1

def solve(s):
    global ans
    n = len(s)
    d = {}
    for i in s:
        d[i] = 1
    f = [1]*26
    f[0] = 0
    dfs(0,"",f,n)
    ans.sort()
    print(len(ans))
    if len(ans) < 10:
        for i in ans:
            print(i)
    else:
        for i in ans[:5]:
            print(i)
        for i in ans[-5:]:
            print(i)
while 1:
    s = input()
    ans = []
    if s == "#":
        break
    solve(s)
"""

#2004_D
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)