Problem: Many schoolchildren look for a job for the summer, and one day, when Gerald was still a schoolboy, he also decided to work in the summer. But as Gerald was quite an unusual schoolboy, he found quite unusual work. A certain Company agreed to pay him a certain sum of money if he draws them three identical circles on a plane. The circles must not interfere with each other (but they may touch each other). He can choose the centers of the circles only from the n options granted by the Company. He is free to choose the radius of the circles himself (all three radiuses must be equal), but please note that the larger the radius is, the more he gets paid. 

Help Gerald earn as much as possible.

Input

The first line contains a single integer n — the number of centers (3 ≤ n ≤ 3000). The following n lines each contain two integers xi, yi ( - 104 ≤ xi, yi ≤ 104) — the coordinates of potential circle centers, provided by the Company.

All given points are distinct.

Output

Print a single real number — maximum possible radius of circles. The answer will be accepted if its relative or absolute error doesn't exceed 10 - 6.

Examples

Input

3
0 1
1 0
1 1


Output

0.50000000000000000000


Input

7
2 -3
-2 -3
3 0
-3 -1
1 -2
2 -2
-1 0


Output

1.58113883008418980000

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const long double eps = 1e-6;
inline long long dcmp(long double first) {
  if (fabs(first) < eps)
    return 0;
  else
    return first < 0 ? -1 : 1;
}
struct Point {
  long double first, second;
  Point(long double first = 0, long double second = 0)
      : first(first), second(second) {}
  void read() { cin >> first >> second; }
  void write() { cout << '(' << first << ',' << second << ')' << endl; }
  bool operator==(const Point& u) const {
    return dcmp(first - u.first) == 0 && dcmp(second - u.second) == 0;
  }
  bool operator!=(const Point& u) const { return !(*this == u); }
  bool operator<(const Point& u) const {
    return dcmp(first - u.first) < 0 ||
           (dcmp(first - u.first) == 0 && dcmp(second - u.second) < 0);
  }
  bool operator>(const Point& u) const { return u < *this; }
  bool operator<=(const Point& u) const { return *this < u || *this == u; }
  bool operator>=(const Point& u) const { return *this > u || *this == u; }
  Point operator+(const Point& u) {
    return Point(first + u.first, second + u.second);
  }
  Point operator-(const Point& u) {
    return Point(first - u.first, second - u.second);
  }
  Point operator*(const long double u) { return Point(first * u, second * u); }
  Point operator/(const long double u) { return Point(first / u, second / u); }
  long double operator*(const Point& u) {
    return first * u.second - second * u.first;
  }
};
long double getDistance(Point a, Point b) {
  long double first = a.first - b.first, second = a.second - b.second;
  return (first * first + second * second);
}
long double getDot(Point a, Point b) {
  return a.first * b.first + a.second * b.second;
}
long double getCross(Point a, Point b) {
  return a.first * b.second - a.second * b.first;
}
long double getLength(Point a) { return sqrt(getDot(a, a)); }
long double getPLength(Point a) { return getDot(a, a); }
long double getAngle(Point u) { return atan2(u.second, u.first); }
long double getAngle(Point a, Point b) {
  return acos(getDot(a, b) / getLength(a) / getLength(b));
}
Point rotate(Point a, long double rad) {
  return Point(a.first * cos(rad) - a.second * sin(rad),
               a.first * sin(rad) + a.second * cos(rad));
}
Point getNormal(Point a) {
  long double l = getLength(a);
  return Point(-a.second / l, a.first / l);
}
long long getConvexHull(Point* p, long long n, Point* ch) {
  long long m = 0;
  for (long long i = 0; i < n; i++) {
    while (m > 1 &&
           dcmp(getCross(ch[m - 1] - ch[m - 2], p[i] - ch[m - 1])) <= 0)
      m--;
    ch[m++] = p[i];
  }
  long long k = m;
  for (long long i = n - 2; i >= 0; i--) {
    while (m > k &&
           dcmp(getCross(ch[m - 1] - ch[m - 2], p[i] - ch[m - 2])) <= 0)
      m--;
    ch[m++] = p[i];
  }
  if (n > 1) m--;
  return m;
}
long double rotatingCalipers(Point* p, long long n) {
  if (n <= 1) return 0.0;
  long double ans = 0.0;
  long long j = 1;
  p[n] = p[0];
  for (long long i = 0; i < n; i++) {
    while (getCross(p[j + 1] - p[i + 1], p[i] - p[i + 1]) >
           getCross(p[j] - p[i + 1], p[i] - p[i + 1]))
      j = (j + 1) % n;
    ans = max(ans, getDistance(p[i], p[j]));
    ans = max(ans, getDistance(p[i + 1], p[j + 1]));
  }
  return ans;
}
Point pts[3007], tmp[3007], ch[3007];
int main() {
  long long n;
  scanf("%lld", &n);
  for (long long i = (0); i < (n); i++) {
    pts[i].read();
  }
  sort(pts, pts + n);
  long double l = 0, r = 30007;
  while ((r - l) > .000001) {
    long double rr = ((l + r) / 2) * ((l + r) / 2);
    long double d = 0;
    for (long long i = (0); i < (n); i++) {
      long long sz = 0;
      for (long long j = (i + 1); j < (n); j++) {
        if (getDistance(pts[i], pts[j]) >= rr) {
          tmp[sz++] = pts[j];
        }
      }
      sz = getConvexHull(tmp, sz, ch);
      d = max(d, rotatingCalipers(ch, sz));
    }
    if (d >= rr)
      l = ((l + r) / 2);
    else
      r = ((l + r) / 2);
  }
  cout << fixed << setprecision(10) << l / 2 << endl;
}