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;
void debug_out() { cerr << endl; }
template <class T>
ostream &prnt(ostream &out, T v) {
  out << v.size() << '\n';
  for (auto e : v) out << e << ' ';
  return out;
}
template <class T>
ostream &operator<<(ostream &out, vector<T> v) {
  return prnt(out, v);
}
template <class T>
ostream &operator<<(ostream &out, set<T> v) {
  return prnt(out, v);
}
template <class T1, class T2>
ostream &operator<<(ostream &out, map<T1, T2> v) {
  return prnt(out, v);
}
template <class T1, class T2>
ostream &operator<<(ostream &out, pair<T1, T2> p) {
  return out << '(' << p.first << ' ' << p.second << ')';
}
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
  cerr << " " << H;
  debug_out(T...);
}
const long double PI = acos(-1);
class Point {
 public:
  long double x, y;
  Point() : x(0), y(0) {}
  Point(long double _x, long double _y) : x(_x), y(_y) {}
  bool operator==(const Point &oth) const { return x == oth.x && y == oth.y; }
  bool operator<(const Point &oth) const {
    return x == oth.x ? y < oth.y : x < oth.x;
  }
  long double dist(Point B) const {
    return sqrt((x - B.x) * (x - B.x) + (y - B.y) * (y - B.y));
  }
  void operator=(const Point &oth) {
    this->x = oth.x;
    this->y = oth.y;
  }
  Point operator+(const Point &oth) const { return {x + oth.x, y + oth.y}; }
  Point operator-(const Point &oth) const { return {x - oth.x, y - oth.y}; }
  Point operator/(const long double value) const {
    return {x / value, y / value};
  }
  Point operator*(const long double value) const {
    return {x * value, y * value};
  }
  friend ostream &operator<<(ostream &output, const Point &P) {
    output << P.x << " " << P.y;
    return output;
  }
  friend istream &operator>>(istream &input, Point &P) {
    input >> P.x >> P.y;
    return input;
  }
};
class Geom {
 public:
  static long double det(Point A, Point B, Point C) {
    return (B.x - A.x) * (C.y - A.y) - (C.x - A.x) * (B.y - A.y);
  }
  static void rotate(vector<Point> &points, long double angle = 0) {
    if (abs(angle) < 0.000000001) {
      unsigned seed1 = chrono::system_clock::now().time_since_epoch().count();
      std::mt19937 generator(seed1);
      std::uniform_real_distribution<long double> distribution(0.0, 3.14);
      angle = distribution(generator);
    }
    for (auto &it : points) {
      long double x = it.x * cos(angle) - it.y * sin(angle);
      long double y = it.x * sin(angle) + it.y * cos(angle);
      it = {x, y};
    }
  }
};
class ConvexHull {
 private:
  static Point bst;
  static bool comp(Point &A, Point &B) {
    if (B == bst) return false;
    int x = Geom::det(bst, A, B);
    if (abs(x) < 0.000000001) return bst.dist(A) < bst.dist(B);
    return x < 0;
  }

 public:
  vector<Point> getConvexHull(vector<Point> points) {
    if (points.size() <= 1) return points;
    bst = points[0];
    for (auto &it : points) bst = min(bst, it);
    sort(points.begin(), points.end(), comp);
    vector<Point> H({points[0], points[1]});
    for (int i = 2; i < (int)points.size(); i++) {
      while (H.size() >= 2 &&
             (Geom::det(H[H.size() - 2], H.back(), points[i]) > 0 ||
              (Geom::det(H[H.size() - 2], H.back(), points[i]) == 0 &&
               H[H.size() - 2].dist(H.back()) <
                   H[H.size() - 2].dist(points[i])))) {
        H.pop_back();
      }
      H.push_back(points[i]);
    }
    return H;
  }
};
Point ConvexHull::bst;
int n;
Point aux;
vector<Point> p;
bitset<3005> B[3005];
struct ceva {
  long double v;
  int a, b;
};
vector<ceva> v;
bool comp(ceva A, ceva B) { return A.v > B.v; }
int main() {
  ios::sync_with_stdio(false);
  ConvexHull ch = ConvexHull();
  cin >> n;
  for (int i = 1; i <= n; i++) cin >> aux, p.push_back(aux);
  for (int i = 0; i < p.size(); i++) {
    for (int j = i + 1; j < p.size(); j++) {
      v.push_back({p[i].dist(p[j]), i, j});
    }
  }
  sort(v.begin(), v.end(), comp);
  for (auto it : v) {
    if ((B[it.a] & B[it.b]).any()) {
      cout << fixed << setprecision(10) << it.v / 2 << '\n';
      return 0;
    }
    B[it.a].set(it.b);
    B[it.b].set(it.a);
  }
  return 0;
}