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>
struct Point {
  long long int x;
  long long int y;
  std::string pToString() {
    return std::to_string(x) + " " + std::to_string(y);
  }
};
bool operator<(Point const &p1, Point const &p2) {
  if (p1.x == p2.x) {
    return p1.y < p2.y;
  }
  return p1.x < p2.x;
}
Point operator-(Point const &p1, Point const &p2) {
  long long x = p1.x - p2.x;
  long long y = p1.y - p2.y;
  Point temp = {x, y};
  return temp;
}
long long int cross(const Point &t1, const Point &t2, const Point &t3) {
  Point a = t2 - t1;
  Point b = t3 - t2;
  return a.x * b.y - b.x * a.y;
}
long long int getDist(Point const &p1, Point const &p2) {
  Point temp = p1 - p2;
  long long int dist = temp.x * temp.x + temp.y * temp.y;
  return dist;
}
struct SortByDist {
  Point _c;
  SortByDist(Point &c) : _c(c) {}
  bool operator()(Point &a, Point &b) const {
    long long int angle = cross(a, _c, b);
    if (angle == 0) {
      return getDist(_c, b) > getDist(_c, a);
    }
    return angle < 0;
  }
};
void printStack(std::vector<Point> points) {
  for (Point p : points) {
    std::cout << p.pToString() << std::endl;
  }
}
std::vector<Point> getStack(std::vector<Point> centers) {
  std::vector<Point> stack;
  if (centers.size() < 3) {
    stack = centers;
    return stack;
  }
  stack.emplace_back(centers[0]);
  int j = 1;
  for (int i = 1; i < centers.size(); i++) {
    while (stack.size() > 2 &&
           cross(stack[j - 2], stack[j - 1], centers[i]) <= 0) {
      j--;
      stack.pop_back();
    }
    stack.emplace_back(centers[i]);
    j++;
  }
  return stack;
}
std::vector<Point> getCompares(std::vector<Point> centers, long long int d,
                               int i) {
  std::vector<Point> compares;
  for (int j = i + 1; j < centers.size(); j++) {
    if (getDist(centers[i], centers[j]) >= d) {
      compares.emplace_back(centers[j]);
    }
  }
  return compares;
}
bool isNewLower(std::vector<Point> stack, long long int d) {
  for (int i = 0; i < stack.size(); i++) {
    long long int max = 0;
    for (int j = i + 1; j < stack.size(); j++) {
      long long int dist = getDist(stack[i], stack[j]);
      if (dist >= d) return true;
      if (dist < max) continue;
      max = dist;
    }
  }
  return false;
}
bool testCheck(std::vector<Point> const &centers, long long int &d) {
  std::vector<Point> compares;
  std::vector<Point> stack;
  for (int i = 0; i < centers.size(); i++) {
    compares = getCompares(centers, d, i);
    printStack(compares);
    stack = getStack(compares);
    printStack(stack);
    if (isNewLower(stack, d)) {
      std::cout << d << std::endl;
      return true;
    } else
      continue;
  }
  return false;
}
bool check(std::vector<Point> const &centers, long long int &d) {
  std::vector<Point> compares;
  std::vector<Point> stack;
  for (int i = 0; i < centers.size(); i++) {
    compares = getCompares(centers, d, i);
    stack = getStack(compares);
    if (isNewLower(stack, d))
      return true;
    else
      continue;
  }
  return false;
}
int main() {
  int numCenters;
  long long int inputX;
  long long int inputY;
  std::vector<Point> centers;
  std::cin >> numCenters;
  for (int i = 0; i < numCenters; i++) {
    std::cin >> inputX >> inputY;
    Point p = {inputX, inputY};
    centers.emplace_back(p);
  }
  auto min = std::min_element(centers.begin(), centers.end());
  std::swap(*centers.begin(), *min);
  Point first = centers[0];
  std::sort(centers.begin()++, centers.end(), SortByDist(first));
  long long int lower = 0;
  long long int upper = 800000000;
  long long int d = 0;
  while (upper - lower > 1) {
    d = (lower + upper) / 2;
    if (check(centers, d)) {
      lower = d;
    } else {
      upper = d;
    }
  }
  std::cout.precision(12);
  std::cout.fixed;
  std::cout << std::sqrt(lower) / 2 << std::endl;
  return 0;
}