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;
pair<int, int> operator-(pair<int, int> a, pair<int, int> b) {
  return {a.first - b.first, a.second - b.second};
}
int distSquared(pair<int, int> a, pair<int, int> b) {
  pair<int, int> d = b - a;
  return d.first * d.first + d.second * d.second;
}
int cross(pair<int, int> a, pair<int, int> b) {
  return a.first * b.second - a.second * b.first;
}
int cross(pair<int, int> base, pair<int, int> a, pair<int, int> b) {
  return cross(a - base, b - base);
}
void radialSort(vector<pair<int, int>> &a) {
  size_t n = a.size();
  int ind = 0;
  pair<int, int> leftPoint = a[0];
  for (int i = 1; i < n; ++i) {
    if (a[i] < leftPoint) {
      ind = i;
      leftPoint = a[i];
    }
  }
  swap(a[ind], a[0]);
  sort(a.begin() + 1, a.end(),
       [&leftPoint](const pair<int, int> &a, const pair<int, int> &b) {
         pair<int, int> v1 = a - leftPoint;
         pair<int, int> v2 = b - leftPoint;
         int c = cross(v1, v2);
         return c == 0 ? v1.first == v2.first ? v1.second < v2.second
                                              : v1.first < v2.first
                       : c < 0;
       });
}
vector<pair<int, int>> getConvexHull(vector<pair<int, int>> a) {
  if (a.size() < 3) {
    return a;
  }
  size_t n = a.size();
  vector<pair<int, int>> hullStack{a[0]};
  for (int i = 1; i <= n; ++i) {
    if (i == n && hullStack.size() == 2) {
      break;
    }
    while (hullStack.size() > 1) {
      pair<int, int> n1 = hullStack.back(),
                     n2 = hullStack[hullStack.size() - 2];
      if (cross(a[i % n], n1, n2) > 0) {
        break;
      }
      hullStack.pop_back();
    }
    if (i != n) hullStack.emplace_back(a[i % n]);
  }
  return hullStack;
}
bool isEdgePairGood(pair<int, int> start1, pair<int, int> start2,
                    pair<int, int> end1, pair<int, int> end2) {
  pair<int, int> v1 = start2 - start1;
  pair<int, int> v2 = end2 - end1;
  return cross(v1, v2) <= 0;
}
int getCaliperDistance(vector<pair<int, int>> &hull) {
  if (hull.size() < 2) {
    return 0;
  }
  if (hull.size() == 2) {
    return distSquared(hull[0], hull[1]);
  }
  size_t n = hull.size();
  pair<int, int> bp1, bp2;
  int maxDist = 0;
  for (int i = 0, j = 1; i < n - 1; ++i) {
    while (
        isEdgePairGood(hull[i], hull[i + 1], hull[j % n], hull[(j + 1) % n])) {
      j = (j + 1) % (int)n;
    }
    j = (j + (int)n - 1) % (int)n;
    int dist1 = distSquared(hull[i], hull[(j + 1) % n]);
    int dist2 = distSquared(hull[i + 1], hull[(j + 1) % n]);
    int dist3 = distSquared(hull[i], hull[j]);
    int dist4 = distSquared(hull[i + 1], hull[j]);
    int dist = max({dist1, dist2, dist3, dist4});
    if (dist > maxDist) {
      maxDist = dist;
      if (dist1 == maxDist)
        bp1 = hull[i], bp2 = hull[(j + 1) % n];
      else if (dist2 == maxDist)
        bp1 = hull[i + 1], bp2 = hull[(j + 1) % n];
      else if (dist3 == maxDist)
        bp1 = hull[i], bp2 = hull[j];
      else if (dist4 == maxDist)
        bp1 = hull[i + 1], bp2 = hull[j];
    }
  }
  return maxDist;
}
bool isGuessValid(vector<pair<int, int>> &a, int r) {
  for (auto &p : a) {
    vector<pair<int, int>> goodPoints;
    for (auto &q : a) {
      if (p != q && distSquared(p, q) >= r) {
        goodPoints.push_back(q);
      }
    }
    vector<pair<int, int>> hull = getConvexHull(goodPoints);
    if (getCaliperDistance(hull) >= r) {
      return true;
    }
  }
  return false;
}
int solve(vector<pair<int, int>> &a, int n) {
  radialSort(a);
  int base = 0;
  for (int jump = 1e9; jump > 0; jump /= 2) {
    while (isGuessValid(a, base + jump)) {
      base += jump;
    }
  }
  return base;
}
int bruteForce(vector<pair<int, int>> &a, int n) {
  int mx = 0;
  for (int i = 2; i < n; ++i) {
    for (int j = 1; j < i; ++j) {
      for (int k = 0; k < j; ++k) {
        int d1 = distSquared(a[i], a[j]);
        int d2 = distSquared(a[j], a[k]);
        int d3 = distSquared(a[i], a[k]);
        mx = max(mx, min({d1, d2, d3}));
        cout << "";
      }
    }
  }
  return mx;
}
void printCase(vector<pair<int, int>> &a) {
  cout << a.size() << endl;
  for (auto &p : a) {
    cout << p.first << ' ' << p.second << endl;
  }
  cout << endl;
}
void runTests() {
  const int tests = 1000;
  const int n = 20;
  const int maxDist = 10;
  for (int test = 0; test < tests; ++test) {
    vector<pair<int, int>> a(n);
    for (int i = 0; i < n; ++i) {
      a[i].first = rand() % (maxDist * 2 + 1) - maxDist;
      a[i].second = rand() % (maxDist * 2 + 1) - maxDist;
    }
    int found = solve(a, n);
    int actual = bruteForce(a, n);
    if (found != actual) {
      cout << "Test case failed!" << endl;
      printCase(a);
      cout << "Found: " << found << endl;
      cout << "Actual: " << actual << endl;
      return;
    }
  }
  cout << "All test cases passed." << endl;
}
int main() {
  cout.precision(15);
  cout << fixed;
  int n;
  cin >> n;
  vector<pair<int, int>> a(n);
  for (int i = 0; i < n; ++i) {
    cin >> a[i].first >> a[i].second;
  }
  cout << sqrt((long double)solve(a, n)) / 2 << endl;
  return 0;
}