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;
struct pt {
  long long first, second;
  pt() {}
  pt(long long xx, long long yy) : first(xx), second(yy) {}
  pt(const pt &s) : first(s.first), second(s.second) {}
  pt operator-(const pt &r) const {
    return pt(first - r.first, second - r.second);
  }
  friend long long scal(const pt &l, const pt &r) {
    return l.first * r.first + l.second * r.second;
  }
  long long dist(const pt &r) const {
    pt tmp(*this - r);
    return scal(tmp, tmp);
  }
};
long long d[3000][3000];
unsigned long long bit[3000][50];
char con[3000][3000];
inline void put(unsigned long long i, unsigned long long j) {
  bit[i][j >> 6ull] |= (1ull << (j & 63ull));
}
inline bool check_and(unsigned long long i, unsigned long long j) {
  for (int k = 0; k < 50; ++k) {
    if (bit[i][k] & bit[j][k]) return true;
  }
  return false;
}
int main() {
  ios_base::sync_with_stdio(false);
  int n;
  cin >> n;
  pt a[n];
  for (int i = 0; i < (int)n; ++i) cin >> a[i].first >> a[i].second;
  long long l = 0, r = 1e9;
  for (int i = 0; i < (int)n; ++i) {
    for (int j = (int)i + 1; j <= (int)n - 1; ++j) {
      d[i][j] = a[i].dist(a[j]);
    }
  }
  while (l < r) {
    long long m = (l + r + 1) >> 1;
    memset(bit, 0, sizeof(bit));
    for (int i = 0; i < (int)n; ++i) {
      for (int j = (int)i + 1; j <= (int)n - 1; ++j) {
        con[i][j] = 0;
        if (d[i][j] >= m) {
          con[i][j] = 1;
          put(i, j);
        }
      }
    }
    bool fl = false;
    for (int i = 0; i < n && !fl; ++i) {
      for (int j = i + 1; j < n && !fl; ++j) {
        if (con[i][j]) {
          if (check_and(i, j)) fl = true;
        }
      }
    }
    if (fl)
      l = m;
    else
      r = m - 1;
  }
  cout << setprecision(10) << fixed << sqrt((long double)l) / 2.0 << endl;
  return 0;
}