Problem: For given n points in metric space, find the distance of the closest points.

Constraints

* 2 ≤ n ≤ 100,000
* -100 ≤ x, y ≤ 100

Input


n
x0 y0
x1 y1
:
xn-1 yn-1


The first integer n is the number of points.

In the following n lines, the coordinate of the i-th point is given by two real numbers xi and yi. Each value is a real number with at most 6 digits after the decimal point.

Output

Print the distance in a line. The output values should be in a decimal fraction with an error less than 0.000001.

Examples

Input

2
0.0 0.0
1.0 0.0


Output

1.000000


Input

3
0.0 0.0
2.0 0.0
1.0 1.0


Output

1.41421356237

Solution (in CPP):

Solution:
// includes
#include <bits/stdc++.h>

// macros
#define ll long long int
#define pb emplace_back
#define mk make_pair
#define pq priority_queue
#define FOR(i, a, b) for(int i=(a);i<(b);++i)
#define rep(i, n) FOR(i, 0, n)
#define rrep(i, n) for(int i=((int)(n)-1);i>=0;i--)
#define irep(itr, st) for(auto itr = (st).begin(); itr != (st).end(); ++itr)
#define irrep(itr, st) for(auto itr = (st).rbegin(); itr != (st).rend(); ++itr)
#define vrep(v, i) for(int i = 0; i < (v).size(); i++)
#define all(x) (x).begin(),(x).end()
#define sz(x) ((int)(x).size())
#define UNIQUE(v) v.erase(unique(v.begin(), v.end()), v.end())
#define FI first
#define SE second
#define dump(a, n) for(int i = 0; i < n; i++)cout << a[i] << "\n "[i + 1 != n];
#define dump2(a, n, m) for(int i = 0; i < n; i++)for(int j = 0; j < m; j++)cout << a[i][j] << "\n "[j + 1 != m];
#define bit(n) (1LL<<(n))
#define INT(n) int n; cin >> n;
#define LL(n) ll n; cin >> n;
#define DOUBLE(n) double n; cin >> n;
using namespace std;

//  types
typedef pair<int, int> P;
typedef pair<ll, int> Pl;
typedef pair<ll, ll> Pll;
typedef pair<double, double> Pd;
typedef complex<double> cd;
 
// constants
const int inf = 1e9;
const ll linf = 1LL << 50;
const double EPS = 1e-10;
const int mod = 1e9 + 7;
const int dx[4] = {-1, 0, 1, 0};
const int dy[4] = {0, -1, 0, 1};

// solve
template <class T>bool chmax(T &a, const T &b){if(a < b){a = b; return 1;} return 0;}
template <class T>bool chmin(T &a, const T &b){if(a > b){a = b; return 1;} return 0;}
template <typename T> istream &operator>>(istream &is, vector<T> &vec){for(auto &v: vec)is >> v; return is;}
template <typename T> ostream &operator<<(ostream &os, const vector<T>& vec){for(int i = 0; i < vec.size(); i++){ os << vec[i]; if(i + 1 != vec.size())os << " ";} return os;}
template <typename T> ostream &operator<<(ostream &os, const set<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;}
template <typename T> ostream &operator<<(ostream &os, const unordered_set<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;}
template <typename T> ostream &operator<<(ostream &os, const multiset<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;}
template <typename T> ostream &operator<<(ostream &os, const unordered_multiset<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;}
template <typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &p){os << p.first << " " << p.second; return os;}
template <typename T1, typename T2> ostream &operator<<(ostream &os, const map<T1, T2> &mp){for(auto itr = mp.begin(); itr != mp.end(); ++itr){ os << itr->first << ":" << itr->second; auto titr = itr; if(++titr != mp.end())os << " "; } return os;}
template <typename T1, typename T2> ostream &operator<<(ostream &os, const unordered_map<T1, T2> &mp){for(auto itr = mp.begin(); itr != mp.end(); ++itr){ os << itr->first << ":" << itr->second; auto titr = itr; if(++titr != mp.end())os << " "; } return os;}

struct point2d{
  double x, y;
  point2d(){}
  point2d(double x, double y): x(x), y(y){}
  point2d operator+(const point2d &r) const{
    return point2d(x + r.x, y + r.y);
  }
  point2d operator-(const point2d &r) const{
    return point2d(x - r.x, y - r.y);
  }
  point2d& operator+=(const point2d &r){
    *this = *this + r;
    return *this;
  }
  point2d& operator-=(const point2d &r){
    *this = *this - r;
    return *this;
  }
  bool operator==(const point2d &r) const{
    return abs(x - r.x) < EPS && abs(y - r.y) < EPS;
  }
  bool operator!=(const point2d &r) const{
    return !(*this == r);
  }
  bool operator<(const point2d &r) const{
    if(abs(x - r.x) >= EPS)return x < r.x;
    return y < r.y;
  }
};

point2d operator*(double x, const point2d &p){
  return point2d(x * p.x, x * p.y);
}

point2d operator/(const point2d &p, double x){
  return point2d(p.x / x, p.y / x);
}

double norm(const point2d &a){
  return sqrt(a.x * a.x + a.y * a.y);
}

double dis(const point2d &a, const point2d &b){
  point2d c = a - b;
  return norm(c);
}

double inner_product(const point2d &a, const point2d &b){
  return a.x * b.x + a.y * b.y;
}

double outer_product(const point2d &a, const point2d &b){
  return a.x * b.y - a.y * b.x;
}

double cosine(const point2d &a, const point2d &b){
  return inner_product(a, b) / norm(a) / norm(b);
}

double closest_pair(vector<point2d> &a, int l, int r){
  double d = numeric_limits<double>::max();
  if(r - l == 1)return d;

  int m = (l + r) / 2;
  double x = a[m].x;
  d = min(closest_pair(a, l, m), closest_pair(a, m, r));
  inplace_merge(a.begin() + l, a.begin() + m, a.begin() + r, [](const point2d &u, const point2d &v){
      return u.y < v.y;
      });

  vector<point2d> v;
  for(int i = l; i < r; i++){
    if(abs(x - a[i].x) >= d)continue;
    for(int j = 0; j < v.size(); j++){
      double dx = a[i].x - v[v.size()-j-1].x;
      double dy = a[i].y - v[v.size()-j-1].y;
      if(dy >= d)break;
      d = min(d, sqrt(dx * dx + dy * dy));
    }
    v.push_back(a[i]);
  }
  return d;
}

double closest_pair(vector<point2d> &a){
  sort(a.begin(), a.end(), [](const point2d &u, const point2d &v){
      if(u.x != v.x)return u.x < v.x;
      return u.y < v.y;
      });
  return closest_pair(a, 0, int(a.size()));
}

int main(int argc, char const* argv[])
{
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout << fixed << setprecision(20);
  INT(n);
  vector<point2d> v(n);
  rep(i, n)cin >> v[i].x >> v[i].y;
  cout << closest_pair(v) << endl;
  return 0;
}