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:
#include <iostream>
#include <complex>
#include <sstream>
#include <string>
#include <algorithm>
#include <deque>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <vector>
#include <set>
#include <limits>
#include <cstdio>
#include <cctype>
#include <cmath>
#include <cstring>
#include <cstdlib>
#include <ctime>
using namespace std;
#define REP(i, j) for(int i = 0; i < (int)(j); ++i)
#define FOR(i, j, k) for(int i = (int)(j); i < (int)(k); ++i)
#define SORT(v) sort((v).begin(), (v).end())
#define REVERSE(v) reverse((v).begin(), (v).end())
typedef complex<double> P;
//typedef pair<double, double> P;
#define X real()
#define Y imag()
#define curr(P, i) P[i]
#define next(P, i) P[(i+1)%P.size()]
#define prev(P, i) P[(i+P.size()-1) % P.size()]
#define diff(P, i) (next(P, i) - curr(P, i))
const double EPS = 1e-8;
const double INF = 1e12;
namespace std {
  bool operator < (const P& a, const P& b) {
    return real(a) != real(b) ? real(a) < real(b) : imag(a) < imag(b);
  }
}

typedef vector<P> G;

double compare_x(const P &a, const P &b){
  return a.X != b.X ? a.X < b.X : a.Y < b.Y;
}

double compare_y(const P &a, const P &b){
  return a.Y != b.Y ? a.Y < b.Y : a.X < b.X;
}

double length_of_the_nearest_point_to(P a[100000], int n){
    if(n<=1)return 999999999.9;
    int m=n/2;
    double x=a[m].X;
    double d=min(length_of_the_nearest_point_to(a, m), length_of_the_nearest_point_to(a+m, n-m));
    sort(a, a+n, compare_y);
    vector<P> b;
    for(int i=0; i<n; i++){
        if(fabs(a[i].X-x)>=d)continue;
        for(int j=0; j<b.size(); j++){
            double dx=a[i].X-b[b.size()-j-1].X;
            double dy=a[i].Y-b[b.size()-j-1].Y;
            if(dy>=d)break;
            d=min(d,sqrt(dx*dx+dy*dy));
             
        }
        b.push_back(a[i]);
    }
    return d;
}

int main() {
  int N; cin >>N;
  G g(N);
  REP(i, N){
    double x, y; cin >>x >>y;
    g[i] = P(x, y);
  }
  sort(g.begin(), g.end(), compare_x);
  printf("%.10lf\n", length_of_the_nearest_point_to(&g[0], N));
  return 0;
}