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 <cmath>
#include <cstdio>
#include <algorithm>

using namespace std;

int main()
{
    int n; double x[100000], y[100000];
    
    scanf("%d", &n);
    
    for(int i = 0; i < n; i++)
    {
        scanf("%lf", &x[i]);
        scanf("%lf", &y[i]);
    }
    
    pair<double, double> p1[100000], p2[100000];
    
    for(int i = 0; i < n; i++)
    {
        p1[i] = make_pair(x[i], y[i]);
    }
    
    for(int i = 0; i < n; i++)
    {
        p2[i] = make_pair(y[i], x[i]);
    }
    
    sort(p1, p1 + n);
    sort(p2, p2 + n);
    
    double sqr_ans = 100000000.0;
    
    const int loops = 125;
    
    for(int i = 0; i < n - 1; i++)
    {
        int r = min(loops, n - i - 1);
        
        for(int j = 1; j <= r; j++)
        {
            double distance_ = (p1[i + j].first - p1[i].first) * (p1[i + j].first - p1[i].first) + (p1[i + j].second - p1[i].second) * (p1[i + j].second - p1[i].second);
        
            sqr_ans = min(distance_, sqr_ans);
        }
    }
    
    for(int i = 0; i < n - 1; i++)
    {
        int r = min(loops, n - i - 1);
        
        for(int j = 1; j <= r; j++)
        {
            double distance_ = (p2[i + j].first - p2[i].first) * (p2[i + j].first - p2[i].first) + (p2[i + j].second - p2[i].second) * (p2[i + j].second - p2[i].second);
        
            sqr_ans = min(distance_, sqr_ans);
        }
    }
    
    printf("%.15f\n", sqrt(sqr_ans));
    
    return 0;
}