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 <cstdio>
#include <utility>
#include <vector>
#include <complex>
#include <cmath>
#include <algorithm>
#include <functional>

using namespace std;

static const double EPS=1e-12;
static const double INF=1e24;

using Point=complex<double>;
using Plane=vector<Point>;
using Polygon=vector<Point>;

bool operator<(const Point &a, const Point &b) {
    return real(a)!=real(b)? real(a)<real(b) : imag(a)<imag(b);
}

double cross_prod(const Point &a, const Point &b) {
    return imag(conj(a)*b);
}

double dot_prod(const Point &a, const Point &b) {
    return real(conj(a)*b);
}

enum {
    ONLINE_FRONT=-2,
    CLOCKWISE,
    ON_SEGMENT,
    COUNTER_CLOCKWISE,
    ONLINE_BACK,
};

int ccwise(Point a, Point b, Point c) {
    b -= a; c -= a;

    if (cross_prod(b, c) > 0) {
        return COUNTER_CLOCKWISE;
    } else if (cross_prod(b, c) < 0) {
        return CLOCKWISE;
    } else if (dot_prod(b, c) < 0) {
        return ONLINE_BACK;
    } else if (norm(b) < norm(c)) {
        return ONLINE_FRONT;
    } else {
        return ON_SEGMENT;
    }
}

template <class LineType>
int ccwise(LineType l, Point p) {
    return ccwise(l.first, l.second, p);
}

struct Line: public pair<Point, Point> {
    Line() {}
    Line(const Point &a, const Point &b) {
        first = a;
        second = b;
    }
};

struct LineSeg: public pair<Point, Point> {
    LineSeg() {}
    LineSeg(const Point &a, const Point &b) {
        first = a;
        second = b;
    }
};

pair<Point, Point> closest_pair(Polygon g) {
    size_t V=g.size(), s=0, t=1, m=2;
    vector<size_t> S(V);
    sort(g.begin(), g.end(), [](const Point &a, const Point &b) {
        return real(a)!=real(b)? real(a)<real(b) : imag(a)<imag(b);
    });

    double res=abs(g[s]-g[t]);
    for (size_t i=2; i<V; S[m++]=i++)
        for (size_t j=0; j<m; ++j) {
            if (res > abs(g[S[j]]-g[i]))
                res = abs(g[s=S[j]]-g[t=i]);

            if (real(g[S[j]]) < real(g[i]-res))
                S[j--] = S[--m];
        }

    return make_pair(g[s], g[t]);
}

template <class RandomIt>
pair<Point, Point> closest_pair(RandomIt first, RandomIt last) {
    size_t n=last-first;
    if (n < 2)
        return make_pair(Point(-INF, -INF), Point(INF, INF));

    RandomIt mid=first+n/2;
    double x=real(*mid);
    pair<Point, Point> p1=closest_pair(first, mid);
    pair<Point, Point> p2=closest_pair(mid, last);
    inplace_merge(first, mid, last, [](const Point &lhs, const Point &rhs) {
        return imag(lhs) < imag(rhs);
    });

    double d1=norm(p1.first-p1.second), d2=norm(p2.first-p2.second);
    double d=(d1<d2? d1:d2);
    pair<Point, Point> res=(d1<d2? p1:p2);

    vector<Point> b;
    for (RandomIt it=first; it<last; ++it) {
        if (norm(real(*it)-x) >= d) continue;

        for (size_t j=0; j<b.size(); ++j) {
            Point e=*it-b[b.size()-j-1];
            if (imag(e) >= sqrt(d)) break;

            if (d > norm(e)) {
                d = norm(e);
                res = make_pair(*it, b[b.size()-j-1]);
            }
        }
        b.push_back(*it);
    }

    return res;
}

int main() {
    size_t n;
    scanf("%zu", &n);

    Polygon g(n);
    for (size_t i=0; i<n; ++i) {
        double x, y;
        scanf("%lf %lf", &x, &y);
        g[i] = Point(x, y);
    }

    sort(g.begin(), g.end(), [](const Point &lhs, const Point &rhs) {
        return real(lhs)!=real(rhs)? real(lhs)<real(rhs) : imag(lhs)<imag(rhs);
    });

    pair<Point, Point> p=closest_pair(g.begin(), g.end());
    printf("%.9f\n", abs(p.first-p.second));
    return 0;
}