#include <bits/stdc++.h>
using namespace std;

#define dump(...) cout<<"# "<<#__VA_ARGS__<<'='<<(__VA_ARGS__)<<endl
#define repi(i,a,b) for(int i=int(a);i<int(b);i++)
#define peri(i,a,b) for(int i=int(b);i-->int(a);)
#define rep(i,n) repi(i,0,n)
#define per(i,n) peri(i,0,n)
#define all(c) begin(c),end(c)
#define mp make_pair
#define mt make_tuple

typedef unsigned int uint;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> pii;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<double> vd;
typedef vector<vd> vvd;
typedef vector<string> vs;

template<typename T1,typename T2>
ostream& operator<<(ostream& os,const pair<T1,T2>& p){
	return os<<'('<<p.first<<','<<p.second<<')';
}

template<typename Tuple>
void print_tuple(ostream&,const Tuple&){}
template<typename Car,typename... Cdr,typename Tuple>
void print_tuple(ostream& os,const Tuple& t){
	print_tuple<Cdr...>(os,t);
	os<<(sizeof...(Cdr)?",":"")<<get<sizeof...(Cdr)>(t);
}
template<typename... Args>
ostream& operator<<(ostream& os,const tuple<Args...>& t){
	print_tuple<Args...>(os<<'(',t);
	return os<<')';
}

template<typename Ch,typename Tr,typename C>
basic_ostream<Ch,Tr>& operator<<(basic_ostream<Ch,Tr>& os,const C& c){
	os<<'[';
	for(auto i=begin(c);i!=end(c);++i)
		os<<(i==begin(c)?"":" ")<<*i;
	return os<<']';
}

constexpr int INF=1e9;
constexpr int MOD=1e9+7;
constexpr double EPS=1e-9;

struct Point{
	double x,y;
	Point(){}
	Point(double x,double y):x(x),y(y){}
	Point& operator+=(Point p){x+=p.x,y+=p.y; return *this;}
	Point& operator-=(Point p){x-=p.x,y-=p.y; return *this;}
	Point& operator*=(double c){x*=c,y*=c; return *this;}
	Point& operator/=(double c){x/=c,y/=c; return *this;}
};
Point operator+(Point a,Point b){return a+=b;}
Point operator-(Point a,Point b){return a-=b;}
Point operator*(Point a,double c){return a*=c;}
Point operator*(double c,Point a){return a*=c;}
Point operator/(Point a,double c){return a/=c;}
bool operator==(Point a,Point b){return abs(a.x-b.x)<EPS && abs(a.y-b.y)<EPS;}
bool operator!=(Point a,Point b){return !(a==b);}

struct Circle{
	Point center;
	double radius;
	Circle(){}
	Circle(Point c,double r):center(c),radius(r){}
	Circle(double x,double y,double r):center(x,y),radius(r){}
};

double Abs(Point p){
	return sqrt(p.x*p.x+p.y*p.y);
}
Point Rot(Point p,double t){
	return Point(cos(t)*p.x-sin(t)*p.y,sin(t)*p.x+cos(t)*p.y);
}

pair<Point,Point> InterPointCC(Circle c1,Circle c2){
	const double PI=acos(-1);
	Point p1=c1.center,p2=c2.center;
	double r1=c1.radius,r2=c2.radius;
	double d=Abs(p1-p2);
	double a=(d*d+r1*r1-r2*r2)/(2*d);
	double s=sqrt(r1*r1-a*a);
	return mp(p1+a/d*(p2-p1)+s*Rot((p2-p1)/d,PI/2),
			  p1+a/d*(p2-p1)-s*Rot((p2-p1)/d,PI/2));
}

ostream& operator<<(ostream& os,const Point& p){
	return os<<'('<<p.x<<','<<p.y<<')';
}
ostream& operator<<(ostream& os,const Circle& c){
	return os<<'('<<c.center.x<<','<<c.center.y<<','<<c.radius<<')';
}

int main()
{
	for(int n;cin>>n && n;){
		vector<Point> ps(n);
		vd vs(n);
		rep(i,n) cin>>ps[i].x>>ps[i].y>>vs[i];
		
		double lo=0,hi=100;
		rep(_,50){
			double t=(lo+hi)/2;
			vector<Circle> cs;
			rep(i,n) cs.emplace_back(ps[i],vs[i]*t);
			vector<Point> is;
			rep(i,n) is.push_back(cs[i].center);
			rep(i,n) repi(j,i+1,n){
				Circle c1=cs[i],c2=cs[j];
				if(c1.radius>c2.radius) swap(c1,c2);
				double d=Abs(c2.center-c1.center);
				
				if(c1.radius+c2.radius<d-EPS)
					continue;
				else if(c2.radius+c2.radius<d+EPS)
					is.push_back((c2.radius*c1.center+c1.radius*c2.center)/d);
				else if(d+c1.radius<c2.radius-EPS)
					continue;
				else if(d+c1.radius<c2.radius+EPS)
					is.push_back((c2.radius*c1.center-c1.radius*c2.center)/d);
				else{
					auto t=InterPointCC(c1,c2);
					is.push_back(get<0>(t));
					is.push_back(get<1>(t));
				}
			}
			bool ok=false;
			for(auto p:is){
				bool flg=true;
				for(auto c:cs)
					flg&=Abs(p-c.center)<c.radius+EPS;
				ok|=flg;
			}
			(ok?hi:lo)=t;
		}
		printf("%.9f\n",lo);
	}
}
### Prompt

Please formulate a CPP solution to the following problem:

Problem

KND is a student programmer at the University of Aizu. He is known to be a sweet tooth. He will be staying in a city for a year and wants to visit all N sweets shops in the city during that time. So I think the best place to live for the past year is the best place to go around the sweets shop. As his neighbor, you have to find a place that minimizes the worst travel time to each sweets shop. The city where this sweets shop is located is represented by a two-dimensional plane for the sake of simplicity. He travels a different distance per unit time depending on his motivation for the desired sweets shop. He also intends to live anywhere (even in the same place as the sweets shop). KND is uncompromising when it comes to sweetness.

Constraints

The input satisfies the following conditions.

* All inputs are integers.
* 2 ≤ N ≤ 100
* 0 ≤ xi, yi ≤ 100
* 1 ≤ vi ≤ 100 (1 ≤ i ≤ N)
* xi ≠ xj or yi ≠ yj (where 1 ≤ i <j ≤ N)

Input

The input consists of multiple test cases. One test case is given in the following format. Indicates the end of input when N = 0.


N
x1 y1 v1
x2 y2 v2
...
xN yN vN


here,

* N: Number of sweets shops
* xi: x-coordinate of the i-th sweetener
* yi: y coordinate of the i-th sweets shop
* vi: Distance traveled per unit time when moving to the i-th sweets shop



Is.

Output

Output the minimum travel time for each test case on one line. This value should not differ more than 10-5 from the value of the judge output.

Example

Input

2
1 1 1
2 2 1
4
1 1 3
3 1 3
4 2 1
1 5 3
0


Output

0.70710678
1.06066017

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;

#define dump(...) cout<<"# "<<#__VA_ARGS__<<'='<<(__VA_ARGS__)<<endl
#define repi(i,a,b) for(int i=int(a);i<int(b);i++)
#define peri(i,a,b) for(int i=int(b);i-->int(a);)
#define rep(i,n) repi(i,0,n)
#define per(i,n) peri(i,0,n)
#define all(c) begin(c),end(c)
#define mp make_pair
#define mt make_tuple

typedef unsigned int uint;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> pii;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<double> vd;
typedef vector<vd> vvd;
typedef vector<string> vs;

template<typename T1,typename T2>
ostream& operator<<(ostream& os,const pair<T1,T2>& p){
	return os<<'('<<p.first<<','<<p.second<<')';
}

template<typename Tuple>
void print_tuple(ostream&,const Tuple&){}
template<typename Car,typename... Cdr,typename Tuple>
void print_tuple(ostream& os,const Tuple& t){
	print_tuple<Cdr...>(os,t);
	os<<(sizeof...(Cdr)?",":"")<<get<sizeof...(Cdr)>(t);
}
template<typename... Args>
ostream& operator<<(ostream& os,const tuple<Args...>& t){
	print_tuple<Args...>(os<<'(',t);
	return os<<')';
}

template<typename Ch,typename Tr,typename C>
basic_ostream<Ch,Tr>& operator<<(basic_ostream<Ch,Tr>& os,const C& c){
	os<<'[';
	for(auto i=begin(c);i!=end(c);++i)
		os<<(i==begin(c)?"":" ")<<*i;
	return os<<']';
}

constexpr int INF=1e9;
constexpr int MOD=1e9+7;
constexpr double EPS=1e-9;

struct Point{
	double x,y;
	Point(){}
	Point(double x,double y):x(x),y(y){}
	Point& operator+=(Point p){x+=p.x,y+=p.y; return *this;}
	Point& operator-=(Point p){x-=p.x,y-=p.y; return *this;}
	Point& operator*=(double c){x*=c,y*=c; return *this;}
	Point& operator/=(double c){x/=c,y/=c; return *this;}
};
Point operator+(Point a,Point b){return a+=b;}
Point operator-(Point a,Point b){return a-=b;}
Point operator*(Point a,double c){return a*=c;}
Point operator*(double c,Point a){return a*=c;}
Point operator/(Point a,double c){return a/=c;}
bool operator==(Point a,Point b){return abs(a.x-b.x)<EPS && abs(a.y-b.y)<EPS;}
bool operator!=(Point a,Point b){return !(a==b);}

struct Circle{
	Point center;
	double radius;
	Circle(){}
	Circle(Point c,double r):center(c),radius(r){}
	Circle(double x,double y,double r):center(x,y),radius(r){}
};

double Abs(Point p){
	return sqrt(p.x*p.x+p.y*p.y);
}
Point Rot(Point p,double t){
	return Point(cos(t)*p.x-sin(t)*p.y,sin(t)*p.x+cos(t)*p.y);
}

pair<Point,Point> InterPointCC(Circle c1,Circle c2){
	const double PI=acos(-1);
	Point p1=c1.center,p2=c2.center;
	double r1=c1.radius,r2=c2.radius;
	double d=Abs(p1-p2);
	double a=(d*d+r1*r1-r2*r2)/(2*d);
	double s=sqrt(r1*r1-a*a);
	return mp(p1+a/d*(p2-p1)+s*Rot((p2-p1)/d,PI/2),
			  p1+a/d*(p2-p1)-s*Rot((p2-p1)/d,PI/2));
}

ostream& operator<<(ostream& os,const Point& p){
	return os<<'('<<p.x<<','<<p.y<<')';
}
ostream& operator<<(ostream& os,const Circle& c){
	return os<<'('<<c.center.x<<','<<c.center.y<<','<<c.radius<<')';
}

int main()
{
	for(int n;cin>>n && n;){
		vector<Point> ps(n);
		vd vs(n);
		rep(i,n) cin>>ps[i].x>>ps[i].y>>vs[i];
		
		double lo=0,hi=100;
		rep(_,50){
			double t=(lo+hi)/2;
			vector<Circle> cs;
			rep(i,n) cs.emplace_back(ps[i],vs[i]*t);
			vector<Point> is;
			rep(i,n) is.push_back(cs[i].center);
			rep(i,n) repi(j,i+1,n){
				Circle c1=cs[i],c2=cs[j];
				if(c1.radius>c2.radius) swap(c1,c2);
				double d=Abs(c2.center-c1.center);
				
				if(c1.radius+c2.radius<d-EPS)
					continue;
				else if(c2.radius+c2.radius<d+EPS)
					is.push_back((c2.radius*c1.center+c1.radius*c2.center)/d);
				else if(d+c1.radius<c2.radius-EPS)
					continue;
				else if(d+c1.radius<c2.radius+EPS)
					is.push_back((c2.radius*c1.center-c1.radius*c2.center)/d);
				else{
					auto t=InterPointCC(c1,c2);
					is.push_back(get<0>(t));
					is.push_back(get<1>(t));
				}
			}
			bool ok=false;
			for(auto p:is){
				bool flg=true;
				for(auto c:cs)
					flg&=Abs(p-c.center)<c.radius+EPS;
				ok|=flg;
			}
			(ok?hi:lo)=t;
		}
		printf("%.9f\n",lo);
	}
}
```