#include <iostream>
#include <cstdio>
#include <vector>
#include <list>
#include <cmath>
#include <fstream>
#include <algorithm>
#include <string>
#include <queue>
#include <set>
#include <map>
#include <complex>
#include <iterator>
#include <cstdlib>
#include <cstring>
#include <sstream>
#include <stack>
#include <climits>
#include <deque>
#include <bitset>
#include <cassert>
#include <ctime>
using namespace std;

typedef long long ll;
typedef pair<int,int> pii;
const int dy[]={-1,0,1,0},dx[]={0,1,0,-1};
// adjust problem by problem
const double EPS=1e-8;
const double PI=acos(-1.0);
#ifdef __GNUC__
int popcount(int n){return __builtin_popcount(n);}
int popcount(ll n){return __builtin_popcountll(n);}
#endif
#ifndef __GNUC__
template<class T> int popcount(T n){int cnt=0;while(n){if(n%2)cnt++;n/=2;}return cnt;}
#endif
template<class T>int SIZE(T a){return a.size();}
template<class T>string IntToString(T num){string res;stringstream ss;ss<<num;return ss.str();}
template<class T>T StringToInt(string str){T res=0;for(int i=0;i<SIZE(str);i++)res=(res*10+str[i]-'0');return res;}
template<class T>T gcd(T a,T b){if(b==0)return a;return gcd(b,a%b);}
template<class T>T lcm(T a,T b){return a/gcd(a,b)*b;}
template<class T> void PrintSeq(T &a,int sz){for(int i=0;i<sz;i++){cout<<a[i];if(sz==i+1)cout<<endl;else cout<<' ';}}
bool EQ(double a,double b){return abs(a-b)<EPS;}
void fastStream(){cin.tie(0);std::ios_base::sync_with_stdio(0);}
vector<string> split(string str,char del){
  vector<string> res;
  for(int i=0,s=0;i<SIZE(str);i++){
    if(str[i]==del){if(i-s!=0)res.push_back(str.substr(s,i-s));s=i+1;}
    else if(i==SIZE(str)-1){res.push_back(str.substr(s));}
  }
  return res;
}

typedef complex<double> P;
// 座標の回転(座標pにある点を,半時計回りにa(ラジアン)回転)
P roundPoint(P p,double a){
  return P(cos(a)*p.real()-sin(a)*p.imag(),sin(a)*p.real()+cos(a)*p.imag());
}

// 2円の交点を求める
// 2円が交点を持つすることが前提となっていることに注意
// 重解は２つの同じ点が返る
// 交点を持たないかどうかはr1+r2とabs(c1-c2)を比較
pair<P,P> crossPointsTwoCircle(P c1,double r1,P c2,double r2){
  double a=abs(c1-c2);
  double tmp=((r1*r1-r2*r2+a*a)/(2*a));
  double b=sqrt(r1*r1-tmp*tmp);
  P p=c1-c2;p/=abs(p);
  p=roundPoint(p,PI/2);
  P p1=p;
  P p2=p;p2*=-1;
  p1*=b;p2*=b;
  P cp=(c2*tmp+c1*(a-tmp));
  cp*=(1.0/a);
  P res1=cp+p1;
  P res2=cp+p2;
  return make_pair(res1,res2);
}

int N;
double XS[101];
double YS[101];
P cs[101];
double VS[101];

bool check(double time){
  for(int i=0;i<N;i++){
    for(int j=i+1;j<N;j++){
      // 今選択している２円の交点を求めて、その交点を候補として計算
      // 円が内包される場合は、適当な代表点を候補点として利用
      const double r1=VS[i]*time,r2=VS[j]*time;
      const P &p1=cs[i],&p2=cs[j];
      double dist=abs(p1-p2);
      P cand[2];
      // 内包
      if(!EQ(abs(r1-r2),dist)&&abs(r1-r2)>dist){
        // 円1が含まれる場合
        if(r1<r2)cand[0]=cand[1]=P(p1.real()+r1,p1.imag());
        // 円2が含まれる場合
        else cand[0]=cand[1]=P(p2.real()+r2,p2.imag());
      }
      // 距離が半径の和以下なら１つ以上の交点を持つ
      else if(EQ(dist,r1+r2)||dist<r1+r2){
        pair<P,P> ps=crossPointsTwoCircle(p1,r1,p2,r2);
        cand[0]=ps.first,cand[1]=ps.second;
      }
      // 交点をもたないかつ内包もしない場合は計算しない
      else continue;
      // 2つの候補点についてvalidか調べる
      for(int k=0;k<2;k++){
        bool ok=true;
        for(int l=0;l<N;l++){
          double d=abs(cand[k]-cs[l]);
          double r=time*VS[l];
          if(!(EQ(d,r)||d<r)){
            ok=false;
            break;
          }
        }
        if(ok)return true;
      }
    }
  }
  return false;
}

int main(){
  while(cin>>N&&N){
    for(int i=0;i<N;i++){
      cin>>XS[i]>>YS[i]>>VS[i];
      cs[i]=P(XS[i],YS[i]);
    }
    double ub=1e+10;
    double lb=0;
    for(int ite=0;ite<200;ite++){
      double mid=(ub+lb)/2;
      if(check(mid))ub=mid;
      else lb=mid;
    }
    printf("%.10f\n",ub);
  }

  return 0;
}
### Prompt

Develop a solution in Cpp to the problem described below:

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 <iostream>
#include <cstdio>
#include <vector>
#include <list>
#include <cmath>
#include <fstream>
#include <algorithm>
#include <string>
#include <queue>
#include <set>
#include <map>
#include <complex>
#include <iterator>
#include <cstdlib>
#include <cstring>
#include <sstream>
#include <stack>
#include <climits>
#include <deque>
#include <bitset>
#include <cassert>
#include <ctime>
using namespace std;

typedef long long ll;
typedef pair<int,int> pii;
const int dy[]={-1,0,1,0},dx[]={0,1,0,-1};
// adjust problem by problem
const double EPS=1e-8;
const double PI=acos(-1.0);
#ifdef __GNUC__
int popcount(int n){return __builtin_popcount(n);}
int popcount(ll n){return __builtin_popcountll(n);}
#endif
#ifndef __GNUC__
template<class T> int popcount(T n){int cnt=0;while(n){if(n%2)cnt++;n/=2;}return cnt;}
#endif
template<class T>int SIZE(T a){return a.size();}
template<class T>string IntToString(T num){string res;stringstream ss;ss<<num;return ss.str();}
template<class T>T StringToInt(string str){T res=0;for(int i=0;i<SIZE(str);i++)res=(res*10+str[i]-'0');return res;}
template<class T>T gcd(T a,T b){if(b==0)return a;return gcd(b,a%b);}
template<class T>T lcm(T a,T b){return a/gcd(a,b)*b;}
template<class T> void PrintSeq(T &a,int sz){for(int i=0;i<sz;i++){cout<<a[i];if(sz==i+1)cout<<endl;else cout<<' ';}}
bool EQ(double a,double b){return abs(a-b)<EPS;}
void fastStream(){cin.tie(0);std::ios_base::sync_with_stdio(0);}
vector<string> split(string str,char del){
  vector<string> res;
  for(int i=0,s=0;i<SIZE(str);i++){
    if(str[i]==del){if(i-s!=0)res.push_back(str.substr(s,i-s));s=i+1;}
    else if(i==SIZE(str)-1){res.push_back(str.substr(s));}
  }
  return res;
}

typedef complex<double> P;
// 座標の回転(座標pにある点を,半時計回りにa(ラジアン)回転)
P roundPoint(P p,double a){
  return P(cos(a)*p.real()-sin(a)*p.imag(),sin(a)*p.real()+cos(a)*p.imag());
}

// 2円の交点を求める
// 2円が交点を持つすることが前提となっていることに注意
// 重解は２つの同じ点が返る
// 交点を持たないかどうかはr1+r2とabs(c1-c2)を比較
pair<P,P> crossPointsTwoCircle(P c1,double r1,P c2,double r2){
  double a=abs(c1-c2);
  double tmp=((r1*r1-r2*r2+a*a)/(2*a));
  double b=sqrt(r1*r1-tmp*tmp);
  P p=c1-c2;p/=abs(p);
  p=roundPoint(p,PI/2);
  P p1=p;
  P p2=p;p2*=-1;
  p1*=b;p2*=b;
  P cp=(c2*tmp+c1*(a-tmp));
  cp*=(1.0/a);
  P res1=cp+p1;
  P res2=cp+p2;
  return make_pair(res1,res2);
}

int N;
double XS[101];
double YS[101];
P cs[101];
double VS[101];

bool check(double time){
  for(int i=0;i<N;i++){
    for(int j=i+1;j<N;j++){
      // 今選択している２円の交点を求めて、その交点を候補として計算
      // 円が内包される場合は、適当な代表点を候補点として利用
      const double r1=VS[i]*time,r2=VS[j]*time;
      const P &p1=cs[i],&p2=cs[j];
      double dist=abs(p1-p2);
      P cand[2];
      // 内包
      if(!EQ(abs(r1-r2),dist)&&abs(r1-r2)>dist){
        // 円1が含まれる場合
        if(r1<r2)cand[0]=cand[1]=P(p1.real()+r1,p1.imag());
        // 円2が含まれる場合
        else cand[0]=cand[1]=P(p2.real()+r2,p2.imag());
      }
      // 距離が半径の和以下なら１つ以上の交点を持つ
      else if(EQ(dist,r1+r2)||dist<r1+r2){
        pair<P,P> ps=crossPointsTwoCircle(p1,r1,p2,r2);
        cand[0]=ps.first,cand[1]=ps.second;
      }
      // 交点をもたないかつ内包もしない場合は計算しない
      else continue;
      // 2つの候補点についてvalidか調べる
      for(int k=0;k<2;k++){
        bool ok=true;
        for(int l=0;l<N;l++){
          double d=abs(cand[k]-cs[l]);
          double r=time*VS[l];
          if(!(EQ(d,r)||d<r)){
            ok=false;
            break;
          }
        }
        if(ok)return true;
      }
    }
  }
  return false;
}

int main(){
  while(cin>>N&&N){
    for(int i=0;i<N;i++){
      cin>>XS[i]>>YS[i]>>VS[i];
      cs[i]=P(XS[i],YS[i]);
    }
    double ub=1e+10;
    double lb=0;
    for(int ite=0;ite<200;ite++){
      double mid=(ub+lb)/2;
      if(check(mid))ub=mid;
      else lb=mid;
    }
    printf("%.10f\n",ub);
  }

  return 0;
}
```