1 #include<iostream>
 2 #include<cstdio>
 3 #include<cstring>
 4 #include<string>
 5 #include<stack>
 6 #include<algorithm>
 7 #include<cmath>
 8 #define PI acos(-1.0)
 9 #define INF 0x3f3f3f3f
10 using namespace std;
11 
12 int n;
13 double A,B,C1,C2;
14 struct Circle{
15     double x,y,r;
16 }p[1005];
17 
18 double map[1005][1005];
19 double vis[1005];
20 double dis[1005];
21 
22 double dist1(Circle a,Circle b){
23     return sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y))-a.r-b.r;
24 }
25 
26 double dist2(double a,double b,double c,Circle d){
27     return (fabs(a*d.x+b*d.y+c)/sqrt(a*a+b*b)-d.r);
28 }
29 
30 void Dijstra(){
31     for(int i=1;i<=n+2;i++){
32         dis[i]=map[1][i];
33         vis[i]=0;
34     }
35     vis[1]=1;
36     dis[1]=0;
37     for(int i=1;i<n+2;i++){
38         double minn=INF;
39         int pos=0;
40         for(int j=1;j<=n+2;j++){
41             if(!vis[j]&&dis[j]<minn){
42                 minn=dis[j];
43                 pos=j;
44             }
45         }
46         vis[pos]=1;
47         for(int j=1;j<=n+2;j++){
48             if(!vis[j]&&dis[j]>minn+map[pos][j]){
49                 dis[j]=minn+map[pos][j];
50             }
51         }
52     }
53     cout<<dis[n+2]<<endl;
54 }
55 
56 int main(){
57     std::ios::sync_with_stdio(false);
58     cin>>n>>A>>B>>C1>>C2;
59     for(int i=0;i<1005;i++){
60         for(int j=0;j<1005;j++){
61             map[i][j]=INF;
62         }
63     }
64     for(int i=2;i<=n+1;i++){
65         cin>>p[i].x>>p[i].y>>p[i].r;
66     }
67     double tmp;
68     for(int i=2;i<=n+1;i++){
69         for(int j=i+1;j<=n+1;j++){
70             tmp=dist1(p[i],p[j]);
71             if(tmp>0)
72                 map[i][j]=map[j][i]=tmp;
73             else
74                 map[i][j]=map[j][i]=0;
75         }
76     }
77     for(int i=2;i<=n+1;i++){
78         tmp=dist2(A,B,C1,p[i]);
79         if(tmp>0)
80             map[1][i]=map[i][1]=tmp;
81         else
82             map[1][i]=map[i][1]=0;
83         tmp=dist2(A,B,C2,p[i]);
84         if(tmp>0)
85             map[n+2][i]=map[i][n+2]=tmp;
86         else
87             map[n+2][i]=map[i][n+2]=0;
88     }
89     map[1][n+2]=map[n+2][1]=fabs(C1-C2)/sqrt(A*A+B*B);
90     Dijstra();
91 
92 }