Problem:
Score : 600 points

Problem Statement

On the xy-plane, Snuke is going to travel from the point (x_s, y_s) to the point (x_t, y_t).
He can move in arbitrary directions with speed 1.
Here, we will consider him as a point without size.

There are N circular barriers deployed on the plane.
The center and the radius of the i-th barrier are (x_i, y_i) and r_i, respectively.
The barriers may overlap or contain each other.

A point on the plane is exposed to cosmic rays if the point is not within any of the barriers.

Snuke wants to avoid exposure to cosmic rays as much as possible during the travel.
Find the minimum possible duration of time he is exposed to cosmic rays during the travel.

Constraints

All input values are integers.

-10^9 ≤ x_s, y_s, x_t, y_t ≤ 10^9

(x_s, y_s) ≠ (x_t, y_t)

1≤N≤1,000

-10^9 ≤ x_i, y_i ≤ 10^9

1 ≤ r_i ≤ 10^9

Input

The input is given from Standard Input in the following format:

x_s y_s x_t y_t
N
x_1 y_1 r_1
x_2 y_2 r_2
:
x_N y_N r_N

Output

Print the minimum possible duration of time Snuke is exposed to cosmic rays during the travel.
The output is considered correct if the absolute or relative error is at most 10^{-9}.

Sample Input 1

-2 -2 2 2
1
0 0 1

Sample Output 1

3.6568542495

An optimal route is as follows:

Sample Input 2

-2 0 2 0
2
-1 0 2
1 0 2

Sample Output 2

0.0000000000

An optimal route is as follows:

Sample Input 3

4 -2 -2 4
3
0 0 2
4 0 1
0 4 1

Sample Output 3

4.0000000000

An optimal route is as follows:

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

//#pragma GCC optimize("Ofast")
#include<bits/stdc++.h>
using namespace::std;
//struct __INIT{__INIT(){cin.tie(0);ios::sync_with_stdio(false);cout<<fixed<<setprecision(15);}} __init;
__attribute__((constructor))
void init(){
	cin.tie(0);
	ios::sync_with_stdio(false);
	cout<<fixed<<setprecision(15);
}
// random_device rd;
// mt19937 mt(rd());
// #include <boost/numeric/interval.hpp>
// #include <boost/numeric/interval/io.hpp>
// #include <boost/intrusive/rbtree.hpp>
// #include <boost/dynamic_bitset.hpp>
// #include <boost/geometry.hpp>
// #include <boost/geometry/geometries/linestring.hpp>
// #include <boost/geometry/geometries/polygon.hpp>
// #include <boost/geometry/geometries/point_xy.hpp>
// #include <boost/math/tools/minima.hpp>
// using boost::math::tools::brent_find_minima;
// #include <boost/multiprecision/cpp_dec_float.hpp>
// #include <boost/multiprecision/cpp_int.hpp>
// namespace mp = boost::multiprecision;
// typedef mp::number<mp::cpp_dec_float<256>> cdouble;
// typedef mp::cpp_int cint;

#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/priority_queue.hpp>
#include<ext/pb_ds/tag_and_trait.hpp>
using namespace __gnu_pbds;
template<typename T=long long>using pbds=tree<T,null_type,less<T>,rb_tree_tag,tree_order_statistics_node_update>;
template<typename T=long long>using pbds_map=tree<T,T,less<T>,rb_tree_tag,tree_order_statistics_node_update>;
template<typename T=long long>using pqueue =__gnu_pbds::priority_queue<T, less<T>,rc_binomial_heap_tag>;
typedef long long lint;
typedef long long ll;
typedef long double ldouble;
typedef vector<lint> vec;
typedef vector<vector<lint>> mat;
typedef vector<vector<vector<lint>>> mat3;
typedef vector<double> dvec;
typedef vector<vector<double>> dmat;
typedef vector<vector<vector<double>>> dmat3;
typedef vector<string> svec;
typedef vector<vector<string>> smat;
typedef vector<vector<vector<string>>> smat3;
typedef vector<pair<lint,lint>> pvec;
typedef vector<vector<pair<lint,lint>>> pmat;
typedef vector<vector<vector<pair<lint,lint>>>> pmat3;
#define rep(i, n) for(lint i = 0; i < (lint)(n); i++)
#define irep(i) for(lint i = 0;; i++)
#define irep1(i) for(lint i = 1;; i++)
#define irep2(i) for(lint i = 2;; i++)
#define rrep(i, n) for(lint i = (lint)(n-1); i >-1; i--)
#define rrepi(i,a,b) for(lint i = (lint)(b-1); i >a-1; i--)
#define repi(i,a,b) for(lint i=lint(a);i<lint(b);i++)
#define rep2(i,a,b,c) for(lint i=lint(a);i>lint(b);i+=c)
#define all(x) (x).begin(),(x).end()
#define PI 3.141592653589793
#define dist(x1,y1,x2,y2) (pow(pow(x2-x1,2)+pow(y2-y1,2),0.5))
#define output(v) do{bool f=0;for(auto i:v){cout<<(f?" ":"");if(i>INF/2)cout<<"INF";else cout<<i;f=1;}cout<<"\n";}while(0);
#define output2(v) for(auto j:v)output(j);
#define _output(v) do{bool f=0;rep(i,v.size()){cout<<(f?" ":"");if(v[i]>INF/2)cout<<"INF";else cout<<v[i];f=1;}cout<<"\n";}while(0)
#define _output2(v) rep(j,v.size()){_output(v[j]);}
#define input(a,n) lint n;cin>>n;vector<lint>a(n);rep(i,n)cin>>a[i];
#define SUM(v) accumulate(all(v),0LL)
#define INF (1LL<<60)
#define IINF (1<<30)
#define EPS (1e-10)
#define LINF 9223372036854775807
#define MOD 998244353LL
#define endl "\n"
template<typename T=lint>T in(){return *istream_iterator<T>(cin);}
inline lint gcd(lint a,lint b){return b?gcd(b,a%b):a;}
template<typename T=lint>inline T lcm(T a,T b){return a/gcd(a,b)*b;}
template<typename T=lint>inline T add(T a,T b){return a+b;}
template<typename T=lint>inline T minq(T a,T b){return min(a,b);}
inline bool chmin(auto& s,const auto& t){bool res=s>t;s=min(s,t);return res;}
inline bool chmax(auto& s,const auto& t){bool res=s<t;s=max(s,t);return res;}
vector<lint> dx={-1,1,0,0,1,1,-1,-1};
vector<lint> dy={0,0,-1,1,1,-1,1,-1};



// template<typename T,typename E>
// struct RBST{
// 	struct node{
// 		int cnt=1,l=-1,r=-1;
// 		T key;E val;
// 		node(){}
// 		node(T key,E val):key(key),val(val){}
// 	};
// 	vector<node> v;
// 	RBST(){
// 	}
// 	int root=1;
// 	int count(int idx){return idx==-1?0:v[idx].cnt;}
// 	int update(int idx){
// 		if(idx!=-1)v[idx].cnt=1+count(v[idx].l)+count(v[idx].r);
// 		return idx;
// 	}
// 	private:
// 	inline int merge(int l,int r){
//         if(l==-1||r==-1)return l==-1?r:l;
//         if((unsigned long)count(v[l])>rnd()%(unsigned long)(count(v[l])+count(v[r]))){
//             v[l].r=merge(v[l].r,r);
//             return update(l);
//         }else{
//             v[r].l=merge(l,v[r].l);
//             return update(r);
//         }
//     }
// 	inline pair<int,int> split(int t,int k){
//         if(t==-1)return make_pair(-1,-1);
//         if(k<=count(v[t].l)){
//             auto s=split(v[t].l,k);
//             v[t].l=s.second;
//             return make_pair(s.first,update(t));
//         }else{
//             auto s=split(v[t].r,k-count(v[t].l)-1);
//             v[t].r=s.first;
//             return make_pair(update(t),s.second);
//         }
//     }
// 	inline unsigned long rnd() {
//         static unsigned long x=123456789, y=362436069, z=521288629, w=88675123;
//         unsigned long t=(x^(x<<11));
//         x=y; y=z; z=w;
//         return ( w=(w^(w>>19))^(t^(t>>8)) );
//     }
// };

int main(){
    lint xs,ys,xt,yt;
    cin>>xs>>ys>>xt>>yt;
    lint n;
    cin>>n;
    vec x(n),y(n),r(n);
    rep(i,n){
        cin>>x[i]>>y[i]>>r[i];
    }
    vector<vector<pair<lint,double>>> v(n+2);
    rep(i,n)rep(j,n){
        double tmp=max(0.,dist(x[i],y[i],x[j],y[j])-r[i]-r[j]);
        v[i].push_back(make_pair(j,tmp));
        v[j].push_back(make_pair(i,tmp));
    }
    rep(i,n){
        double tmp=max(0.,dist(xs,ys,x[i],y[i])-r[i]);
        v[n].push_back(make_pair(i,tmp));
    }
    rep(i,n){
        double tmp=max(0.,dist(xt,yt,x[i],y[i])-r[i]);
        v[i].push_back(make_pair(n+1,tmp));
    }
    std::priority_queue<pair<double,lint>,vector<pair<double,lint>>,greater<pair<double,lint>>>que;
    vector<double>diff(n+2,INF);
    diff[n]=0;
    que.push(make_pair(0.,n));
    while(!que.empty()){
        auto d=que.top();
        que.pop();
        double x;lint now;
        tie(x,now)=d;
        for(auto d2:v[now]){
            double sa;lint to;
            tie(to,sa)=d2;
            if(chmin(diff[to],diff[now]+sa))que.emplace(diff[to],to);
        }
    }
    cout<<diff[n+1]<<endl;
}