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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.PriorityQueue;
import java.util.StringTokenizer;

public class Main {

    static BufferedReader in;
    static PrintWriter out;
    static StringTokenizer tok;

    void solve() throws IOException {
        int xs = ni();
        int ys = ni();
        int xt = ni();
        int yt = ni();

        int n = ni();

        int[] x = new int[n];
        int[] y = new int[n];
        int[] r = new int[n];
        for (int i = 0; i < n; i++) {
            x[i] = ni();
            y[i] = ni();
            r[i] = ni();
        }

        ArrayList<ArrayList<Edge>> G = new ArrayList<>();
        for (int i = 0; i < n + 2; i++) {
            G.add(new ArrayList<>());
        }

        for (int i = 0; i < n; i++) {
            for (int j = i + 1; j < n; j++) {
                double t = d(x[i], y[i], x[j], y[j]);
                if (t > r[i] + r[j]) {
                    G.get(i).add(new Edge(j, t - r[i] - r[j]));
                    G.get(j).add(new Edge(i, t - r[i] - r[j]));
                } else {
                    G.get(i).add(new Edge(j, 0));
                    G.get(j).add(new Edge(i, 0));
                }
            }
        }

        for (int i = 0; i < n; i++) {
            double t = d(xs, ys, x[i], y[i]);
            if (t > r[i]) {
                G.get(n).add(new Edge(i, t - r[i]));
            } else {
                G.get(n).add(new Edge(i, 0));
            }
        }

        for (int i = 0; i < n; i++) {
            double t = d(xt, yt, x[i], y[i]);
            if (t > r[i]) {
                G.get(i).add(new Edge(n + 1, t - r[i]));
            } else {
                G.get(i).add(new Edge(n + 1, 0));
            }
        }

        G.get(n).add(new Edge(n + 1, d(xs, ys, xt, yt)));

        Dijkstra dijk = new Dijkstra(G);
        double[] dist = dijk.getDist(n);

        out.println(dist[n + 1]);
    }

    double d(double x1, double y1, double x2, double y2) {
        return Math.sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2));
    }


    class Dijkstra {
        int n;
        ArrayList<ArrayList<Edge>> G;

        int INF = Integer.MAX_VALUE / 3;

        public Dijkstra(ArrayList<ArrayList<Edge>> G) {
            n = G.size();
            this.G = G;
        }

        double[] getDist(int s) {
            PriorityQueue<Pair> Q = new PriorityQueue<>();
            Q.add(new Pair(s, 0));
            double[] dist = new double[n];
            Arrays.fill(dist, INF);
            boolean[] used = new boolean[n];
            while (!Q.isEmpty()) {
                Pair p = Q.poll();
                if (used[p.x]) continue;
                used[p.x] = true;
                dist[p.x] = p.y;

                for (Edge e : G.get(p.x)) {
                    Q.add(new Pair(e.to, p.y + e.cost));
                }
            }
            return dist;
        }

        public class Pair implements Comparable<Pair> {
            int x;
            double y;

            public Pair(int x, double y) {
                this.x = x;
                this.y = y;
            }

            public int compareTo(Pair p) {
                return Double.compare(y, p.y);
            }
        }
    }

    class Edge implements Comparable<Edge> {
        int to;
        double cost;

        public Edge(int to, double cost) {
            this.to = to;
            this.cost = cost;
        }

        public int compareTo(Edge edge) {
            return Double.compare(cost, edge.cost);
        }
    }

    String ns() throws IOException {
        while (!tok.hasMoreTokens()) {
            tok = new StringTokenizer(in.readLine(), " ");
        }
        return tok.nextToken();
    }

    int ni() throws IOException {
        return Integer.parseInt(ns());
    }

    long nl() throws IOException {
        return Long.parseLong(ns());
    }

    double nd() throws IOException {
        return Double.parseDouble(ns());
    }

    String[] nsa(int n) throws IOException {
        String[] res = new String[n];
        for (int i = 0; i < n; i++) {
            res[i] = ns();
        }
        return res;
    }

    int[] nia(int n) throws IOException {
        int[] res = new int[n];
        for (int i = 0; i < n; i++) {
            res[i] = ni();
        }
        return res;
    }

    long[] nla(int n) throws IOException {
        long[] res = new long[n];
        for (int i = 0; i < n; i++) {
            res[i] = nl();
        }
        return res;
    }

    public static void main(String[] args) throws IOException {
        in = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        tok = new StringTokenizer("");
        Main main = new Main();
        main.solve();
        out.close();
    }
}