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: Time Limit Exceeded)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.util.stream.IntStream;
import java.util.Arrays;
import java.util.PriorityQueue;
import java.util.OptionalInt;
import java.io.BufferedOutputStream;
import java.util.AbstractCollection;
import java.nio.charset.Charset;
import java.util.StringTokenizer;
import java.io.OutputStreamWriter;
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.UncheckedIOException;
import java.util.stream.Stream;
import java.io.Writer;
import java.io.BufferedReader;
import java.util.Comparator;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author mikit
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        LightScanner in = new LightScanner(inputStream);
        LightWriter out = new LightWriter(outputStream);
        ECosmicRays solver = new ECosmicRays();
        solver.solve(1, in, out);
        out.close();
    }

    static class ECosmicRays {
        private static final double EPS = 1e-10;

        public void solve(int testNumber, LightScanner in, LightWriter out) {
            double sx = in.doubles(), sy = in.doubles(), gx = in.doubles(), gy = in.doubles();
            int n = in.ints();
            double[] x = new double[n], y = new double[n], r = new double[n];
            in.doubles(x, y, r);
            double[] dist = new double[n];
            PriorityQueue<Integer> q = new PriorityQueue<>(Comparator.comparing(p -> dist[p]));
            for (int i = 0; i < n; i++) {
                dist[i] = Math.max(0.0, dist(sx, sy, x[i], y[i]) - r[i]);
                q.offer(i);
            }
            while (!q.isEmpty()) {
                int p = q.poll();
                for (int i = 0; i < n; i++) {
                    double d = Math.max(0.0, dist(x[p], y[p], x[i], y[i]) - r[i] - r[p]);
                    if (dist[p] + d < dist[i] - EPS) {
                        dist[i] = dist[p] + d;
                        q.offer(i);
                    }
                }
            }
            double ans = dist(sx, sy, gx, gy);
            for (int i = 0; i < n; i++) {
                ans = Math.min(ans, dist[i] + Math.max(0.0, dist(gx, gy, x[i], y[i]) - r[i]));
            }
            out.ans(ans, 10).ln();
        }

        private static double dist(double x1, double y1, double x2, double y2) {
            double dx = x1 - x2, dy = y1 - y2;
            return Math.sqrt(dx * dx + dy * dy);
        }

    }

    static class LightScanner {
        private BufferedReader reader = null;
        private StringTokenizer tokenizer = null;

        public LightScanner(InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
        }

        public String string() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new UncheckedIOException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int ints() {
            return Integer.parseInt(string());
        }

        public double doubles() {
            return Double.parseDouble(string());
        }

        public void doubles(double[]... arrays) {
            int l = Arrays.stream(arrays).mapToInt(a -> a.length).min().orElse(0);
            for (int i = 0; i < l; i++) {
                for (int j = 0; j < arrays.length; j++) {
                    arrays[j][i] = doubles();
                }
            }
        }

    }

    static class LightWriter implements AutoCloseable {
        private final Writer out;
        private boolean autoflush = false;
        private boolean breaked = true;

        public LightWriter(Writer out) {
            this.out = out;
        }

        public LightWriter(OutputStream out) {
            this(new OutputStreamWriter(new BufferedOutputStream(out), Charset.defaultCharset()));
        }

        public LightWriter print(char c) {
            try {
                out.write(c);
                breaked = false;
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
            return this;
        }

        public LightWriter print(String s) {
            try {
                out.write(s, 0, s.length());
                breaked = false;
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
            return this;
        }

        public LightWriter ans(double x, int n) {
            if (!breaked) {
                print(' ');
            }
            if (x < 0) {
                print('-');
                x = -x;
            }
            x += Math.pow(10, -n) / 2;
            print(Long.toString((long) x)).print('.');
            x -= (long) x;
            for (int i = 0; i < n; i++) {
                x *= 10;
                print((char) ('0' + ((int) x)));
                x -= (int) x;
            }
            return this;
        }

        public LightWriter ln() {
            print(System.lineSeparator());
            breaked = true;
            if (autoflush) {
                try {
                    out.flush();
                } catch (IOException ex) {
                    throw new UncheckedIOException(ex);
                }
            }
            return this;
        }

        public void close() {
            try {
                out.close();
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
        }

    }
}