Problem: 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}.

Examples

Input

-2 -2 2 2
1
0 0 1


Output

3.6568542495


Input

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


Output

0.0000000000


Input

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


Output

4.0000000000

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.io.BufferedWriter;
import java.util.PriorityQueue;
import java.util.Collection;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.Queue;
import java.io.InputStream;

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

    static class ECosmicRays {
        public void solve(int testNumber, InputReader in, OutputWriter out) {
            ECosmicRays.Circle c0 = new ECosmicRays.Circle(ECosmicRays.Point.read(in), 0);
            ECosmicRays.Circle c1 = new ECosmicRays.Circle(ECosmicRays.Point.read(in), 0);
            int n = in.readInt();
            ECosmicRays.Circle[] a = new ECosmicRays.Circle[n + 2];
            for (int i = 0; i < n; i++) a[i] = ECosmicRays.Circle.read(in);
            a[n] = c0;
            a[n + 1] = c1;
            double ans = findDistance(a);
            out.printFormat("%.20f", ans);
        }

        double findDistance(ECosmicRays.Circle[] a) {
            int n = a.length;
            int from = n - 2;
            double[] dist = new double[n];
            Arrays.fill(dist, Double.POSITIVE_INFINITY);
            dist[from] = 0;
            Queue<DoubleIntPair> q = new PriorityQueue<>();
            q.add(DoubleIntPair.makePair(0, from));
            while (!q.isEmpty()) {
                DoubleIntPair cur = q.poll();
                int v = cur.second;
                if (dist[v] != cur.first) continue;
                for (int i = 0; i < n; i++) {
                    double d1 = dist[v] + a[v].distance(a[i]);
                    if (dist[i] > d1) {
                        dist[i] = d1;
                        q.add(DoubleIntPair.makePair(dist[i], i));
                    }
                }
            }
            return dist[n - 1];
        }

        static class Point {
            double x;
            double y;

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

            static ECosmicRays.Point read(InputReader in) {
                double x = in.readDouble();
                double y = in.readDouble();
                return new ECosmicRays.Point(x, y);
            }

            double distance(ECosmicRays.Point p) {
                double dx = p.x - x;
                double dy = p.y - y;
                return Math.sqrt(dx * dx + dy * dy);
            }

        }

        static class Circle {
            ECosmicRays.Point center;
            double r;

            public Circle(ECosmicRays.Point center, double r) {
                this.center = center;
                this.r = r;
            }

            static ECosmicRays.Circle read(InputReader in) {
                ECosmicRays.Point center = ECosmicRays.Point.read(in);
                double r = in.readDouble();
                return new ECosmicRays.Circle(center, r);
            }

            double distance(ECosmicRays.Circle c) {
                return Math.max(0, c.center.distance(center) - (r + c.r));
            }

        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void printFormat(String format, Object... objects) {
            writer.printf(format, objects);
        }

        public void close() {
            writer.close();
        }

    }

    static class DoubleIntPair implements Comparable<DoubleIntPair> {
        public final double first;
        public final int second;

        public static DoubleIntPair makePair(double first, int second) {
            return new DoubleIntPair(first, second);
        }

        public DoubleIntPair(double first, int second) {
            this.first = first;
            this.second = second;
        }

        public boolean equals(Object o) {
            if (this == o) {
                return true;
            }
            if (o == null || getClass() != o.getClass()) {
                return false;
            }

            DoubleIntPair pair = (DoubleIntPair) o;

            return first == pair.first && second == pair.second;
        }

        public int hashCode() {
            int result = Double.hashCode(first);
            result = 31 * result + Integer.hashCode(second);
            return result;
        }

        public String toString() {
            return "(" + first + "," + second + ")";
        }

        public int compareTo(DoubleIntPair o) {
            int value = Double.compare(first, o.first);
            if (value != 0) {
                return value;
            }
            return Integer.compare(second, o.second);
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int readInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public double readDouble() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E') {
                    return res * Math.pow(10, readInt());
                }
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E') {
                        return res * Math.pow(10, readInt());
                    }
                    if (c < '0' || c > '9') {
                        throw new InputMismatchException();
                    }
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }
}