Problem: Fifa and Fafa are sharing a flat. Fifa loves video games and wants to download a new soccer game. Unfortunately, Fafa heavily uses the internet which consumes the quota. Fifa can access the internet through his Wi-Fi access point. This access point can be accessed within a range of r meters (this range can be chosen by Fifa) from its position. Fifa must put the access point inside the flat which has a circular shape of radius R. Fifa wants to minimize the area that is not covered by the access point inside the flat without letting Fafa or anyone outside the flat to get access to the internet.

The world is represented as an infinite 2D plane. The flat is centered at (x1, y1) and has radius R and Fafa's laptop is located at (x2, y2), not necessarily inside the flat. Find the position and the radius chosen by Fifa for his access point which minimizes the uncovered area.

Input

The single line of the input contains 5 space-separated integers R, x1, y1, x2, y2 (1 ≤ R ≤ 105, |x1|, |y1|, |x2|, |y2| ≤ 105).

Output

Print three space-separated numbers xap, yap, r where (xap, yap) is the position which Fifa chose for the access point and r is the radius of its range. 

Your answer will be considered correct if the radius does not differ from optimal more than 10 - 6 absolutely or relatively, and also the radius you printed can be changed by no more than 10 - 6 (absolutely or relatively) in such a way that all points outside the flat and Fafa's laptop position are outside circle of the access point range.

Examples

Input

5 3 3 1 1


Output

3.7677669529663684 3.7677669529663684 3.914213562373095


Input

10 5 5 5 15


Output

5.0 5.0 10.0

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.io.BufferedWriter;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author chaku
 */
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);
        TaskC solver = new TaskC();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskC {
        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int R = in.nextInt();
            int x1 = in.nextInt();
            int y1 = in.nextInt();
            int x2 = in.nextInt();
            int y2 = in.nextInt();

            if (!checkIns(x1, y1, x2, y2, R)) {
                out.println(x1 + " " + y1 + " " + R);
                return;
            }
            if (x2 == x1) {
                double[] roots = new double[]{x1, x1};
                double[] yrts = new double[]{y1 + R, y1 - R};
                double dis1 = dis(x2, y2, roots[0], yrts[0]);
                double dis2 = dis(x2, y2, roots[1], yrts[1]);
                if (dis1 > dis2) {
                    double cx = (roots[0] + x2) / 2;
                    double cy = (yrts[0] + y2) / 2;
                    out.println(cx + " " + cy + " " + (dis1 / 2));
                } else {
                    double cx = (roots[1] + x2) / 2;
                    double cy = (yrts[1] + y2) / 2;
                    out.println(cx + " " + cy + " " + (dis2 / 2));
                }
                return;
            }
            if (y2 == y1) {
                double[] roots = new double[]{x1 + R, x1 - R};
                double[] yrts = new double[]{y1, y1};
                double dis1 = dis(x2, y2, roots[0], yrts[0]);
                double dis2 = dis(x2, y2, roots[1], yrts[1]);
                if (dis1 > dis2) {
                    double cx = (roots[0] + x2) / 2;
                    double cy = (yrts[0] + y2) / 2;
                    out.println(cx + " " + cy + " " + (dis1 / 2));
                } else {
                    double cx = (roots[1] + x2) / 2;
                    double cy = (yrts[1] + y2) / 2;
                    out.println(cx + " " + cy + " " + (dis2 / 2));
                }
                return;
            }
            double m = Double.MAX_VALUE;
            if ((x2 - x1) != 0) m = ((double) y2 - y1) / (x2 - x1);
            double c = 0;
            if (m != Double.MAX_VALUE) c = y1 - m * x1;
            double a = 1 + Math.pow(m, 2);
            double b = 2 * (m * (c - y1) - x1);
            double cc = Math.pow(x1, 2) + Math.pow(c - y1, 2) - Math.pow(R, 2);
            double[] roots = root(a, b, cc);
            double[] yrts = new double[]{m * roots[0] + c, m * roots[1] + c};
            double dis1 = dis(x2, y2, roots[0], yrts[0]);
            double dis2 = dis(x2, y2, roots[1], yrts[1]);
            if (dis1 > dis2) {
                double cx = (roots[0] + x2) / 2;
                double cy = (yrts[0] + y2) / 2;
                out.println(cx + " " + cy + " " + (dis1 / 2));
            } else {
                double cx = (roots[1] + x2) / 2;
                double cy = (yrts[1] + y2) / 2;
                out.println(cx + " " + cy + " " + (dis2 / 2));
            }
        }

        static double dis(double x1, double y1, double x2, double y2) {
            return Math.pow(Math.pow(x2 - x1, 2) + Math.pow(y2 - y1, 2), 0.5);
        }

        static double[] root(double a, double b, double c) {
            double first = Math.pow(Math.pow(b, 2) - 4 * a * c, 0.5);
            double sec = -b - first;
            first -= b;
            first /= 2 * a;
            sec /= 2 * a;
            return new double[]{first, sec};
        }

        static boolean checkIns(double x1, double y1, double x2, double y2, int R) {
            double val = Math.pow(x2 - x1, 2) + Math.pow(y2 - y1, 2) - Math.pow(R, 2);
            if (val < 0) return true;
            return false;
        }

    }

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

        }

    }

    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 print(Object... objects) {
            for (int i = 0; i < objects.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(objects[i]);
            }
        }

        public void println(Object... objects) {
            print(objects);
            writer.println();
        }

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

    }
}