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.PrintWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

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

  static class TaskC {
    int dx;
    int dy;

    void print(double x, double y, double r, PrintWriter out) {
      out.println(String.format("%.12f %.12f %.12f", dx + x, dy + y, r));
    }

    public void solve(int testNumber, InputReader in, PrintWriter out) {
      int R = in.readInt();
      int x1 = in.readInt();
      int y1 = in.readInt();
      int x2 = in.readInt() - x1;
      int y2 = in.readInt() - y1;

      dx = x1;
      dy = y1;
      x1 = y1 = 0;

      Point originPoint = new Point(0, 0);
      Point badPoint = new Point(x2, y2);

      if (x2 == 0 && y2 == 0) {
        print(R / 2.0, 0.0, R / 2.0, out);
      } else {
        Segment seg = new Segment(originPoint, badPoint);
        if (seg.length() >= R) {
          print(0, 0, R, out);
        } else {
          Circle circle = new Circle(originPoint, R);
          Point[] inters = seg.line().intersect(circle);

          double d0 = new Segment(badPoint, inters[0]).length();
          double d1 = new Segment(badPoint, inters[1]).length();
          Point furtherPoint = inters[d0 > d1 ? 0 : 1];

          print((furtherPoint.x + badPoint.x) / 2.0, (furtherPoint.y + badPoint.y) / 2.0, Math.max(d0, d1) / 2.0, out);
        }
      }
    }

  }

  static class Circle {
    public final Point center;
    public final double radius;

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

  }

  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 interface SpaceCharFilter {
      public boolean isSpaceChar(int ch);

    }

  }

  static class GeometryUtils {
    public static double epsilon = 1e-8;

    public static double fastHypot(double x, double y) {
      return Math.sqrt(x * x + y * y);
    }

  }

  static class Point {
    public final double x;
    public final double y;


    public String toString() {
      return "(" + x + ", " + y + ")";
    }

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

    public Line line(Point other) {
      if (equals(other)) {
        return null;
      }
      double a = other.y - y;
      double b = x - other.x;
      double c = -a * x - b * y;
      return new Line(a, b, c);
    }


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

      Point point = (Point) o;

      return Math.abs(x - point.x) <= GeometryUtils.epsilon && Math.abs(y - point.y) <= GeometryUtils.epsilon;
    }


    public int hashCode() {
      int result;
      long temp;
      temp = x != +0.0d ? Double.doubleToLongBits(x) : 0L;
      result = (int) (temp ^ (temp >>> 32));
      temp = y != +0.0d ? Double.doubleToLongBits(y) : 0L;
      result = 31 * result + (int) (temp ^ (temp >>> 32));
      return result;
    }

    public double distance(Point other) {
      return GeometryUtils.fastHypot(x - other.x, y - other.y);
    }

  }

  static class Line {
    public final double a;
    public final double b;
    public final double c;

    public Line(Point p, double angle) {
      a = Math.sin(angle);
      b = -Math.cos(angle);
      c = -p.x * a - p.y * b;
    }

    public Line(double a, double b, double c) {
      double h = GeometryUtils.fastHypot(a, b);
      this.a = a / h;
      this.b = b / h;
      this.c = c / h;
    }

    public Point intersect(Line other) {
      if (parallel(other)) {
        return null;
      }
      double determinant = b * other.a - a * other.b;
      double x = (c * other.b - b * other.c) / determinant;
      double y = (a * other.c - c * other.a) / determinant;
      return new Point(x, y);
    }

    public boolean parallel(Line other) {
      return Math.abs(a * other.b - b * other.a) < GeometryUtils.epsilon;
    }

    public Line perpendicular(Point point) {
      return new Line(-b, a, b * point.x - a * point.y);
    }

    public double value(Point point) {
      return a * point.x + b * point.y + c;
    }

    public Point[] intersect(Circle circle) {
      double distance = distance(circle.center);
      if (distance > circle.radius + GeometryUtils.epsilon) {
        return new Point[0];
      }
      Point intersection = intersect(perpendicular(circle.center));
      if (Math.abs(distance - circle.radius) < GeometryUtils.epsilon) {
        return new Point[]{intersection};
      }
      double shift = Math.sqrt(circle.radius * circle.radius - distance * distance);
      return new Point[]{new Point(intersection.x + shift * b, intersection.y - shift * a),
          new Point(intersection.x - shift * b, intersection.y + shift * a)};
    }

    public double distance(Point center) {
      return Math.abs(value(center));
    }


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

      Line line = (Line) o;

      if (!parallel(line)) {
        return false;
      }
      if (Math.abs(a * line.c - c * line.a) > GeometryUtils.epsilon ||
          Math.abs(b * line.c - c * line.b) > GeometryUtils.epsilon) {
        return false;
      }

      return true;
    }

  }

  static class Segment {
    public final Point a;
    public final Point b;
    private double distance = Double.NaN;
    private Line line = null;

    public Segment(Point a, Point b) {
      this.a = a;
      this.b = b;
    }

    public double length() {
      if (Double.isNaN(distance)) {
        distance = a.distance(b);
      }
      return distance;
    }

    public Line line() {
      if (line == null) {
        line = a.line(b);
      }
      return line;
    }

  }
}