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:
/* package whatever; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

	import java.util.Arrays;
import java.util.Collections;
import java.util.List;

/* Name of the class has to be "Main" only if the class is public. */
public class main
{

    public static Point getCircleLineIntersectionPoint(Point pointA,
            Point pointB, Point center, double radius) {
        double baX = pointB.x - pointA.x;
        double baY = pointB.y - pointA.y;
        double caX = center.x - pointA.x;
        double caY = center.y - pointA.y;

        double a = baX * baX + baY * baY;
        double bBy2 = baX * caX + baY * caY;
        double c = caX * caX + caY * caY - radius * radius;

        double pBy2 = bBy2 / a;
        double q = c / a;

        double disc = pBy2 * pBy2 - q;
        //if (disc < 0) {
        //    return Collections.emptyList();
        //}
        // if disc == 0 ... dealt with later
        double tmpSqrt = Math.sqrt(disc);
        double abScalingFactor1 = -pBy2 + tmpSqrt;
        double abScalingFactor2 = -pBy2 - tmpSqrt;

        Point p1 = new Point(pointA.x - baX * abScalingFactor1, pointA.y
                - baY * abScalingFactor1);
        if (disc == 0) { // abScalingFactor1 == abScalingFactor2
            return p1;
        }
        Point p2 = new Point(pointA.x - baX * abScalingFactor2, pointA.y
                - baY * abScalingFactor2);
        //pb: center
        //p1 and pa
        double d1 = (p1.x-pointA.x)*(p1.x-pointA.x) + (p1.y-pointA.y)* (p1.y-pointA.y);
        //p2 and pa
        double d2 = (p2.x-pointA.x)*(p2.x-pointA.x) + (p2.y-pointA.y)* (p2.y-pointA.y);
        if(d1 <= d2) return p2;
        return p1;
    }

    static class Point {
        double x, y;

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

        @Override
        public String toString() {
            return "Point [x=" + x + ", y=" + y + "]";
        }
    }


	public static void main (String[] args)
	{
		Scanner in = new Scanner(System.in);
		int R = in.nextInt();
		int x1 = in.nextInt();
		int y1 = in.nextInt();
		int x2 = in.nextInt();
		int y2 = in.nextInt();
		double val = (x2-x1)*1.0*(x2-x1) + (y2-y1)*1.0*(y2-y1);
		double r2 = R*1.0*R;
		if(x1==x2 && y1==y2)
		{
			double xx = x1+R;
			System.out.printf("%.9f %.9f %.9f" , (x1+xx)/2.0, y1*1.0, R/2.0);
		}
		else if(val >= r2)
		{
			System.out.printf("%d %d %d" , x1, y1, R);
		}
		else{
			Point o = getCircleLineIntersectionPoint(new Point(x2,y2), new Point(x1,y1), new Point(x1,y1), R);
			double ans = (o.x-x2*1.0)*(o.x-x2*1.0) + (o.y-y2*1.0)*(o.y-y2*1.0);
			ans = Math.sqrt(ans);
			double x0 = (x2+o.x)/2.0;
			double y0 = (y2+o.y)/2.0;
			System.out.printf("%.9f %.9f %.9f" , x0, y0, ans/2.0);
		}
	}
}