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

public class C {

	public static void main(String[] args) throws Exception {
		FinalScanner sc = new FinalScanner(); 
		PrintWriter out = new PrintWriter(System.out);
		double R = sc.nextDouble();
		double x1 = sc.nextDouble();
		double y1 = sc.nextDouble();
		double x2 = sc.nextDouble();
		double y2 = sc.nextDouble();
		
		double ansx = 0,ansy = 0,ansr = 0;
		
		double FD =dist(x1,y1,x2,y2);
		if(FD==0){
			ansx=x1 +(R/2.0);
			ansy=y1;
			ansr = (R/2.0);
		}
		else if(FD>=R){
			ansr=R;
			ansx=x1;
			ansy=y1;
		}
		else{
			ansr=(R+FD)/2.0;
			// F to C
			Vector FC = new Vector(x1,y1).sub((new Vector(x2,y2)));
			Vector A = FC.normalize().scale(ansr);
			ansx=A.x+x2;
			ansy=A.y+y2;
		}
		
		out.println(ansx+" "+ansy+" "+ansr);
		out.close();
	}

	static class Vector {
		final double x, y, z;
		static final double eps = 1e-10;

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

		public Vector(double x, double y) {
			this(x, y, 0);
		}

		public double mag2() {
			return this.dot(this);
		}

		public double mag() {
			return Math.sqrt(this.mag2());
		}

		public Vector add(Vector that) {
			return new Vector(this.x + that.x, this.y + that.y, this.z + that.z);
		}

		public Vector sub(Vector that) {
			return new Vector(this.x - that.x, this.y - that.y, this.z - that.z);
		}

		public double dist2(Vector that) {
			return this.sub(that).mag2();
		}

		public double dist(Vector that) {
			return this.sub(that).mag();
		}

		public double dot(Vector that) {
			return this.x * that.x + this.y * that.y + this.z * that.z;
		}

		public double cross2d(Vector that) {
			return this.x * that.y - this.y * that.x;
		}

		public Vector cross(Vector that) {
			return new Vector(this.y * that.z - this.z * that.y,
							  this.z * that.x - this.x * that.z,
							  this.x * that.y - this.y * that.x);
		}
		
		public Vector scale(double s) {
			return new Vector(this.x*s, this.y*s, this.z*s);
		}
		
		public Vector normalize() {
			return scale(1/this.mag());
		}
		
		public double angle(Vector that) {
			return Math.atan2(this.cross(that).mag(), this.dot(that));
		}
		
		public double angle2d(Vector that) {
			return this.angle(that, new Vector(0, 0, 1));
		}
		
		public double angle(Vector that, Vector up) {
			double sign = Math.signum(this.cross(that).dot(up));
			return sign*this.angle(that);
		}
		
		public Vector project(Vector that) {
			return that.scale(this.dot(that)/that.dot(that));
		}

		public double det(Vector v1, Vector v2, Vector v3){
			double aMul =	v2.y * v3.z - v3.y * v2.z;
			double bMul =	v1.y * v3.z - v3.y * v1.z;
			double cMul =	v1.y * v2.z - v2.y * v1.z;
			return aMul * v1.x + bMul * v2.x + cMul * v3.x;
		}
		
		public String toString() {
			return String.format("(%.3f, %.3f)", x, y);
		}
	}

	
	

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

	static class FinalScanner{
		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;
		
		public FinalScanner(){
			stream = System.in;
			//stream = new FileInputStream(new File("dec.in"));

		}
		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++];
		}
		
		boolean isSpaceChar(int c){
			return c==' '||c=='\n'||c=='\r'||c=='\t'||c==-1;
		}
		boolean isEndline(int c){
			return c=='\n'||c=='\r'||c==-1;
		}
		int nextInt(){
			return Integer.parseInt(next());
		}
		int[] nextInt(int v){
			int[] temp = new int[v];
			for(int a=0;a<v;a++)temp[a]=nextInt();
			return temp;
		}
		long nextLong(){
			return Long.parseLong(next());
		}
		long[] nextLong(int v){
			long[] temp = new long[v];
			for(int a=0;a<v;a++)temp[a]=nextLong();
			return temp;
		}
		double nextDouble(){
			return Double.parseDouble(next());
		}
		double[] nextDouble(int v){
			double[] temp = new double[v];
			for(int a=0;a<v;a++)temp[a]=nextDouble();
			return temp;
		}
		String next(){
			int c = read();
			while(isSpaceChar(c))
				c=read();
			StringBuilder res = new StringBuilder();
			do{
				res.appendCodePoint(c);
				c=read();
			} while(!isSpaceChar(c));
			return res.toString();
		}
		String[] next(int v){
			String[] temp = new String[v];
			for(int a=0;a<v;a++)temp[a]=next();
			return temp;
		}
		String nextLine(){
			int c = read();
			while(isEndline(c))
				c=read();
			StringBuilder res = new StringBuilder();
			do{
				res.appendCodePoint(c);
				c = read();
			}while(!isEndline(c));
			return res.toString();
		}
		String[] nextLine(int v){
			String[] temp = new String[v];
			for(int a=0;a<v;a++)temp[a]=nextLine();
			return temp;
		}
	}
}