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.*;
 
public class Main {
	public static void main(String[] args) {
		InputReader in = new InputReader();
		PrintWriter out = new PrintWriter(System.out);
		Thread th = new Thread(null, new Runnable(){public void run(){new Task1().solve(in, out);}},"Task1",1<<24);
		try{
			th.start();
			th.join();
		} catch(InterruptedException e){}
		out.close();
	}

	static class Task1{
		static final int MAX = 1000001;

		public void solve(InputReader in, PrintWriter out){
			double R = Double.parseDouble(in.next());
			double x1 = Double.parseDouble(in.next());
			double y1 = Double.parseDouble(in.next());
			double x2 = Double.parseDouble(in.next());
			double y2 = Double.parseDouble(in.next());

			if((x2-x1)*(x2-x1)+(y2-y1)*(y2-y1) >= R*R){
				out.println(x1+" "+y1+" "+R);
				return;
			}
			if(x1==x2 && y1==y2){
				out.println((x1+R/2)+" "+y1+" "+R/2);
				return;
			}
			boolean inverted = false;
			if(x1==x2){
				double temp1 = x1, temp2 = x2;
				x1 = y1;
				x2 = y2;
				y1 = temp1;
				y2 = temp2;
				inverted = true;
			}

			double d = Math.sqrt((x2-x1)*(x2-x1)+(y2-y1)*(y2-y1));
			double m = (y2-y1)/(x2-x1);
			double P = x2*m;

			double A = 1+m*m;
			double B = -2*P*m-2*x2;
			double C = P*P+x2*x2-((R+d)*(R+d))/4;

			double xc1 = (-B+Math.sqrt(B*B - 4*A*C))/(2*A);
			double xc2 = (-B-Math.sqrt(B*B - 4*A*C))/(2*A);
			double yc1 = y1+m*(xc1-x1);
			double yc2 = y1+m*(xc2-x1);

			double d1 = (xc1-x1)*(xc1-x1)+(yc1-y1)*(yc1-y1);
			double d2 = (xc2-x1)*(xc2-x1)+(yc2-y1)*(yc2-y1);
			if(d1<=d2){
				double r = Math.sqrt((xc1-x2)*(xc1-x2)+(yc1-y2)*(yc1-y2));
				if(inverted){
					out.println(yc1+" "+xc1+" "+r);
				} else{
					out.println(xc1+" "+yc1+" "+r);
				}
			} else {
				double r = Math.sqrt((xc2-x2)*(xc2-x2)+(yc2-y2)*(yc2-y2));
				if(inverted){
					out.println(yc2+" "+xc2+" "+r);
				} else{
					out.println(xc2+" "+yc2+" "+r);
				}
			}
		}
		
		long gcd(long a, long b){
			while(a>0){
				long rem = b%a;
				b = a;
				a = rem;
			}
			return b;
		}
		long expo(long a, long b, long MOD){
			long result = 1;
			while (b>0){
				if (b%2==1) result=(result*a)%MOD;
				b>>=1;
				a=(a*a)%MOD;
			}
			return result%MOD;
		}
		long inverseModullo(long numerator, long denominator, long MOD){
			return ((numerator )*(expo(denominator, MOD-2, MOD))) ;
		}
	}
 	
	static class InputReader{
		final InputStream stream;
		final byte[] buf = new byte[8192];
		int curChar, numChars;
		SpaceCharFilter filter;
		public InputReader(){
			this.stream = System.in;
		}
		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 long nextLong(){
			int c = read();
			while(isSpaceChar(c)) c = read();
			int sgn = 1;
			if(c == '-'){
				sgn = -1;
				c = read();
			}
			long 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 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();
		}
		public boolean isSpaceChar(int c){
			if(filter != null) return filter.isSpaceChar(c);
			return c==' ' || c=='\n' || c=='\r' || c=='\t' || c==-1;
		}
		public interface SpaceCharFilter{
			public boolean isSpaceChar(int ch);
		}
	}
}