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.*;
import java.util.*;

public class Solution{
    InputStream is;
    static PrintWriter out;
    String INPUT = "";
    static long mod = (long)1e9+7L;
    
    public void solve(){
        double R = nd(), fx = nd(), fy=nd(), px=nd(), py=nd();

                                   //y = mx+c;

if(!isInside(fx, fy, R, px, py)){
    out.println(fx+" "+fy+" "+R);
    return;
}
        if(px == fx){
            double ans, ansx, ansy;
            if(fy > py){
                ans=(R+fy-py)/2.0;
                ansx=px;
                ansy=(fy+R-py)/2.0;
            }
            else{
                ans = (R+py-fy)/2.0;
                ansx=px;
                ansy=((py)-(R-fy))/2.0;
            }
            out.println(ansx+" "+ansy+" "+ans);
            return;
        }

        double m = (py - fy)/(px - fx);
        double c = py - m*px;
//out.println(m+" "+c);
        int ct = 40;
        double l = px, r= px+2.0*R;
//out.println(l+" "+r);
        while(ct-->0 && l<r){
            double mid = l+(r-l)/2.0;
            if(isInside(fx, fy, R, mid, m*mid+c)){
                l = mid;
            }
            else{
                r= mid;
            }
        }

        double ans1R = dist(px, py, l, m*l+c)/2.0;
        double ans1x = (l+px)/2.0;
        double ans1y = (py+(m*l+c))/2.0;
        
/*out.println(l);
out.println(ans1R+" "+ans1x+" "+ans1y);
out.println(px+" "+py+" "+l+" "+(m*l+c));
out.println(dist(1, 1, 6.5, 6.5));
*/
        r=px; l=px-2.0*R; ct=40;
//out.println(l+" "+r+" "+ct);
        while(ct-->0 && l<r){
            //out.println(l+" "+r);
            double mid = l+(r-l)/2.0;
            if(isInside(fx, fy, R, mid, m*mid+c)){
                r=mid;
            }
            else{
                l=mid;
            }
        }
//out.println(l);
        double ans2R = dist(px, py, l, m*l+c)/2.0;
        double ans2x = (px+l)/2.0;
        double ans2y = (py+(m*l+c))/2.0;

        if(ans1R < ans2R){
            out.println(ans2x+" "+ans2y+" "+ans2R);
        }
        else{
            out.println(ans1x+" "+ans1y+" "+ans1R);
        }

    }
    double dist(double x1, double y1, double x2, double y2){
        return (double)Math.sqrt((x1-x2)*(x1-x2) + (y1-y2)*(y1-y2));
    }
    boolean isInside(double cx, double cy, double r, double x, double y){
        if ((x - cx)*(x-cx) + (y - cy)*(y - cy) < r*r){
            return true;
        }
        else return false;
    }    

   /* bool isInside(int circle_x, int circle_y, int rad, int x, int y)
{
    // Compare radius of circle with distance of its center from 
    // given point
    if ((x - circle_x)*(x - circle_x) + 
        (y - circle_y)*(y - circle_y) <= rad*rad)
        return true;
    else
        return false;
}*/

    void run(){
        is = new DataInputStream(System.in);
        out = new PrintWriter(System.out);
        int t=1;while(t-->0)solve();
        out.flush();
    }
    public static void main(String[] args)throws Exception{new Solution().run();}
    long mod(long v, long m){if(v<0){long q=(Math.abs(v)+m-1L)/m;v=v+q*m;}return v%m;}
    long mod(long v){if(v<0){long q=(Math.abs(v)+mod-1L)/mod;v=v+q*mod;}return v%mod;}
    //Fast I/O code is copied from uwi code.
    private byte[] inbuf = new byte[1024];
    public int lenbuf = 0, ptrbuf = 0;
    private int readByte(){
        if(lenbuf == -1)throw new InputMismatchException();
        if(ptrbuf >= lenbuf){
            ptrbuf = 0;
            try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
            if(lenbuf <= 0)return -1;
        }
        return inbuf[ptrbuf++];
    }
    private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
    private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
    private double nd() { return Double.parseDouble(ns()); }
    private char nc() { return (char)skip(); }
    private String ns(){
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    private char[] ns(int n){
        char[] buf = new char[n];
        int b = skip(), p = 0;
        while(p < n && !(isSpaceChar(b))){
            buf[p++] = (char)b;
            b = readByte();
        }
        return n == p ? buf : Arrays.copyOf(buf, p);
    }
    private char[][] nm(int n, int m){
        char[][] map = new char[n][];
        for(int i = 0;i < n;i++)map[i] = ns(m);
        return map;
    }
    private int[] na(int n){
        int[] a = new int[n];
        for(int i = 0;i < n;i++)a[i] = ni();
        return a;
    }
    private int ni(){
        int num = 0, b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-'){
            minus = true;
            b = readByte();
        }
        while(true){
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            }else{
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    private long nl(){
        long num = 0;
        int b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-'){
            minus = true;
            b = readByte();
        }        
        while(true){
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            }else{
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    static  int i(long x){return (int)Math.round(x);}
    static class Pair implements Comparable<Pair>{
        long fs,sc;
        Pair(long a,long b){
            fs=a;sc=b;
        }
        public int compareTo(Pair p){
            if(this.fs>p.fs)return 1;
            else if(this.fs<p.fs)return -1;
            else{
                return i(this.sc-p.sc);
            }
            //return i(this.sc-p.sc);
        }
        public String toString(){
            return "("+fs+","+sc+")";
        }    
    }
    
}