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

public class Solution2 {

    //(x - a)^2 + (y - b)^2 = vR

    // y = kx + m

    private void solve() throws IOException {
        double R = in.nextDouble();
        double x1 = in.nextDouble();
        double y1 = in.nextDouble();
        double x2 = in.nextDouble();
        double y2 = in.nextDouble();
        if ((x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1) >= R * R) {
            System.out.println(x1 + " " + y1 + " " + R);
            return;
        }
        /** obrabotat` sluchai korda x1 = x2 && y1 == y2**/
        // m = y1 - kx1;
        // m = y2 - kx2;
        //y1 - kx1 = y2 - kx2
        // y1 - y2 = kx1 - kx2
        // k = y1 - y2 / x1 - x2
        double x_circle, y_circle;
        double k = y1 - y2;
        if (x1 != x2) {
            k /= (x1 - x2);
        }
        else {
            x_circle = x1;
            double a = 1;
            double b = -2 * y1;
            double c = y1 * y1 - R * R;
            double y_1 = (-b + Math.sqrt(b * b - 4 * a * c)) / (2 * a);
            double y_2 = (-b - Math.sqrt(b * b - 4 * a * c)) / (2 * a);
            if (distance(x_circle, y_1, x_circle, y2) > distance(x_circle, y_2, x_circle, y2)) {
                y_circle = y_1;
            }
            else {
                y_circle = y_2;
            }
            double x_center = x_circle + x2;
            x_center /= 2;
            double y_center = y_circle + y2;
            y_center /= 2;
            double dist = distance(x_center, y_center, x_circle, y_circle);
            System.out.println(x_center + " " + y_center + " " + dist);
            return;
        }
        double m = y1 - k * x1;
        // y = kx + m
        // vR = (x - a)^2 + (y - b)^2
        // vR = x^2 - 2ax + a^2 + (kx + m)^ 2 - 2b(kx + m) + b^2
        // vR = x^2 - 2ax + a^2 + k^2x^2 + 2kxm + m^2 - 2bkx -2bm + b^2
        // (1 + k^2)x^2 - (2a + 2bk - 2km)x + a^2 + m^2 + b^2 - 2bm - vR
        double a = 1 + k * k;
        double b = -2 * (x1 + y1 * k - k * m);
        double c = x1 * x1 + m * m + y1 * y1 - 2 * y1 * m - R * R;
        //ax^2 + bx + c = 0
        double x_1 = -b + Math.sqrt(b * b - 4 * a * c);
        x_1 /= (2 * a);
        double x_2 = -b - Math.sqrt(b * b - 4 * a * c);
        x_2 /= (2 * a);
        double y_1 = k * x_1 + m;
        double y_2 = k * x_2 + m;
        if (distance(x_1, y_1, x2, y2) > distance(x_2, y_2, x2, y2)) {
            x_circle = x_1;
            y_circle = y_1;
        }
        else {
            x_circle = x_2;
            y_circle = y_2;
        }
        double x_center = x_circle + x2;
        x_center /= 2;
        double y_center = y_circle + y2;
        y_center /= 2;
        double dist = distance(x_center, y_center, x_circle, y_circle);
        System.out.println(x_center + " " + y_center + " " + dist);
    }

    private double distance(double x1, double y1, double x2, double y2) {
        return  Math.sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2));
    }

    private String filename = "";
    private PrintWriter out;
    MyScanner in;

    private void run() throws IOException {
        in = new MyScanner();
        out = new PrintWriter(System.out);
        solve();
        in.close();
        out.close();
    }

    private class MyScanner {
        private BufferedReader br;
        private StringTokenizer st;

        public MyScanner() throws IOException {
            this.br = new BufferedReader(new InputStreamReader(System.in));
        }

        public MyScanner(String fileTitle) throws IOException {
            this.br = new BufferedReader(new FileReader(fileTitle));
        }

        public String nextLine() throws IOException {
            String s = br.readLine();
            return s == null ? "-1" : s;
        }

        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens()) {
                String s = br.readLine();
                if (s == null) {
                    return "-1";
                }
                st = new StringTokenizer(s);
            }
            return st.nextToken();
        }

        public Integer nextInt() throws IOException {
            return Integer.parseInt(this.next());
        }

        public Long nextLong() throws IOException {
            return Long.parseLong(this.next());
        }

        public Double nextDouble() throws IOException {
            return Double.parseDouble(this.next());
        }

        public void close() throws IOException {
            this.br.close();
        }
    }

    public static void main(String[] args) throws IOException {
        Locale.setDefault(Locale.US);
        new Solution2().run();
    }
}