/******************************************************************************
 *  Compilation:  javac Sphere.java
 *  Execution:    java Sphere N
 *  Dependencies  StdRandom.java
 *  
 *  Computes a random point on the surface of an N-dimensional sphere
 *  with radius 1 using Brown's method. Brown's method is to compute
 *  N independent variables x[0], ..., x[N-1] from a standard Gaussian
 *  distribution. Then
 * 
 *         ( x[0]/r, x[1]/r, ..., x[N-1]/r )
 *
 *  has the desired distribution, where r = sqrt(x[0]^2 + ... + x[N-1]^2).
 *
 *
 *  % java Sphere 1
 *  1.0
 *
 *  % java Sphere 1
 *  -1.0
 *
 *  % java Sphere 2
 *  -0.2239806529364283
 *  0.9745935907393252
 *
 *  % java Sphere 5
 *  0.953736056675788
 *  0.2233325012832955
 *  0.15023547754201239
 *  0.13387920998076436
 *  -0.00397322157886321
 *
 ******************************************************************************/


public class Sphere {

    public static void main(String[] args) { 
        int N = Integer.parseInt(args[0]);

        double[] x = new double[N];
        double r = 0.0;

        // generate N variables from Gaussian distribution
        for (int i = 0; i < N; i++)
            x[i] = StdRandom.gaussian();

        // compute Euclidean norm of vector x[]
        for (int i = 0; i < N; i++)
            r = r + x[i]*x[i];
        r = Math.sqrt(r);

        // print scaled vector
        for (int i = 0; i < N; i++)
            StdOut.println(x[i] / r);
   }
}