Problem: A long time ago in a galaxy, far, far away, there were N spheres with various radii. Spheres were mirrors, that is, they had reflective surfaces . . . .

You are standing at the origin of the galaxy (0, 0, 0), and emit a laser ray to the direction (u,v, w). The ray travels in a straight line.

When the laser ray from I hits the surface of a sphere at Q, let N be a point outside of the sphere on the line connecting the sphere center and Q. The reflected ray goes to the direction towards R that satisfies the following conditions: (1) R is on the plane formed by the three points I, Q and N , (2) ∠ IQN = ∠ NQR, as shown in Figure 1.

<image>
---
Figure 1: Laser ray reflection

After it is reflected several times, finally it goes beyond our observation. Your mission is to write a program that identifies the last reflection point.



Input

The input consists of multiple datasets, each in the following format.


N
u v w
x1 y1 z1 r1
.
.
.
xN yN zN rN


The first line of a dataset contains a positive integer N which is the number of spheres. The next line contains three integers u, v and w separated by single spaces, where (u, v, w) is the direction of the laser ray initially emitted from the origin.

Each of the following N lines contains four integers separated by single spaces. The i-th line corresponds to the i-th sphere, and the numbers represent the center position (xi, yi, zi ) and the radius ri .

N, u, v, w, xi, yi, zi and ri satisfy the following conditions.

1 ≤ N ≤ 100
−100 ≤ u, v, w ≤ 100
−100 ≤ xi, yi, zi ≤ 100
5 ≤ ri ≤ 30
u2 + v2 + w2 > 0


You can assume that the distance between the surfaces of any two spheres is no less than 0.1. You can also assume that the origin (0, 0, 0) is located outside of any sphere, and is at least 0.1 distant from the surface of any sphere.

The ray is known to be reflected by the sphere surfaces at least once, and at most five times. You can assume that the angle between the ray and the line connecting the sphere center and the reflection point, which is known as the angle of reflection (i.e. θ in Figure 1), is less than 85 degrees for each point of reflection.

The last dataset is followed by a line containing a single zero.

Output

For each dataset in the input, you should print the x-, y- and z-coordinates of the last reflection point separated by single spaces in a line. No output line should contain extra characters.

No coordinate values in the output should have an error greater than 0.01.

Example

Input

3
-20 -20 -24
100 100 100 30
10 8 3 5
-70 -70 -84 5
4
0 47 84
-23 41 42 8
45 -10 14 19
-5 28 47 12
-27 68 34 14
0


Output

79.0940 79.0940 94.9128
-21.8647 54.9770 34.1761

Solution (in CPP):

Solution:
#include <bits/stdc++.h>

using namespace std;

constexpr double EPS = 1e-8;
constexpr double INF = 1LL << 55;

struct Point3D {
    double x, y, z;
    Point3D(){}
    Point3D(double x, double y, double z) : x{x}, y{y}, z{z} {}
  
    Point3D operator + (const Point3D& p) const
    {
        return Point3D(x + p.x, y + p.y, z + p.z);
    }
    
    Point3D operator - (const Point3D& p) const
    {
        return Point3D(x - p.x, y - p.y, z - p.z);
    }
    
    Point3D operator * (double k) const
    {
        return Point3D(x * k, y * k, z * k);
    }    
    
    Point3D operator / (double k) const
    {
        return Point3D(x / k, y / k, z / k);
    }    
};

using Vector3D = Point3D;

istream& operator >> (istream& is, Point3D& p)
{
    return is >> p.x >> p.y >> p.z;
}

double dot(const Point3D& a, const Point3D& b)
{
    return a.x * b.x + a.y * b.y + a.z * b.z;
}

double norm(const Point3D& p)
{
    return dot(p, p);
}

double abs(const Point3D& p)
{
    return sqrt(norm(p));
}

double cross(const Point3D& a, const Point3D& b)
{
    return abs(Point3D(a.y * b.z - a.z * b.y,
                       a.z * b.x - a.x * b.z,
                       a.x * b.y - a.y * b.x));
}

double dist(const Point3D& a, const Point3D& b)
{
    return abs(a - b);
}

constexpr int COUNTER_CLOCKWISE = +1;
constexpr int CLOCKWISE         = -1;
constexpr int ONLINE_BACK       = +2;
constexpr int ONLINE_FRONT      = -2;
constexpr int ON_SEGMENT        = +0;
using Vector3D = Point3D;
 
int ccw(const Point3D& p0, const Point3D& p1, const Point3D& p2)
{
    Vector3D a = p1 - p0;
    Vector3D b = p2 - p0;
    if (abs(cross(a, b)) > EPS)  return COUNTER_CLOCKWISE;
    if (abs(cross(a, b)) < -EPS) return CLOCKWISE;
    if (dot(a, b) < -EPS)        return ONLINE_BACK;
    if (norm(a) < norm(b))       return ONLINE_FRONT;
    return ON_SEGMENT;
}

struct Line {
    Point3D s, t;
    Line() {}
    Line(Point3D s, Point3D t) : s{s}, t{t} {}
};

Point3D proj(const Line &l, const Point3D &p)
{
    Point3D b = l.t - l.s;
    double t = dot(p - l.s, b) / norm(b);
    return l.s + b * t;
}

Point3D refl(const Line& l, const Point3D& p)
{    
    return p + (proj(l, p) - p) * 2.0;
}

double distance_LP(const Line& l, const Point3D& p)
{
    return abs(p - proj(l, p));
}

struct Sphere {
    Point3D p;
    double r;
    Sphere() {}
    Sphere(Point3D p, double r) : p{p}, r{r} {}
};

istream& operator >> (istream& is, Sphere& sp)
{
    return is >> sp.p >> sp.r;
}

bool intersect_SL(const Sphere& s, const Line& l)
{
    return distance_LP(l, s.p) <= s.r + EPS;
}

Point3D crosspoint_SL(const Sphere& s, const Line& l)
{
    Point3D x = proj(l, s.p);
    Vector3D vp = x - s.p;
    Vector3D uv = (l.t - l.s) / abs(l.t - l.s);
    double t = sqrt(s.r * s.r - norm(vp));
    return x - uv * t;
}

int main()
{
    int N;
    while (cin >> N, N > 0) {
        Point3D p, pp{0, 0, 0};
        cin >> p;
        vector<Sphere> sp(N);
        for (int i = 0; i < N; i++) {
            cin >> sp[i];
        }

        Line l{pp, p};
        
        bool update = 1;
        while (update) {
            update = 0;
            
            double min = INF;
            int min_idx = -1;
            Point3D np{};
            
            for (int i = 0; i < N; i++) {
                if (!intersect_SL(sp[i], l)) continue;
                Point3D cp = crosspoint_SL(sp[i], l);

                double d = dist(pp, cp);
                
                if (d < min &&
                    (ccw(l.s, l.t, cp) == ON_SEGMENT || ccw(l.s, l.t, cp) == ONLINE_FRONT)) {
                    min = d;
                    min_idx = i;
                    np = cp;
                }
            }

            if (min_idx != -1) {
                update = 1;

                l = Line{np, refl({np, sp[min_idx].p}, pp)};
                pp = np;
            }
        }
        
        printf("%.15f %.15f %.15f\n", pp.x, pp.y, pp.z);
    }
    return 0;
}