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>
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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:
#define _USE_MATH_DEFINES
#define INF 0x3f3f3f3f

#include <iostream>
#include <cstdio>
#include <sstream>
#include <cmath>
#include <cstdlib>
#include <algorithm>
#include <queue>
#include <stack>
#include <limits>
#include <map>
#include <string>
#include <cstring>
#include <set>
#include <deque>
#include <bitset>
#include <list>
#include <cctype>
#include <utility>
#include <assert.h>
  
using namespace std;
  
typedef long long ll;
typedef pair <int,int> P;
typedef pair <double,P> PP;
  
static const double EPS = 1e-8;

class Point {
public:
  double x;
  double y;
  double z;
  Point (double x,double y,double z) :
    x(x), y(y), z(z) {}
  Point () : x(0), y(0), z(0) {}
  Point operator-(const Point& p) const {
    return Point(this->x - p.x,
                 this->y - p.y,
                 this->z - p.z);
  }
  Point operator+(const Point& p) const {
    return Point(this->x + p.x,
                 this->y + p.y,
                 this->z + p.z);
  }
  void operator+=(const Point& p) const {
    this->x + p.x;
    this->y + p.y;
    this->z + p.z;
  }
  Point operator*(const double t) const {
    return Point(this->x * t,
                 this->y * t,
                 this->z * t);
  }
  Point operator*(const Point&p) const {
    return Point(this->x * p.x,
                 this->y * p.y,
                 this->z * p.z);
  }
  Point operator/(const double t) const {
    return Point(this->x / t,
                 this->y / t,
                 this->z / t);
  }
  void operator/=(const double t) {
    this->x /= t;
    this->y /= t;
    this->z /= t;
  }
  void print_vec() const{
    printf("(%lf,%lf,%lf)\n",this->x,this->y,this->z);
  }
};

class Line : public vector<Point> {
public:
  Line(const Point& p1,const Point& p2) {
    push_back(p1);
    push_back(p2);
  }
};

class Circle {
public:
  Point p;
  double r;
  Circle(const Point& p,double r) : p(p),r(r) {}
};

double norm(const Point& p){
  return p.x * p.x + p.y * p.y + p.z * p.z;
}

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

Point unit(const Point& p){
  return p/abs(p);
}

double dot(const Point& p1,const Point& p2){
  return p1.x * p2.x + p1.y * p2.y + p1.z * p2.z;
}

Point cross(const Point& p1,const Point& p2){
  return Point(p1.y * p2.z - p1.z * p2.y,
               p1.z * p2.x - p1.x * p2.z,
               p1.x * p2.y - p1.y * p2.x);
}

Point projection(const Line& l,const Point& p){
  double t = dot(p - l[0],l[0]-l[1]) / norm(l[0] - l[1]);
  return l[0] + (l[0] - l[1]) * t;
}

bool EQ(const Point& s,const Point& t) {
  if((t.x - EPS <= s.x && s.x <= t.x + EPS)
     && (t.y - EPS <= s.y && s.y <= t.y + EPS)
     && (t.z - EPS <= s.z && s.z <= t.z + EPS)) return true;
  return false;
}

bool parallelLL(const Line &l, const Line &m) {
  return EQ(cross(l[1]-l[0], m[1]-m[0]),Point(0,0,0));
}

bool intersectLP(const Line &l, const Point &p) {
  return (abs(cross(l[1]-p, l[0]-p)) < EPS);
}

double distanceLP(const Line& l,const Point& p){
  if(intersectLP(l,p)) return 0;
  return abs(p - projection(l,p));
}

double distanceLL(const Line& l,const Line& m){
  if(parallelLL(l,m)) return distanceLP(l,m[0]);

  const Point V1 = l[1] - l[0];
  const Point V2 = m[1] - m[0];
  const Point V3 = m[0] - l[0];
  return abs(dot(cross(V1,V2),V3)/abs(cross(V1,V2)));
}

double distancePP(const Point& s,const Point& t) {
  if(EQ(s,t)) return 0;
  return abs(Point(s.x - t.x,s.y - t.y,s.z - t.z));
}

vector<Point> crosspointLC(const Line& l,const Circle& ci){
  Point dir = unit(l[1] - l[0]);
  // a * t^2 + b * t + c = 0
  double a = norm(dir);
  double b = dot(l[0] - ci.p,dir);
  double c = norm(l[0] - ci.p) - ci.r * ci.r;
  double D = b * b - a * c;

  vector<Point> res;
  if(D < EPS) return res;
  double t1 = (-b - sqrt(D))/a;
  double t2 = (-b + sqrt(D))/a;

  if(abs(t1) < abs(t2)){
    res.push_back(l[0] + dir * t1);
  }
  else{
    res.push_back(l[0] + dir * t2);
  }
  return res;
}

Point reflection(const Line& l,const Point& p){
  return p + (projection(l,p) - p) * 2.0;
}

int main(){
  int num_of_spheres;
  while(~scanf("%d",&num_of_spheres)){
    if(num_of_spheres == 0) break;

    double u,v,w;
    scanf("%lf %lf %lf",&u,&v,&w);

    vector<Circle> spheres;
    for(int sphere_i = 0; sphere_i < num_of_spheres; sphere_i++){
      double x,y,z,r;
      scanf("%lf %lf %lf %lf",&x,&y,&z,&r);
      spheres.push_back(Circle(Point(x,y,z),r));
    }

    Line laser(Point(0,0,0),Point(u,v,w));
    Point reflection_point;

    int prev_sphere = -1;
    for(int round = 0; round < 5; round++){
      double min_abs = numeric_limits<double>::max();
      int current_sphere = -1;
      for(int sphere_i = 0; sphere_i < num_of_spheres; sphere_i++){
        if(prev_sphere == sphere_i) continue;
        vector<Point> p = crosspointLC(laser,spheres[sphere_i]);
        for(int i = 0; i < p.size(); i++){
          if(dot(laser[1] - laser[0],p[i] -laser[0]) < EPS) continue;
          if(abs(p[i] - laser[0]) < min_abs){
            reflection_point = p[i];
            current_sphere = sphere_i;
            min_abs = abs(p[i] - laser[0]);
          }
        }
      }
      if(current_sphere == -1) break;

      Line nv(reflection_point,spheres[current_sphere].p);

      laser = Line(reflection_point,
                   reflection(nv,laser[0]));

      prev_sphere = current_sphere;
    }

    printf("%.4lf %.4lf %.4f\n",
           reflection_point.x,
           reflection_point.y,
           reflection_point.z);

  }
}