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:

#include<bits/stdc++.h>
 
#define REP(i,s,n) for(int i=s;i<n;i++)
#define rep(i,n) REP(i,0,n)
#define IINF (INT_MAX)
#define EPS (1e-7)
#define equals(a,b) (fabs((a)-(b))<EPS)
#define MAX 110
 
using namespace std;
 
//作成中 VerifyしたものにはVerifyと書いてある
 
//Verify AOJ 0115
class Point3d{
public:
  double x,y,z;
 
  Point3d(double x=0,double y=0,double z=0):x(x),y(y),z(z){}
 
  Point3d operator + (const Point3d& a){
    return Point3d(x+a.x,y+a.y,z+a.z);
  }
  Point3d operator - (const Point3d& a){
    return Point3d(x-a.x,y-a.y,z-a.z);
  }
  Point3d operator * (const double& d){
    return Point3d(x*d,y*d,z*d);
  }
  Point3d operator / (const double& d){
    return Point3d(x/d,y/d,z/d);
  }
 
  bool operator < (const Point3d& p)const{
    return !equals(x,p.x)?x<p.x:((!equals(y,p.y))?y<p.y:z<p.z);
  }
 
  bool operator == (const Point3d& p)const{
    return equals(x,p.x) && equals(y,p.y) && equals(z,p.z);
  }
 
};
 
//Verify AOJ 0115
struct Segment3d{
  Point3d p[2];
  Segment3d(Point3d p1=Point3d(),Point3d p2=Point3d()){
    p[0] = p1, p[1] = p2;
  }
  bool operator == (const Segment3d& seg)const{
    return p[0] == seg.p[0] && p[1] == seg.p[1];
  }
};
 
typedef Point3d Vector3d;
typedef Segment3d Line3d;
 
 
 
 
ostream& operator << (ostream& os,const Point3d& p){
  os << "(" << p.x << "," << p.y << "," << p.z << ")";
}
 
ostream& operator << (ostream& os,const Segment3d& seg){
  os << "(" << seg.p[0] << "," << seg.p[1] << ")";
}
 
//Verify AOJ 0115
double dot(const Point3d& a,const Point3d& b){
  return a.x*b.x + a.y*b.y + a.z*b.z;
}
 
//Verify AOJ 0115
Vector3d cross(const Point3d& a,const Point3d& b){
  return Vector3d(a.y*b.z-a.z*b.y,a.z*b.x-a.x*b.z,a.x*b.y-a.y*b.x);
}
 
//Verify AOJ 0115
inline double norm(const Point3d &p){
  return p.x*p.x + p.y*p.y + p.z*p.z;
}
 
//Verify AOJ 0115
inline double abs(const Point3d &p){
  return sqrt(norm(p));
}
 
inline double toRad(double theta){
  return theta * M_PI / 180.0;
}
 
 
 
bool on_line3d(Line3d line,Point3d p){
  return equals(abs(cross(p-line.p[0],line.p[1]-line.p[0])),0);
}
 
bool on_segment3d(Segment3d seg,Point3d p){
  if( !on_line3d(seg,p) ) return false;
  double dist[3] = { abs(seg.p[1]-seg.p[0]), abs(p-seg.p[0]), abs(p-seg.p[1]) };  
  return on_line3d(seg,p) && equals(dist[0],dist[1]+dist[2]);
}
 
//Verify AOJ 0115
bool point_on_the_triangle3d(Point3d tri1,Point3d tri2,Point3d tri3,Point3d p){
 
  //線分上にpがあった場合、三角形内とみなす
  //if( on_segment3d(Segment3d(tri1,tri2),p) ) return true;
  //if( on_segment3d(Segment3d(tri2,tri3),p) ) return true;
  //if( on_segment3d(Segment3d(tri3,tri1),p) ) return true;
 
  Vector3d v1 = tri2 - tri1;
  Vector3d v2 = tri3 - tri2;
  Vector3d v3 = tri1 - tri3;
 
  Vector3d cp[3] = { cross(v1,p-tri1), cross(v2,p-tri2), cross(v3,p-tri3) };
  double d1 = dot(cp[0],cp[1]);
  double d2 = dot(cp[0],cp[2]);
 
  // 線分上にpがあった場合,三角形内とはみなさない
  //if( ( !equals(d1,0.0) && d1 > 0 ) && ( !equals(d2,0.0) && d2 > 0 ) ) return true;
 
  // 線分上にpがあった場合,三角形内とみなす
  if( ( equals(d1,0.0) || d1 > 0 ) && ( equals(d2,0.0) || d2 > 0 ) ) return true;
  return false;
}
 
inline Point3d rotateX(Point3d p,double rad){
  return Point3d(p.x,p.y*cos(rad)-p.z*sin(rad),p.y*sin(rad)+p.z*cos(rad));
}
 
inline Point3d rorateY(Point3d p,double rad){
  return Point3d(p.x*cos(rad)+p.z*sin(rad),p.y,-p.x*sin(rad)+p.z*cos(rad));
}
 
inline Point3d rorateZ(Point3d p,double rad){
  return Point3d(p.x*cos(rad)-p.y*sin(rad),p.x*sin(rad)+p.y*cos(rad),p.z);
}
 
inline Point3d rotateEuler(Point3d p,double alpha,double beta,double gamma){
  return Point3d( (cos(alpha)*cos(beta)*cos(gamma)-sin(alpha)*sin(gamma)) * p.x + (-cos(alpha)*cos(beta)*sin(gamma)-sin(alpha)*cos(gamma)) * p.y + (cos(alpha)*sin(beta)) * p.z,
		  (sin(alpha)*cos(beta)*cos(gamma)+cos(alpha)*sin(gamma)) * p.x + (-sin(alpha)*cos(beta)*sin(gamma)+cos(alpha)*cos(gamma)) * p.y + (sin(alpha)*sin(beta)) * p.z,
		  (-sin(beta)*cos(gamma)) * p.x + (sin(beta)*sin(gamma)) * p.y + (cos(beta)) * p.z);
}
 
inline Point3d rotateRollPitchYaw(Point3d p,double roll,double pitch,double yaw){
  return Point3d( ( cos(roll) * cos(pitch) ) * p.x + ( cos(roll) * sin(pitch) * sin(yaw) - sin(roll) * cos(yaw) ) * p.y + ( cos(roll) * sin(pitch) * cos(yaw) + sin(roll) * sin(yaw) ) * p.z,
		  ( sin(roll) * cos(pitch) ) * p.x + ( sin(roll) * sin(pitch) * sin(yaw) + cos(roll) * cos(yaw) ) * p.y + ( sin(roll) * sin(pitch) * cos(yaw) - cos(roll) * sin(yaw) ) * p.z,
		  -sin(pitch) * p.x + cos(pitch) * sin(yaw) * p.y + cos(pitch) * cos(yaw) * p.z);
}
 
 
class Plane3d{
public:
  Point3d normal_vector; //法線ベクトル
  double d; // 平面方程式 normal_vector.x * x + normal_vector.y * y + normal_vector.z * z + d = 0
 
  Plane3d(Point3d normal_vector=Point3d(),double d=0):normal_vector(normal_vector),d(d){}
  Plane3d(Vector3d a,Vector3d b,Vector3d c){
    Vector3d v1 = b - a;
    Vector3d v2 = c - a;
    Vector3d tmp = cross(v1,v2);
    normal_vector = tmp / abs(tmp);
    set_d(a);
  }
 
  //Verify AOJ 0115
  //法線ベクトルnormal_vectorと平面上の１点からdを計算する
  void set_d(Point3d p){
    d = dot(normal_vector,p);
  }
 
  //平面と点pの距離を求める
  double distanceP(Point3d p){
    Point3d a = normal_vector * d;//平面上の適当な点をつくる
    return abs( dot(p-a,normal_vector) );
  }
 
  //平面上でもっとも点pと近い点を求める
  Point3d nearest_point(Point3d p){
    Point3d a = normal_vector * d;
    return p - ( normal_vector * dot(p-a,normal_vector) );
  }
 
  //Verify AOJ 0115
  //平面と線分が交差するか
  bool intersectS(Segment3d seg){
    Point3d a = normal_vector * d;
    double res1 = dot(a-seg.p[0],normal_vector);
    double res2 = dot(a-seg.p[1],normal_vector);
    if( res1 > res2 ) swap(res1,res2);
    //cout << res1 << " < " << res2 << endl;
    if( ( equals(res1,0.0) || res1 < 0 ) && ( equals(res2,0.0) || res2 > 0 ) ) return true;
    return false;
  }
 
  //Verify AOJ 0115
  //平面と線分の交点を求める
  Point3d crosspointS(Segment3d seg){
    Point3d a = normal_vector * d;
    double dot_p0a = fabs(dot( seg.p[0]-a,normal_vector ));
    double dot_p1a = fabs(dot( seg.p[1]-a,normal_vector ));
    if( equals(dot_p0a+dot_p1a,0) ) return seg.p[0];
    return seg.p[0] + ( seg.p[1] - seg.p[0] ) * ( dot_p0a / ( dot_p0a + dot_p1a ) );
  }
 
};
 
double distanceLP(Line3d line,Point3d p){
  return abs(cross(line.p[1]-line.p[0],p-line.p[0])) / abs(line.p[1]-line.p[0]);
}

double distanceSP(Segment3d seg,Point3d p){
  double res = dot(seg.p[1]-seg.p[0],p-seg.p[0]);
  if( !equals(res,0.0) && res < 0.0 ) return abs( p - seg.p[0] );
  res = dot(seg.p[0]-seg.p[1],p-seg.p[1]);
  if( !equals(res,0.0) && res < 0.0 ) return abs( p - seg.p[1] );
  return distanceLP(seg,p);
}
 
Point3d project(Segment3d seg,Point3d p){
  Vector3d base = seg.p[1] - seg.p[0];
  double t = dot(p-seg.p[0],base) / norm(base);
  return seg.p[0] + base * t;
}
 
Point3d reflect(Segment3d seg,Point3d p){
  return p + (project(seg,p)-p) * 2.0;
}

//Verify AOJ 2081
bool isParallel(Line3d l1,Line3d l2){
  Vector3d A = l1.p[0], B = l1.p[1], C = l2.p[0], D = l2.p[1];
  Vector3d AB = B - A, CD = D - C;
  Vector3d n1 = AB / abs(AB), n2 = CD / abs(CD);
  double tmp = dot(n1,n2);
  tmp = 1 - tmp*tmp;
  return equals(tmp,0.0);
}
 
//Verify AOJ 2081 
//l1,l2が平行な時には使用できないので注意
Segment3d nearest_segmentLL(Line3d l1,Line3d l2){
  assert(!isParallel(l1,l2)); // 平行な場合は使用不可
  // l1.p[0] = A, l1.p[1] = B, l2.p[0] = C, l2.p[1] = D
  Vector3d AB = l1.p[1] - l1.p[0];
  Vector3d CD = l2.p[1] - l2.p[0];
  Vector3d AC = l2.p[0] - l1.p[0];
  Vector3d n1 = AB / abs(AB), n2 = CD / abs(CD);
  double d1 = (dot(n1,AC)-dot(n1,n2)*dot(n2,AC)) / (1.0-pow(dot(n1,n2),2));
  double d2 = (dot(n1,n2)*dot(n1,AC)-dot(n2,AC)) / (1.0-pow(dot(n1,n2),2));
  return Segment3d(l1.p[0]+n1*d1,l2.p[0]+n2*d2);
}
 
//Verify AOJ 2081
bool intersectLL(Line3d l1,Line3d l2){
  Vector3d A = l1.p[0], B = l1.p[1], C = l2.p[0], D = l2.p[1];
 
  //そもそもl1,l2が直線じゃない
  if( equals(abs(B-A),0.0) || equals(abs(D-C),0.0) ){
    /*
      この場合は注意
      そもそも与えられた線分が線分になっていないので、交差するかどうかは判定できない
    */
    return false;
  }
 
  Vector3d AB = B - A, CD = D - C;
  Vector3d n1 = AB / abs(AB), n2 = CD / abs(CD);
  double tmp = dot(n1,n2);
  tmp = 1 - tmp*tmp;
 
  if( equals(tmp,0.0) ) return 0; // 直線が平行
 
  Segment3d ns = nearest_segmentLL(l1,l2);
  if( ns.p[0] == ns.p[1] ) return true;
  return false;
}

bool intersectSS(Segment3d seg1,Segment3d seg2){
  if( isParallel(seg1,seg2) ) return false;
  Segment3d seg = nearest_segmentLL(seg1,seg2);
  if( !( seg.p[0] == seg.p[1] ) ) return false;
  Point3d cp = seg.p[1];
  return on_segment3d(seg1,cp) && on_segment3d(seg2,cp);
}


int N;
Segment3d ururu_beam;
Point3d Circle[MAX];
double R[MAX];

inline void Input3d(Point3d &p){ cin >> p.x >> p.y >> p.z; }

inline void compute(){
  int skip = -1;
  bool update = true;
  while(update){
    update = false;
    Point3d tmp_p0,tmp_p1;
    int tmp_skip = -1;
    double tmp_dist = IINF;
    Vector3d vect = ( ururu_beam.p[1] - ururu_beam.p[0] ) / abs( ururu_beam.p[1] - ururu_beam.p[0] );
    Vector3d rvect = ( ururu_beam.p[0] - ururu_beam.p[1] ) / abs( ururu_beam.p[0] - ururu_beam.p[1] );
    ururu_beam.p[1] = ururu_beam.p[0] + vect * 500;
    rep(i,N){
      if( i == skip ) continue;

      double dist = distanceSP(ururu_beam,Circle[i]);
      if( !equals(dist,R[i]) && dist > R[i] ) continue;

      Point3d on_seg = project(ururu_beam,Circle[i]);

      dist = sqrt(pow(R[i],2.0)-norm(on_seg-Circle[i]));
      double x = R[i] * R[i] - norm(on_seg-Circle[i]);
      if( x == 0 ) dist = 0;
      else if( x < 0 ) continue;

      Point3d cp = on_seg + rvect * dist;
      Line3d line = Line3d(Circle[i],cp);

      dist = abs(ururu_beam.p[0]-cp);
      if( tmp_dist > dist ){
        tmp_p0 = cp, tmp_p1 = reflect(line,ururu_beam.p[0]);
        tmp_dist = dist;
        tmp_skip = i;
      }
      update = true;
    }
    if( update ){
      ururu_beam = Segment3d(tmp_p0,tmp_p1);
      skip = tmp_skip;
    }
  }
  printf("%.4f %.4f %.4f\n",ururu_beam.p[0].x,ururu_beam.p[0].y,ururu_beam.p[0].z);
}

int main(){
  while( cin >> N, N ){
    ururu_beam.p[0] = Point3d(0,0,0);
    Input3d(ururu_beam.p[1]);
    rep(i,N){
      Input3d(Circle[i]);
      cin >> R[i];
    }
    compute();
  }
  return 0;
}