The input consists of multiple datasets, each in the following format.
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.
in Figure 6), is less than 85 degrees for each point of reflection.
The last dataset is followed by a line containing a single zero.