The input consists of one or more datasets. The number of datasets is less than 50. Each dataset describes stars and the parameters of the telescopes used.
The first line of a dataset contains a positive integer n not exceeding 500, meaning the number of stars. Each of the n lines following it contains three decimal fractions, sx, sy, and sz. They give the position (sx, sy, sz) of the star described in Euclidean coordinates. You may assume −1000 ≤ sx ≤ 1000, −1000 ≤ sy ≤ 1000, −1000 ≤ sz ≤ 1000, and (sx, sy, sz) ≠ (0, 0, 0).
Then comes a line containing a positive integer m not exceeding 50, meaning the number of telescopes. Each of the following m lines contains four decimal fractions, tx, ty, tz and ψ, describing a telescope.
The first three numbers represent the direction of the telescope. All the telescopes are at the origin of the coordinate system (0, 0, 0) (we ignore the size of the planet). The three numbers give the point (tx, ty, tz) which can be see in the center of the sight through the telescope. You may assume −1000 ≤ tx ≤ 1000, −1000 ≤ ty ≤ 1000, −1000 ≤ tz ≤ 1000, and (tx, ty, tz) ≠ (0, 0, 0).
The fourth number ψ (0 ≤ ψ ≤ π ⁄ 2) gives the angular radius, radians, of the sight field of the telescope. Let us define that θi,j is the angle between the direction of the i-th star and the center direction of the j-th telescope and ψj is the angular radius of the sight field of the j-th telescope. the i-th star is observable through the j-th telescope if and only if θi,j is less than ψj. You may assume that |θi,j − ψj| > 0.00000001 for all pairs of i and j.
Figure 1: Direction and angular radius of a telescope
The end of the input is indicated with a line containing a single zero.
3
100 0 500
-500.243 -200.1 -300.5
0 300 200
2
1 1 1 0.65
-1 0 0 1.57
3
1 0 0
0 1 0
0 0 1
4
1 -1 -1 0.9553
-1 1 -1 0.9554
-1 -1 1 0.9553
-1 1 -1 0.9554
3
1 0 0
0 1 0
0 0 1
4
1 -1 -1 0.9553
-1 1 -1 0.9553
-1 -1 1 0.9553
-1 1 -1 0.9553
0
2
1
0