Finally some geometry! Maybe very easy though.

Currently I am undergoing the College Entrance Exam(GK) so I don't have many ideas for Competitive Programming problems. This problem is inspired by some math problem in GK Simulation.

Of course, this is only a very rough and primitive idea. Enjoy solving open problems. 🙂

Line Banquet

There are N lines in the 3-dimensional space indexed from 1 to N. The angle between line i(i\geq 2) and line F_i(F_i<i) is \theta_i(0\degree\leq\theta_i\leq90\degree)

There are Q queries. For each query, given line x,y, find the range of the possible angle between line x and y.

Example

F_2=1,F_3=1
\theta_2=90\degree,\theta_3=30\degree
Q={(2,3)}
Returns {[60\degree,90\degree]}