A maze can be constructed from a series of concentric circles. Between the circles there are walls placed, and around the circles there are doors. The walls divide the areas between the circles into...

A maze can be constructed from a series of concentric circles. Between the circles there are walls placed, and around the circles there are doors. The walls divide the areas between the circles into chambers, and the doors permit movement between chambers. The positions of the doors and walls are given in degrees measured counterclockwise from the horizontal. For example, the maze shown on the left can be described as follows:

Write a program that inputs a description of a maze in this format and finds the shortest path from the outside to the innermost circle. The shortest path is the one that goes through the smallest number of chambers.