Please give a thorough and complete explenation. Also, be sure to justify the answer per the instructions.

Given a set A of n activities a_i = [s_i, f_i], i = 1, 2, ..., n, where s_i is the start time and f_i is the finish time for i-th activity, the problem is to schedule the maximum number of activities for two classrooms. The activities scheduled for the same classroom must be non-conflicting. Consider the following algorithm: assign as many activities as possible to the first classroom, then assign as many activities as possible to the second classroom (not using the activities already assigned to the first classroom). Does it always solve the problem? Justify your answer (prove or disprove)