Assume that event A takes place at intervals that are IID exponential, and event B takes place at intervals that are IID exponential. Here, the parameters denote the hazard rates, the means being their reciprocals. Assume that a timer is started when event B takes place (call it the 0-th occurrence of B) and it is stopped when event B takes place three more times. Let N be the number of times event A takes place while the timer is on. Determine the distribution of N.