Statement

At Luci di Nochia, the most important company producing flash lights for smartphones, the proportions between bosses and employees are very regular. Luca, the CEO, is the leader of the company. Under his control there are A_0 direct subordinates; under each of them there are other A_1 people, and so on. Generalizing, every person at level i has exactly A_i direct subordinates. Luca, who is a bit greedy, is worried that this structure has led to a company with too many employees: he has even lost the count of them! Given all the values A_i for i = 0 … N-1, count how many people work at his company.