You are a conference organiser and you are asked to organise a conference for a company. The capacity of the conference room is limited and hence you would want to minimise the number of people invited to the conference. To make the conference useful for the entire company, you need to make sure that if an employee is not invited, then every employee who is an immediate subordinate of this employee gets the invitation (if an employee is invited, then you may or may not invite a subordinate). The company has a typical hierarchical tree structure, where every employee except the CEO has exactly one immediate boss. Design an algorithm for this problem. You are given as input an integer array B[1...n], where B[i] is the immediate boss of the ith employee of the company. The CEO is employee number 1 and B[1] = 1. The output of your algorithm is a subset S C{1,.., n} of invited employees. Give running time analysis and proof of correctness.