You are working at a major social networking company, designing their recommendation system. You have been tasked with finding pairs of people to recommend. The social network is represented as a undirected graph G = (V, E), where V = {1, 2, . . . , n} and the edges denoted friendship. A pair (u, v) is a called a potential recommendation if it satisfied the following properties: (u, v) is not an edge and u and v have at least 3 common friends (neighbors).

Write an algorithm that outputs all potential recommendations. Assume that n is the number of vertices and m is the number of edges.