CF920E Connected Components?

You are given an undirected graph consisting of $ n $ vertices and  edges. Instead of giving you the edges that exist in the graph, we give you $ m $ unordered pairs ( $ x,y $ ) such that there is no edge between $ x $ and $ y $ , and if some pair of vertices is not listed in the input, then there is an edge between these vertices. You have to find the number of connected components in the graph and the size of each component. A connected component is a set of vertices $ X $ such that for every two vertices from this set there exists at least one path in the graph connecting these vertices, but adding any other vertex to $ X $ violates this rule.

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