Given a simple connected undirected graph with $$$n$$$ vertices and $$$m$$$ edges, you may add as many edges (possibly zero) as you want and count the number of different ways modulo $$$998\,244\,353$$$ to make the graph biconnected while keeping it simple. Two ways of adding edges are considered different, if and only if there exists at least an edge $$$(u,v)$$$ added in one way and not added in the other.

Note that:

• A simple graph contains no self-loops and no multiple edges.
• For any two different vertices in a connected graph, there always exists at least a path from one vertex to the other.
• For any two different vertices in a biconnected graph, there always exist two or more paths sharing no common edges from one vertex to the other.

Figure: a simple graph, a connected graph, and a biconnected graph

As shown above, the graph on the left is simple but not connected because the $$$3$$$rd vertex can't reach any other vertex by a path, while the graph in the middle is connected but not biconnected because it's impossible to find two paths sharing no common edges from the $$$3$$$rd vertex to any other vertex.