You are given a connected undirected graph having N nodes numbered from 1 to N and M edges between its nodes. It is guaranteed that the input graph is connected and consists of no self-loops and no multiple edges between two vertices. An edge is special if it is removed then the number of connected components in the graph increases. Determine the number of unordered_pair {u, v} such that each and every Simple path (path with no edges repeated) between the node u and node v consists of exactly 1 special edge.

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