You are given an undirected graph consisting of n vertices and m edges. It is guaranteed that the given graph is connected (i. e. it is possible to reach any vertex from any other vertex) and there are no self-loops ( ) (i.e. there is no edge between a node and itself, and no multiple edges in the graph (i.e. if there is an edge between vertices vi, and vj, then it is only one edge). Your task is to calculate the number of simple paths of length at least 2 in the given graph. Note that paths that differ only by their direction are considered the same (i. e. you have to calculate the number of undirected paths). For example, paths v1, v2, v3 and v3, v2, v1 are considered the same. Recall that a path in the graph is a sequence of vertices v1,v2,,vk such that each pair of adjacent (consecutive) vertices in this sequence is connected by an edge. The length of the path is the number of edges in it. A simple path is such a path that all vertices in it are distinct (e.g. the path v1, v2, v3, v4 is a simple path while the path v1, v2, v3, v2, v4 is not a simple path because v2 appears twice). The user inputs the number of vertices and the number of edges and then inputs edges in the form: i, j (i and j are positive integers <=n) to mean there is an edge between vertex i and vertex j.