Given a forest of trees containing \(N\) nodes and \(M\) bidirectional edges, output the number of paths in the forest of trees. A path is defined as a sequence of nodes which are connected by edges in the forest of trees, and the sequence contains at least one node. A path is different from another path if the starting or ending nodes differ. For example, a path from \(a\) to \(b\) is different from a path from \(b\) to \(a\).
The first line will contain \(2\) integers, \(N, M\ (1 \le N \le 10^6, 0 \le M < N)\), the number of nodes and the number of edges respectively.
The next \(M\) lines will each contain \(2\) integers, \(a, b\ (1 \le a \le b \le N)\), indicating that node \(a\) and node \(b\) are connected by a single edge. It is guaranteed that there will be no cycles in the forest of trees.
Output one integer, the number of paths in the forest of trees.
Sample Input 1
5 2 1 3 2 3
Sample Output 1
Sample Input 2
Sample Output 2