Tree Subsets

You are given a multiset of $N + 1$ edges on $N$ vertices. Your task is to count the number of subsets of these $N + 1$ edges that form a tree. Obviously, all such subsets must have size $N - 1$. $2$ subsets are different if there exists some index $i$ such that the $i$-th edge is included in the first subset but not the second. ### Input - The first line of input will contain a single integer