Stefan loves exploring forests but he usually gets lost in them. This time, he went a little too deep into the forest and no longer knows if he is even in a forest still. Help Stefan find out how many trees there are in the forest, or tell him that he is not in a forest anymore and is walking in circles. (Just to clarify, a forest is a graph that is not necessarily connected and contains no cycles. In other words, it is a collection of trees).
The first line contains two integers: N (The number of nodes in the graph) and M (The number of edges in the graph).
The next M lines contain two integers: u, v indicating that there is an undirected edge connecting the nodes u and v (1 ≤ u, v ≤ N)
If the graph given is a forest, print
Stefan is in a forest with T trees
where T is the number of trees in the forest.
Otherwise, Stefan is walking in cycles, and you should print
middle of nowhere.
For all cases: 1 ≤ N, M ≤ 10^5
For batch 1 (30 points): 1 ≤ N ≤ 500
For batch 2 (10 points): Stefan is guaranteed to be in a forest
For batch 3 (60 points): No additional constraints
Stefan is in a forest with 3 trees
Stefan is in a forest with 1 trees
Explanation for Sample Case 2:
Stefan is in a forest with 1 tree (still considered a forest I guess)
Middle of nowhere
Explanation for Sample Case 3:
One of the components of the graph contains a cycle, so Stefan is no longer in a forest