Walking in circles

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).


Input Specification


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)


Output Specification


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.


Constraints (and partial points)


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


Sample Input 1


9 6
1 2
2 3
2 4
5 6
5 7
8 9


Output for Sample Input 1


Stefan is in a forest with 3 trees


Sample Input 2


7 6
1 2
2 3
3 4
3 5
2 6
3 7


Output for Sample Input 2


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)


Sample Input 3


6 5
1 2
2 3
3 1
4 5
5 6


Output for Sample Input 3


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

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