Cactus or not

A cactus is an undirected graph in which every vertex lies on at most one simple cycle. A simple cycle is a closed walk that returns to the vertex it started from without visiting any vertex twice.

If two cycles share a vertex, that vertex lies on two simple cycles, so the graph is not a cactus. Two triangles that meet at a single vertex already fail the condition.

You are given a connected graph. Decide whether it is a cactus.

The first line contains two integers $N$ and $M$, the number of vertices and the number of edges, separated by a space. ($1 \le N, M \le 100\,000$)

Each of the next $M$ lines contains two integers $x$ and $y$, the endpoints of one edge, separated by a space. ($1 \le x, y \le N$, $x \ne y$)

No edge is given twice, and a path exists between every pair of vertices.

Print Cactus if the given graph is a cactus, and Not cactus otherwise.