As the only *Oni* (a kind of fabulous creature with incredible strength and power) living on the surface of *Gensokyo*, *Ibuki Suika* always wears a powerful and mysterious chain. The chain is a symbolization of *Oni*.

Not surprisingly, *Suika's* chain looks very different from her friends' chains. There are three small magical artifacts hanging on the chain:

- The ball. It means "vacuos", or "diffusion", "sparseness".
- The tetrahedron. It means "ordo", or "collection", "denseness".
- The block. It means "aeternus", or "ego".

One day, you have discovered an ancient tome recording the history of *Gensokyo*. On the 725th page of the tome, you were attracted by a stange graph consists of `N` points and `M` edges. Each edge connects two points. After a short time of reasearch, you have realized that the graph may represents the chain of *Suika*.

An ordinary chain is a graph consists of a sequential of (at least two) points. Each two adjacent points are connected by an edge. *Suika's* chain looks slightly different. There are three sub-chains extended from the main chain from three different points. At the end of each sub-chain, there is a simple cycle with length 3, 4 or 5, represents the tetrahedron, the block and the ball respectively. There must be no other points or edges in the graph of *Suika's* chain.

Checking the graph manually seems to be an inefficient method. So you decide to write a small program to judge whether the graph represents the chain of *Suika* or not.

There are multiple test cases. For each test case:

The first line contains two integers `N` (1 <= `N` <= 50) and `M` indicating the number of points and edges in the graph.

Then followed by M lines, each line contains two integers `X _{i}` and

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