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Micro and Permutations

Problem

Editorial

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Micro is having a graph having $$N$$ vertices numbered from $$1$$ to $$N$$ and $$M$$ edges. All the edges are bidirectional. Micro wants to find out the number of lucky permutations in the graph.

A permutation of the vertices $$[v_1, v_2, v_3,...., v_n ]$$ is called lucky permutation, if for every vertex $$v_i $$, where $$1 \le i \le N-1$$, there is an edge between $$v_i$$ and $$v_{i+1}$$.
Help Micro find out the number of lucky permutations in the graph.

**Input:**

First line consists of two space separated integers denoting $$N$$ and $$M$$.

$$M$$ lines follow each consisting of two space separated integers $$X$$ and $$Y$$ denoting there is an edge between vertices numbered $$X$$ and $$Y$$.

**Output:**

Print the number of lucky permutations in the graph.

**Constraints:**

$$1 \le N \le 10$$

$$1 \le M \le 100$$

$$1 \le X, Y \le N$$

Explanation

The two possible lucky permutations are 1-2-3 and 3-2-1.

Time Limit:
5.0 sec(s)
for each input file.

Memory Limit:
256 MB

Source Limit:
1024 KB

Marking Scheme:
Marks are awarded when all the testcases pass.

Allowed Languages:
C,
C++,
C++14,
Clojure,
C#,
D,
Erlang,
F#,
Go,
Groovy,
Haskell,
Java,
Java 8,
JavaScript(Rhino),
JavaScript(Node.js),
Julia,
Lisp,
Lisp (SBCL),
Lua,
Objective-C,
OCaml,
Octave,
Pascal,
Perl,
PHP,
Python,
Python 3,
R(RScript),
Racket,
Ruby,
Rust,
Scala,
Swift,
Visual Basic,
Kotlin

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