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# Cyclic Components

2000ms 262144K

## Description:

You are given an undirected graph consisting of $n$ vertices and $m$ edges. Your task is to find the number of connected components which are cycles.

Here are some definitions of graph theory.

An undirected graph consists of two sets: set of nodes (called vertices) and set of edges. Each edge connects a pair of vertices. All edges are bidirectional (i.e. if a vertex $a$ is connected with a vertex $b$, a vertex $b$ is also connected with a vertex $a$). An edge can't connect vertex with itself, there is at most one edge between a pair of vertices.

Two vertices $u$ and $v$ belong to the same connected component if and only if there is at least one path along edges connecting $u$ and $v$.

A connected component is a cycle if and only if its vertices can be reordered in such a way that:

• the first vertex is connected with the second vertex by an edge,
• the second vertex is connected with the third vertex by an edge,
• ...
• the last vertex is connected with the first vertex by an edge,
• all the described edges of a cycle are distinct.

A cycle doesn't contain any other edges except described above. By definition any cycle contains three or more vertices.

There are $6$ connected components, $2$ of them are cycles: $[7, 10, 16]$ and $[5, 11, 9, 15]$.

## Input:

The first line contains two integer numbers $n$ and $m$ ($1 \le n \le 2 \cdot 10^5$, $0 \le m \le 2 \cdot 10^5$) — number of vertices and edges.

The following $m$ lines contains edges: edge $i$ is given as a pair of vertices $v_i$, $u_i$ ($1 \le v_i, u_i \le n$, $u_i \ne v_i$). There is no multiple edges in the given graph, i.e. for each pair ($v_i, u_i$) there no other pairs ($v_i, u_i$) and ($u_i, v_i$) in the list of edges.

## Output:

Print one integer — the number of connected components which are also cycles.

## Sample Input:

5 41 23 45 43 5

## Sample Output:

1

## Sample Input:

17 151 81 125 1111 99 1515 54 133 134 310 167 1016 714 314 417 6

## Sample Output:

2

## Note:

In the first example only component $[3, 4, 5]$ is also a cycle.

The illustration above corresponds to the second example.

Info

Provider CodeForces

Code CF977E

Tags

dfs and similardsugraphs

Submitted 33

Passed 22

AC Rate 66.67%

Date 03/04/2019 16:23:58

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