100752: [AtCoder]ABC075 C - Bridge

Problem Statement

You are given an undirected connected graph with $N$ vertices and $M$ edges that does not contain self-loops and double edges.
The $i$-th edge $(1 \leq i \leq M)$ connects Vertex $a_i$ and Vertex $b_i$.

An edge whose removal disconnects the graph is called a bridge.
Find the number of the edges that are bridges among the $M$ edges.

Notes

• A self-loop is an edge $i$ such that $a_i=b_i$ $(1 \leq i \leq M)$.
• Double edges are a pair of edges $i,j$ such that $a_i=a_j$ and $b_i=b_j$ $(1 \leq i<j \leq M)$.
• An undirected graph is said to be connected when there exists a path between every pair of vertices.

Constraints

• $2 \leq N \leq 50$
• $N-1 \leq M \leq min(N(N−1)⁄2,50)$
• $1 \leq a_i<b_i \leq N$
• The given graph does not contain self-loops and double edges.
• The given graph is connected.

Input

Input is given from Standard Input in the following format:

$N$ $M$  
$a_1$ $b_1$  
$a_2$ $b_2$
$:$  
$a_M$ $b_M$

Output

Print the number of the edges that are bridges among the $M$ edges.

Sample Input 1

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

Sample Output 1

4

The figure below shows the given graph:

The edges shown in red are bridges. There are four of them.

Sample Input 2

3 3
1 2
1 3
2 3

Sample Output 2

0

It is possible that there is no bridge.

Sample Input 3

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

Sample Output 3

5

It is possible that every edge is a bridge.