Problem:
Score : 300 points

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.

Solution in Ruby (2.3.3) (judge verdict: Accepted)

$n, $m = gets.chomp.split(' ').map(&:to_i)

$graph = {}
$path_list = []

$m.times do
  s, t = gets.chomp.split(' ').map(&:to_i)
  $path_list << [s, t]
  $graph[s] = [] unless $graph[s]
  $graph[s] << t

  $graph[t] = [] unless $graph[t]
  $graph[t] << s
end

def dfs(point, remove_path)
  stack = [point]

  until stack.empty?
    current_point = stack.pop
    next if $visited[current_point]

    $visited[current_point] = true

    $graph[current_point].each do |next_point|
      stack << next_point unless [[current_point, next_point], [next_point, current_point]].include?(remove_path)
    end
  end
end

res = 0
$path_list.each do |remove_path|
  $visited = {}
  count = 0
  $graph.keys.each do |point|
    next if $visited[point]
    dfs(point, remove_path)
    count += 1
    if count > 1
      res += 1
      break
    end
  end
end

puts res