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.split.map(&:to_i)

$visited = Array.new(n+1,false)
$graph = Array.new(n+1){Array.new(n+1, false)}


edge = []

0.upto(m-1) do |i|
  edge[i] = gets.split.map(&:to_i)
end

#隣接行列
0.upto(m-1) do |i|
  $graph[edge[i][0]][edge[i][1]] = $graph[edge[i][1]][edge[i][0]] = true
end


#深さ優先探索
def dfs(v)
  $visited[v] = true
  $graph[v].each_with_index do |b, i|
    dfs(i)  if !$visited[i] & b && i!= 0
  end
  return
end

ans = 0

0.upto(m-1) do |i|
  $visited = Array.new(n+1,false)
  $visited[0] = true
  $graph[edge[i][0]][edge[i][1]] = $graph[edge[i][1]][edge[i][0]] = false
  dfs(1)
  if $visited.include?(false)
    ans += 1
  end
  $graph[edge[i][0]][edge[i][1]] = $graph[edge[i][1]][edge[i][0]] = true
end

puts ans