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)

def dfs(edges, curr, visited = {})
  visited[curr] = true
  next_edges = edges[curr] || []
  next_edges.each do |node|
    next if visited[node]
    dfs(edges, node, visited)
  end
  visited
end

def bridge?(n, abs, i)
  edges = {}
  abs.each_with_index do |ab, j|
    next if j == i
    a, b = ab
    edges[a] ||= []
    edges[b] ||= []
    edges[a] << b
    edges[b] << a
  end
  visited = dfs(edges, abs[0][0])
  visited.keys.length < n
end

n, m = STDIN.gets.split(" ").map(&:to_i)

abs = []
m.times do
  a, b = STDIN.gets.split(" ").map(&:to_i)
  abs << [a, b]
end

ans = 0
for i in 0...m
  ans += 1 if bridge?(n, abs, i)
end
puts ans