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 bfs(graph, start, rm)
  visited = {}
  count = 0
  queue = [start]
  until queue.empty? do
    p = queue.shift
    neighbors = graph[p]
    neighbors.each do |n|
      next if visited[n]
      next if (p == rm[0] && n == rm[1]) || (p == rm[1] && n == rm[0])
      visited[n] = true
      queue.push(n)
      count += 1
    end
  end
  count
end

@visited = {}
@count = 0
def dfs(graph, now, rm)
  @visited[now] = true
  @count += 1
  neighbors = graph[now]
  neighbors.each do |n|
    next if @visited[n]
    next if (now == rm[0] && n == rm[1]) || (now == rm[1] && n == rm[0])
    dfs(graph, n, rm)
  end
end

n, m = gets.strip.split.map(&:to_i)
graph = {}
(1..n).each do |i|
  graph[i] = []
end

edges = []
m.times do
  a, b = gets.strip.split.map(&:to_i)
  graph[a] << b
  graph[b] << a
  edges << [a, b]
end

num_bridges = 0
edges.each do |e|
  @visited = {}
  @count = 0
  dfs(graph, 1, e)
  #count = bfs(graph, 1, e)
  num_bridges += 1 if @count < n
end

puts num_bridges