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 (2.7.1) (judge verdict: Accepted)

require "set"
n,m = gets.chomp.split(" ").map(&:to_i)
ab_arr = m.times.map{gets.chomp.split(" ").map(&:to_i)}

hash = {}
edge = []
# 無向グラフを作成
ab_arr.each do |(a, b)|
  hash[a] ||= []
  hash[a] << b
  hash[b] ||= []
  hash[b] << a
  # 辺は小さい順に並べたほうが都合が良い(a == bはあり得ないので考慮しなくてOK)
  edge << [a, b] if a < b
  edge << [b, a] if b < a
end

count = 0
# 各辺を取り除いたときに, 全頂点がたどれるかを確認
edge.each do |(e_a, e_b)|
  bfs = [1]
  node_set = Set.new([1])
  edge_set = Set.new
  while bfs.length > 0 do
    a = bfs.shift
    hash[a].each do |b|
      # 小さい順に並べたほうが都合が良い
      in_a, in_b = a, b if a < b
      in_a, in_b = b, a if b < a
      # 通れない辺
      next if e_a == in_a && e_b == in_b
      # すでに通った辺
      next if edge_set.include?([in_a, in_b])
      bfs << b
      node_set << b
      edge_set << [in_a, in_b]
    end
  end
  # 全頂点通れないなら橋としてカウント
  count += 1 if node_set.length != n
end

puts count