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)

class UnionFind
  attr_accessor(:table)

  def initialize(n)
    @table = Array.new(n, -1)
  end

  def root(x)
    st = []
    tb = @table
    while tb[x] >= 0
      st.push(x)
      x = tb[x]
    end
    
    st.each do |y|
      @table[y] = x
    end
    
    return x
  end
  
  def find(x, y)
    return root(x) == root(y)
  end

  def unite(x, y)
    r1 = root(x)
    r2 = root(y)
    return if r1 == r2
    
    d1 = @table[r1]
    d2 = @table[r2]
    if d1 <= d2
      @table[r2] = r1
      @table[r1] += d2
    else
      @table[r1] = r2
      @table[r2] += d1
    end
  end
end

n, m = $stdin.readline.chomp.split.map(&:to_i)
e = []

m.times do
  a, b = $stdin.readline.chomp.split.map(&:to_i)
  e << [a - 1, b - 1]
end

res = 0
m.times do |i|
  uf = UnionFind.new(n)
  m.times do |j|
    next if i == j
    uf.unite(*e[j])
  end
  res += 1 if uf.table.min != - n
end
puts res