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: Wrong Answer)

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

tree = Hash.new([])
m.times do
  a, b = gets.chomp.split.map(&:to_i)
  tree[a] += [b]
  tree[b] += [a]
end

cnt = 0
checked_sides = Set.new([])

if n-1 == m
  puts m
else
  n.times do |i|
    tree[i + 1].each do |node|
      next if checked_sides.include? [i + 1, node].sort
      checked_sides.add [i + 1, node].sort
      tree[i + 1].delete node
      tree[node].delete (i + 1)

      queue = [node]
      visited = Set.new([])
      until queue.empty? do
        now = queue.pop
        tree[now].each do |node2|
          next if visited.include? node2
          visited.add node2
          queue.push node2
        end
      end

      if visited.size != n
        cnt += 1
        p "i+1: #{i+1}, node: #{node}"
      end
      tree[i + 1].push node
      tree[node].push (i + 1)
    end
  end
  puts cnt
end