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: Runtime Error)

#!/usr/bin/env ruby


require 'pry'



class MyNode
  attr_accessor :flag
  attr_reader :connections


  def initialize
    @connections = []
  end


  def connect(my_node)
    @connections << my_node
    @connections.uniq!
  end


  def disconnect(my_node)
    @connections.delete(my_node)
  end


  def propagate_flag
    @flag = true

    @connections.each do |my_node|
      if my_node.flag
        next
      else
        my_node.flag = true
        my_node.propagate_flag
      end
    end

    @connections
  end
end




class MyGraph
  def initialize
    @nodes = {}
    @edges = []
  end


  def add_edge(from, to)
    @nodes[from] ||= MyNode.new
    @nodes[to] ||= MyNode.new

    a = @nodes[from]
    b = @nodes[to]

    a.connect(b)
    b.connect(a)


    @edges << [a, b]
  end


  def bridges
    @edges.select{|a, b|
      # Remove edge information from nodes
      a.disconnect(b)
      b.disconnect(a)

      a.propagate_flag
      result = b.flag

      a.connect(b)
      b.connect(a)

      @nodes.each{|id, my_node| my_node.flag = false }

      ! result
    }
  end
end


N, M = gets.chomp.split(" ").map(&:to_i)

graph = MyGraph.new

M.times do
  a, b = gets.chomp.split(" ").map(&:to_i)

  graph.add_edge(a, b)
end

puts graph.bridges.size