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)

$n,m=gets.split.map(&:to_i)
ab = []
m.times do
  ab.push gets.split.map(&:to_i)
end

def node(h, n)
  h.each do |k, v|
    return k if v.include?(n)
  end
  nil
end

def disconnected?(br)
  h = {}
  (1..$n).each do |i|
    h[i] = []
  end
  br.each do |b|
    src = b.first
    dst = b.last
    src_n = node(h, src)
    dst_n = node(h, dst)
    if h[src] && !h[src].empty?
      h[src] += [dst]
      h.delete(dst) if h[dst].empty?
    elsif h[dst] && !h[dst].empty?
      h[dst] += [src]
      h.delete(src) if h[src].empty?
    elsif src_n && dst_n
      if src_n != dst_n
        h[src_n] += ([dst] + [dst_n]).flatten
        h.delete(src)
        h.delete(dst)
        h.delete(dst_n)
      end
    elsif src_n
      h[src_n] += [dst]
      h.delete(src)
      h.delete(dst)
    elsif dst_n
      h[dst_n] += [src]
      h.delete(src)
    else
      h[src] += [dst]
      h.delete(dst)
    end
  end
  h.size == 1 ? false : true
end
count = 0
0.upto(m-1) do |i|
  b = ab.dup
  b.delete_at(i)
  count += 1 if disconnected?(b)
end
puts count