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)

n,m = gets.chomp.split(" ").map(&:to_i)
edge = m.times.map{gets.chomp.split(" ").map(&:to_i)}
mtr = Array.new(n).map{Array.new(n,2)}
count = 0
n.times do |i|
  mtr[i][i] = 0
end
for i in 0..m-1
  mtr[edge[i][0]-1][edge[i][1]-1] = 1
  mtr[edge[i][1]-1][edge[i][0]-1] = 1
end
cpmtr = []
for i in 0..m-1
  cpmtr = Marshal.load(Marshal.dump(mtr))
  cpmtr[edge[i][0]-1][edge[i][1]-1] = n
  cpmtr[edge[i][1]-1][edge[i][0]-1] = n
  list = [0]
  s = 0
  while s != list.size
    for j in s..list.size-1
      s = list.size
      for k in 0..n-1
        if cpmtr[list[j]][k] == 1 && !(list.include?(k))
          list << k
        end
      end
    end
  end
  if list.size != n
    count += 1
  end
end
puts count