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=gets.to_i
$list = *0..$N
$rank = [].fill(0,0..$N)

def root(i)
  i == $list[i] ? i : $list[i] = root($list[i])
end

def unite(i,j)
  x = root(i)
  y = root(j)
  if x != y
    $list[x] = $list[y] = [x,y,x][$rank[x]<=>$rank[y]]
    $rank[x] += 1 if $rank[x] == $rank[y]
  end
end


ans=0
$a=  $<.map{|x|x.split.map &:to_i}
$N.times{|k|
  $list = *0..$N
  $rank = [].fill(0,0..$N)
  tmp=$a.pop
  $a.map{|x,y|unite(x,y)}
  $a.unshift(tmp)
  ans -= 1 - (1..$N).map{|x|root(x)}.minmax.uniq.size >> 31
}
p ans