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: Accepted)

def root(a, x)
  a[x] < 0 ? x : a[x] = root(a, a[x])
end

def unite(a, x, y)
  x, y = root(a, x), root(a, y)
  if x != y
    x, y = y, x if a[y] < a[x]
    a[x] += a[y]
    a[y] = x
  end
end

def connected?(a)
  a.any?{|e| e == -N}
end

N, M = gets.split.map(&:to_i)
ABs = readlines.map{|l| l.split.map(&:to_i)}

ans = 0
ABs.each do |a, b|
  @p = Array.new(N + 1, -1)
  (ABs - [[a, b]]).each{|c, d| unite(@p, c, d)}
  ans += 1 unless connected?(@p)
end
puts ans