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)

N, M = gets.split(' ').map(&:to_i)
require 'pp'
def debug obj
  PP.pp obj, STDERR
end

debug [N,M]
@nodes = {} # key node番号, value keyのnodeから生えてるedgeの向き先配列
@result = 0
@visits = {}
@ords = []
@lows = []
@step = 0

M.times do
  a, b = gets.split(' ').map(&:to_i)
  @nodes[a] ||= []
  @nodes[b] ||= []
  @nodes[a].push(b)
  @nodes[b].push(a) 
end

def dfs node,parent=-1
debug @lows
  @visits[node] = true
  @ords[node] = @step
  @lows[node] = @step
  @nodes[node].each do |target|
    if target == parent
      next
    end
    if @visits[target]
      if @ords[target] < @lows[node]
        @lows[node] = @ords[target]
      end
    else
      @step += 1
      dfs(target, node)
      if @lows[target] < @lows[node]
        @lows[node] = @lows[target]
      end
      if @ords[node] < @lows[target]
        @result += 1
      end
    end
  end
end

dfs(1)
debug @nodes
debug @ords
debug @lows
puts @result