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)

class Array
    def graphify(node)
        out = Array.new(node){Array.new(node,false)}
        self.each do |i,j|
            out[i-1][j-1]=true
            out[j-1][i-1]=true
        end
        return out
    end
end

def dfs(node)
    return if @visited[node]
    @visited[node]=true
    @graph[node].each_with_index do |e,i|
        dfs(i) if e
    end
    return
end

N,M = gets.split.map &:to_i
as = M.times.map{gets.split.map(&:to_i)}
ORIGEN=as.graphify(N)
cnt=0
as.each do |i,j|
    @graph=Marshal.load(Marshal.dump(ORIGEN))
    @graph[i-1][j-1]=false
    @graph[j-1][i-1]=false
    @visited=Array.new(N,false)
    dfs(0)
    cnt+=1 if !@visited.all?
end
puts cnt