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 (2.7.1) (judge verdict: Accepted)

N,M=gets.split.map(&:to_i)
E=Array.new(N+1){[]}
l=[]
M.times{
	a,b=gets.split.map(&:to_i)
	E[a] << b
	E[b] << a
	l << [a,b]
}
c=0
l.each{|e|
	s=e[0]
	f=Array.new(N+1){false}
	f[s]=true
	q=[]
	E[s].each{|x|
		next if x==e[1]
		q.push(x)
	}
	until q.empty?
		n=q.shift
		next if f[n]
		f[n]=true
		break if n==e[1]
		E[n].each{|x|
			next if f[x]
			q.push(x)
		}
	end
	#warn e.inspect
	#warn f.inspect
	if !f[e[1]]
		c+=1
	end
}
puts c