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 Julia (0.5.0) (judge verdict: Accepted)

function find(parent,u)
	if u==parent[u]
		u
	else
		parent[u]=find(parent,parent[u])
	end
end
function check(E,N)
	parent=collect(1:N)
	size=ones(Int,N)
	for (u,v)=E
		u=find(parent,u)
		v=find(parent,v)
		if u!=v
			if size[u]<size[v]
				parent[u]=v
				size[v]+=size[u]
			else
				parent[v]=u
				size[u]+=size[v]
			end
		end
	end
	length(unique(find(parent,i) for i=1:N))==1
end
function main()
	lines=readlines()
	N,M=map(x->parse(Int,x),split(shift!(lines)))
	E=Pair{Int,Int}[]
	for s=lines
		x,y=map(x->parse(Int,x),split(s))
		push!(E,x=>y)
	end
	cnt=0
	for i=1:M
		F=Pair{Int,Int}[]
		for j=1:i-1
			push!(F,E[j])
		end
		for j=i+1:M
			push!(F,E[j])
		end
		if !check(F,N)
			cnt+=1
		end
	end
	println(cnt)
end
main()