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)

require 'set'
N, M = gets.split.map(&:to_i)
E = $<.map{|ab| ab.split.map(&:to_i) }

Tr = Hash.new{|h,k| h[k]=[] }
E.each{|a,b|
	Tr[a] << b
	Tr[b] << a
}

Cycle = (CycleDetector = lambda{|vs|
	ret = []
	Tr[vs[-1]].each{|b|
		pb = vs.index(b)
		if pb.nil?
			vs << b
			ret.concat CycleDetector[vs]
			vs.pop
		elsif vs.length - pb <= 2
		else
			ret << Set[*vs[pb,vs.length-pb]]
		end
	}
	return ret
}).call [1]

V = Cycle + (1..N).map{|v| Set[v] }
i = -1
until (i+=1) == V.length
	j = V.length
	until (j-=1) == i
		V[i].merge(V.delete_at(j)) if V[i].intersect?(V[j])
	end
end
br, nbr = E.partition{|ab|
	i, j = ab.map{|c| V.index{|v| v.include? c } }.sort
	V[i].merge V.delete_at j if i != j
	next i != j
}
p br.size