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)

def dfs( graph, u, visited )
	if visited[u] then
		return 0
	end

	visited[u] = true

	res = 1
	graph[u].each do |v|
		res += dfs( graph, v, visited )
	end

	return res
end

def solve( n, es, rem )
	m = es.size

	graph = Array.new( n ) do
		Array.new
	end


	m.times do |i|
		if i == rem then
			next
		end

		u, v = es[i]
		graph[u] << v
		graph[v] << u
	end


	visited = Array.new( N )
	return dfs( graph, 0, visited ) == N ? 0 : 1
end

N, M = gets.split.map( &:to_i )
E = Array.new( M ) do
	gets.split.map( &:to_i ).map( &:pred )
end

res = 0
M.times do |i|
	res += solve( N, E.dup, i )
end

puts res