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)

s = gets.chomp.split(" ")
$n = s[0].to_i
$m = s[1].to_i
$list = Array.new($n).map{Array.new($n,false)}
$visited = Array.new($n,false)

for i in 0..$m-1 do
    s = gets.chomp.split(" ")
    a = s[0].to_i-1 
    b = s[1].to_i-1
    $list[a][b] = $list[b][a] = true
end

def check( i=0 )
    $visited[i] = true
    for j in 0..$n-1 do
        check(j) if $list[i][j] and $visited[j] == false
    end

    if $visited.count {|num| num == false } >= 1 then return false
    else return true end
end

count = 0
for i in 0..$n-1 do
    for j in 0..i do
        if $list[i][j] then
            $list[i][j] = $list[j][i] = false
            $visited.map!{false}
            count += 1 if check() == false
            $list[i][j] = $list[j][i] = true
        end
    end
end

puts count