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 Lua (Lua 5.3.5) (judge verdict: Accepted)

local n,m=io.read("n","n")
local a={}
local b={}
local visited={}
local graph={}
for i=1,n do
    graph[i]={}
    for j=1,n do
        graph[i][j]=false
    end
end

local function dfs(x)
    visited[x]=true
    for y=1,n do
        if graph[x][y]==false then
            goto continue
        end
        if visited[y]==true then
            goto continue
        end
        dfs(y)
        ::continue::
    end
end

for i=1,m do
    local x,y=io.read("n","n")
    a[i]=x
    b[i]=y
    graph[x][y]=true
    graph[y][x]=true
end

local counter=0
for i=1,m do
    graph[a[i]][b[i]]=false
    graph[b[i]][a[i]]=false
    for j=1,n do
        visited[j]=false
    end
    dfs(1)
    local bridge=false
    for j=1,n do
        if visited[j]==false then
            bridge=true
        end
    end
    if bridge==true then
        counter=counter+1
    end
    graph[a[i]][b[i]]=true
    graph[b[i]][a[i]]=true
end
print(counter)