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 (LuaJIT 2.1.0) (judge verdict: Accepted)

local par={}
local rank={}
local size={}

local function init(n)
    for i=1,n do
        par[i]=i
        rank[i]=1
        size[i]=1
    end
end

local function root(x)
    return par[x]==x and x or root(par[x])
end

local function same(x,y)
    return root(x)==root(y)
end

local function unite(x,y)
    x=root(x)
    y=root(y)
    if x==y then
        return
    end
    if rank[x]>rank[y] then
        par[x]=y
        size[y]=size[y]+size[x]
    else
        par[x]=y
        size[y]=size[y]+size[x]
        if rank[x]==rank[y] then
            rank[y]=rank[y]+1
        end
    end
end

local function getsize(x)
    return size[root(x)]
end

----------

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

local counter=0
for i=1,m do
    init(n)
    for j=1,m do
        if i~=j then
            unite(a[j],b[j])
        end
    end
    if not same(a[i],b[i]) then
        counter=counter+1
    end
end
print(counter)