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 Julia (0.5.0) (judge verdict: Accepted)

parseInt(x) = parse(Int, x)
parseBigInt(x) = parse(BigInt, x)
parseFloat(x) = parse(Float64, x)
parseBigFloat(x) = parse(BigFloat, x)
parseMap(x::Array{SubString{String},1}) = map(parseInt, x)

function root(par::Vector{Int},x::Int)
    index=par[x]
    while par[index]!=index
        index=par[index]
    end
    return index
end

function unite(par::Vector{Int},x::Int,y::Int)
    rx,ry=root(par,x),root(par,y)
    if rx==ry
        return
    elseif rx>ry
        rx,ry=ry,rx
    end
    par[ry]=rx
end

function same(par::Vector{Int},x::Int,y::Int)
    return root(par,x)==root(par,y)
end

function main()
    n,m=parseMap(split(readline()))
    data=[parseMap(split(readline())) for i in 1:m]
    ans=0
    # 取り除く辺を全探索してUnion-Findを構築
    for ng in 1:m
        par=[i for i in 1:n]
        for i in 1:m
            if i==ng
                continue
            end
            unite(par,data[i][1],data[i][2])
        end
        renketsu=true
        r=root(par,1)
        for i in 2:n
            if root(par,i)!=r
                renketsu=false
                break
            end
        end
        if !renketsu
            ans+=1
        end
    end
    println(ans)
end
main()