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 C++14 (Clang 3.8.0) (judge verdict: Accepted)

#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;

vector<vector<int>> G;
vector<int> preorder;
vector<int> low;
using P = pair<int,int>;

void lowlink(int v,int prev, int &pre, vector<P>& ans){
  preorder[v]=pre;
  low[v]=pre;
  for(auto to:G[v]){
    if(preorder[to]==-1){
      lowlink(to,v,++pre,ans);
      if(low[to]==preorder[to]){
        ans.emplace_back(min(v,to),max(v,to));
      }
      low[v]=min(low[v],low[to]);
    }else if(to!=prev){
      low[v]=min(low[v],preorder[to]);
    }
  }
}

int main(){
  int V,E;
  cin>>V>>E;
  G.resize(V);
  preorder.resize(V,-1);
  low.resize(V);

  for(int i=0;i<E;i++){
    int s,t;
    cin>>s>>t;
    s--;t--;
    G[s].push_back(t);
    G[t].push_back(s);
  }
  int p=1;
  vector<P> ans;
  lowlink(0,-1,p,ans);
  cout<<ans.size()<<endl;
}