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 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
//---------------------------
using namespace std;
//---------------------------
#define REP(i,n) for(int i = 0; i < (n); i++)
#define P(x) cout << (x) << "\n"

#define MOD 1e9+7
#define PI acos(-1.0)
#define ll long long
#define INF 1000000001

int dx[4]={1,-1,0,0};
int dy[4]={0,0,1,-1};
//---------------------------
bool edge[51][51];
bool visited[51];
int n,m;

void dfs(int v){
  visited[v]=true;
  REP(v2, n){
    if(edge[v][v2]==false)continue;
    if(visited[v2]==true)continue;
    dfs(v2);
  }
}

int main(){
  std::ios::sync_with_stdio(false);
  std::cin.tie(0);

  // ifstream in("input.txt");
  // cin.rdbuf(in.rdbuf());

  cin>>n>>m;
  int a[51],b[51];
  REP(i,m){
    cin>>a[i]>>b[i];
    a[i]--; b[i]--;
    edge[a[i]][b[i]]=true;
    edge[b[i]][a[i]]=true;
  }
  int ans=0;
  REP(i,m){
    edge[a[i]][b[i]]=false;
    edge[b[i]][a[i]]=false;

    REP(j,51)visited[j]=false;
    dfs(0);
    bool flag=false;
    REP(j,n)if(visited[j]==false)flag=true;
    if(flag)ans++;

    edge[a[i]][b[i]]=true;
    edge[b[i]][a[i]]=true;
  }
  P(ans);
  return 0;
}