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,j,n) for(int i=(j);i<(n);i++)
#define erep(i,j,n) for(int i=(j);i<=(n);i++)
#define all(i) i.begin(),i.end()
#define rall(i) i.rbegin(),i.rend()
#define INF 1e9
const int mod = 1e9+7;

typedef vector<int> vi;
typedef vector<string> vs;
typedef vector<vi> vvi;
typedef pair<int, int> pi;
typedef long long i64;

int n, m;
vi a;
vi b;

void dfs(int num, int p, vector<bool> &v) {
  if(v[p]) return;
  v[p] =true;

  rep(i, 0, m) {
    if(i == num) continue;
    
    if(a[i] == p) dfs(num, b[i], v);
    else if(b[i] == p) dfs(num, a[i], v);
  }
}

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

  cin >> n >> m;
  a.resize(m);
  b.resize(m);
  rep(i, 0, m) cin >> a[i] >> b[i];

  int ans = 0;
  rep(i, 0, m) {
    vector<bool> visited(n + 1, false);
    visited[0] = true;
    dfs(i, 1, visited);
    if(count(all(visited), false)) ans++;
  }
  cout << ans << endl;
}