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)

typedef long long ll;
typedef pair<ll, ll> P;

const int MAX = 1e5 + 10;
const int INF = 1e9;
const int MOD = 1e9 + 7;

class edge{
    public:
        int to, from;
};

int N, M;
vector<int> G[MAX];
vector<edge> E;
bool vis[MAX];

void dfs(int n, edge e){
    vis[n] = true;
    for(int i : G[n]){
        if( (n == e.to && i == e.from) or (n == e.from && i == e.to) ){

        } else if(!vis[i]) {
            dfs(i, e);
        }
    }
}

int main(){
    cin >> N >> M;
    rep(i, M){
        int a, b;
        cin >> a >> b;
        a--, b--;
        edge e;
        e.from = a;
        e.to = b;
        E.push_back(e);
        G[a].push_back(b);
        G[b].push_back(a);
    }

    int ans = 0;
    rep(i, M){
        rep(j, N) vis[j] = false;
        dfs(0, E[i]);
        bool flg = true;
        rep(j, N){
            if(!vis[j]) flg = false;
        }
        if(!flg) ans++;
    }

    cout << ans << endl;
}