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 ALL(v) v.begin(), v.end()
#define V vector
#define P pair
typedef long long ll;
const int INT_INF = 1e9;
const ll INF = 1LL << 30;
const ll MOD = 1e9 + 7;

using Graph = vector<vector<int>>;
vector<bool> seen;
void dfs(const Graph &g, int v, P<int, int> &p){
    seen[v] = true;
    for(auto next_v : g[v]){
        if(seen[next_v]) continue;
        if(p.first == v && p.second == next_v) continue;
        if(p.second == v && p.first == next_v) continue;
        dfs(g, next_v, p);
    }
}

int main() {
    int n, m; cin >> n >> m;
    Graph g(n);
    V<P<int, int> > p(m);
    for(int i = 0; i < m; i++){
        int a, b; cin >> a >> b;
        a--, b--;
        g[a].push_back(b);
        g[b].push_back(a);
        p[i] = make_pair(a, b);
    }

    int ans = 0;
    seen.assign(n, false);
    for(int i = 0; i < m; i++){
        dfs(g, 0, p[i]);

        bool flag = false;
        for(int i = 0; i < n; i++){
            if(seen[i]) continue;
            flag = true;
            break;
        }
        if(flag) ans++;
        seen.assign(n, false);
    }

    cout << ans << endl;
}