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 all(v) (v).begin(),(v).end()
#define chmin(x,y) x = min(x,y)
typedef pair<int, int> P;
typedef long long ll;
const int INF = 1001001001;
const ll LINF = 1001002003004005006ll;
const ll MOD = 1e9+7;

const int MAXN = 50;
int N, M;
vector<int> a(MAXN), b(MAXN);
vector<vector<bool>> graph(MAXN, vector<bool>(MAXN));
vector<bool> visited(MAXN);

void dfs(int v) {
    visited[v] = true;
    rep(v2, N) {
        if (graph[v][v2] == false) continue;
        if (visited[v2] == true) continue;
        dfs(v2);
    }
}

int main() {
	cin >> N >> M;
    rep(i, M) {
        cin >> a[i] >> b[i];
        a[i]--, b[i]--;
        graph[a[i]][b[i]] = graph[b[i]][a[i]] = true;
    }

    int ans = 0;

    rep(i, M) {
        graph[a[i]][b[i]] = graph[b[i]][a[i]] = false;
        rep(j, N) visited[j] = false;
        dfs(0);
        bool bridge = false;
        rep(j, N) if(visited[j] == false) bridge = true;
        if(bridge) ans++;
        graph[a[i]][b[i]] = graph[b[i]][a[i]] = true;
    }

	cout << ans << endl;
	return 0;
}