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 debug(x) cout<<#x<<"="<<x<<endl
#define RD(x) freopen((x),"r",stdin)
#define WT(x) freopen((x),"w",stdout)
#define pii pair<int,int>
#define PQ priority_queue
#define ll long long
#define pb push_back
#define mp make_pair
const int INF=0x7fffffff;

int n,m,ans;
vector <int> g[53];
bool vis[53];
pii e[53];

bool check_union(){
	bool f=true;
	for (int i=1;i<=n;i++){
		f&=vis[i];
		vis[i]=0;
	}
	return !f;
}

void dfs(int x,int y){
	vis[x]=1;
	for (int i=0;i<g[x].size();i++){
		if (!vis[g[x][i]] && !((x==e[y].first && g[x][i]==e[y].second) || (x==e[y].second && g[x][i]==e[y].first))){
			dfs(g[x][i],y);
		}
	}
}

int main(){
	cin>>n>>m;
	for (int i=0;i<m;i++){
		cin>>e[i].first>>e[i].second;
		g[e[i].first].pb(e[i].second);
		g[e[i].second].pb(e[i].first);
	}
	for (int i=0;i<m;i++){
		dfs(1,i);
		ans+=check_union();
	}
	cout<<ans;
	return 0;
}