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 reps(i,n) for(int i = 1; i <= n; i++)
#define rrep(i,n) for(int i = n-1; i >= 0; i--)
#define rreps(i,n) for(int i = n; i >= 1; i--)
#define mrep(i,from,n) for(int i = from; i < n; i++)
#define mreps(i,from,n) for(int i = from; i <= n; i++)
#define all(x) (x).begin(),(x).end()
#define sz(x) ((int)(x).size())
#define ERASE(x,val) x.erase(remove(ALL(x), val), x.end())
typedef long long ll;
typedef pair<ll, ll> P;
template<class T>inline bool chmax(T& a, T b) { if (a < b) { a = b; return true; }return false; }
template<class T>inline bool chmin(T& a, T b) { if (a > b) { a = b; return true; }return false; }
ll MOD = 1000000007;
int INF = 1001001001;

//Union-Find tree
struct UnionFind
{
	vector<int> par;
	vector<int> rank;

	UnionFind(int n) : par(n),rank(n)
	{
		for (int i = 0; i < n; i++)
		{
			par[i] = i;
			rank[i] = 0;
		}
	}
	int root(int x)
	{
		if (par[x] == x)
		{
			return x;
		}
		else
		{
			return par[x] = root(par[x]);
		}
	}
	void unite(int x, int y)
	{
		int rx = root(x);
		int ry = root(y);
		if (rx == ry)return;
		if (rank[rx] < rank[ry])
		{
			par[rx] = ry;
		}
		else
		{
			par[ry] = rx;
			if (rank[rx] == rank[ry])rank[rx]++;
		}
	}
	bool same(int x, int y)
	{
		return root(x) == root(y);
	}
};

void solve()
{
	int n, m; cin >> n >> m;
	vector<int> a(m), b(m);
	rep(i, m) cin >> a[i] >> b[i];
	int ans = 0;
	rep(i ,m)
	{
		UnionFind uf(n);
		rep(j, m)if(i != j)
		{
			uf.unite(a[j]-1,b[j]-1);
		}
		rep(j ,n)
		{
			bool ok = true;
			rep(k, n)if(!uf.same(0, k)) ok = false;
			if(!ok)
			{
				ans++;
				break;
			}
		}
	}	
	cout << ans << endl;
	return;
}

int main()
{
	cin.tie(0);
	ios::sync_with_stdio(false);
	cout << fixed << setprecision(15);
	solve();
	return 0;
}