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# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;

class ABC075C
{
	static bool[,] connected;
	static bool[] check;
	static int N, M;
	static public void Main(string[] args)
	{
		string[] vals = Console.ReadLine().Split(' ');
		N = int.Parse(vals[0]);
		M = int.Parse(vals[1]);
		int[] a = new int[M+1];
		int[] b = new int[M+1];
		connected = new bool[N+1, N+1];
		for(int i=1; i<=M; i++)
		{
			vals = Console.ReadLine().Split(' ');
			a[i] = int.Parse(vals[0]);
			b[i] = int.Parse(vals[1]);
			connected[a[i],b[i]] = true;
			connected[b[i],a[i]] = true;
		}

		int ans = 0;
		for(int i=1; i<=M; i++)
		{
			connected[a[i],b[i]] = false;
			connected[b[i],a[i]] = false;
			if(!isConnected())
				ans++;
			connected[a[i],b[i]] = true;
			connected[b[i],a[i]] = true;
		}
		Console.WriteLine(ans);
		
	}

	static bool isConnected()
	{
		check = new bool[N+1];
		dfs(1);
		bool ret = true;
		for(int i=1; i<=N; i++)
		{
			if(check[i] == false)
			{
				ret = false;
				break;
			}
		}
		return ret;
	}

	static void dfs(int n)
	{
		check[n] = true;
		for(int m = 1; m<=N; m++)
		{
			if(connected[n,m] && check[m] == false)
			{
				dfs(m);
			}
		}
	}
}