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;
using System.Collections.Generic;
using System.Linq;
using static System.Console;
using System.Runtime.CompilerServices;
using static MyUtil;

class MyUtil
{
    public static int[] ReadIntArray()
    {
	return ReadLine().Split().Select(x => int.Parse(x)).ToArray();
    }
}

class Program
{
    static bool[,] edges;
    static bool[] visited;
    static int n;

    static void dfs(int x)
    {
	visited[x] = true;
	for (int i = 0; i < n; i++)
	{
	    if((!visited[i]) && edges[x, i])
	    {
		dfs(i);
	    }
	}
    }
    
    public static void Main()
    {
	var tmp = ReadIntArray();
	n = tmp[0]; int m = tmp[1];

	edges = new bool[n, n];
	int[] a = new int[m];
	int[] b = new int[m];

	for (int i = 0; i < m; i++)
	{
	    tmp = ReadIntArray();
	    a[i] = tmp[0] - 1;
	    b[i] = tmp[1] - 1;
	    edges[a[i], b[i]] = true;
	    edges[b[i], a[i]] = true;
	}
	
	visited = new bool[n];

	int ans = 0;
	for (int i = 0; i < m; i++)
	{
	    edges[a[i], b[i]] = false;
	    edges[b[i], a[i]] = false;

	    for (int j = 0; j < n; j++){ visited[j] = false; }

	    dfs(0);

	    for (int j = 0; j < n; j++)
	    {
		if (!visited[j])
		{
		    ans++;
		    break;
		}
	    }
		
	    edges[a[i], b[i]] = true;
	    edges[b[i], a[i]] = true;
	}

	WriteLine(ans);
    }
}