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 static System.Convert;
using static System.Math;
//using static System.Globalization.CultureInfo;

class Program
{
    struct P
    {
        public int index;
        public List<int> ad;
        public P(int index)
        {
            this.index = index;
            ad = new List<int>();
        }
    }
    static void Main(string[] args)
    {
        var nm = Array.ConvertAll(ReadLine().Split(' '), int.Parse);
        var ab = new int[nm[1]][];
        for (var i = 0; i < nm[1]; i++)
            ab[i] = Array.ConvertAll(ReadLine().Split(' '), int.Parse);
        var res = 0;
        for (var i = 0; i < nm[1]; i++)
        {
            var ps = new P[nm[0]];
            for (var j = 0; j < nm[0]; j++)
                ps[j] = new P(j);
            for(var j = 0; j < nm[1]; j++)
            {
                if (i == j) continue;
                ps[ab[j][0] - 1].ad.Add(ab[j][1] - 1);
                ps[ab[j][1] - 1].ad.Add(ab[j][0] - 1);
            }
            var set = new HashSet<int>();
            dfs(set, ps, 0);
            if (set.Count != nm[0]) res++;
        }
        WriteLine(res);
    }
    private static void dfs(HashSet<int> set,P[] ps,int index)
    {
        set.Add(index);
        foreach (var ad in ps[index].ad)
            if (!set.Contains(ad))
                dfs(set, ps, ad);
        
    }
    private const string ALFA = "abcdefghijklmnopqrstuvwxyz";
    private const int MOD = 1000000007;
}