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.Text;
using System.Linq;
using System.Collections;
using System.Collections.Generic;
using static System.Console;
using static System.Math;

namespace NotFounds
{
    public class Program
    {
        public static void Main(string[] args)
        {
            var sw = new System.IO.StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);
            new Program().Solve(new ConsoleInput(Console.In, ' '));
            Console.Out.Flush();
        }

        public void Solve(ConsoleInput cin)
        {
            var N = cin.ReadInt;
            var M = cin.ReadInt;

            var e = new List<Pair>();
            var g = new bool[N, N];
            for (int i = 0; i < M; ++i)
            {
                var a = cin.ReadInt - 1;
                var b = cin.ReadInt - 1;
                e.Add(new Pair(a, b));
                g[a, b] = g[b, a] = true;
            }

            Func<int> IsLink = () => {
                var visited = new bool[N];
                visited[0] = true;
                var q = new Queue<int>();
                q.Enqueue(0);
                while (q.Any())
                {
                    var now = q.Dequeue();
                    visited[now] = true;
                    for (int i = 0; i < N; ++i)
                    {
                        if (i == now) continue;
                        if (visited[i]) continue;
                        if (g[now, i]) q.Enqueue(i);
                    }
                }
                return visited.All(x => x) ? 0 : 1;
            };

            var cnt = 0;
            foreach (var edge in e)
            {
                g[edge.First, edge.Second] = false;
                g[edge.Second, edge.First] = false;
                if (IsLink() == 1)
                {
                    Error.WriteLine($"{edge.First + 1} {edge.Second + 1}");
                    cnt++;
                }
                g[edge.First, edge.Second] = true;
                g[edge.Second, edge.First] = true;
            }

            WriteLine(cnt);
        }
    }

    public class Pair
    {
        public int First { get; set; }
        public int Second { get; set; }
        public Pair(int f, int s) { First = f; Second = s; }
    }

    public class ConsoleInput
    {
        private readonly System.IO.TextReader _stream;
        private char _separator = ' ';
        private Queue<string> inputStream;
        public ConsoleInput(System.IO.TextReader stream, char separator = ' ')
        {
            this._separator = separator;
            this._stream = stream;
            inputStream = new Queue<string>();
        }
        public string Read
        {
            get
            {
                if (inputStream.Count != 0) return inputStream.Dequeue();
                string[] tmp = _stream.ReadLine().Split(_separator);
                for (int i = 0; i < tmp.Length; ++i)
                    inputStream.Enqueue(tmp[i]);
                return inputStream.Dequeue();
            }
        }
        public string ReadLine { get { return _stream.ReadLine(); }}
        public int ReadInt { get { return int.Parse(Read); }}
        public long ReadLong { get { return long.Parse(Read); }}
        public double ReadDouble { get { return double.Parse(Read); }}
        public string[] ReadStrArray(long N) { var ret = new string[N]; for (long i = 0; i < N; ++i) ret[i] = Read; return ret;}
        public int[] ReadIntArray(long N) { var ret = new int[N]; for (long i = 0; i < N; ++i) ret[i] = ReadInt; return ret;}
        public long[] ReadLongArray(long N) { var ret = new long[N]; for (long i = 0; i < N; ++i) ret[i] = ReadLong; return ret;}
        public void ReadIntArrays(long N, out int[] A, out int[] B) { A = new int[N]; B = new int[N]; for (long i = 0; i < N; ++i) { A[i] = ReadInt; B[i] = ReadInt; }}
        public void ReadLongArrays(long N, out long[] A, out long[] B) { A = new long[N]; B = new long[N]; for (long i = 0; i < N; ++i) { A[i] = ReadLong; B[i] = ReadLong; }}
    }
}