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 Yorukatsu018.Questions;
using Yorukatsu018.Extensions;
using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Text;

namespace Yorukatsu018.Questions
{
    public class QuestionD : AtCoderQuestionBase
    {
        int n;
        int m;
        List<int?>[] nodes;

        public override IEnumerable<object> Solve(TextReader inputStream)
        {
            var nm = inputStream.ReadIntArray();
            n = nm[0];
            m = nm[1];

            nodes = Enumerable.Range(0, n).Select(_ => new List<int?>()).ToArray();
            var inputs = new int[m][];

            for (int i = 0; i < m; i++)
            {
                var ab = inputStream.ReadIntArray().Select(x => x - 1).ToArray();
                inputs[i] = ab;
                var a = ab[0];
                var b = ab[1];
                nodes[a].Add(b);
                nodes[b].Add(a);
            }

            var bridgesCount = 0;
            foreach (var input in inputs)
            {
                var a = input[0];
                var b = input[1];

                var indexA = nodes[a].IndexOf(b);
                var indexB = nodes[b].IndexOf(a);
                nodes[a][indexA] = null;
                nodes[b][indexB] = null;
                if (!GraphIsConnected())
                {
                    bridgesCount++;
                }
                nodes[a][indexA] = b;
                nodes[b][indexB] = a;
            }

            yield return bridgesCount;
        }

        private bool GraphIsConnected()
        {
            var seen = new bool[n];
            seen[0] = true;
            var todo = new Queue<int>();
            todo.Enqueue(0);

            while (todo.Any())
            {
                var current = todo.Dequeue();
                foreach (var nextNode in nodes[current].Where(i => i.HasValue && !seen[i.Value]).Select(i => i.Value))
                {
                    seen[nextNode] = true;
                    todo.Enqueue(nextNode);
                }
            }

            return seen.All(b => b);
        }
    }
}


namespace Yorukatsu018
{
    class Program
    {
        static void Main(string[] args)
        {
            IAtCoderQuestion question = new QuestionD();    // 問題に合わせて書き換え
            var answers = question.Solve(Console.In);
            foreach (var answer in answers)
            {
                Console.WriteLine(answer);
            }
        }
    }
}

#region Base Classes

namespace Yorukatsu018.Questions
{

    public interface IAtCoderQuestion
    {
        IEnumerable<object> Solve(string input);
        IEnumerable<object> Solve(TextReader inputStream);
    }

    public abstract class AtCoderQuestionBase : IAtCoderQuestion
    {
        public IEnumerable<object> Solve(string input)
        {
            var stream = new MemoryStream(Encoding.Unicode.GetBytes(input));
            var reader = new StreamReader(stream, Encoding.Unicode);

            return Solve(reader);
        }

        public abstract IEnumerable<object> Solve(TextReader inputStream);
    }

}

#endregion

#region Extensions

namespace Yorukatsu018.Extensions
{
    internal static class TextReaderExtensions
    {
        internal static int ReadInt(this TextReader reader) => int.Parse(ReadString(reader));
        internal static long ReadLong(this TextReader reader) => long.Parse(ReadString(reader));
        internal static double ReadDouble(this TextReader reader) => double.Parse(ReadString(reader));
        internal static string ReadString(this TextReader reader) => reader.ReadLine();

        internal static int[] ReadIntArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(int.Parse).ToArray();
        internal static long[] ReadLongArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(long.Parse).ToArray();
        internal static double[] ReadDoubleArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(double.Parse).ToArray();
        internal static string[] ReadStringArray(this TextReader reader, char separator = ' ') => reader.ReadLine().Split(separator);
    }
}

#endregion