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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;

namespace atcoder
{
    class Program
    {
        static void Main(string[] args)
        {
            var NM = Console.ReadLine().Split(' ');
            var N = int.Parse(NM[0]);
            var M = int.Parse(NM[1]);

            Dictionary<int, List<int>> dic = new Dictionary<int, List<int>>();
            for(int i = 0; i < M; i++)
            {
                var line = Console.ReadLine().Split(' ');
                int key = int.Parse(line[0]);
                int val = int.Parse(line[1]);
                if (dic.ContainsKey(key))
                {
                    dic[key].Add(val);
                }
                else
                {
                    dic.Add(key, new List<int>() { val });
                }
            }

            int count = 0;
            foreach(var d in dic)
            {
                if (d.Value.Count >= 2 && (dic.Where(p => p.Value.Contains(d.Key)).Count() > 0)) continue;
                foreach(var tgt in d.Value)
                {
                    // tgt より大きい値がValueにいない
                    bool c1 = (d.Value.Where(p => p > tgt).Count() > 0) ? true : false;

                    //  かつ tgtをValueに含み、Valueにも含むdicがない
                    bool c2 = ((dic.Where(p => p.Key != d.Key && d.Value.Contains(p.Key) && p.Value.Contains(tgt)).Count() > 0)
                                || (dic.Where(p => p.Key != d.Key && p.Value.Contains(d.Key) && p.Value.Contains(tgt)).Count() > 0) )? true : false;

                    if (!c1 && !c2)
                        count++;
                }
            }

            Console.WriteLine(count.ToString());

        }
    }
}