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 System.Text;
using System.Threading.Tasks;

namespace AtCoder.Abc
{
    class QuestionD
    {
        public static void Main(string[] args)
        {
            var sw = new System.IO.StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);

            // 整数配列の入力
            var nm = Console.ReadLine().Split(' ').Select(i => long.Parse(i)).ToArray();

            var ab = new long[nm[1], 2];
            var nodes = new List<long>[nm[0]];

            for(int i = 0; i < nodes.Length; i++) {
                nodes[i] = new List<long>();
            }

            for (int i = 0; i < nm[1]; i++) {
                var d = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
                ab[i, 0] = d[0] - 1;
                ab[i, 1] = d[1] - 1;
                nodes[d[0] - 1].Add(d[1] - 1);
                nodes[d[1] - 1].Add(d[0] - 1);
            }
            var num = 0;
            for(int i = 0; i < nm[1]; i++) {
                if(DFS(nodes, nodes.Length, ab[i, 0], ab[i, 1])) {
                    num++;
                }
            }

            Console.WriteLine(nm[1] - num);

            Console.Out.Flush();
        }

        public static bool DFS(List<long>[] maps, int nodes, long removeA, long removeB)
        { 
            var reachMaps = new bool[nodes];
            DFSCore(0, maps, reachMaps, removeA, removeB);

            foreach(var isReached in reachMaps) {
                if(isReached == false) {
                    return false;
                }
            }

            return true;
        }

        public static void DFSCore(long nodeIndex, List<long>[] maps, bool[] reachMaps, long removeA, long removeB)
        {
            if(reachMaps[nodeIndex] == false) {
                reachMaps[nodeIndex] = true;
                foreach(var next in maps[nodeIndex]) {
                    if (nodeIndex == removeA && next == removeB) {
                        continue;
                    }
                    if (nodeIndex == removeB && next == removeA) {
                        continue;
                    }

                    DFSCore(next, maps, reachMaps, removeA, removeB);
                }
            }
        }
    }
}