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;

class Program
{
    static string InputPattern = "InputX";

    static List<string> GetInputList()
    {
        var WillReturn = new List<string>();

        if (InputPattern == "Input1") {
            WillReturn.Add("7 7");
            WillReturn.Add("1 3");
            WillReturn.Add("2 7");
            WillReturn.Add("3 4");
            WillReturn.Add("4 5");
            WillReturn.Add("4 6");
            WillReturn.Add("5 6");
            WillReturn.Add("6 7");
            //4
        }
        else if (InputPattern == "Input2") {
            WillReturn.Add("3 3");
            WillReturn.Add("1 2");
            WillReturn.Add("1 3");
            WillReturn.Add("2 3");
            //0
        }
        else if (InputPattern == "Input3") {
            WillReturn.Add("6 5");
            WillReturn.Add("1 2");
            WillReturn.Add("2 3");
            WillReturn.Add("3 4");
            WillReturn.Add("4 5");
            WillReturn.Add("5 6");
            //5
        }
        else {
            string wkStr;
            while ((wkStr = Console.ReadLine()) != null) WillReturn.Add(wkStr);
        }
        return WillReturn;
    }

    struct EdgeInfo
    {
        internal int A;
        internal int B;
    }

    static int N;
    static List<EdgeInfo> mEdgeList = new List<EdgeInfo>();

    static void Main()
    {
        List<string> InputList = GetInputList();

        int[] wkArr = { };
        Action<string> SplitAct = pStr =>
            wkArr = pStr.Split(' ').Select(X => int.Parse(X)).ToArray();

        SplitAct(InputList[0]);
        N = wkArr[0];

        foreach (string EachStr in InputList.Skip(1)) {
            SplitAct(EachStr);
            EdgeInfo WillAdd;
            WillAdd.A = wkArr[0];
            WillAdd.B = wkArr[1];
            mEdgeList.Add(WillAdd);
        }
        int HashiCnt = 0;
        for (int I = 0; I <= mEdgeList.Count - 1; I++) {
            if (IsHashi(I)) HashiCnt++;
        }
        Console.WriteLine(HashiCnt);
    }

    struct JyoutaiDef
    {
        internal int CurrPos;
    }

    //辺の添字を指定して、橋かを判定
    static bool IsHashi(int pSoeji)
    {
        var Stk = new Stack<JyoutaiDef>();
        JyoutaiDef WillPush;
        WillPush.CurrPos = 1;

        var VisitedSet = new HashSet<int>();
        VisitedSet.Add(1);
        Stk.Push(WillPush);

        while (Stk.Count > 0) {
            JyoutaiDef Popped = Stk.Pop();

            Action<int> PushSyori = pToInd =>
            {
                if (VisitedSet.Add(pToInd) == false) return;
                WillPush.CurrPos = pToInd;
                Stk.Push(WillPush);
            };

            for(int I=0;I<=mEdgeList.Count-1;I++){
                if (I == pSoeji) continue;
                EdgeInfo CurrEdge=mEdgeList[I];
                if (CurrEdge.A == Popped.CurrPos) PushSyori(CurrEdge.B);
                if (CurrEdge.B == Popped.CurrPos) PushSyori(CurrEdge.A);
            }
        }
        return VisitedSet.Count < N;
    }
}