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;

namespace ABC075C
{
    class Program
    {
        static int INFTY = 0x30000000;

        static void Main(string[] args)
        {
            string[] bufs = Console.ReadLine().Split(' ');
            int N = int.Parse(bufs[0]);
            int M = int.Parse(bufs[1]);

            int[] a = new int[M];
            int[] b = new int[M];

            int[,] cost = new int[N, N];

            for (int i = 0; i < M; i++)
            {
                bufs = Console.ReadLine().Split(' ');
                a[i] = int.Parse(bufs[0]) - 1;
                b[i] = int.Parse(bufs[1]) - 1;
            }

            // END Initialize

            int res = 0;

            for (int cut = 0; cut < M; cut++)
            {
                // Cost Reset
                for (int i = 0; i < N; i++)
                {
                    cost[i, i] = 0;
                    for (int j = i + 1; j < N; j++)
                    {
                        cost[i, j] = cost[j, i] = INFTY;
                    }
                }

                for (int m = 0; m < M; m++)
                {
                    if(m != cut)
                    {
                        cost[a[m], b[m]] = cost[b[m], a[m]] = 1;
                    }
                }
                // END Cost Reset

                // WF Method
                for (int k = 0; k < N; ++k)
                {
                    for (int i = 0; i < N; ++i)
                    {
                        for (int j = 0; j < N; ++j)
                        {
                            int wc = cost[i, k] + cost[k, j];
                            if (wc < cost[i, j])
                            {
                                cost[i, j] = wc;
                            }
                        }
                    }
                }

                // Check
                bool disconnected = false;

                for (int i = 0; i < N; i++)
                {
                    for (int j = i + 1; j < N; j++)
                    {
                        if (cost[i, j] >= INFTY)
                        {
                            disconnected = true;
                        }
                    }
                }

                if (disconnected)
                {
                    res++;
                }

            }


            Console.WriteLine(res);
        }
    }
}