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.Linq;
using System.Collections.Generic;
using static System.Console;
using System.Text;
using System.IO;
using static System.Math;
namespace AtCoder
{
    class Program
    {
        static public long[] Sarray() { return ReadLine().Split().Select(long.Parse).ToArray(); }
        static public List<long> Slist() { return ReadLine().Split().Select(long.Parse).ToList(); }
        static long Mod = (long)1e9 + 7;
        static void Main(string[] args)
        {
            //SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
            var NM = Sarray();
            var N = NM[0];
            var M = NM[1];
            var A = new long[M];
            var B = new long[M];

            for (var i = 0; i < M; ++i)
            {
                var ab = Sarray();
                A[i] = ab[0] - 1;
                B[i] = ab[1] - 1;
            }
            var ans = 0L;
            for (var i = 0; i < M; ++i)
            {
                var graph = new long[N, N];
                for (var j = 0; j < M; ++j)
                {
                    if (j == i) continue;
                    graph[A[j], B[j]] = 1;
                    graph[B[j], A[j]] = 1;
                }
                var cmp = new bool[N];
                dfs(graph, cmp, 0);
                if (cmp.Count(c => c) != N)
                    ++ans;
            }
            WriteLine(ans);
            //Out.Flush();
        }
        static void dfs(long[,] graph, bool[] cmp, long r)
        {
            if (cmp[r]) return;
            cmp[r] = true;
            for (var i = 0; i < graph.GetLength(1); ++i)
            {
                if (graph[r, i] != 0)
                    dfs(graph, cmp, i);
            }
        }
    }
}