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;

namespace AtCoder
{
    class Program
    {
        private const int MODULO = 1000000007;
        private static string Read() { return Console.ReadLine(); }
        private static int ReadInt() { return int.Parse(Read()); }
        private static long ReadLong() { return long.Parse(Read()); }
        private static double ReadDouble() { return double.Parse(Read()); }
        private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
        private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }
        private static double[] ReadDoubles() { return Array.ConvertAll(Read().Split(), double.Parse); }

        class Node<T>
        {
            private int m_height;
            private Node<T> m_parent;
            public T Item { get; private set; }
            public Node(T item)
            {
                m_height = 0;
                m_parent = this;
                Item = item;
            }
            public Node<T> Find()
            {
                if (m_parent == this) { return this; }

                Node<T> parent = m_parent.Find();
                m_parent = parent;
                return parent;
            }
            public static void Unite(Node<T> a, Node<T> b)
            {
                Node<T> p = a.Find();
                Node<T> q = b.Find();
                if (p.m_height < q.m_height)
                {
                    p.m_parent = q;
                    q.m_height = Math.Max(p.m_height + 1, q.m_height);
                }
                else
                {
                    q.m_parent = p;
                    p.m_height = Math.Max(q.m_height + 1, p.m_height);
                }
            }
        }
        static int Solve(int N, int M, Tuple<int, int>[] paths)
        {
            int count = 0;
            for (int i = 0; i < M; ++i)
            {
                var nodes = Enumerable.Range(0, N).Select(j => new Node<int>(j)).ToArray();
                for (int j = 0; j < M; ++j)
                {
                    if (i != j)
                    {
                        int a = paths[j].Item1;
                        int b = paths[j].Item2;
                        Node<int>.Unite(nodes[a], nodes[b]);
                    }
                }
                var parents = new HashSet<int>();
                foreach (int j in nodes.Select(node => node.Find().Item)) { parents.Add(j); }
                if (parents.Count > 1) { ++count; }
            }
            return count;
        }
        static void Main(string[] args)
        {
            int[] v1 = ReadInts();
            int N = v1[0];
            int M = v1[1];
            var paths = new Tuple<int, int>[M];
            for (int i = 0; i < M; ++i)
            {
                var v2 = ReadInts();
                paths[i] = new Tuple<int, int>(v2[0] - 1, v2[1] - 1);
            }
            Console.WriteLine(Solve(N, M, paths));
        }
    }
}