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: Runtime Error)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading;

namespace algorithm
{
	class Program
	{
		public static void Main()
		{
			int[] nm = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
			int[][] q = new int[nm[0]][];
			for (int i = 0; i < nm[1]; i++)
			{
				q[i] = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
			}
			Dictionary<int, List<int>> dic = new Dictionary<int, List<int>>();
			for (int i = 0; i < nm[1]; i++)
			{
				if (!dic.ContainsKey(q[i][0]))
					dic.Add(q[i][0], new List<int>());

				if (!dic.ContainsKey(q[i][1]))
					dic.Add(q[i][1], new List<int>());
				dic[q[i][0]].Add(q[i][1]);
				dic[q[i][1]].Add(q[i][0]);
			}

			Console.WriteLine(dic.Count(x => x.Value.Count <= 2)-1);
		}
	}

}