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.IO;
using System.Linq;
using System.Runtime.CompilerServices;
using System.Text;

namespace AtCoder
{
	public class Program
	{
		static void Main()
		{
			var nm = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
			int n = nm[0];
			int m = nm[1];
			var ab = new Tuple<int, int>[m];
			for (int i = 0; i < m; i++) {
				var temp = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
				ab[i] = new Tuple<int, int>(temp[0] - 1, temp[1] - 1);
			}

			int ans = 0;
			for (int i = 0; i < m; i++) {
				ans += Check(n, m, ab, i);
			}

			Console.WriteLine(ans);
		}

		static int Check(int n, int m, Tuple<int, int>[] edges, int target)
		{
			var to = new List<int>[n];
			for (int i = 0; i < n; i++) {
				to[i] = new List<int>();
			}

			for (int i = 0; i < m; i++) {
				if (i == target) {
					continue;
				}

				to[edges[i].Item1].Add(edges[i].Item2);
				to[edges[i].Item2].Add(edges[i].Item1);
			}

			var done = new bool[n];
			var q = new Queue<int>();
			q.Enqueue(0);
			while (q.Count > 0) {
				int cur = q.Dequeue();
				if (done[cur]) {
					continue;
				}

				done[cur] = true;
				foreach (var next in to[cur]) {
					q.Enqueue(next);
				}
			}

			for (int i = 0; i < n; i++) {
				if (done[i] == false) {
					return 1;
				}
			}

			return 0;
		}
	}
}