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;

namespace Algorithm
{
    class Program
    {
        static void Main(string[] args)
        {
            var NM = Console.ReadLine().Split().Select(int.Parse).ToArray();
            var a = new int[NM[1]];
            var b = new int[NM[1]];

            for (var i = 0; i < NM[1]; i++)
            {
                var tmp = Console.ReadLine().Split().Select(int.Parse).ToArray();
                a[i] = tmp[0];
                b[i] = tmp[1];
            }

            var ans = 0;
            for (var i = 0; i < NM[1]; i++)
            {
                var uf = new UnionFind(NM[0]+1);

                for (var j = 0; j < NM[1]; j++)
                {
                    if (i == j) continue;
                    uf.Unite(a[j], b[j]);
                }
                if (uf.GetSize(a[i]) != NM[0]) ans++;
            }
            Console.WriteLine(ans);
        }
    }


    class UnionFind
    {
        public int Size { get; set; } = 0;
        List<int> parent;
        List<int> sizes;

        public UnionFind(int count)
        {
            parent = new List<int>(count);
            sizes = new List<int>(count);
            ExtendSize(count);
        }

        public bool Unite(int x, int y)
        {
            var xp = Find(x);
            var yp = Find(y);
            if (yp == xp) return false;
            if (sizes[xp] < sizes[yp])
            {
                var tmp = xp;
                xp = yp;
                yp = tmp;
            }
            parent[yp] = xp;
            sizes[xp] += sizes[yp];
            return true;
        }

        public IEnumerable<int> AllParents => parent.Where(x => x == parent[x]);
        public int GetSize(int x) => sizes[Find(x)];
        public int Find(int x) => parent[x] == parent[parent[x]] ? parent[x] : parent[x] = Find(parent[x]);
        public void ExtendSize(int treeSize)
        {
            if (treeSize <= Size) return;
            parent.Capacity = treeSize;
            sizes.Capacity = treeSize;
            while (Size < treeSize)
            {
                parent.Add(Size);
                sizes.Add(1);
                Size++;
            }
        }
    }
}