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;

class Program{

    const int INT_MAX = 2147483647;
    static void Main(string[] args)
    {
        // ufは連結は出来るけど後戻りが出来ない<incremental?というのか>
        int[] nm = Scan.IntArray(2);
        int n, m;
        n = nm[0];
        m = nm[1];
        int[,] edge = Scan.IntSquareArray(m, 2);
        int cnt = 0;
        for (int i = 0; i < m; i++)
        {
            // i が取り除く<辺を張らない>インデックス
            UnionFind uf = new UnionFind();
            uf.Init(n);
            for (int j = 0; j < m; j++)
            {
                if(i != j)
                {
                    uf.Unite(edge[j, 0], edge[j, 1], 0);
                }
            }
            if (!uf.Same(edge[i, 0], edge[i, 1]))
            {
                cnt++;
            }
        }
        Out.Num(cnt);
    }
}

public class Scan
{
    public static int[] IntArray(int t)
    {
        string[] str = Console.ReadLine().Split(' ');
        int[] ar = new int[t];
        for (int i = 0; i < t; i++)
        {
            ar[i] = int.Parse(str[i]);
        }
        return ar;
    }

    public static int[,] IntSquareArray(int h, int w)
    {
        int[,] resAr = new int[h, w];
        for (int i = 0; i < h; i++)
        {
            int[] ar = Scan.IntArray(w);
            for (int j = 0; j < w; j++)
            {
                resAr[i, j] = ar[j];
            }
        }
        return resAr;
    }
}

public class Out
{
    public static void Num<T>(T a)
    {
        Console.WriteLine(a);
    }
}

public class UnionFind
{
    public int[] parent;
    public int[] rank;
    public long[] weightDiff;

    public void Init(int size)
    {
        parent = new int[size + 5];
        rank = new int[size + 5];
        weightDiff = new long[size + 5];
        for (int i = 0; i < size; i++)
        {
            parent[i] = i;
            rank[i] = 0;
            weightDiff[i] = 0;
        }
    }

    public int Root(int x)
    {
        if(parent[x] == x)
        {
            return x;
        }
        else
        {
            int r = Root(parent[x]);
            weightDiff[x] += weightDiff[parent[x]];
            return parent[x] = r;
        }
    }

    public bool Unite(int x, int y, long w) // Add edge x <- y (weight: w)
    {
        w = w + GetWeight(x) - GetWeight(y);
        x = Root(x);
        y = Root(y);
        if (x == y) return false;
        if(rank[x] < rank[y])
        {
            int tmp = x; x = y; y = tmp;
            w *= -1;
        }
        if(rank[x] == rank[y])
        {
            ++rank[x];
        }
        parent[y] = x;
        weightDiff[y] = w;
        return true;
    }

    public bool Same(int x, int y)
    {
        return Root(x) == Root(y);
    }

    public long GetWeight(int x)
    {
        Root(x);
        return weightDiff[x];
    }

    public long Diff(int x, int y) // x -> y
    {
        return GetWeight(y) - GetWeight(x);
    }
}