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++ (GCC 9.2.1) (judge verdict: Accepted)

// 問題の URL を書いておく
// 

#include <algorithm>
#include <array>
#include <bitset>
#include <cmath>
#include <iostream>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <vector>

using namespace std;

//#define ENABLE_PRINT

#if defined(ENABLE_PRINT)

#define Print(v) \
do {\
    cout << #v << ": " << v << endl; \
}while(0)

#define PrintVec(v) \
do {\
    for(int __i = 0; __i < v.size(); ++__i) \
    { \
        cout << #v << "[" << __i << "]: " << v[__i] << endl; \
    }\
}while(0)

#else

#define Print(v) ((void)0)
#define PrintVec(v) ((void)0)

#endif

#define rep(i, n) for(int i = 0; i < (int)(n); ++i)

struct Edge
{
    int a;
    int b;
};

struct Vertex
{
    int id;
    int parent;
    int root(vector<Vertex>& v)
    {
        if(parent == -1)
        {
            return id;
        }
        auto r = v[parent].root(v);
        parent = r;
        return r;
    }
};

int main(int, const char**)
{
    int n, m;
    cin >> n >> m;
    vector<Edge> e(m);
    rep(i, m)
    {
        int a, b;
        cin >> a >> b;
        a--; b--;
        e[i] = {a, b};
    }

    int count = 0;
    rep(i, m)
    {
        vector<Vertex> v(n);
        rep(j, n) v[j] = {j, -1};
        rep(j, m)
        {
            if(i == j)
            {
                continue;
            }
            auto& t = e[j];
            if(v[t.a].root(v) != v[t.b].root(v))
            {
                v[v[t.a].root(v)].parent = t.b;
            }
        }
        bool valid = true;
        rep(j, n - 1)
        {
            auto a = v[j].root(v);
            auto b = v[j + 1].root(v);
            if(!(a != -1 && b != -1 && a == b))
            {
                valid = false;
                break;
            }
        }
        if(!valid)
        {
            count++;
        }
    }
    cout << count << endl;
    return 0;
}