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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
#include <vector>
#include <algorithm>
#include <queue>
using namespace std;

int main()
{
    int n,m;
    cin >> n >> m;
    vector<int> a(m);
    vector<int> b(m);
    vector<vector<int>> graph(n,vector<int>(n,0));
    int i,j;
    for(i = 0;i < m;++i){
        cin >> a.at(i) >> b.at(i);
        graph.at(a.at(i)-1).at(b.at(i)-1) = 1;
        graph.at(b.at(i)-1).at(a.at(i)-1) = 1;
    }
    int ans = 0;
    int tmp;
    for(i = 0;i < m;++i){
        graph.at(a.at(i)-1).at(b.at(i)-1) = 0;
        graph.at(b.at(i)-1).at(a.at(i)-1) = 0;
        vector<bool> bridge(n,false);
        queue<int> ten;
        bridge.at(0) = true;
        for(j = 0;j < n;++j){
            if(graph.at(0).at(j)){
                bridge.at(j) = true;
                ten.push(j);
            }
        }
        vector<bool> check(n,false);
        check.at(0) = true;
        while(ten.size()){
            tmp = ten.front();
            ten.pop();
            for(j = 0;j < n;++j){
                if(graph.at(tmp).at(j)){
                    bridge.at(j) = true;
                    if(!check.at(j)){
                        ten.push(j);
                    }
                }
            }
            check.at(tmp) = true;
        }
        bool flag = false;
        for(j = 0;j < n;++j){
            if(!bridge.at(j)){
                flag = true;
                break;
            }
        }
        if(flag){
            ++ans;
        }
        graph.at(a.at(i)-1).at(b.at(i)-1) = 1;
        graph.at(b.at(i)-1).at(a.at(i)-1) = 1;
    }
    cout << ans << endl;
    return 0;
}