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<bits/stdc++.h>
#include<iostream>
#include<algorithm>
#include<math.h>
#include<stdio.h>
using namespace std;
int dfn[503],low[503];
int n,m,u,v,dep,ans;
int head[503],to[1003],nxt[1003],tot;
inline void add(int a,int b){
	to[++tot]=b;  nxt[tot]=head[a];  head[a]=tot;
}
void tarjan(int u,int fa){
    dfn[u]=low[u]=++dep;
    for(int i=head[u];i;i=nxt[i]){
        int v=to[i];
        if(!dfn[v]){
            tarjan(v,u);
            low[u]=min(low[u],low[v]);
            if(low[v]>dfn[u]){
            	ans++;
			}
        }else if(v!=fa){
        	low[u]=min(low[u],dfn[v]);
		}
    }
}
int main(){
	cin>>n>>m;
    for(int i=0;i<m;i++){
        cin>>u>>v;
        add(u,v),add(v,u);
    }
    tarjan(1,-1);
    cout<<ans<<endl;
    return 0;
}
/*

in:
7 7
1 3
2 7
3 4
4 5
4 6
5 6
6 7

out:
4

*/