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 5.4.1) (judge verdict: Wrong Answer)

#include<stdio.h>

int main(){
  int N,M,i,j,k,res=0;
  scanf("%d%d",&N,&M);
  long long A[M],tmp,a,b,m;

  for(i=0;i<M;++i){
    scanf("%lld%lld",&a,&b);
    A[i]=(1<<--b)|(1<<--a);
  }

  m=(1<<N)-1;
  
  for(k=0;k<M;++k){
    tmp=A[(k+1)%M];
    for(i=0;i<M;++i){
      for(j=0;j<k;++j)  if(tmp&A[j])tmp|=A[j];
      for(j=k+1;j<M;++j)if(tmp&A[j])tmp|=A[j];
    }
    if(tmp-m)++res;
  }
  printf("%d\n",res);
}