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 Python (3.4.3) (judge verdict: Wrong Answer)

n,m=map(int,input().split())
graph=[[] for i in range(n)]
for i in range(m):
    a,b=map(int,input().split())
    a-=1;b-=1
    graph[a].append(b)
    graph[b].append(a)
#print(graph)#受け取り終了

#ぐるっと一周を除く
c=0
for i in range(n):
  if len(graph[i])!=2:
    c+=1
if c==0:
  print(0)

else:
  cnt=0;p=0;q=0
  for i in range(n):
    if len(graph[i])==2:
        p+=1
        x=graph[i][0]
        y=graph[i][1]
        if (x in graph[y]) and (y in graph[x]):
            cnt+=0
        elif len(graph[x])==2 or len(graph[y])==2:
            cnt+=1
        else:
            cnt+=2
    elif len(graph[i])==1:
        q+=1
  if p+q==n and q>0:
      cnt+=1
  print(cnt)