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: Accepted)

n,m = map(int,input().split())
a=[]
b=[]
vector=[[False for i in range(n)] for j in range(n)]

visited = [False]*n
for i in range(m):
  x,y=map(int,input().split())
  a.append(x-1)
  b.append(y-1)
  vector[x-1][y-1]=vector[y-1][x-1]=True
  


def dfs(v):
  visited[v]=True
  for i in range(n):
    if not vector[v][i]:continue
    if visited[i]:continue
    dfs(i)
      
def main():
  ans=0
  for i in range(m):
    vector[a[i]][b[i]]=vector[b[i]][a[i]]=False
  
    for j in range(n):visited[j]=False
   
    dfs(0)
    
    bridge=False
    for j in range(1,n):
      if visited[j]==False:
        bridge=True
    if bridge:
      ans+=1
    vector[a[i]][b[i]]=vector[b[i]][a[i]]=True
    
  print(ans)

if __name__=='__main__':
  main()