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 (3.8.2) (judge verdict: Accepted)

class UnionFind():
  def __init__(self,n):
    self.n=n
    self.parents =[-1]*n

  def find(self, x):
    if self.parents[x]<0:
      return x
    else:
      self.parents[x]=self.find(self.parents[x])
      return self.parents[x]

  def union(self, x, y):
    x=self.find(x)
    y=self.find(y)
    if x==y:
      return
    if self.parents[x]>self.parents[y]:
      x,y=y,x
    self.parents[x]+=self.parents[y]
    self.parents[y]=x
    
  def size(self, x):
    return -self.parents[self.find(x)]

  def same(self, x, y):
    return self.find(x)==self.find(y)

  def members(self, x):
    root=self.find(x)
    return list(i for i in range(self.n) if self.find(i) == root)

  def roots(self):
    return list(i for i, x in enumerate(self.parents) if x < 0)

  def group_count(self):
    return len(self.roots)

  def all_group_members(self):
    return {r: self.members(r) for r in self.roots()}

  def __str__(self):
    return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())

adj=[]
N, M = map(int, input().split())
for m in range(M):
  a,b=map(int, input().split())
  adj.append([a-1,b-1])

ans = 0
for i in range(M):
  uf = UnionFind(N)
  for j in range(M):
    if i == j:
      continue
    uf.union(*adj[j])
  if len(set(uf.roots()))!=1:
    ans += 1
print(ans)