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)

N,M = map(int,input().split())
es = []
for i in range(M):
    a,b = map(int,input().split())
    a,b = a-1, b-1
    es.append((a,b))
 
parent = None
def root(a):
    if parent[a] == a:
        return a
    else:
        parent[a] = root(parent[a])
        return parent[a]
def is_same(a,b):
    return root(a) == root(b)
def unite(a,b):
    ra = root(a)
    rb = root(b)
    if ra == rb: return
    parent[ra] = rb;
 
ans = 0
for i in range(M):
    parent = [k for k in range(N)]
    for j,e in enumerate(es):
        if j == i: continue
        a,b = e
        unite(a,b)
    a,b = es[i]
    if not is_same(a,b):
        ans += 1
print(ans)