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())
f, t = [], []

for i in range(M) :
    a, b = map(int, input().split())
    
    f.append(a)
    t.append(b)
    
def get_root(idx) :
    if idx == u[idx] :
        return idx
    else :
        u[idx] = get_root(u[idx])
        return u[idx]
    
def union(a, b) :
    if get_root(a) <= get_root(b) :
        u[get_root(b)] = get_root(a)
    else :
        u[get_root(a)] = get_root(b)
cnt = 0 

for i in range(M) :
    u = [x for x in range(N)]
    
    for j in range(M) :
        if i != j :
            union(f[j] - 1, t[j] - 1)
    
    u_sets = set()
    for j in range(N) :
        u_sets.add(get_root(j))
        
    # print("DBG : ", u_sets)
    if len(list(u_sets)) != 1 :
        cnt += 1
        
print(cnt)