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 PyPy3 (2.4.0) (judge verdict: Accepted)

n, m = map(int, input().split())
d = [[float("inf")] * n for i in range(n)]
edge = []
for i in range(m):
    a, b = map(int, input().split())
    edge.append((a, b))
    d[a - 1][b - 1] = 1
    d[b - 1][a - 1] = 1
ans = 0
for a in range(m):
    d_s = [x[:] for x in d]
    x, y = edge[a]
    d_s[x - 1][y - 1] = float("inf")
    d_s[y - 1][x - 1] = float("inf")
    for k in range(n):
        for i in range(n):
            for j in range(n):
                d_s[i][j] = min(d_s[i][j], d_s[i][k] + d_s[k][j])
    flag = 0
    for i in range(n):
        if flag:
            break
        for j in range(n):
            if flag:
                break
            if d_s[i][j] == float("inf"):
                ans += 1
                flag = 1
print(ans)