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)

from typing import List, Tuple


def main():
    n, m = map(int, input().split())
    g = []
    for _ in range(m):
        a, b = map(int, input().split())
        g.append((a, b))
    print(bb(n, m, g))


def bb(n: int, m: int, g: List[Tuple[int, int]]):
    ret = 0
    for i in range(m):
        v = set()
        w = [1]
        while w:
            now = w.pop()
            v.add(now)
            for j, node in enumerate(g):
                if j == i:
                    continue
                if node[0] == now and node[1] not in v:
                    w.append(node[1])
                elif node[1] == now and node[0] not in v:
                    w.append(node[0])
        if len(v) != n:
            ret += 1
    return ret


if __name__ == '__main__':
    main()