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 (7.3.0) (judge verdict: Accepted)

class DisjointSet:
    def __init__(self, size):
        self.size = [0 for i in range(size)]
        self.p = [0 for i in range(size)]
        for i in range(size):
            self.makeSet(i)
    
    def makeSet(self, x):
        self.p[x] = x
        self.size[x] = 1

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

    def unite(self, x, y):
        self.link(self.findSet(x), self.findSet(y))

    def link(self, x, y):
        if self.size[x] > self.size[y]:
            self.p[y] = x
            self.size[x] += self.size[y]
        else:
            self.p[x] = y
            self.size[y] += self.size[x]
    
    def findSet(self, x):
        if x != self.p[x]:
            self.p[x] = self.findSet(self.p[x])
        return self.p[x]

    def getSize(self, x):
        return self.size[ds.findSet(x)]

N, M = map(int, input().split())
A = []
B = []
for i in range(M):
    a, b = map(int, input().split())
    A += [a]
    B += [b]
ans = 0
for i in range(M):
    ds = DisjointSet(N+1)
    for j, (a, b) in enumerate(zip(A, B)):
        if i == j:
            continue
        ds.unite(a, b)
    if len(set([ds.findSet(j) for j in range(1, N+1)])) != 1:
        ans += 1
print(ans)