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)

import copy

# Union-Find
def find(x):
    if par[x] < 0:
        return x
    else:
        par[x] = find(par[x])
        return par[x]


def unite(x, y):
    x = find(x)
    y = find(y)
    if x == y:
        return False
    if par[x] > par[y]:
        x, y = y, x
    par[y] = x
    return True


def same(x, y):
    return find(x) == find(y)


def size(x):
    return -par[find(x)]


N, M = map(int, input().split())
Road = [tuple(map(int, input().split())) for _ in range(M)]
ans = 0
for i in range(M):
    Roadi = copy.deepcopy(Road)
    par = [-1] * N
    for j, r in enumerate(Road):
        if i == j:
            continue
        ra, rb = r
        ra -= 1
        rb -= 1
        unite(ra, rb)
    if par.count(-1) > 1:
        ans += 1

print(ans)