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 = list(map(int, input().split()))

G = [[0] * N for i in range(N)]
for i in range(M):
    a, b = list(map(int, input().split()))
    a = a - 1
    b = b - 1
    G[a][b] = 1
    G[b][a] = 1

def isConnected(a, b):
    used = [0] * N
    def dfs(pos, pre):
        if used[pos]:
            return
        
        used[pos] = 1
        for to in range(N):
            if (pos == a and to == b) or (pos == b and to == a) or (G[pos][to] == 0):
                continue
            dfs(to, pos)
    dfs(0, -1)
    return used.count(1) != N

ans = 0
for a in range(N):
    for b in range(a+1, N):
        if G[a][b] == 0:
            continue
        ans = ans + isConnected(a, b)
    
print (ans)