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: Wrong Answer)

def ABC075C_dfs(root, graph, frm, now):
    
    for dst in graph[now]:
        if dst != frm:
           if dst in root:
               base = root.index(dst)
               return len(root) - base + 1
           else:
              root.append(now)
              ret = ABC075C_dfs(root, graph, now, dst)
              if ret == 0:
                  root.remove(now)
              else:
                  return ret
 
    return 0

def ABC075C_Bridge():
    N, M = map(int, input().strip().split())
    graph = [[] for i in range(N)]

    for i in range(M):
        a1, b1 = list(map(int, input().strip().split()))
        a1 -= 1
        b1 -= 1
        graph[a1].append(b1)
        graph[b1].append(a1)

    root = []
    print(M - ABC075C_dfs(root, graph, -1, 0))
        


def main():
    ABC075C_Bridge()

if __name__ == "__main__":
    main()