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(Nāˆ’1)ā„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:

570677a9809fd7a5b63bff11e5d9bf79.png

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.