Given a simple, undirected graph with $n$ vertices and $m$ edges, determine the maximum number of bridges that can be reduced after adding an edge to the graph.
### Input
- The first line contains 2 integers $n,m$.
- The next $m$ lines, each line contains two integers $u, v$, there is an edge between $u$ and $v$.
### Output
- Print the maximum number of bridges can be reduced.
### Constraints
- $1 \le n,m \le 10^5$.
- $1 \le u,v \le n$.
### Example
Input:
```
6 5
1 3
2 3
3 4
4 5
4 6
```
Output:
```
3
```