Given a tree of $n$ vertices, each vertex is initially white. Determine the maximum number of vertices that can be colored black, subject to the constraint that no two adjacent vertices can be black.
### Input
- The first line contains an integer $n$.
- The next $n - 1$ lines, each line contains 2 integers $u, v$, there is an edge between $u$ and $v$.
### Output
- Print the maximum number of vertices can be colored black.
### Constraints
- $1 \le n \le 10^5$.
- $1 \le u, v \le n$.
### Example
Input:
```
5
1 2
2 3
1 4
4 5
```
Output:
```
3
```