Given a tree of $n$ vertices. Calculate the diameter of the given tree. The diameter of graph is the maximum distance between any pair of vertices.
### 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 a single integer, the diameter of the tree.
### Constraints
- $1 \le n \le 10^5$.
- $1 \le u, v \le n$.
### Example
Input:
```
6
1 2
2 3
3 4
4 5
5 6
```
Output:
```
5
```
