Given a tree of $n$ vertices. You can choose the root arbitrarily, find the maximum number of leaves in the tree.
### Input
- The first line contains an integers $n$.
- The next $n - 1$ lines, each line contains two integers $u,v$, there is an edge between $u$ and $v$.
### Output
- Print the maximum number of leaves.
### Constraints
- $1 \le n \le 10^5$.
- $1 \le u, v \le n$.
### Example
Input:
```
3
1 2
1 3
```
Output:
```
2
```
