Given a tree of $n$ vertices. Count the number of way to color vertices in 3 colors so that no 2 adjacent vertices having the same color.
### 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 number ways to color the tree, modulo $10^9+7$.
### Constraints
- $1 \le n \le 10^5$.
- $1 \le u, v \le n$.
### Example
Input:
```
5
1 2
1 3
2 4
2 5
```
Output:
```
48
```