Given a tree of $n$ vertices, vertex $i$ has the number $A_i$ on it. Find a simple path with maximum sum.
### Input
- The first line contains an integer $n$.
- The second line contains $n$ integers $A_i$.
- The next $n - 1$ lines, each line contains 2 integers $u, v$, there is an edge between $u$ and $v$.
### Output
- Print the maximum sum.
### Constraints
- $1 \le n \le 10^5$.
- $0 \le |A_i| \le 10^9$.
### Example
Input:
```
5
1 -2 3 4 -5
1 2
2 3
3 4
4 5
```
Output:
```
7
```