Given a tree of $n$ vertices. On vertex $i$ there is an integer $A_i$. You can apply the following operation unlimitedly:
- Select a set of connected vertices that contains vertex $1$, increase or decrease all these vertices by $1$.
What's the minimum number of operations needed to make all numbers become $0$.
### 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 minimum number of operations.
### Constraints
- $1 \le n \le 10^5$.
- $0 \le |A_i| \le 10^9$.
- $1 \le u, v \le n$.
### Example
Input:
```
3
1 -1 1
1 2
1 3
```
Output:
```
3
```