The Human Village can be represented by a simple graph with $n$ locations and $m$ roads. The previous festival was very successful, so Reimu wants to organize an even grander festival. Specifically, she will choose a road to host the festival.
There are $k$ people who want to attend the festival, and person number $i$ is currently at location $p_i$. Help Reimu choose a road to host the festival in such a way that the total distance the $k$ people have to travel to get to the festival is minimized. Each person only needs to travel to one end of the chosen road to reach the festival.
### Input
- The first line contains three integers $n$, $m$, and $k$.
- The second line contains $k$ integers $p_i$.
- The next $m$ lines each contain two integers $u$ and $v$, representing an edge between vertices $u$ and $v$.
### Output
- Print the minimum total distance.
### Constraints
- $1 \le n,k \le 10^3$.
- $1 \le m \le 3000$.
- $1 \le u, v, p_i \le n$.
### Example
Input:
```
4 4 3
1 3 4
1 2
2 3
3 4
4 1
```
Output:
```
1
```
