Opening Portals

Description:

Input:

The first line contains two space-separated integers n and m (1 ≤ n ≤ 10⁵, 0 ≤ m ≤ 10⁵) that show how many cities and roads are in the game.

Each of the next m lines contains the description of a road as three space-separated integers x_i, y_i, w_i (1 ≤ x_i, y_i ≤ n, x_i ≠ y_i, 1 ≤ w_i ≤ 10⁹) — the numbers of the cities connected by the i-th road and the time needed to go from one city to the other one by this road. Any two cities are connected by no more than one road. It is guaranteed that we can get from any city to any other one, moving along the roads of the country.

The next line contains integer k (1 ≤ k ≤ n) — the number of portals.

The next line contains k space-separated integers p₁, p₂, ..., p_k — numbers of the cities with installed portals. Each city has no more than one portal.

Output:

Print a single number — the minimum time a player needs to open all portals.

Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams or the %I64d specifier.

Sample Input:

3 3
1 2 1
1 3 1
2 3 1
3
1 2 3

Sample Output:

2

Sample Input:

4 3
1 2 1
2 3 5
2 4 10
3
2 3 4

Sample Output:

16

Sample Input:

4 3
1 2 1000000000
2 3 1000000000
3 4 1000000000
4
1 2 3 4

Sample Output:

3000000000

Note:

In the second sample the player has to come to city 2, open a portal there, then go to city 3, open a portal there, teleport back to city 2 and finally finish the journey in city 4.