Codeforces celebrates 10 years! We are pleased to announce the crowdfunding-campaign. Congratulate us by the link https://codeforces.com/10years.
×

Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

E. Opening Portals

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputPavel plays a famous computer game. A player is responsible for a whole country and he can travel there freely, complete quests and earn experience.

This country has *n* cities connected by *m* bidirectional roads of different lengths so that it is possible to get from any city to any other one. There are portals in *k* of these cities. At the beginning of the game all portals are closed. When a player visits a portal city, the portal opens. Strange as it is, one can teleport from an open portal to an open one. The teleportation takes no time and that enables the player to travel quickly between rather remote regions of the country.

At the beginning of the game Pavel is in city number 1. He wants to open all portals as quickly as possible. How much time will he need for that?

Input

The first line contains two space-separated integers *n* and *m* (1 ≤ *n* ≤ 10^{5}, 0 ≤ *m* ≤ 10^{5}) 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} ≤ 10^{9}) — 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 *p*_{1}, *p*_{2}, ..., *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.

Examples

Input

3 3

1 2 1

1 3 1

2 3 1

3

1 2 3

Output

2

Input

4 3

1 2 1

2 3 5

2 4 10

3

2 3 4

Output

16

Input

4 3

1 2 1000000000

2 3 1000000000

3 4 1000000000

4

1 2 3 4

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.

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Feb/21/2020 19:28:08 (g1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|