\problemname{Doomsday}
\illustration{.3}{mountain_trails}{\href{https://www.flickr.com/photos/42034606@N05/27076955039}{Public domain, Munds Mountain Trail by Coconino NF Photography via Flickr}}%
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Doomsday is near! Or at least that’s what your brother is telling you. 
In his preparations he has constructed a clever network of well concealed food depots and water depots far out in a mountainous region. 
You are in your base, and the alarm goes off: how quickly can you fetch both food and water supplies?
% He has asked you to find the most efficient route starting from base such that you can visit at least one food depot and at least one water depot and then return to the base.

\section*{Input}
The first line contains four integers $n$, $m$, $w$, $f$, where $1 \leq n \leq 50\,000$ is the number of hidden locations, $0 \leq m \leq 150\,000$ is the number of trails in the network,
$1 \leq w \leq n$ is the number of water depots in total, and $1 \leq f \leq n$ is the number of food depots in total. Your base is at location $0$.
The second line contains $w$ space-separated integers $u_1, u_2, \ldots, u_w$, which represents the (distinct) locations of the water depots ($0 \leq u_i < n$ for each $i$).
The third line contains $f$ space-separated integers $v_1, v_2, \ldots, v_f$, which represents the (distinct) locations of the food depots ($0 \leq v_i < n$ for each $i$).

The next $m$ lines each describe a (bidirectional) trail in the network.
The $i^{\text{th}}$ such line contains three space-separated integers $a_i$, $b_i$ and $t_i$ indicating that there is a trail between location $a_i$ and $b_i$ which takes $t_i$ hours to traverse ($0 \leq a_i, b_i < n$ and $0 \leq t_i < 100$ for each $i$).

% The objective is to find the shortest path such that you visit at least one water depot and at least one food depot and return back to base (the order in which you visit them does not matter).

\section*{Output}
Output a single integer, the minimum number of hours required to fetch both food and water and bring it back to base.
