#include<bits/stdc++.h>
#define int long long
#define nl endl
using namespace std;
int n;
tuple<int,int,int> MultiDijkstra(vector<pair<int,int> > graph[], vector<int> spec, vector<tuple<int,int,int> > el){
vector<int> dist(n+1, 1e18);
vector<int> head(n+1, -1);
vector<int> vis(n+1, 0);
priority_queue<tuple<int,int,int>, vector<tuple<int,int,int> >, greater<tuple<int,int,int> > > pq;
for(int i=0; i<spec.size(); i++){
pq.push({0, spec[i], spec[i]});
dist[spec[i]] = 0;
head[spec[i]] = spec[i];
}
while(!pq.empty()){
auto [d, v, h] = pq.top();
pq.pop();
if(vis[v]) continue;
vis[v] = 1;
for(auto [ch, wt] : graph[v]){
if(d + wt < dist[ch]){
head[ch] = h;
dist[ch] = d + wt;
pq.push({dist[ch], ch, head[ch]});
}
}
}
int ans = 1e18, n1, n2;
for(int i=0; i<el.size(); i++){
auto [u, v, wt] = el[i];
if(head[u] != head[v]){
if(dist[u] + wt + dist[v] < ans){
ans = dist[u] + wt + dist[v];
n1 = head[u], n2 = head[v];
}
}
}
return {n1, n2, ans};
}
tuple<int,int,int,int> Dijkstra(vector<pair<int,int> > graph[], vector<int> spec, int src){
vector<int> dist(n+1, 1e18);
vector<int> vis(n+1, 0);
priority_queue<pair<int,int>, vector<pair<int,int> >, greater<pair<int,int> > > pq;
pq.push({0, src});
dist[src] = 0;
while(!pq.empty()){
auto [d, v] = pq.top();
pq.pop();
if(vis[v]) continue;
vis[v] = 1;
for(auto [ch, wt] : graph[v]){
if(d + wt < dist[ch]){
dist[ch] = d + wt;
pq.push({dist[ch], ch});
}
}
}
vector<pair<int,int> > v;
for(int i=0; i<spec.size(); i++){
v.push_back({dist[spec[i]], spec[i]});
}
sort(v.begin(), v.end());
return {v[0].second, v[0].first, v[1].second, v[1].first};
}
signed main(){
ios_base::sync_with_stdio(0);
cin.tie(NULL);cout.tie(NULL);
int m, k;
cin>>n>>m>>k;
vector<pair<int,int> > graph[n+1];
vector<tuple<int,int,int> > el(m);
for(int i=0; i<m; i++){
int a, b, c;
cin>>a>>b>>c;
graph[a].push_back({b, c});
graph[b].push_back({a, c});
el[i] = {a, b, c};
}
vector<int> spec(k);
for(int i=0; i<k; i++) cin>>spec[i];
auto [u, v, mini] = MultiDijkstra(graph, spec, el);
vector<pair<int,int> > graph2[n+1];
for(int i=1; i<=n; i++){
for(auto x : graph[i]){
if(x.first != u and x.first != v) graph2[i].push_back(x);
}
}
vector<int> spec2;
for(int i=0; i<k; i++){
if(spec[i] != u and spec[i] != v) spec2.push_back(spec[i]);
}
vector<tuple<int,int,int> > el2;
for(int i=0; i<m; i++){
auto [x, y, wt] = el[i];
if(x != u and x != v and y != u and y != v) el2.push_back(el[i]);
}
auto [u2, v2, mini2] = MultiDijkstra(graph2, spec2, el2);
int ans = mini + mini2;
auto [s1, d1, s2, d2] = Dijkstra(graph, spec2, u);
auto [s3, d3, s4, d4] = Dijkstra(graph, spec2, v);
if(s3 != s1){
ans = min(ans, d1 + d3);
}else{
ans = min(ans, min(d1 + d4, d2 + d3));
}
//cout<<s1<<" "<<d1<<nl<<s2<<" "<<d2<<nl<<s3<<" "<<d3<<nl<<s4<<" "<<d4<<nl<<mini<<" "<<mini2<<nl;
cout<<ans;
return 0;
}
