#include <bits/stdc++.h>
using namespace std;
constexpr int MAXN=100'000;
vector<pair<int,int>> adjlist[MAXN];
int spec[MAXN];
bool is_spec[MAXN];
pair<int,int> nearest[MAXN]; // dist, owner
int bnear[MAXN];
int main(){
ios_base::sync_with_stdio(false);
int n,m,k;
cin>>n>>m>>k;
for(int i=0;i<m;++i){
int u,v,w;
cin>>u>>v>>w;
--u;--v;
adjlist[u].emplace_back(v,w);
adjlist[v].emplace_back(u,w);
}
for(int i=0;i<k;++i){
cin>>spec[i];
--spec[i];
is_spec[spec[i]]=true;
}
int ansu, ansv, ansdist=numeric_limits<int>::max()>>1, ansother=numeric_limits<int>::max()>>1, ansu1, ansu1dist=numeric_limits<int>::max()>>1, ansu2dist=numeric_limits<int>::max()>>1, ansv1, ansv1dist=numeric_limits<int>::max()>>1, ansv2dist=numeric_limits<int>::max()>>1;
struct pq_item{
int index;
int dist;
int owner;
};
struct pq_item_comp{
bool operator()(const pq_item& a, const pq_item& b) const {
return a.dist>b.dist;
}
};
struct b_item{
int index;
int dist;
};
struct b_item_comp{
bool operator()(const b_item& a, const b_item& b) const {
return a.dist>b.dist;
}
};
{
fill(nearest,nearest+n,make_pair(-1,-1));
priority_queue<pq_item,vector<pq_item>,pq_item_comp> pq;
for(int i=0;i<k;++i){
pq.push({spec[i],0,spec[i]});
}
while(!pq.empty()){
pq_item tmp = pq.top();
pq.pop();
if(nearest[tmp.index].first!=-1){
if(nearest[tmp.index].second!=tmp.owner){
break;
}
continue;
}
nearest[tmp.index]={tmp.dist, tmp.owner};
for(const pair<int,int>& pr : adjlist[tmp.index]) {
if(nearest[pr.first].first==-1||nearest[pr.first].second!=tmp.owner){
int pdist;
if(nearest[pr.first].first!=-1&&(pdist=tmp.dist+pr.second+nearest[pr.first].first)<ansdist){
ansu=tmp.owner;
ansv=nearest[pr.first].second;
ansdist=pdist;
}
pq.push({pr.first,tmp.dist+pr.second,tmp.owner});
}
}
}
}
{
fill(nearest,nearest+n,make_pair(-1,-1));
priority_queue<pq_item,vector<pq_item>,pq_item_comp> pq;
for(int i=0;i<k;++i){
if(spec[i]!=ansu&&spec[i]!=ansv){
pq.push({spec[i],0,spec[i]});
}
}
while(!pq.empty()){
pq_item tmp = pq.top();
pq.pop();
if(nearest[tmp.index].first!=-1){
if(nearest[tmp.index].second!=tmp.owner){
break;
}
continue;
}
nearest[tmp.index]={tmp.dist, tmp.owner};
for(const pair<int,int>& pr : adjlist[tmp.index]) {
if(nearest[pr.first].first==-1||nearest[pr.first].second!=tmp.owner){
if(nearest[pr.first].first!=-1)ansother=min(ansother,tmp.dist+pr.second+nearest[pr.first].first);
pq.push({pr.first,tmp.dist+pr.second,tmp.owner});
}
}
}
}
{
fill(bnear,bnear+n,-1);
bool counter=false;
priority_queue<b_item,vector<b_item>,b_item_comp> pq;
pq.push({ansu,0});
while(!pq.empty()){
b_item tmp = pq.top();
pq.pop();
if(bnear[tmp.index]!=-1)continue;
if(is_spec[tmp.index]&&tmp.index!=ansu&&tmp.index!=ansv){
if(!counter){
ansu1=tmp.index;
ansu1dist=tmp.dist;
counter=true;
}
else{
ansu2dist=tmp.dist;
break;
}
}
bnear[tmp.index]=tmp.dist;
for(const pair<int,int>& pr : adjlist[tmp.index]) {
if(bnear[pr.first]==-1){
pq.push({pr.first,tmp.dist+pr.second});
}
}
}
}
{
fill(bnear,bnear+n,-1);
bool counter=false;
priority_queue<b_item,vector<b_item>,b_item_comp> pq;
pq.push({ansv,0});
while(!pq.empty()){
b_item tmp = pq.top();
pq.pop();
if(bnear[tmp.index]!=-1)continue;
if(is_spec[tmp.index]&&tmp.index!=ansu&&tmp.index!=ansv){
if(!counter){
ansv1=tmp.index;
ansv1dist=tmp.dist;
counter=true;
}
else{
ansv2dist=tmp.dist;
break;
}
}
bnear[tmp.index]=tmp.dist;
for(const pair<int,int>& pr : adjlist[tmp.index]) {
if(bnear[pr.first]==-1){
pq.push({pr.first,tmp.dist+pr.second});
}
}
}
}
cout<<min(ansdist+ansother, (ansu1!=ansv1) ? (ansu1dist+ansv1dist) : min(ansu1dist+ansv2dist, ansu2dist+ansv1dist));
//cout<<ansu<<' '<<ansv<<' '<<ansdist<<' '<<ansother<<' '<<ansu1<<' '<<ansu1dist<<' '<<ansu2dist<<' '<<ansv1<<' '<<ansv1dist<<' '<<ansv2dist<<endl;
}
