#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#define MAXN (100005)
ll dist[MAXN], distA[MAXN], distB[MAXN];
ll source[MAXN];
vector<pair<ll,ll> > v[MAXN];
int main() {
ios_base::sync_with_stdio(false);cin.tie(0);
ll N,M,K;
cin>>N>>M>>K;
vector<pair<ll,pair<ll,ll> > > edges;
for(ll i = 0;i < M;i++){
ll a,b,c;
cin>>a>>b>>c;
a--;
b--;
v[a].push_back({c,b});
v[b].push_back({c,a});
edges.push_back({c,{a,b}});
}
priority_queue<pair<ll,pair<ll,ll> >,vector<pair<ll,pair<ll,ll> > >,greater<pair<ll,pair<ll,ll> > > > pq;
ll special[K];
memset(dist,-1,sizeof(dist));
memset(source,-1,sizeof(source));
for(ll i = 0;i < K;i++){
cin>>special[i];
special[i]--;
pq.push({0,{special[i],special[i]}}); //d, cur node, source
dist[special[i]] = 0;
source[special[i]] = special[i];
}
while(!pq.empty()){
ll d = pq.top().first;
ll x = pq.top().second.first;
ll Source = pq.top().second.second;
pq.pop();
if(d != dist[x]){
continue;
}
for(auto u : v[x]){
if(dist[u.second] == -1 || d + u.first < dist[u.second]){
pq.push({d + u.first,{u.second,Source}});
dist[u.second] = d + u.first;
source[u.second] = Source;
}
}
}
ll A = -1, B = -1, minimum = 1e18;
for(auto u : edges){
ll a = u.second.first;
ll b = u.second.second;
ll c = u.first;
if(dist[a] == -1 || dist[b] == -1 || source[a] == source[b]){
continue;
}
if(dist[a] + c + dist[b] <= minimum){
minimum = dist[a] + c + dist[b];
A = source[a];
B = source[b];
}
}
ll sum = 1e18;
//Case 1: First Pair (A, B) fixed, Second pair (C, D) unknown
memset(dist,-1,sizeof(dist));
memset(source,-1,sizeof(source));
for(ll i = 0;i < K;i++){
if(special[i] != A && special[i] != B){
//cout<<"SOURCE: "<<special[i]<<'\n';
pq.push({0,{special[i],special[i]}}); //d, cur node, source
dist[special[i]] = 0;
source[special[i]] = special[i];
}
}
while(!pq.empty()){
ll d = pq.top().first;
ll x = pq.top().second.first;
ll Source = pq.top().second.second;
pq.pop();
if(x == A || x == B) continue;
if(d != dist[x]){
continue;
}
for(auto u : v[x]){
if(u.second == A || u.second == B) continue;
if(dist[u.second] == -1 || d + u.first < dist[u.second]){
pq.push({d + u.first,{u.second,Source}});
dist[u.second] = d + u.first;
source[u.second] = Source;
}
}
}
ll C = -1, D = -1, minimum2 = 1e18;
for(auto u : edges){
ll a = u.second.first;
ll b = u.second.second;
ll c = u.first;
if(dist[a] == -1 || dist[b] == -1 || source[a] == source[b]){
continue;
}
if(dist[a] + c + dist[b] <= minimum2){
minimum2 = dist[a] + c + dist[b];
C = source[a];
D = source[b];
}
}
sum = min(sum,minimum + minimum2);
//cout<<"Case 1 SUM: "<<minimum + minimum2<<" "<<A<<" with "<<B<<" , "<<C<<" with "<<D<<'\n';
//Case 2: Half of both pairs are known (A, C) and (B, D)
memset(distA,-1,sizeof(distA));
pq.push({0,{A,A}}); //d, cur node, source
distA[A] = 0;
source[A] = A;
while(!pq.empty()){ //dikjstra from A
ll d = pq.top().first;
ll x = pq.top().second.first;
ll Source = pq.top().second.second;
pq.pop();
if(d != distA[x]){
continue;
}
for(auto u : v[x]){
if(distA[u.second] == -1 || d + u.first < distA[u.second]){
pq.push({d + u.first,{u.second,Source}});
distA[u.second] = d + u.first;
source[u.second] = Source;
}
}
}
pair<ll,ll> C1 = {-1,1e18}, C2 = {-1,1e18}; //first-best choice for C, second-best choice for C
for(ll i = 0;i < K;i++){
ll x = special[i];
if(distA[x] == -1 || x == A || x == B) continue;
if(distA[x] <= C1.second){
C2 = C1;
C1 = {x,distA[x]};
}else if(distA[x] <= C2.second){
C2 = {x,distA[x]};
}
}
memset(distB,-1,sizeof(distB));
pq.push({0,{B,B}}); //d, cur node, source
distB[B] = 0;
source[B] = B;
while(!pq.empty()){ //dikjstra from B
ll d = pq.top().first;
ll x = pq.top().second.first;
ll Source = pq.top().second.second;
pq.pop();
if(d != distB[x]){
continue;
}
for(auto u : v[x]){
if(distB[u.second] == -1 || d + u.first < distB[u.second]){
pq.push({d + u.first,{u.second,Source}});
distB[u.second] = d + u.first;
source[u.second] = Source;
}
}
}
for(ll i = 0;i < K;i++){
ll D = special[i];
if(D == A || D == B || C1.first == -1 || distB[D] == -1) continue;
if(D == C1.first){
if(C2.first == -1) continue;
sum = min(sum,C2.second + distB[D]);
//cout<<"Case 2 SUM: "<<C2.second + distB[D]<<" "<<A<<" with "<<C2.first<<" , "<<B<<" with "<<D<<'\n';
}else{
sum = min(sum,C1.second + distB[D]);
//cout<<"Case 2 SUM: "<<C1.second + distB[D]<<" "<<A<<" with "<<C1.first<<" , "<<B<<" with "<<D<<'\n';
}
}
cout<<sum<<'\n';
}
