#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const ll INF = 1e18;
struct Edge {
int to, w;
};
struct State {
ll d;
int u, src;
bool operator>(const State &o) const {
return d > o.d;
}
};
int main(){
ios::sync_with_stdio(false);
cin.tie(nullptr);
int N, M, K;
cin >> N >> M >> K;
vector<vector<Edge>> graph(N+1);
for (int i = 0; i < M; i++){
int u, v, w;
cin >> u >> v >> w;
graph[u].push_back({v, w});
graph[v].push_back({u, w});
}
vector<int> special(K);
vector<bool> isSpecial(N+1, false);
for (int i = 0; i < K; i++){
cin >> special[i];
isSpecial[special[i]] = true;
}
vector<vector<pair<ll,int>>> best(N+1);
priority_queue<State, vector<State>, greater<State>> pq;
for (int s : special) {
best[s].push_back({0, s});
pq.push({0, s, s});
}
while(!pq.empty()){
State st = pq.top();
pq.pop();
if(st.d != best[st.u][0].first && best[st.u].size() && st.d > best[st.u][0].first)
continue;
int u = st.u;
for(auto &edge : graph[u]){
int v = edge.to;
ll nd = st.d + edge.w;
bool canPush = false;
bool already = false;
for(auto &p : best[v]){
if(p.second == st.src){
if(nd < p.first){
p.first = nd;
canPush = true;
}
already = true;
break;
}
}
if(!already){
best[v].push_back({nd, st.src});
canPush = true;
}
if(best[v].size() > 2){
sort(best[v].begin(), best[v].end());
best[v].resize(2);
}
if(canPush)
pq.push({nd, v, st.src});
}
}
map<pair<int,int>, ll> cand;
for (int u = 1; u <= N; u++){
if(best[u].size() >= 2){
sort(best[u].begin(), best[u].end());
ll cost = best[u][0].first + best[u][1].first;
int a = best[u][0].second, b = best[u][1].second;
if(a > b) swap(a, b);
if(cand.find({a,b}) == cand.end() || cost < cand[{a,b}])
cand[{a,b}] = cost;
}
}
for (int u = 1; u <= N; u++){
for(auto &edge : graph[u]){
int v = edge.to;
// Với mỗi cặp (u,v), xem xét tất cả các khả năng đến từ u và v.
for(auto &p1 : best[u]){
for(auto &p2 : best[v]){
if(p1.second == p2.second) continue;
ll cost = p1.first + edge.w + p2.first;
int a = p1.second, b = p2.second;
if(a > b) swap(a, b);
if(cand.find({a,b}) == cand.end() || cost < cand[{a,b}])
cand[{a,b}] = cost;
}
}
}
}
vector<tuple<ll,int,int>> pairs;
for(auto &entry : cand){
pairs.push_back({entry.second, entry.first.first, entry.first.second});
}
sort(pairs.begin(), pairs.end());
ll ans = INF;
int sz = pairs.size();
int L = min(sz, 5000);
for (int i = 0; i < L; i++){
ll cost1;
int a, b;
tie(cost1, a, b) = pairs[i];
for (int j = i+1; j < L; j++){
ll cost2;
int c, d;
tie(cost2, c, d) = pairs[j];
// Kiểm tra 2 cặp có giao nhau không
if(a == c || a == d || b == c || b == d)
continue;
ans = min(ans, cost1 + cost2);
break;
}
}
cout << ans << "\n";
return 0;
}
