/**
* Author : Nguyen Tuan Vu
* Created : 12.01.2023
**/
#pragma GCC optimize("O2")
#pragma GCC target("avx,avx2,fma")
#include<bits/stdc++.h>
#define MASK(x) ((1ll)<<(x))
#define BIT(x, i) (((x)>>(i))&(1))
#define ALL(v) (v).begin(), (v).end()
#define REP(i, n) for (int i = 0, _n = (n); i < _n; ++i)
#define FOR(i, a, b) for (int i = (a), _b = (b); i <= _b; ++i)
#define FORD(i, b, a) for (int i = (b), _a = (a); i >= _a; --i)
#define db(val) "["#val" = "<<(val)<<"] "
#define TIME (1.0 * clock() / CLOCKS_PER_SEC)
template <class X, class Y> bool minimize(X &a, Y b) {
if (a > b) return a = b, true;
return false;
}
template <class X, class Y> bool maximize(X &a, Y b) {
if (a < b) return a = b, true;
return false;
}
using namespace std;
mt19937 jdg(chrono::steady_clock::now().time_since_epoch().count());
int Rand(int l, int r) {return l + jdg() % (r - l + 1);}
void file(){
#define TASK "TASK"
if(fopen(TASK".inp", "r")) {
freopen(TASK".inp", "r", stdin);
freopen(TASK".out", "w", stdout);
}
}
const int N = 1e5 + 5;
const int INF = 1e9 + 7;
int n, m, K, head[N], dist[N], MIN[2][4], dist2[N];
vector <pair <int, int>> adj[N];
vector <int> Spe, new_Spe;
void dijkstra(vector <int> Spe) {
FOR(i, 1, n) dist[i] = INF;
priority_queue <pair <int, int>, vector <pair <int, int>>, greater <pair <int, int>>> heap;
for (auto x : Spe) {
head[x] = x;
heap.push({dist[x] = 0, x});
}
while (heap.size()) {
int du = heap.top().first;
int u = heap.top().second;
heap.pop();
if (du != dist[u]) continue;
for (auto v : adj[u]) if (minimize(dist[v.second], dist[u] + v.first)) {
heap.push({dist[v.second], v.second});
head[v.second] = head[u];
}
}
}
int shortest_path(vector <int> Spe) {
dijkstra(Spe);
int D = INF;
FOR(u, 1, n) for (auto x : adj[u]) {
int v = x.second;
if (head[v] != head[u]) {
minimize(D, dist[v] + dist[u] + x.first);
}
}
return D;
}
void dijkstra2(int x, int MIN[], int dist[]) {
FOR(i, 1, n) dist[i] = INF;
priority_queue <pair <int, int>, vector <pair <int, int>>, greater <pair <int, int>>> heap;
heap.push({dist[x] = 0, x});
while (heap.size()) {
int du = heap.top().first;
int u = heap.top().second;
heap.pop();
if (du != dist[u]) continue;
for (auto v : adj[u]) if (minimize(dist[v.second], dist[u] + v.first)) {
heap.push({dist[v.second], v.second});
head[v.second] = head[u];
}
}
MIN[0] = MIN[1] = MIN[2] = INF;
for (auto z : Spe) if (z != x) {
if (dist[z] < MIN[0]) {
MIN[3] = MIN[2];
MIN[2] = MIN[1];
MIN[1] = MIN[0];
MIN[0] = dist[z];
}
else if (dist[z] < MIN[1]) {
MIN[3] = MIN[2];
MIN[2] = MIN[1];
MIN[1] = dist[z];
}
else if (dist[z] < MIN[2]) {
MIN[3] = MIN[2];
MIN[2] = dist[z];
}
else minimize(MIN[3], dist[z]);
}
}
int main()
{
ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
file();
cin >> n >> m >> K;
FOR(i, 1, m) {
int u, v, w; cin >> u >> v >> w;
adj[u].push_back({w, v});
adj[v].push_back({w, u});
}
FOR(i, 1, K) {
int x; cin >> x;
Spe.push_back(x);
}
dijkstra(Spe);
int A = 0, B = 0, D = INF;
FOR(u, 1, n) for (auto x : adj[u]) {
int v = x.second;
if (head[v] != head[u] && minimize(D, dist[v] + dist[u] + x.first)) {
A = head[u];
B = head[v];
}
}
//cout << A << ' ' << B << '\n';
for (auto x : Spe) if (x != A && x != B) new_Spe.push_back(x);
int res = 2 * INF;
minimize(res, shortest_path(Spe) + shortest_path(new_Spe));
dijkstra2(A, MIN[0], dist);
dijkstra2(B, MIN[1], dist2);
for (auto x : Spe) if (x != A && x != B) {
int cost = dist2[x];
int bonus = 0;
if (MIN[0][0] == dist[x] || MIN[0][0] == dist[A] || MIN[0][0] == dist[B]) {
if (MIN[0][1] == dist[x] || MIN[0][1] == dist[A] || MIN[0][1] == dist[B]) {
if (MIN[0][2] == dist[x] || MIN[0][2] == dist[A] || MIN[0][2] == dist[B]) {
bonus = MIN[0][3];
}
else bonus = MIN[0][2];
}
else bonus = MIN[0][1];
}
else bonus = MIN[0][0];
minimize(res, cost + bonus);
}
cout << res;
cerr << "Time elapsed: " << TIME << " s.\n";
return 0;
}
/*
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INPUT: |
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OUTPUT: |
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*/
