#include <bits/stdc++.h>
using namespace std;
#define FOR(i, l, r) for(int i = (l); i < (r); ++i)
#define ROF(i, r, l) for(int i = (r)-1; i >= (l); --i)
#define mp make_pair
#define mt make_tuple
#define ff first
#define ss second
#define all(v) begin(v), end(v)
#define rall(v) rbegin(v), rend(v)
#define sz(v) (int)v.size()
#define pb push_back
#define eb emplace_back
#define compact(v) v.erase(unique(all(v)), end(v))
#define dbg(x) "[" #x " = " << (x) << "]"
template<typename T>
bool minimize(T& a, const T& b){
if(a > b) return a = b, true;
return false;
}
template<typename T>
bool maximize(T& a, const T& b){
if(a < b) return a = b, true;
return false;
}
typedef long long ll;
using db = double;
using ull = unsigned long long;
using pi = pair<int, int>;
using pl = pair<ll, ll>;
using pd = pair<db, db>;
using vi = vector<int>;
using vl = vector<ll>;
using vc = vector<char>;
using vd = vector<db>;
using vb = vector<bool>;
using vpi = vector<pi>;
using vpl = vector<pl>;
void setIO(){
ios_base::sync_with_stdio(0); cin.tie(0);
#ifdef LOCAL
freopen("task.inp", "r", stdin);
freopen("task.out", "w", stdout);
#endif
}
const int MAX = 1e5 + 5;
const int inf = 1e9 + 9;
int N, M, K, A[MAX], cnt_vis[MAX];
vpi adj[MAX];
vector<tuple<int, int, int>> important_pairs;
bool is_special[MAX], done[MAX];
vector<pi> top[MAX];
vi pos[MAX];
int count_prefix(int i, int r){
return upper_bound(all(pos[i]), r) - pos[i].begin();
}
bool can(int v, int org, int cost){
if(v == org) return false;
if(top[v].empty()) {
top[v].eb(cost, org);
return true;
}
for(auto &[tot, st] : top[v]){
if(st == org){
if(tot > cost){
tot = cost;
sort(all(top[v]));
return true;
} else return false;
}
}
if(sz(top[v]) < 4){
top[v].eb(cost, org);
sort(all(top[v]));
return true;
}
if(top[v][0].ff > cost){
top[v][0] = mp(cost, org);
sort(all(top[v]));
return true;
}
return false;
}
bool in_four_best(int u, int org){
for(auto [cost, st] : top[u]) if(st == org) return true;
return false;
}
int main(){
setIO();
cin >> N >> M >> K;
FOR(i, 0, M){
int u, v, w;
cin >> u >> v >> w;
adj[u].eb(v, w); adj[v].eb(u, w);
}
using node = tuple<int, int, int>;
priority_queue<node, vector<node>, greater<node>> pq;
while(K--){
int u;
cin >> u;
is_special[u] = true;
pq.push(mt(0, u, u));
}
while(!pq.empty()){
int dist, u, org;
tie(dist, u, org) = pq.top(); pq.pop();
for(auto [v, w] : adj[u]){
if(can(v, org, dist + w)){
pq.push(mt(dist + w, v, org));
}
}
}
vector<tuple<int, int, int>> matches;
FOR(i, 1, N+1){
if(is_special[i]){
for(auto [cost, org] : top[i]){
matches.eb(cost, min(i, org), max(i, org));
// cout << dbg(cost) << dbg(i) << dbg(org) << '\n';
}
}
}
sort(all(matches)); compact(matches);
int ans = inf;
FOR(i, 0, sz(matches)){
int cost, u, v; tie(cost, u, v) = matches[i];
if(i>0){
int l = 0, r = i-1, pos = -1;
while(l <= r){
int mid = l + r >> 1;
if(count_prefix(u, mid) + count_prefix(v, mid) == mid + 1){
l = mid + 1;
} else{
pos = mid;
r = mid - 1;
}
}
if(pos != -1){
int pre = get<0>(matches[pos]);
minimize(ans, pre + cost);
}
}
pos[u].pb(i);
pos[v].pb(i);
}
cout << ans << '\n';
return 0;
}
