This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#pragma GCC optimize("Ofast")
#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#ifdef ENABLE_DEBUG
#include <debug.h>
#else
#define DEBUG(...) do {} while (0)
#endif
using namespace std;
using namespace __gnu_pbds;
using ll = long long;
using ull = unsigned long long;
using lll = __int128;
using ulll = unsigned __int128;
using ld = long double;
template<typename T, size_t N> using ar = array<T, N>;
template<typename T, typename Cmp = less<T>>
using iset = tree<T, null_type, Cmp, rb_tree_tag,
tree_order_statistics_node_update, allocator<T>>;
#define REPSI(name, start, stop, step) for (ll name = start; name < (ll)stop; name += step)
#define REPS(name, start, stop) REPSI(name, start, stop, 1)
#define REP(name, stop) REPS(name, 0, stop)
#define RREPSI(name, start, stop, step) for (ll name = stop-1; name >= (ll)start; name -= step)
#define RREPS(name, start, stop) RREPSI(name, start, stop, 1)
#define RREP(name, stop) RREPS(name, 0, stop)
template<typename T> void cins(T &first) { cin >> first; }
template<typename T, typename... Ts> void cins(T &first, T &second, Ts&... rest) {
cin >> first;
cins(second, rest...);
}
#define GET(type, ...) type __VA_ARGS__; cins(__VA_ARGS__)
#define GETI(...) GET(int, __VA_ARGS__)
#define GETLL(...) GET(ll, __VA_ARGS__)
#define GETS(...) GET(string, __VA_ARGS__)
#define GETD(...) GET(double, __VA_ARGS__)
#define GETC(...) GET(char, __VA_ARGS__)
struct hsh {
size_t operator()(uint64_t x) const {
static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
x += FIXED_RANDOM;
x += 0x9e3779b97f4a7c15;
x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
return x ^ (x >> 31);
}
};
const ll mxN = 1e5;
vector<ar<ll, 2>> g[mxN];
int main() {
ios::sync_with_stdio(0);cin.tie(0);
GETI(n, m, k);
REP(mm, m) {
GETI(i, j, w); --i, --j;
g[i].push_back({j, w});
g[j].push_back({i, w});
}
vector<ll> a(k);
REP(i, k) cin >> a[i], --a[i];
vector<bool> special(n);
for (ll x : a) special[x] = true;
vector<ll> vis_cnt(n);
vector<ar<ll, 2>> vis(n, {-1, -1}), dist(n, {-1, -1});
priority_queue<ar<ll, 3>, vector<ar<ll, 3>>, greater<ar<ll, 3>>> pq;
for (ll cur : a) for (auto [nxt, w] : g[cur])
pq.push({w, nxt, cur});
while (pq.size()) {
auto [dhere, cur, source] = pq.top();
pq.pop();
if (vis_cnt[cur]==2) continue;
DEBUG(cur);
DEBUG(vis_cnt[cur]);
DEBUG(vis[cur]);
DEBUG(dist[cur]);
bool ok = true;
REP(p, vis_cnt[cur]) if (vis[cur][p] == source) ok = false;
if (!ok) continue;
vis[cur][vis_cnt[cur]] = source;
dist[cur][vis_cnt[cur]] = dhere;
++vis_cnt[cur];
for (auto [nxt, w] : g[cur]) {
if (vis_cnt[nxt] == 2) continue;
if (nxt == source) continue;
bool ok = true;
REP(p, vis_cnt[nxt]) if (vis[nxt][p] == source) ok = false;
if (!ok) continue;
pq.push({dhere+w, nxt, source});
}
}
vector<ar<ll, 3>> pairs;
REP(i, n)
if (special[i])
REP(p, vis_cnt[i])
if (vis[i][p] != i) pairs.push_back({dist[i][p], min(i, vis[i][p]), max(i, vis[i][p])});
sort(pairs.begin(), pairs.end());
pairs.erase(unique(pairs.begin(), pairs.end()), pairs.end());
DEBUG(pairs);
int P = pairs.size();
ll ans = 1LL<<60;
REP(p0, min(P, 100)) {
auto [d0, i0, j0] = pairs[p0];
REP(p1, min(P, 100)) {
auto [d1, i1, j1] = pairs[p1];
if (i0 == i1) continue;
if (i0 == j1) continue;
if (j0 == i1) continue;
if (j0 == j1) continue;
ans = min(ans, d0+d1);
break;
}
}
cout << ans << '\n';
}
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