#include using namespace std; #include using namespace atcoder; //using mint = modint998244353; using mint = modint1000000007; using ll = long long; using ld = long double; using pll = pair; using tlll = tuple; constexpr ll INF = 1LL << 60; template bool chmin(T& a, T b) {if (a > b) {a = b; return true;} return false;} template bool chmax(T& a, T b) {if (a < b) {a = b; return true;} return false;} ll safemod(ll A, ll M) {return (A % M + M) % M;} ll divfloor(ll A, ll B) {if (B < 0) {return divfloor(-A, -B);} return (A - safemod(A, B)) / B;} ll divceil(ll A, ll B) {if (B < 0) {return divceil(-A, -B);} return divfloor(A + B - 1, B);} #define FINALANS(A) do {cout << (A) << '\n'; exit(0);} while (false) template class graph { public: struct edge { ll to; T cost; edge(ll to, T cost) : to(to), cost(cost) {} }; ll N; vector> G; graph(ll n) { N = n; G.resize(N); } void connect(ll sv, ll gv, T c) { G.at(sv).push_back(edge(gv, c)); } void connect2(ll v0, ll v1, T c) { connect(v0, v1, c), connect(v1, v0, c); } vector _01bfs(ll sv) { vector costs(N, INF); costs.at(sv) = 0; deque> deq; for (auto e : G.at(sv)) { if (e.cost == 0) deq.push_front(make_tuple(e.cost, sv, e.to)); else deq.push_back(make_tuple(e.cost, sv, e.to)); } while (!deq.empty()) { auto [c, pv, v] = deq.front(); deq.pop_front(); if (chmin(costs.at(v), costs.at(pv) + c)) { for (auto e : G.at(v)) { if (e.cost == 0) deq.push_front(make_tuple(e.cost, v, e.to)); else deq.push_back(make_tuple(e.cost, v, e.to)); } } } return costs; } vector dijkstra(ll sv) { vector costs(N, INF); costs.at(sv) = 0; priority_queue, vector>, greater>> pque; pque.emplace(make_pair(0, sv)); while (!pque.empty()) { auto [c, v] = pque.top(); pque.pop(); if (costs.at(v) < c) continue; for (auto e : G.at(v)) { T nc = c + e.cost; if (costs.at(e.to) > nc) { costs.at(e.to) = nc; pque.emplace(nc, e.to); } } } return costs; } }; int main() { ll N, M, K; cin >> N >> M >> K; vector R(K); for (ll i = 0; i < K; i++) { cin >> R.at(i); R.at(i)--; } graph gr(N); vector A(M), B(M), C(M); for (ll i = 0; i < M; i++) { ll a, b, c; cin >> a >> b >> c; a--, b--; A.at(i) = a, B.at(i) = b, C.at(i) = c; gr.connect2(a, b, c); } vector V = {0, N - 1}; for (ll i = 0; i < K; i++) { ll a = A.at(R.at(i)), b = B.at(R.at(i)); V.push_back(a), V.push_back(b); } sort(V.begin(), V.end()); V.erase(unique(V.begin(), V.end()), V.end()); ll L = V.size(); /* for (auto v : V) cerr << v << " "; cerr << endl; //*/ vector invV(N, -1); for (ll i = 0; i < L; i++) { invV.at(V.at(i)) = i; } vector> dists(L); for (ll i = 0; i < L; i++) { dists.at(i) = gr.dijkstra(V.at(i)); /* for (ll v = 0; v < N; v++) { cerr << dists.at(i).at(v) << " "; } cerr << endl; //*/ } vector dp(L, vector(1LL << K, INF)); dp.at(0).at(0) = 0; for (ll b = 0; b < (1LL << K); b++) { for (ll i = 0; i < L; i++) { for (ll j = 0; j < K; j++) { ll nb = b | (1LL << j); ll v1 = A.at(R.at(j)), v2 = B.at(R.at(j)); ll ni1 = invV.at(v1), ni2 = invV.at(v2); ll d2 = dists.at(i).at(v1), d1 = dists.at(i).at(v2); ll d = C.at(R.at(j)); chmin(dp.at(ni1).at(nb), dp.at(i).at(b) + d1 + d); chmin(dp.at(ni2).at(nb), dp.at(i).at(b) + d2 + d); //cerr << bitset<2>(b) << " " << i << " " << j << " " << bitset<2>(nb) << " " << v1 << " " << v2 << " " << ni1 << " " << ni2 << " " << d1 << " " << d2 << endl; } } } ll ans = INF; for (ll i = 0; i < L; i++) { ll tmp = dp.at(i).at((1LL << K) - 1) + dists.at(i).at(N - 1); chmin(ans, tmp); } cout << ans << endl; /* for (ll b = 0; b < (1LL << K); b++) { for (ll i = 0; i < L; i++) { cerr << (bitset<2>)b << " " << i << " " << dp.at(i).at(b) << endl; } } //*/ }