#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using namespace atcoder; typedef long long ll; #define rep(i, n) for (int i = 0; i < (int)(n); i++) #define repr(i, n) for (int i = (int)(n) - 1; i >= 0; i--) #define repk(i, k, n) for (int i = k; i < (int)(n); i++) #define all(v) v.begin(), v.end() #define mod1 1000000007 #define mod2 998244353 #define mod3 100000007 #define vi vector #define vs vector #define vc vector #define vl vector #define vb vector #define vvi vector> #define vvc vector> #define vvl vector> #define vvb vector> #define vvvi vector>> #define vvvl vector>> #define pii pair #define pil pair #define pli pair #define pll pair #define vpii vector> #define vpll vector> #define vvpii vector>> #define vvpll vector>> // using mint = modint998244353; template void debug(T e) { cerr << e << endl; } template void debug(vector &v) { rep(i, v.size()) { cerr << v[i] << " "; } cerr << endl; } template void debug(vector> &v) { rep(i, v.size()) { rep(j, v[i].size()) { cerr << v[i][j] << " "; } cerr << endl; } } template void debug(vector> &v) { rep(i, v.size()) { cerr << v[i].first << " " << v[i].second << endl; } } template void debug(set &st) { for (auto itr = st.begin(); itr != st.end(); itr++) { cerr << *itr << " "; } cerr << endl; } template void debug(multiset &ms) { for (auto itr = ms.begin(); itr != ms.end(); itr++) { cerr << *itr << " "; } cerr << endl; } template void debug(map &mp) { for (auto itr = mp.begin(); itr != mp.end(); itr++) { cerr << itr->first << " " << itr->second << endl; } } void debug_out() { cerr << endl; } template void debug_out(Head H, Tail... T) { cerr << H << " "; debug_out(T...); } using mint = modint998244353; void debug_mint1(vector &vec) { for (int i = 0; i < vec.size(); i++) { cerr << vec[i].val() << " "; } cerr << endl; } void debug_mint2(vector> &vec) { for (int i = 0; i < vec.size(); i++) { for (int j = 0; j < vec[i].size(); j++) { cerr << vec[i][j].val() << " "; } cerr << endl; } } void dijkstra(vvpll &graph, ll v, vl &dist) { priority_queue> pque; pque.push(pll(0, v)); dist[v] = 0; while (pque.size()) { pll p = pque.top(); pque.pop(); if (dist[p.second] != p.first) { continue; } for (auto x : graph[p.second]) { if (dist[x.first] > dist[p.second] + x.second) { dist[x.first] = dist[p.second] + x.second; pque.push(pll(dist[x.first], x.first)); } } } } int main() { ll N, M, K; cin >> N >> M >> K; vector R(K); for (ll i = 0; i < K; i++) { cin >> R[i]; R[i]--; } vector A(M); vector B(M); vector C(M); for (ll i = 0; i < M; i++) { cin >> A[i] >> B[i] >> C[i]; A[i]--; B[i]--; } vector> graph(N, vector(0)); for (ll i = 0; i < M; i++) { graph[A[i]].push_back(make_pair(B[i], i)); graph[B[i]].push_back(make_pair(A[i], i)); } vector> graph2(N, vector(0)); for (ll i = 0; i < M; i++) { graph2[A[i]].push_back(make_pair(B[i], C[i])); graph2[B[i]].push_back(make_pair(A[i], C[i])); } map mp; mp[0]++; mp[N - 1]++; for (ll i = 0; i < K; i++) { mp[A[R[i]]]++; mp[B[R[i]]]; } vector ids(0); ll now = 0; for (auto it = mp.begin(); it != mp.end(); it++) { ids.push_back(it->first); it->second = now; now++; } ll len = ids.size(); ll INF = 10000000000000023; vector> dists(len, vector(N, INF)); for (ll i = 0; i < ids.size(); i++) { dijkstra(graph2, ids[i], dists[i]); } // とりあえずこの完全グラフを作る vector> dist2(len, vector(len, INF)); for (ll i = 0; i < len; i++) { for (ll j = 0; j < len; j++) { dist2[i][j] = dists[i][ids[j]]; } } vector> num_r(len, vector(len, make_pair(-1, -1))); for (ll i = 0; i < K; i++) { num_r[mp[A[R[i]]]][mp[B[R[i]]]] = make_pair(i, C[R[i]]); num_r[mp[B[R[i]]]][mp[A[R[i]]]] = make_pair(i, C[R[i]]); } // さて、ここからスタート vector> ans_dist(len, vector(1 << K, INF)); ans_dist[0][0] = 0; priority_queue, greater> pque; pque.push(make_pair(0, 0)); while (pque.size()) { pll pp = pque.top(); pque.pop(); ll d = pp.first; ll px = pp.second / (1 << K); ll py = pp.second % (1 << K); // debug_out(d, px, py); if (ans_dist[px][py] < d) { continue; } for (ll i = 0; i < len; i++) { ll nd = d + dist2[px][i]; ll ny = py; if (ans_dist[i][ny] > nd) { ans_dist[i][ny] = nd; pque.push(make_pair(nd, i * (1 << K) + ny)); } if (num_r[px][i].first != -1) { ny |= (1 << num_r[px][i].first); nd = d + num_r[px][i].second; if (ans_dist[i][ny] > nd) { ans_dist[i][ny] = nd; pque.push(make_pair(nd, i * (1 << K) + ny)); } } } } cout << ans_dist[len - 1][(1 << K) - 1] << endl; }