#include #include #include #include #define rep(i, l, n) for (int i = (l); i < (n); i++) using namespace std; using Pair = pair; template using V = vector; template using VV = V >; const int inf = 2000000000; VV dijkstra(int n, VV& edge, V& R, VV& route) { VV dist(n, V(0)); V st = { 0,n - 1 }; rep(i, 0, R.size()) { st.push_back(edge[R[i]][0]); st.push_back(edge[R[i]][1]); } rep(i, 0, st.size()) { int k = st[i]; V di(n, -1); priority_queue, greater > pq; pq.push({ 0,k }); int cnt = 0; while (pq.size() && cnt < n) { Pair p = pq.top(); pq.pop(); int d = p.first; int v = p.second; if (di[v] == -1) { cnt++; di[v] = d; rep(j, 0, route[v].size()) { Pair p = { d + route[v][j].second,route[v][j].first }; pq.push(p); } } } dist[k] = di; } return dist; } int main(void) { int N, M, K; cin >> N >> M >> K; V R(K); rep(i, 0, K) { cin >> R[i]; R[i] -= 1; } VV edge(M, V(3)); VV route(N, V(0)); rep(i, 0, M) { rep(j, 0, 3) { cin >> edge[i][j]; } edge[i][0] -= 1; edge[i][1] -= 1; route[edge[i][0]].push_back({ edge[i][1],edge[i][2] }); route[edge[i][1]].push_back({ edge[i][0],edge[i][2] }); } int ans = inf; int rsum = 0; rep(i, 0, R.size()) { rsum += edge[R[i]][2]; } VV dist = dijkstra(N, edge, R, route); V > dp(1 << K, VV(K, V(2, inf))); rep(i, 0, K) { rep(j, 0, 2) { dp[1 << i][i][j] = rsum + dist[0][edge[R[i]][j]]; } } rep(bit, 1, 1 << K) { rep(s, 0, K) { if ((bit & (1 << s)) == 0) { continue; } rep(i, 0, 2) { rep(t, 0, K) { if (bit & (1 << t)) { continue; } int b = bit | (1 << t); rep(j, 0, 2) { int p = edge[R[t]][j]; int d = dp[bit][s][i ^ 1] + dist[edge[R[s]][i]][edge[R[t]][j]]; if (dp[b][t][j] > d) { dp[b][t][j] = d; } } } } } } ans = inf; rep(i, 0, K) { rep(j, 0, 2) { int d = dp[(1 << K) - 1][i][j ^ 1] + dist[edge[R[i]][j]][N - 1]; if (ans > d) { ans = d; } } } cout << ans << endl; return 0; }