#include using namespace std; template class Kruskal { vector data; int N; bool unite(int x, int y) { x = root(x), y = root(y); if (x == y) return (false); if (data[x] > data[y]) swap(x, y); data[x] += data[y]; data[y] = x; return (true); } int root(int k) { if (data[k] < 0) return (k); return (data[k] = root(data[k])); } bool same(int x, int y) { return root(x) == root(y); } int size(int k) { return (-data[root(k)]); } // public: struct edge { int from, to; T cost; bool used; edge(int from, int to, T cost) : from(from), to(to), cost(cost), used(false) {} }; vector edges; Kruskal(int n) : N(n) { data.assign(n, -1); } void add_edge(int from, int to, T cost = 1) { edges.emplace_back(from, to, cost); } void build() { sort(edges.begin(), edges.end(), [](const edge& a, const edge& b) { return a.cost < b.cost; }); } T solve(long long bit) { T ret = 0; for (auto& e : edges) { if (bit & (1ll << e.from) && bit & (1ll << e.to)) if (unite(e.from, e.to)) ret += e.cost; } if (size(__builtin_ffsll(bit) - 1) != __builtin_popcountll(bit)) { return T(-1); } else return ret; } void reset() { data.assign(N, -1); } }; template struct Steiner { vector> dist; vector> dp; vector terminal; const T inf = numeric_limits::max() / 10; int N; Steiner(int n) : N(n), dist(n, vector(n)) { for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) { if (i != j) dist[i][j] = inf; } } } void add_edge(int u, int v, T cost) { dist[u][v] = cost; dist[v][u] = cost; } void add_terminal(int u) { terminal.emplace_back(u); } T build() { int t = (int)terminal.size(); if (t == 0) return (T)0; dp.resize((1 << t), vector(N, inf)); for (int i = 0; i < t; i++) { dp[(1 << i)][terminal[i]] = 0; } for (int k = 0; k < N; k++) { for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) { dist[i][j] = min(dist[i][j], dist[i][k] + dist[k][j]); } } } for (int mask = 0; mask < (1 << t); mask++) { for (int i = 0; i < N; i++) { for (int bit = mask; bit > 0; bit = (bit - 1) & mask) { dp[mask][i] = min(dp[mask][i], dp[bit][i] + dp[bit ^ mask][i]); } } for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) { dp[mask][i] = min(dp[mask][i], dp[mask][j] + dist[j][i]); } } } return dp[(1 << t) - 1][terminal[0]]; } }; int main() { int N, M, T, a[1500], b[1500], c[1500], v[40]; cin >> N >> M >> T; for (int i = 0; i < M; i++) { cin >> a[i] >> b[i] >> c[i]; a[i]--; b[i]--; } for (int i = 0; i < T; i++) { cin >> v[i]; v[i]--; } if (T < 16) { Steiner st(N); for (int i = 0; i < M; i++) { st.add_edge(a[i], b[i], c[i]); } for (int i = 0; i < T; i++) { st.add_terminal(v[i]); } cout << st.build() << endl; } else { int ans = 1e7; long long mask = 0; for (int i = 0; i < T; i++) { mask |= (1ll << v[i]); } Kruskal krs(N); for (int i = 0; i < M; i++) { krs.add_edge(a[i], b[i], c[i]); krs.add_edge(b[i], a[i], c[i]); } krs.build(); for (long long bit = mask; bit < (1ll << N); bit = (bit + 1) | mask) { int tmp = krs.solve(bit); krs.reset(); if (tmp == -1) continue; ans = min(ans, tmp); } cout << ans << endl; } }