// includes #include using namespace std; // macros #define pb emplace_back #define mk make_pair #define FOR(i, a, b) for(int i=(a);i<(b);++i) #define rep(i, n) FOR(i, 0, n) #define rrep(i, n) for(int i=((int)(n)-1);i>=0;i--) #define irep(itr, st) for(auto itr = (st).begin(); itr != (st).end(); ++itr) #define irrep(itr, st) for(auto itr = (st).rbegin(); itr != (st).rend(); ++itr) #define all(x) (x).begin(),(x).end() #define sz(x) ((int)(x).size()) #define UNIQUE(v) v.erase(unique(v.begin(), v.end()), v.end()) #define bit(n) (1LL<<(n)) // functions template bool chmax(T &a, const T &b){if(a < b){a = b; return 1;} return 0;} template bool chmin(T &a, const T &b){if(a > b){a = b; return 1;} return 0;} template istream &operator>>(istream &is, vector &vec){for(auto &v: vec)is >> v; return is;} template ostream &operator<<(ostream &os, const vector& vec){for(int i = 0; i < vec.size(); i++){ os << vec[i]; if(i + 1 != vec.size())os << " ";} return os;} template ostream &operator<<(ostream &os, const set& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;} template ostream &operator<<(ostream &os, const unordered_set& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;} template ostream &operator<<(ostream &os, const multiset& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;} template ostream &operator<<(ostream &os, const unordered_multiset& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;} template ostream &operator<<(ostream &os, const pair &p){os << p.first << " " << p.second; return os;} template ostream &operator<<(ostream &os, const map &mp){for(auto itr = mp.begin(); itr != mp.end(); ++itr){ os << itr->first << ":" << itr->second; auto titr = itr; if(++titr != mp.end())os << " "; } return os;} template ostream &operator<<(ostream &os, const unordered_map &mp){for(auto itr = mp.begin(); itr != mp.end(); ++itr){ os << itr->first << ":" << itr->second; auto titr = itr; if(++titr != mp.end())os << " "; } return os;} // types using ll = long long int; using P = pair; // constants const int inf = 1e9; const ll linf = 1LL << 50; const double EPS = 1e-10; const int mod = 1000000007; const int dx[4] = {-1, 0, 1, 0}; const int dy[4] = {0, -1, 0, 1}; // io struct fast_io{ fast_io(){ios_base::sync_with_stdio(false); cin.tie(0); cout << fixed << setprecision(20);} } fast_io_; template struct Graph { int n; vector > d; vector > path; Graph(int n): n(n) { d = vector>(n, vector(n, numeric_limits::max() / 10)); path = vector>(n, vector(n, -1)); for(int i = 0; i < n; i++)d[i][i] = 0; } void warshall_floyd(){ for(int k = 0; k < n; k++){ for(int i = 0; i < n; i++){ for(int j = 0; j < n; j++){ if(d[i][j] > d[i][k] + d[k][j]){ d[i][j] = d[i][k] + d[k][j]; path[i][j] = k; } } } } } void adde(int at, int to, T cost){ d[at][to] = cost; } vector& operator[](size_t i){ return d[i]; } }; using GraphI = Graph; using GraphL = Graph; template struct SteinerTree{ int n; vector> d; T inf = numeric_limits::max() / 10; explicit SteinerTree(int n): n(n){ d.resize(n, vector(n, inf)); for(int i = 0; i < n; i++)d[i][i] = 0; } void adde(int from, int to, T cost){ d[from][to] = min(d[from][to], cost); } T steiner_tree(const vector &v){ // warshall floyd Graph g(n); for(int i = 0; i < n; i++){ for(int j = 0; j < n; j++){ if(i != j && d[i][j] != inf)g.adde(i, j, d[i][j]); } } g.warshall_floyd(); int t = v.size(); vector> opt(1 << t, vector(n, inf)); for(int i = 0; i < t; i++){ for(int j = 0; j < n; j++){ opt[1 << i][j] = g.d[v[i]][j]; } } for(int s = 0; s < (1 << t); s++){ if(!(s & (s - 1)))continue; for(int p = 0; p < n; p++){ for(int u = s; ; u = (u - 1) & s){ opt[s][p] = min(opt[s][p], opt[u][p] + opt[s - u][p]); if(u == 0)break; } } for(int p = 0; p < n; p++){ for(int q = 0; q < n; q++){ opt[s][p] = min(opt[s][p], opt[s][q] + g.d[p][q]); } } } T res = inf; for(int s = 0; s < (1 << t); s++){ for(int p = 0; p < n; p++){ res = min(res, opt[s][p] + opt[(1< par, rank_, siz; UnionFind_(){} explicit UnionFind_(int n): rank_(n, 0), siz(n, 1) { par.resize(n); for(int i = 0; i < n; i++)par[i] = i; } int find(int x) { if(par[x] == x)return x; else return par[x] = find(par[x]); } bool same(int x, int y) { if(find(x) == find(y))return true; else return false; } bool unite(int x, int y){ int xp = find(x); int yp = find(y); if(xp == yp)return false; if(rank_[xp] > rank_[yp]){ par[yp] = xp; siz[xp] += siz[yp]; } else if(rank_[xp] < rank_[yp]){ par[xp] = yp; siz[yp] += siz[xp]; } else { par[yp] = xp; siz[xp] += siz[yp]; rank_[xp]++; } return true; } int size(int i){ return siz[find(i)]; } } UnionFind; template struct edge{ int from; int to; T cost; }; template bool comp(const edge &a, const edge &b){ return a.cost < b.cost; } template struct GraphK { int n; vector> es; GraphK(int n_){ n = n_; } void adde(int from, int to, T cost){ es.push_back((edge){from, to, cost}); } T kruskal(){ T res = 0; UnionFind uf(n); sort(es.begin(), es.end(), comp); for(auto e: es){ int from = e.from; int to = e.to; T cost = e.cost; if(uf.same(from, to))continue; res += cost; uf.unite(from, to); } return res; } }; using GraphKI = GraphK; int eds[36][36]; int main(int argc, char const* argv[]) { int n, m, t; cin >> n >> m >> t; if(t <= 15){ SteinerTree st(n); rep(i, m){ int a, b, c; cin >> a >> b >> c, a--, b--; st.adde(a, b, c); st.adde(b, a, c); } vector v(t); cin >> v; rep(i, t)v[i]--; cout << st.steiner_tree(v) << endl; }else{ rep(i, n)rep(j, n)eds[i][j] = inf; rep(i, m){ int a, b, c; cin >> a >> b >> c, a--, b--; eds[a][b] = c; eds[b][a] = c; } vector use(n, false); rep(i, t){ int u; cin >> u, u--; use[u] = true; } vector ve; ll res = linf; rep(i, n)if(!use[i])ve.pb(i); //for(int i = 0; i < (1 << (n - t)); i++){ rrep(i, (1 << (n - t))){ vector used = use; for(int j = 0; j < n - t; j++){ if((i >> j) & 1){ used[ve[j]] = true; } } int curr = 0; vector mp(n, -1); rep(j, n)if(used[j])mp[j] = curr++; vector vex; rep(j, n)if(used[j])vex.pb(j); GraphKI gk(sz(vex)); UnionFind uf(sz(vex)); for(int j = 0; j < sz(vex); j++){ for(int k = 0; k < sz(vex); k++){ if(j != k && eds[vex[j]][vex[k]] != inf){ gk.adde(j, k, eds[vex[j]][vex[k]]); uf.unite(j, k); } } } if(uf.siz[uf.find(0)] != sz(vex)){ continue; } res = min(res, (ll)gk.kruskal()); } cout << res << endl; } return 0; }