#pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; //#define int long long typedef long long ll; typedef unsigned long long ul; typedef unsigned int ui; //constexpr ll mod = 998244353; constexpr ll mod = 1000000007; const ll INF = mod * mod; typedef pairP; #define rep(i,n) for(int i=0;i=0;i--) #define Rep(i,sta,n) for(int i=sta;i=1;i--) #define Rep1(i,sta,n) for(int i=sta;i<=n;i++) #define all(v) (v).begin(),(v).end() typedef pair LP; template void chmin(T& a, T b) { a = min(a, b); } template void chmax(T& a, T b) { a = max(a, b); } template void cinarray(vector& v) { rep(i, v.size())cin >> v[i]; } template void coutarray(vector& v) { rep(i, v.size()) { if (i > 0)cout << " "; cout << v[i]; } cout << "\n"; } ll mod_pow(ll x, ll n, ll m = mod) { if (n < 0) { ll res = mod_pow(x, -n, m); return mod_pow(res, m - 2, m); } if (abs(x) >= m)x %= m; if (x < 0)x += m; //if (x == 0)return 0; ll res = 1; while (n) { if (n & 1)res = res * x % m; x = x * x % m; n >>= 1; } return res; } //mod should be <2^31 struct modint { int n; modint() :n(0) { ; } modint(ll m) { if (m < 0 || mod <= m) { m %= mod; if (m < 0)m += mod; } n = m; } operator int() { return n; } }; bool operator==(modint a, modint b) { return a.n == b.n; } bool operator<(modint a, modint b) { return a.n < b.n; } modint operator+=(modint& a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= (int)mod; return a; } modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += (int)mod; return a; } modint operator*=(modint& a, modint b) { a.n = ((ll)a.n * b.n) % mod; return a; } modint operator+(modint a, modint b) { return a += b; } modint operator-(modint a, modint b) { return a -= b; } modint operator*(modint a, modint b) { return a *= b; } modint operator^(modint a, ll n) { if (n == 0)return modint(1); modint res = (a * a) ^ (n / 2); if (n % 2)res = res * a; return res; } ll inv(ll a, ll p) { return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p); } modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); } modint operator/=(modint& a, modint b) { a = a / b; return a; } const int max_n = 1 << 21; modint fact[max_n], factinv[max_n]; void init_f() { fact[0] = modint(1); for (int i = 0; i < max_n - 1; i++) { fact[i + 1] = fact[i] * modint(i + 1); } factinv[max_n - 1] = modint(1) / fact[max_n - 1]; for (int i = max_n - 2; i >= 0; i--) { factinv[i] = factinv[i + 1] * modint(i + 1); } } modint comb(int a, int b) { if (a < 0 || b < 0 || a < b)return 0; return fact[a] * factinv[b] * factinv[a - b]; } modint combP(int a, int b) { if (a < 0 || b < 0 || a < b)return 0; return fact[a] * factinv[a - b]; } ll gcd(ll a, ll b) { a = abs(a); b = abs(b); if (a < b)swap(a, b); while (b) { ll r = a % b; a = b; b = r; } return a; } using ld = long double; //typedef long double ld; typedef pair LDP; const ld eps = 1e-10; const ld pi = acosl(-1.0); template void addv(vector& v, int loc, T val) { if (loc >= v.size())v.resize(loc + 1, 0); v[loc] += val; } /*const int mn = 2000005; bool isp[mn]; vector ps; void init() { fill(isp + 2, isp + mn, true); for (int i = 2; i < mn; i++) { if (!isp[i])continue; ps.push_back(i); for (int j = 2 * i; j < mn; j += i) { isp[j] = false; } } }*/ //[,val) template auto prev_itr(set& st, T val) { auto res = st.lower_bound(val); if (res == st.begin())return st.end(); res--; return res; } //[val,) template auto next_itr(set& st, T val) { auto res = st.lower_bound(val); return res; } using mP = pair; mP operator+(mP a, mP b) { return { a.first + b.first,a.second + b.second }; } mP operator+=(mP& a, mP b) { a = a + b; return a; } mP operator-(mP a, mP b) { return { a.first - b.first,a.second - b.second }; } mP operator-=(mP& a, mP b) { a = a - b; return a; } LP operator+(LP a, LP b) { return { a.first + b.first,a.second + b.second }; } LP operator+=(LP& a, LP b) { a = a + b; return a; } LP operator-(LP a, LP b) { return { a.first - b.first,a.second - b.second }; } LP operator-=(LP& a, LP b) { a = a - b; return a; } mt19937 mt(time(0)); const string drul = "DRUL"; string senw = "SENW"; //DRUL,or SENW int dx[4] = { 1,0,-1,0 }; int dy[4] = { 0,1,0,-1 }; //----------------------------------------- struct uf { private: vector par, ran; public: uf(int n) { par.resize(n, 0); ran.resize(n, 0); rep(i, n) { par[i] = i; } } int find(int x) { if (par[x] == x)return x; else return par[x] = find(par[x]); } void unite(int x, int y) { x = find(x), y = find(y); if (x == y)return; if (ran[x] < ran[y]) { par[x] = y; } else { par[y] = x; if (ran[x] == ran[y])ran[x]++; } } bool same(int x, int y) { return find(x) == find(y); } }; //O(N3^T+N^22^T) template struct Steiner_Tree { int n; struct edge { int to; T cost; }; vector> G; T sup; Steiner_Tree(int _n,T _sup) { n = _n; sup = _sup; G.resize(n); } void add_edge(int a, int b, T c) { G[a].push_back({ b,c }); G[b].push_back({ a,c }); } T query(vector ids) { if (ids.size() == 1)return 0; int las = ids.back(); ids.pop_back(); int len = ids.size(); vector> dp((1 << len), vector(n,sup)); using speP = pair; priority_queue, greater> q; rep(i, len) { dp[(1 << i)][ids[i]] = 0; } rep(i, (1 << len)) { rep(j, n) { if (dp[i][j] == sup)continue; q.push({ dp[i][j],{i,j} }); } while (!q.empty()) { speP p = q.top(); q.pop(); int x = p.second.first, y = p.second.second; if (dp[x][y] < p.first)continue; //next vertice for (edge e : G[y]) { T nd = e.cost + p.first; int nx = x; int ny = e.to; if (nd < dp[nx][ny]) { dp[nx][ny] = nd; q.push({ nd,{nx,ny} }); } } //merge region int ri = (1 << len) - 1 - i; for (int b = ri;; b = ri & (b - 1)) { if (b == 0)break; if (b < i) { chmin(dp[i | b][y], dp[i][y] + dp[b][y]); } } } } return dp[(1 << len) - 1][las]; } }; void solve() { int n, m, k; cin >> n >> m >> k; if (k <= 16) { Steiner_Tree st(n,mod); rep(i, m) { int a, b, c; cin >> a >> b >> c; a--; b--; st.add_edge(a, b, c); } vector v(k); rep(i, k) { cin >> v[i]; v[i]--; } int ans = st.query(v); cout << ans << "\n"; } else { vector> vp; rep(i, m) { int a, b, c; cin >> a >> b >> c; a--; b--; vp.push_back({ c,{a,b} }); } sort(all(vp)); vector v(k); rep(i, k) { cin >> v[i]; v[i]--; } vector vr; rep(i, n) { bool exi = false; for (int id : v)if (id == i)exi = true; if (!exi) { vr.push_back(i); } } int ans = mod; vector exi(n); rep(i, (1 << vr.size())) { uf u(n); vector ids = v; rep(j, vr.size())if (i & (1 << j))ids.push_back(vr[j]); for (int id : ids)exi[id] = true; int sum = 0; int cnt = 0; for (auto p : vp) { int a = p.second.first, b = p.second.second; if (exi[a]&&exi[b]&&!u.same(a, b)) { cnt++; sum += p.first; u.unite(a, b); if (cnt == ids.size() - 1)break; } } //cout << "?? " << ids.size() << " " << cnt << "\n"; if (cnt == ids.size() - 1) { chmin(ans, sum); } for (int id : ids)exi[id] = false; } cout << ans << "\n"; } } signed main() { ios::sync_with_stdio(false); cin.tie(0); cout << fixed << setprecision(10); //init_f(); //init(); //expr(); //while(true) //int t; cin >> t; rep(i, t) solve(); return 0; }