// >>> TEMPLATES #include using namespace std; using ll = long long; using ld = long double; using i32 = int32_t; using i64 = int64_t; using u32 = uint32_t; using u64 = uint64_t; #define int ll #define rep(i, n) for (int i = 0; i < (int)(n); i++) #define rep1(i, n) for (int i = 1; i <= (int)(n); i++) #define repR(i, n) for (int i = (int)(n)-1; i >= 0; i--) #define rep1R(i, n) for (int i = (int)(n); i >= 1; i--) #define loop(i, a, B) for (int i = a; i B; i++) #define loopR(i, a, B) for (int i = a; i B; i--) #define all(x) begin(x), end(x) #define allR(x) rbegin(x), rend(x) #define rng(x, l, r) begin(x) + (l), begin(x) + (r) #define pb push_back #define eb emplace_back #define fst first #define snd second template constexpr auto mp(A &&a, B &&b) { return make_pair(forward(a), forward(b)); } template constexpr auto mt(T&&... x) { return make_tuple(forward(x)...); } template auto constexpr inf_ = numeric_limits::max()/2-1; auto constexpr INF32 = inf_; auto constexpr INF64 = inf_; auto constexpr INF = inf_; #ifdef LOCAL #include "debug.hpp" #else #define dump(...) (void)(0) #define say(x) (void)(0) #define debug if (0) #endif template struct pque : priority_queue, Comp> { vector &data() { return this->c; } void clear() { this->c.clear(); } }; template using pque_max = pque>; template using pque_min = pque>; template ::value, int> = 0> ostream& operator<<(ostream& os, T const& a) { bool f = true; for (auto const& x : a) os << (f ? "" : " ") << x, f = false; return os; } template ::value, int> = 0> ostream& operator<<(ostream& os, const T (&a)[N]) { bool f = true; for (auto const& x : a) os << (f ? "" : " ") << x, f = false; return os; } template ())), class = typename enable_if::value>::type> istream& operator>>(istream& is, T &a) { for (auto& x : a) is >> x; return is; } template ostream& operator<<(ostream& os, pair const& p) { return os << p.first << " " << p.second; } template istream& operator>>(istream& is, pair& p) { return is >> p.first >> p.second; } struct IOSetup { IOSetup() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); } } iosetup; template struct FixPoint : private F { constexpr FixPoint(F&& f) : F(forward(f)) {} template constexpr auto operator()(T&&... x) const { return F::operator()(*this, forward(x)...); } }; struct MakeFixPoint { template constexpr auto operator|(F&& f) const { return FixPoint(forward(f)); } }; #define MFP MakeFixPoint()| #define def(name, ...) auto name = MFP [&](auto &&name, __VA_ARGS__) template struct vec_impl { using type = vector::type>; template static type make_v(size_t n, U&&... x) { return type(n, vec_impl::make_v(forward(x)...)); } }; template struct vec_impl { using type = T; static type make_v(T const& x = {}) { return x; } }; template using vec = typename vec_impl::type; template auto make_v(Args&&... args) { return vec_impl::make_v(forward(args)...); } template void quit(T const& x) { cout << x << endl; exit(0); } template constexpr bool chmin(T& x, U const& y) { if (x > (T)y) { x = (T)y; return true; } return false; } template constexpr bool chmax(T& x, U const& y) { if (x < (T)y) { x = (T)y; return true; } return false; } template constexpr auto sumof(It b, It e) { return accumulate(b, e, typename iterator_traits::value_type{}); } template int sz(T const& x) { return x.size(); } template int lbd(C const& v, T const& x) { return lower_bound(begin(v), end(v), x)-begin(v); } template int ubd(C const& v, T const& x) { return upper_bound(begin(v), end(v), x)-begin(v); } constexpr ll mod(ll x, ll m) { assert(m > 0); return (x %= m) < 0 ? x+m : x; } constexpr ll div_floor(ll x, ll y) { assert(y != 0); return x/y - ((x^y) < 0 and x%y); } constexpr ll div_ceil(ll x, ll y) { assert(y != 0); return x/y + ((x^y) > 0 and x%y); } constexpr int dx[] = { 1, 0, -1, 0, 1, -1, -1, 1 }; constexpr int dy[] = { 0, 1, 0, -1, 1, 1, -1, -1 }; constexpr int popcnt(ll x) { return __builtin_popcountll(x); } mt19937_64 seed_{random_device{}()}; template Int rand(Int a, Int b) { return uniform_int_distribution(a, b)(seed_); } i64 irand(i64 a, i64 b) { return rand(a, b); } // [a, b] u64 urand(u64 a, u64 b) { return rand(a, b); } // template void shuffle(It l, It r) { shuffle(l, r, seed_); } template V &operator--(V &v) { for (auto &x : v) --x; return v; } template V &operator++(V &v) { for (auto &x : v) ++x; return v; } // <<< struct edge { int to, cost, bit; }; // >>> dijkstra #ifndef EDGE_INFO #define EDGE_INFO constexpr int dest(int v) { return v; } template ().to)> constexpr int dest(E const& e) { return e.to; } constexpr int cost(int) { return 1; } template ().cost)> constexpr auto cost(E const& e) { return e.cost; } template using cost_t = decltype(cost(declval())); #endif vector> dijkstra(vector> const& g, int s, cost_t inf) { rep (x, g.size()) { for (auto const& e : g[x]) { assert(cost(e) >= 0); } } vector> d(g.size(), inf); pque_min, int>> q; d[s] = 0; q.emplace(0, s); while (q.size()) { auto p = q.top(); q.pop(); const int x = p.snd; if (d[x] < p.fst) continue; for (auto const& e : g[x]) { const int y = dest(e); if (chmin(d[y], d[x] + cost(e))) { q.emplace(d[y], y); } } } return d; } // <<< template int sort_unique(vec &v) { sort(begin(v), end(v)); v.erase(unique(begin(v), end(v)), end(v)); return v.size(); } int32_t main() { int n, m, k; cin >> n >> m >> k; vector r(k); cin >> r; --r; vector> g(n); vector a(m), b(m), c(m); rep (i, m) { cin >> a[i] >> b[i] >> c[i], --a[i], --b[i]; g[a[i]].pb({b[i], c[i], 0}); g[b[i]].pb({a[i], c[i], 0}); } vector vs = { 0, n-1 }; for (int i : r) vs.eb(a[i]), vs.eb(b[i]); int N = sort_unique(vs); vector> G(N); rep (i, N) { auto d = dijkstra(g, vs[i], INF); rep (j, N) G[i].pb({j, d[vs[j]], 0}); } rep (j, k) { int i = r[j]; int x = lbd(vs, a[i]); int y = lbd(vs, b[i]); G[x].pb({y, c[i], 1LL<(1LL<> pq; pq.emplace(0, 0, 0); while (pq.size()) { auto [d, now, x] = pq.top(); pq.pop(); if (dist[now][x] < d) continue; for (auto [y, c, bit] : G[x]) { int nxt = now | bit; if (chmin(dist[nxt][y], d + c)) { pq.emplace(d + c, nxt, y); } } } cout << dist[(1LL<