#include using namespace std; struct iofast_t { iofast_t() { ios::sync_with_stdio(false); cin.tie(nullptr); } } iofast; struct uns_t {} uns; template auto vec(Element init, Head arg, Args ...args) { if constexpr (sizeof...(Args) == 0) return vector(arg, init); else return vector(arg, vec(init, args...)); } template auto vec(uns_t, Head arg, Args ...args) { return vec(Element(), arg, args...); } template auto distance(const Container &c, decltype(begin(c)) iter) { return distance(begin(c), iter); } template ::value_type>> auto isort(RIter first, RIter last, Compare comp = Compare()) { vector i(distance(first, last)); iota(begin(i), end(i), 0); sort(begin(i), end(i), [&](auto x, auto y) { return comp(*(first + x), *(first + y)); }); return i; } template typename, typename = void_t<>> struct detect : false_type {}; template typename Check> struct detect>> : true_type {}; template typename Check> constexpr inline bool detect_v = detect::value; template using has_member_sort = decltype(declval().sort()); template > auto sorted(Container c, Compare comp = Compare()) { if constexpr (detect_v) { c.sort(comp); return c; } else { sort(begin(c), end(c), comp); return c; } } template > auto uniqued(Container c, Compare comp = Compare()) { c.erase(unique(begin(c), end(c), comp), end(c)); return c; } template > T &chmin(T &l, T r, Compare &&f = less()) { return l = min(l, r, f); } template > T &chmax(T &l, T r, Compare &&f = less()) { return l = max(l, r, f); } template using pqueue = priority_queue, greater>; int main() { constexpr auto inf = INT_MAX / 2; int n, m, k; cin >> n >> m >> k; auto r = vec(uns, k); for (auto &v : r) { cin >> v; --v; } auto g = vec>(uns, n, 0); auto e = vec>(uns, m); for (auto &[a, b, c] : e) { cin >> a >> b >> c; --a; --b; g[a].push_back({ b, c }); g[b].push_back({ a, c }); } auto dijkstra = [&](int beg) { pqueue> que; auto dist = vec(inf, n); que.push({ 0, beg }); dist[beg] = 0; while (!empty(que)) { auto [d, v] = que.top(); que.pop(); if (dist[v] < d) { continue; } for (auto [u, c] : g[v]) { if (dist[u] <= d + c) { continue; } dist[u] = d + c; que.push({ d + c, u }); } } return dist; }; auto v = vec(uns, 0); for (auto i : r) { auto [a, b, _] = e[i]; v.push_back(a); v.push_back(b); } v.push_back(0); v.push_back(n - 1); v = uniqued(sorted(move(v))); auto vtoi = vec(uns, n); for (int i = 0; i < size(v); ++i) { vtoi[v[i]] = i; } auto dist = vec(uns, size(v), size(v)); for (int i = 0; i < size(v); ++i) { auto d = dijkstra(v[i]); for (int j = 0; j < size(v); ++j) { dist[i][j] = d[v[j]]; } } auto dp = vec(inf, 1 << k, size(v)); dp[0][0] = 0; for (int i = 1; i < (1 << k); ++i) { for (int j = 0; j < k; ++j) { if (!(i & (1 << j))) { continue; } auto [a, b, c] = e[r[j]]; a = vtoi[a]; b = vtoi[b]; for (int k = 0; k < size(v); ++k) { chmin(dp[i][a], dp[i ^ (1 << j)][k] + dist[k][b] + c); chmin(dp[i][b], dp[i ^ (1 << j)][k] + dist[k][a] + c); } } } int ans = inf; for (int i = 0; i < size(v); ++i) { chmin(ans, dp[(1 << k) - 1][i] + dist[i][size(v) - 1]); } cout << ans << endl; }