#include "bits/stdc++.h" #include #include #pragma GCC target("avx2") #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #define ALL(x) (x).begin(), (x).end() #define RALL(x) (x).rbegin(), (x).rend() #define SZ(x) ((lint)(x).size()) #define FOR(i, begin, end) for(lint i=(begin),i##_end_=(end);i=i##_begin_;--i) #define REP(i, n) FOR(i,0,n) #define IREP(i, n) IFOR(i,0,n) #define endk '\n' using namespace std; typedef unsigned long long _ulong; typedef long long int lint; typedef long double ld; typedef pair plint; typedef pair pld; struct fast_ios { fast_ios() { cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(10); }; } fast_ios_; template auto add = [](T a, T b) -> T { return a + b; }; template auto mul = [](T a, T b) -> T { return a * b; }; template auto f_max = [](T a, T b) -> T { return max(a, b); }; template auto f_min = [](T a, T b) -> T { return min(a, b); }; template using V = vector; using Vl = V; using VVl = V; using VVVl = V>; template< typename T > ostream& operator<<(ostream& os, const vector< T >& v) { for (int i = 0; i < (int)v.size(); i++) os << v[i] << (i + 1 != v.size() ? " " : ""); return os; } template< typename T >istream& operator>>(istream& is, vector< T >& v) { for (T& in : v) is >> in; return is; } 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 (b < a) { a = b; return 1; } return 0; } template T div_floor(T a, T b) { if (b < 0) a *= -1, b *= -1; return a >= 0 ? a / b : (a + 1) / b - 1; } template T div_ceil(T a, T b) { if (b < 0) a *= -1, b *= -1; return a > 0 ? (a - 1) / b + 1 : a / b; } template struct rec { F f; rec(F&& f_) : f(std::forward(f_)) {} template auto operator()(Args &&... args) const { return f(*this, std::forward(args)...); } }; lint gcd(lint a, lint b) { if (b == 0) return a; else return gcd(b, a % b); } lint digit(lint a) { return (lint)log10(a); } lint e_dist(plint a, plint b) { return abs(a.first - b.first) * abs(a.first - b.first) + abs(a.second - b.second) * abs(a.second - b.second); } lint m_dist(plint a, plint b) { return abs(a.first - b.first) + abs(a.second - b.second); } bool check_overflow(lint a, lint b, lint limit) { if (b == 0) return false; return a >= limit / b; } // a * b > c => true void Worshall_Floyd(VVl& g) { REP(k, SZ(g)) REP(i, SZ(g)) REP(j, SZ(g)) chmin(g[i][j], g[i][k] + g[k][j]); } const lint MOD1000000007 = 1000000007, MOD998244353 = 998244353, INF = 2e18; lint dx[8] = { 0, -1, 0, 1, 1, -1, 1, -1 }, dy[8] = { -1, 0, 1, 0, -1, -1, 1, 1 }; bool YN(bool flag) { cout << (flag ? "YES" : "NO") << endk; return flag; } bool yn(bool flag) { cout << (flag ? "Yes" : "No") << endk; return flag; } struct Edge { lint from, to; lint cost; Edge() { } Edge(lint u, lint v, lint c) { cost = c; from = u; to = v; } bool operator<(const Edge& e) const { return cost < e.cost; } }; struct WeightedEdge { lint to; lint cost; WeightedEdge(lint v, lint c = 1) { to = v; cost = c; } bool operator<(const WeightedEdge& e) const { return cost < e.cost; } }; using WeightedGraph = V>; typedef pair tlint; typedef pair pld; typedef pair qlint; typedef pair valstr; typedef pair valv; Vl Dijkstra(WeightedGraph& g, int s) { Vl dist(SZ(g), INF); deque visited(SZ(g), false); priority_queue que; que.push({ 0, s }); dist[s] = 0; while (!que.empty()) { plint curr = que.top(); que.pop(); if (visited[curr.second]) continue; visited[curr.second] = true; if (dist[curr.second] < curr.first) continue; for (auto nxt : g[curr.second]) { if (visited[nxt.to]) continue; if (dist[nxt.to] > dist[curr.second] + nxt.cost) { dist[nxt.to] = dist[curr.second] + nxt.cost; que.emplace(-dist[nxt.to], nxt.to); } } } return dist; } int main() { lint N, M, K; cin >> N >> M >> K; Vl arr(K); cin >> arr; lint base_sum = 0; set st; REP(i, K) st.insert(arr[i] - 1); WeightedGraph g(N); V ps; set sts; REP(i, M) { lint u, v, c; cin >> u >> v >> c; u--; v--; if (u > v) swap(u, v); if (st.count(i)) { base_sum += c; ps.push_back({ u, v }); sts.insert(u); sts.insert(v); } g[u].push_back({ v, c }); g[v].push_back({ u, c }); } map fx; for (lint v : sts) fx[v] = SZ(fx); VVl dist(SZ(fx), Vl(SZ(fx))); for (lint v : sts) { auto _dist = Dijkstra(g, v); for (lint _v : sts) { dist[fx[v]][fx[_v]] = _dist[_v]; } } auto s = Dijkstra(g, 0), t = Dijkstra(g, N - 1); VVl dp(1 << K, Vl(SZ(fx), INF)); REP(i, K) { auto [u, v] = ps[i]; dp[1 << i][fx[v]] = s[u]; dp[1 << i][fx[u]] = s[v]; } REP(mask, 1 << K) { REP(i, SZ(fx)) { REP(j, K) { if (mask >> j & 1) continue; auto [u, v] = ps[j]; chmin(dp[mask | (1 << j)][fx[v]], dp[mask][i] + dist[i][fx[u]]); chmin(dp[mask | (1 << j)][fx[u]], dp[mask][i] + dist[i][fx[v]]); } } } lint minv = INF; REP(i, K) { auto [u, v] = ps[i]; chmin(minv, dp[(1 << K) - 1][fx[u]] + t[u] + base_sum); chmin(minv, dp[(1 << K) - 1][fx[v]] + t[v] + base_sum); } cout << minv << endk; }