#include #include #include #include #include #include #include #include #include #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; using lint = long long; using pint = pair; using plint = pair; struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_; #define ALL(x) (x).begin(), (x).end() #define FOR(i, begin, end) for(int 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) template bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; } template bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; } const std::vector> grid_dxs{{1, 0}, {-1, 0}, {0, 1}, {0, -1}}; int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); } template T1 floor_div(T1 num, T2 den) { return (num > 0 ? num / den : -((-num + den - 1) / den)); } template std::pair operator+(const std::pair &l, const std::pair &r) { return std::make_pair(l.first + r.first, l.second + r.second); } template std::pair operator-(const std::pair &l, const std::pair &r) { return std::make_pair(l.first - r.first, l.second - r.second); } template std::vector sort_unique(std::vector vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; } template int arglb(const std::vector &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); } template int argub(const std::vector &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); } template IStream &operator>>(IStream &is, std::vector &vec) { for (auto &v : vec) is >> v; return is; } template OStream &operator<<(OStream &os, const std::vector &vec); template OStream &operator<<(OStream &os, const std::array &arr); template OStream &operator<<(OStream &os, const std::unordered_set &vec); template OStream &operator<<(OStream &os, const pair &pa); template OStream &operator<<(OStream &os, const std::deque &vec); template OStream &operator<<(OStream &os, const std::set &vec); template OStream &operator<<(OStream &os, const std::multiset &vec); template OStream &operator<<(OStream &os, const std::unordered_multiset &vec); template OStream &operator<<(OStream &os, const std::pair &pa); template OStream &operator<<(OStream &os, const std::map &mp); template OStream &operator<<(OStream &os, const std::unordered_map &mp); template OStream &operator<<(OStream &os, const std::tuple &tpl); template OStream &operator<<(OStream &os, const std::vector &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; } template OStream &operator<<(OStream &os, const std::array &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; } template std::istream &operator>>(std::istream &is, std::tuple &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; } template OStream &operator<<(OStream &os, const std::tuple &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; } template OStream &operator<<(OStream &os, const std::unordered_set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::deque &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; } template OStream &operator<<(OStream &os, const std::set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::unordered_multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::pair &pa) { return os << '(' << pa.first << ',' << pa.second << ')'; } template OStream &operator<<(OStream &os, const std::map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::unordered_map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } #ifdef HITONANODE_LOCAL const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m"; #define dbg(x) std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl #define dbgif(cond, x) ((cond) ? std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl : std::cerr) #else #define dbg(x) ((void)0) #define dbgif(cond, x) ((void)0) #endif template ::max() / 2, int INVALID = -1> struct shortest_path { int V, E; bool single_positive_weight; T wmin, wmax; std::vector> tos; std::vector head; std::vector> edges; void build_() { if (int(tos.size()) == E and int(head.size()) == V + 1) return; tos.resize(E); head.assign(V + 1, 0); for (const auto &e : edges) ++head[std::get<0>(e) + 1]; for (int i = 0; i < V; ++i) head[i + 1] += head[i]; auto cur = head; for (const auto &e : edges) { tos[cur[std::get<0>(e)]++] = std::make_pair(std::get<1>(e), std::get<2>(e)); } } shortest_path(int V = 0) : V(V), E(0), single_positive_weight(true), wmin(0), wmax(0) {} void add_edge(int s, int t, T w) { assert(0 <= s and s < V); assert(0 <= t and t < V); edges.emplace_back(s, t, w); ++E; if (w > 0 and wmax > 0 and wmax != w) single_positive_weight = false; wmin = std::min(wmin, w); wmax = std::max(wmax, w); } void add_bi_edge(int u, int v, T w) { add_edge(u, v, w); add_edge(v, u, w); } std::vector dist; std::vector prev; // Dijkstra algorithm // - Requirement: wmin >= 0 // - Complexity: O(E log E) using Pque = std::priority_queue, std::vector>, std::greater>>; template void dijkstra(int s, int t = INVALID) { assert(0 <= s and s < V); build_(); dist.assign(V, INF); prev.assign(V, INVALID); dist[s] = 0; Heap pq; pq.emplace(0, s); while (!pq.empty()) { T d; int v; std::tie(d, v) = pq.top(); pq.pop(); if (t == v) return; if (dist[v] < d) continue; for (int e = head[v]; e < head[v + 1]; ++e) { const auto &nx = tos[e]; T dnx = d + nx.second; if (dist[nx.first] > dnx) { dist[nx.first] = dnx, prev[nx.first] = v; pq.emplace(dnx, nx.first); } } } } }; int main() { int N, A, B, C; cin >> N >> A >> B >> C; shortest_path sp(N * 2); priority_queue, vector>, greater<>> pq; vector dp(N * 2, 1e18); dp.at(1) = 0; pq.emplace(0, 1); auto add_edge = [&](int s, int t, lint w) { if (chmin(dp.at(t), dp.at(s) + w)) pq.emplace(dp.at(t), t); }; vector tos(N * 2); { lint fac = 1; bool is_large = false; for (int i = 0; i < N * 2; ++i) { if (i) fac = fac * i; if (fac >= N) is_large = true; if (is_large) fac %= N; // sp.add_edge(i, fac + (is_large ? N : 0), C); tos.at(i) = fac + (is_large ? N : 0); } } while (pq.size()) { auto [vj, j] = pq.top(); pq.pop(); if (dp.at(j) != vj) continue; const int i = j % N; add_edge(i, i + 1, A); add_edge(i + N, (i + 1) % N + N, A); bool is_large = false; for (lint y = i, cost = B; cost < 1e12; y *= i, cost *= B) { if (y >= N) is_large = true; if (is_large) y %= N; add_edge(i, y + (is_large ? N : 0), cost); add_edge(i + N, y + N, cost); } add_edge(j, tos.at(j), C); } // REP(i, N) { // sp.add_edge(i, i + 1, A); // sp.add_edge(i + N, (i + 1) % N + N, A); // bool is_large = false; // for (lint y = i, cost = B; cost < 1e12 ; y *= i, cost *= B) { // if (y >= N) is_large = true; // if (is_large) y %= N; // sp.add_edge(i, y + (is_large ? N : 0), cost); // sp.add_edge(i + N, y + N, cost); // } // } // sp.dijkstra(1, N); lint ret = dp.at(N); cout << ret << '\n'; }