// #pragma comment(linker, "/stack:200000000") #include #include #include namespace suisen { // ! utility template using constraints_t = std::enable_if_t, std::nullptr_t>; template constexpr decltype(auto) constexpr_if(Then&& then, OrElse&& or_else) { if constexpr (cond_v) { return std::forward(then); } else { return std::forward(or_else); } } // ! function template using is_same_as_invoke_result = std::is_same, ReturnType>; template using is_uni_op = is_same_as_invoke_result; template using is_bin_op = is_same_as_invoke_result; template using is_comparator = std::is_same, bool>; // ! integral template >> constexpr int bit_num = std::numeric_limits>::digits; template struct is_nbit { static constexpr bool value = bit_num == n; }; template static constexpr bool is_nbit_v = is_nbit::value; // ? template struct safely_multipliable {}; template <> struct safely_multipliable { using type = long long; }; template <> struct safely_multipliable { using type = __int128_t; }; template <> struct safely_multipliable { using type = unsigned long long; }; template <> struct safely_multipliable { using type = __uint128_t; }; template <> struct safely_multipliable { using type = float; }; template <> struct safely_multipliable { using type = double; }; template <> struct safely_multipliable { using type = long double; }; template using safely_multipliable_t = typename safely_multipliable::type; } // namespace suisen // ! type aliases using i128 = __int128_t; using u128 = __uint128_t; using ll = long long; using uint = unsigned int; using ull = unsigned long long; template using vec = std::vector; template using vec2 = vec>; template using vec3 = vec>; template using vec4 = vec>; template using pq_greater = std::priority_queue, std::greater>; template using umap = std::unordered_map; // ! macros (capital: internal macro) #define OVERLOAD2(_1,_2,name,...) name #define OVERLOAD3(_1,_2,_3,name,...) name #define OVERLOAD4(_1,_2,_3,_4,name,...) name #define REP4(i,l,r,s) for(std::remove_reference_t>i=(l);i<(r);i+=(s)) #define REP3(i,l,r) REP4(i,l,r,1) #define REP2(i,n) REP3(i,0,n) #define REPINF3(i,l,s) for(std::remove_reference_t>i=(l);;i+=(s)) #define REPINF2(i,l) REPINF3(i,l,1) #define REPINF1(i) REPINF2(i,0) #define RREP4(i,l,r,s) for(std::remove_reference_t>i=(l)+fld((r)-(l)-1,s)*(s);i>=(l);i-=(s)) #define RREP3(i,l,r) RREP4(i,l,r,1) #define RREP2(i,n) RREP3(i,0,n) #define rep(...) OVERLOAD4(__VA_ARGS__, REP4 , REP3 , REP2 )(__VA_ARGS__) #define rrep(...) OVERLOAD4(__VA_ARGS__, RREP4 , RREP3 , RREP2 )(__VA_ARGS__) #define repinf(...) OVERLOAD3(__VA_ARGS__, REPINF3, REPINF2, REPINF1)(__VA_ARGS__) #define CAT_I(a, b) a##b #define CAT(a, b) CAT_I(a, b) #define UNIQVAR(tag) CAT(tag, __LINE__) #define loop(n) for (std::remove_reference_t> UNIQVAR(loop_variable) = n; UNIQVAR(loop_variable) --> 0;) #define all(iterable) (iterable).begin(), (iterable).end() #define input(type, ...) type __VA_ARGS__; read(__VA_ARGS__) // ! I/O utilities // pair template std::ostream& operator<<(std::ostream& out, const std::pair &a) { return out << a.first << ' ' << a.second; } // tuple template std::ostream& operator<<(std::ostream& out, const std::tuple &a) { if constexpr (N >= std::tuple_size_v>) { return out; } else { out << std::get(a); if constexpr (N + 1 < std::tuple_size_v>) { out << ' '; } return operator<<(out, a); } } // vector template std::ostream& operator<<(std::ostream& out, const std::vector &a) { for (auto it = a.begin(); it != a.end();) { out << *it; if (++it != a.end()) out << ' '; } return out; } // array template std::ostream& operator<<(std::ostream& out, const std::array &a) { for (auto it = a.begin(); it != a.end();) { out << *it; if (++it != a.end()) out << ' '; } return out; } inline void print() { std::cout << '\n'; } template inline void print(const Head &head, const Tail &...tails) { std::cout << head; if (sizeof...(tails)) std::cout << ' '; print(tails...); } template auto print_all(const Iterable& v, std::string sep = " ", std::string end = "\n") -> decltype(std::cout << *v.begin(), void()) { for (auto it = v.begin(); it != v.end();) { std::cout << *it; if (++it != v.end()) std::cout << sep; } std::cout << end; } // pair template std::istream& operator>>(std::istream& in, std::pair &a) { return in >> a.first >> a.second; } // tuple template std::istream& operator>>(std::istream& in, std::tuple &a) { if constexpr (N >= std::tuple_size_v>) { return in; } else { return operator>>(in >> std::get(a), a); } } // vector template std::istream& operator>>(std::istream& in, std::vector &a) { for (auto it = a.begin(); it != a.end(); ++it) in >> *it; return in; } // array template std::istream& operator>>(std::istream& in, std::array &a) { for (auto it = a.begin(); it != a.end(); ++it) in >> *it; return in; } template void read(Args &...args) { ( std::cin >> ... >> args ); } // ! integral utilities // Returns pow(-1, n) template constexpr inline int pow_m1(T n) { return -(n & 1) | 1; } // Returns pow(-1, n) template <> constexpr inline int pow_m1(bool n) { return -int(n) | 1; } // Returns floor(x / y) template constexpr inline T fld(const T x, const T y) { return (x ^ y) >= 0 ? x / y : (x - (y + pow_m1(y >= 0))) / y; } template constexpr inline T cld(const T x, const T y) { return (x ^ y) <= 0 ? x / y : (x + (y + pow_m1(y >= 0))) / y; } template > = nullptr> constexpr inline int popcount(const T x) { return __builtin_popcount(x); } template > = nullptr> constexpr inline int popcount(const T x) { return __builtin_popcount(x); } template > = nullptr> constexpr inline int popcount(const T x) { return __builtin_popcountll(x); } template > = nullptr> constexpr inline int count_lz(const T x) { return x ? __builtin_clz(x) : suisen::bit_num; } template > = nullptr> constexpr inline int count_lz(const T x) { return x ? __builtin_clz(x) : suisen::bit_num; } template > = nullptr> constexpr inline int count_lz(const T x) { return x ? __builtin_clzll(x) : suisen::bit_num; } template > = nullptr> constexpr inline int count_tz(const T x) { return x ? __builtin_ctz(x) : suisen::bit_num; } template > = nullptr> constexpr inline int count_tz(const T x) { return x ? __builtin_ctz(x) : suisen::bit_num; } template > = nullptr> constexpr inline int count_tz(const T x) { return x ? __builtin_ctzll(x) : suisen::bit_num; } template constexpr inline int floor_log2(const T x) { return suisen::bit_num - 1 - count_lz(x); } template constexpr inline int ceil_log2(const T x) { return floor_log2(x) + ((x & -x) != x); } template constexpr inline int kth_bit(const T x, const unsigned int k) { return (x >> k) & 1; } template constexpr inline int parity(const T x) { return popcount(x) & 1; } struct all_subset { struct all_subset_iter { const int s; int t; constexpr all_subset_iter(int s) : s(s), t(s + 1) {} constexpr auto operator*() const { return t; } constexpr auto operator++() {} constexpr auto operator!=(std::nullptr_t) { return t ? (--t &= s, true) : false; } }; int s; constexpr all_subset(int s) : s(s) {} constexpr auto begin() { return all_subset_iter(s); } constexpr auto end() { return nullptr; } }; // ! container template > = nullptr> auto priqueue_comp(const Comparator comparator) { return std::priority_queue, Comparator>(comparator); } template auto isize(const Iterable &iterable) -> decltype(int(iterable.size())) { return iterable.size(); } template > = nullptr> auto generate_vector(int n, Gen generator) { std::vector v(n); for (int i = 0; i < n; ++i) v[i] = generator(i); return v; } template auto generate_range_vector(T l, T r) { return generate_vector(r - l, [l](int i) { return l + i; }); } template auto generate_range_vector(T n) { return generate_range_vector(0, n); } template void sort_unique_erase(std::vector &a) { std::sort(a.begin(), a.end()); a.erase(std::unique(a.begin(), a.end()), a.end()); } template auto foreach_adjacent_values(InputIterator first, InputIterator last, BiConsumer f) -> decltype(f(*first++, *last), void()) { if (first != last) for (auto itr = first, itl = itr++; itr != last; itl = itr++) f(*itl, *itr); } template auto foreach_adjacent_values(Container c, BiConsumer f) -> decltype(c.begin(), c.end(), void()){ foreach_adjacent_values(c.begin(), c.end(), f); } // ! other utilities // x <- min(x, y). returns true iff `x` has chenged. template inline bool chmin(T &x, const T &y) { if (y >= x) return false; x = y; return true; } // x <- max(x, y). returns true iff `x` has chenged. template inline bool chmax(T &x, const T &y) { if (y <= x) return false; x = y; return true; } namespace suisen {} using namespace suisen; using namespace std; struct io_setup { io_setup(int precision = 20) { std::ios::sync_with_stdio(false); std::cin.tie(nullptr); std::cout << std::fixed << std::setprecision(precision); } } io_setup_{}; // ! code from here #include #include #include #include namespace suisen::internal::sieve { constexpr std::uint8_t K = 8; constexpr std::uint8_t PROD = 2 * 3 * 5; constexpr std::uint8_t RM[K] = { 1, 7, 11, 13, 17, 19, 23, 29 }; constexpr std::uint8_t DR[K] = { 6, 4, 2, 4, 2, 4, 6, 2 }; constexpr std::uint8_t DF[K][K] = { { 0, 0, 0, 0, 0, 0, 0, 1 }, { 1, 1, 1, 0, 1, 1, 1, 1 }, { 2, 2, 0, 2, 0, 2, 2, 1 }, { 3, 1, 1, 2, 1, 1, 3, 1 }, { 3, 3, 1, 2, 1, 3, 3, 1 }, { 4, 2, 2, 2, 2, 2, 4, 1 }, { 5, 3, 1, 4, 1, 3, 5, 1 }, { 6, 4, 2, 4, 2, 4, 6, 1 }, }; constexpr std::uint8_t DRP[K] = { 48, 32, 16, 32, 16, 32, 48, 16 }; constexpr std::uint8_t DFP[K][K] = { { 0, 0, 0, 0, 0, 0, 0, 8 }, { 8, 8, 8, 0, 8, 8, 8, 8 }, { 16, 16, 0, 16, 0, 16, 16, 8 }, { 24, 8, 8, 16, 8, 8, 24, 8 }, { 24, 24, 8, 16, 8, 24, 24, 8 }, { 32, 16, 16, 16, 16, 16, 32, 8 }, { 40, 24, 8, 32, 8, 24, 40, 8 }, { 48, 32, 16, 32, 16, 32, 48, 8 }, }; constexpr std::uint8_t MASK[K][K] = { { 0x01, 0x02, 0x04, 0x08, 0x10, 0x20, 0x40, 0x80 }, { 0x02, 0x20, 0x10, 0x01, 0x80, 0x08, 0x04, 0x40 }, { 0x04, 0x10, 0x01, 0x40, 0x02, 0x80, 0x08, 0x20 }, { 0x08, 0x01, 0x40, 0x20, 0x04, 0x02, 0x80, 0x10 }, { 0x10, 0x80, 0x02, 0x04, 0x20, 0x40, 0x01, 0x08 }, { 0x20, 0x08, 0x80, 0x02, 0x40, 0x01, 0x10, 0x04 }, { 0x40, 0x04, 0x08, 0x80, 0x01, 0x10, 0x20, 0x02 }, { 0x80, 0x40, 0x20, 0x10, 0x08, 0x04, 0x02, 0x01 }, }; constexpr std::uint8_t OFFSET[K][K] = { { 0, 1, 2, 3, 4, 5, 6, 7, }, { 1, 5, 4, 0, 7, 3, 2, 6, }, { 2, 4, 0, 6, 1, 7, 3, 5, }, { 3, 0, 6, 5, 2, 1, 7, 4, }, { 4, 7, 1, 2, 5, 6, 0, 3, }, { 5, 3, 7, 1, 6, 0, 4, 2, }, { 6, 2, 3, 7, 0, 4, 5, 1, }, { 7, 6, 5, 4, 3, 2, 1, 0, }, }; constexpr std::uint8_t mask_to_index(const std::uint8_t bits) { switch (bits) { case 1 << 0: return 0; case 1 << 1: return 1; case 1 << 2: return 2; case 1 << 3: return 3; case 1 << 4: return 4; case 1 << 5: return 5; case 1 << 6: return 6; case 1 << 7: return 7; default: assert(false); } } } // namespace suisen::internal::sieve namespace suisen { template class SimpleSieve { private: static constexpr unsigned int siz = N / internal::sieve::PROD + 1; static std::uint8_t flag[siz]; public: SimpleSieve() { using namespace internal::sieve; flag[0] |= 1; unsigned int k_max = (unsigned int) std::sqrt(N + 2) / PROD; for (unsigned int kp = 0; kp <= k_max; ++kp) { for (std::uint8_t bits = ~flag[kp]; bits; bits &= bits - 1) { const std::uint8_t mp = mask_to_index(bits & -bits), m = RM[mp]; unsigned int kr = kp * (PROD * kp + 2 * m) + m * m / PROD; for (std::uint8_t mq = mp; kr < siz; kr += kp * DR[mq] + DF[mp][mq], ++mq &= 7) { flag[kr] |= MASK[mp][mq]; } } } } std::vector prime_list(unsigned int max_val = N) const { using namespace internal::sieve; std::vector res { 2, 3, 5 }; res.reserve(max_val / 25); for (unsigned int i = 0, offset = 0; i < siz and offset < max_val; ++i, offset += PROD) { for (uint8_t f = ~flag[i]; f;) { uint8_t g = f & -f; res.push_back(offset + RM[mask_to_index(g)]); f ^= g; } } while (res.size() and (unsigned int) res.back() > max_val) res.pop_back(); return res; } bool is_prime(const unsigned int p) const { using namespace internal::sieve; switch (p) { case 2: case 3: case 5: return true; default: switch (p % PROD) { case RM[0]: return ((flag[p / PROD] >> 0) & 1) == 0; case RM[1]: return ((flag[p / PROD] >> 1) & 1) == 0; case RM[2]: return ((flag[p / PROD] >> 2) & 1) == 0; case RM[3]: return ((flag[p / PROD] >> 3) & 1) == 0; case RM[4]: return ((flag[p / PROD] >> 4) & 1) == 0; case RM[5]: return ((flag[p / PROD] >> 5) & 1) == 0; case RM[6]: return ((flag[p / PROD] >> 6) & 1) == 0; case RM[7]: return ((flag[p / PROD] >> 7) & 1) == 0; default: return false; } } } }; template std::uint8_t SimpleSieve::flag[SimpleSieve::siz]; template class Sieve { private: static constexpr unsigned int base_max = (N + 1) * internal::sieve::K / internal::sieve::PROD; static unsigned int pf[base_max + internal::sieve::K]; public: Sieve() { using namespace internal::sieve; pf[0] = 1; unsigned int k_max = ((unsigned int) std::sqrt(N + 1) - 1) / PROD; for (unsigned int kp = 0; kp <= k_max; ++kp) { const int base_i = kp * K, base_act_i = kp * PROD; for (int mp = 0; mp < K; ++mp) { const int m = RM[mp], i = base_i + mp; if (pf[i] == 0) { unsigned int act_i = base_act_i + m; unsigned int base_k = (kp * (PROD * kp + 2 * m) + m * m / PROD) * K; for (std::uint8_t mq = mp; base_k <= base_max; base_k += kp * DRP[mq] + DFP[mp][mq], ++mq &= 7) { pf[base_k + OFFSET[mp][mq]] = act_i; } } } } } bool is_prime(const unsigned int p) const { using namespace internal::sieve; switch (p) { case 2: case 3: case 5: return true; default: switch (p % PROD) { case RM[0]: return pf[p / PROD * K + 0] == 0; case RM[1]: return pf[p / PROD * K + 1] == 0; case RM[2]: return pf[p / PROD * K + 2] == 0; case RM[3]: return pf[p / PROD * K + 3] == 0; case RM[4]: return pf[p / PROD * K + 4] == 0; case RM[5]: return pf[p / PROD * K + 5] == 0; case RM[6]: return pf[p / PROD * K + 6] == 0; case RM[7]: return pf[p / PROD * K + 7] == 0; default: return false; } } } int prime_factor(const unsigned int p) const { using namespace internal::sieve; switch (p % PROD) { case 0: case 2: case 4: case 6: case 8: case 10: case 12: case 14: case 16: case 18: case 20: case 22: case 24: case 26: case 28: return 2; case 3: case 9: case 15: case 21: case 27: return 3; case 5: case 25: return 5; case RM[0]: return pf[p / PROD * K + 0] ? pf[p / PROD * K + 0] : p; case RM[1]: return pf[p / PROD * K + 1] ? pf[p / PROD * K + 1] : p; case RM[2]: return pf[p / PROD * K + 2] ? pf[p / PROD * K + 2] : p; case RM[3]: return pf[p / PROD * K + 3] ? pf[p / PROD * K + 3] : p; case RM[4]: return pf[p / PROD * K + 4] ? pf[p / PROD * K + 4] : p; case RM[5]: return pf[p / PROD * K + 5] ? pf[p / PROD * K + 5] : p; case RM[6]: return pf[p / PROD * K + 6] ? pf[p / PROD * K + 6] : p; case RM[7]: return pf[p / PROD * K + 7] ? pf[p / PROD * K + 7] : p; default: assert(false); } } /** * Returns a vector of `{ prime, index }`. */ std::vector> factorize(unsigned int n) const { assert(0 < n and n <= N); std::vector> prime_powers; while (n > 1) { int p = prime_factor(n), c = 0; do { n /= p, ++c; } while (n % p == 0); prime_powers.emplace_back(p, c); } return prime_powers; } /** * Returns the divisors of `n`. * It is NOT guaranteed that the returned vector is sorted. */ std::vector divisors(unsigned int n) const { assert(0 < n and n <= N); std::vector divs { 1 }; for (auto [prime, index] : factorize(n)) { int sz = divs.size(); for (int i = 0; i < sz; ++i) { int d = divs[i]; for (int j = 0; j < index; ++j) { divs.push_back(d *= prime); } } } return divs; } }; template unsigned int Sieve::pf[Sieve::base_max + internal::sieve::K]; } // namespace suisen constexpr int M = 100010; Sieve sieve; int main() { input(int, n); long long ans = 0; vector exists(M); rep(i, n) { input(int, v); if (exchange(exists[v], true)) ans += v; } vector vs; rep(i, M) { if (exists[i]) vs.push_back(i); } vector cost(M, numeric_limits::max()); vector coef(M, numeric_limits::max()); auto cmp = [&](int i, int j) { return cost[i] == cost[j] ? i < j : cost[i] < cost[j]; }; set st { cmp }; auto update_cost = [&](int g, long long new_coef) { if (not chmin(coef[g], new_coef)) return; rep(x, g, M, g) { if (not exists[x]) continue; // assert(st.count(x)); if (x * coef[g] < cost[x]) { st.erase(x); chmin(cost[x], x * coef[g]); st.insert(x); } } }; int init = vs[0]; exists[init] = false; for (int d : sieve.divisors(init)) { update_cost(d, init / d); } for (int v : vs) { if (v != init) st.insert(v); } while (st.size()) { auto it = st.begin(); const int u = *it; st.erase(it); exists[u] = false; ans += cost[u]; for (int d : sieve.divisors(u)) { update_cost(d, u / d); } } print(ans); return 0; }