//#define NDEBUG #include #include #include #include #include #include #include namespace n91 { using i8 = std::int_fast8_t; using i32 = std::int_fast32_t; using i64 = std::int_fast64_t; using u8 = std::uint_fast8_t; using u32 = std::uint_fast32_t; using u64 = std::uint_fast64_t; using isize = std::ptrdiff_t; using usize = std::size_t; struct rep { struct itr { usize i; constexpr itr(const usize i) noexcept : i(i) {} void operator++() noexcept { ++i; } constexpr usize operator*() const noexcept { return i; } constexpr bool operator!=(const itr x) const noexcept { return i != x.i; } }; const itr f, l; constexpr rep(const usize f, const usize l) noexcept : f(std::min(f, l)), l(l) {} constexpr auto begin() const noexcept { return f; } constexpr auto end() const noexcept { return l; } }; struct revrep { struct itr { usize i; constexpr itr(const usize i) noexcept : i(i) {} void operator++() noexcept { --i; } constexpr usize operator*() const noexcept { return i; } constexpr bool operator!=(const itr x) const noexcept { return i != x.i; } }; const itr f, l; constexpr revrep(const usize f, const usize l) noexcept : f(l - 1), l(std::min(f, l) - 1) {} constexpr auto begin() const noexcept { return f; } constexpr auto end() const noexcept { return l; } }; template auto md_vec(const usize n, const T &value) { return std::vector(n, value); } template auto md_vec(const usize n, Args... args) { return std::vector(n, md_vec(args...)); } template constexpr T difference(const T &a, const T &b) noexcept { if (a < b) { return b - a; } else { return a - b; } } template void chmin(T &a, const T &b) noexcept { if (b < a) { a = b; } } template void chmax(T &a, const T &b) noexcept { if (a < b) { a = b; } } template class fix_point : private F { public: explicit constexpr fix_point(F &&f) : F(std::forward(f)) {} template constexpr decltype(auto) operator()(Args &&... args) const { return F::operator()(*this, std::forward(args)...); } }; template constexpr decltype(auto) make_fix(F &&f) { return fix_point(std::forward(f)); } template T scan() { T ret; std::cin >> ret; return ret; } } // namespace n91 #include #include #include #include #include namespace n91 { class prime_sieve { public: using size_type = std::size_t; private: std::vector prime, factor; public: prime_sieve() {} explicit prime_sieve(const size_type size) : prime(), factor(size) { if (size == 0) { return; } std::iota(factor.begin(), factor.end(), static_cast(0)); factor[0] = 1; if (size == 1) { return; } factor[1] = 0; prime.reserve(size); for (size_type i{2}; i != size; ++i) { const size_type fi{factor[i]}; if (fi == i) { prime.push_back(i); } for (const size_type p : prime) { if (p > fi) { break; } const size_type ip{i * p}; if (ip >= size) { break; } factor[ip] = p; } } prime.shrink_to_fit(); } size_type len() const noexcept { return factor.size(); } bool is_prime(const size_type i) const noexcept { assert(i < len()); return factor[i] == i; } std::vector factorize(size_type i) const noexcept { assert(i != 0); std::vector ret; while (i != 1) { ret.push_back(factor[i]); i /= factor[i]; } return std::move(ret); } template void divisor_zeta(C &c) const noexcept { const size_type n{c.size()}; assert(n <= len()); for (size_type i{0}; i != prime.size() && prime[i] < n; ++i) { for (size_type j{1}; j * prime[i] < n; ++j) { c[j * prime[i]] += c[j]; } } } template void divisor_mobius(C &c) const noexcept { const size_type n{c.size()}; assert(n <= len()); for (size_type i{0}; i != prime.size() && prime[i] < n; ++i) { for (size_type j{(n - 1) / prime[i]}; j != 0; --j) { c[j * prime[i]] -= c[j]; } } } template void multiple_zeta(C &c) const noexcept { const size_type n{c.size()}; assert(n <= len()); for (size_type i{0}; i != prime.size() && prime[i] < n; ++i) { for (size_type j{(n - 1) / prime[i]}; j != 0; --j) { c[j] += c[j * prime[i]]; } } } template void multiple_mobius(C &c) const noexcept { const size_type n{c.size()}; assert(n <= len()); for (size_type i{0}; i != prime.size() && prime[i] < n; ++i) { for (size_type j{1}; j * prime[i] < n; ++j) { c[j] -= c[j * prime[i]]; } } } }; } // namespace n91 #include #include #include namespace n91 { void main_() { /* std::ios::sync_with_stdio(false); std::cin.tie(nullptr); //*/ const usize n = scan(); std::vector a(n); for (auto &e : a) { std::cin >> e; } const usize am = *std::max_element(a.cbegin(), a.cend()) + 1; const auto get = [](const usize a, const usize i) -> bool { return a >> i & 1; }; const auto gcd = [get](usize a, usize b) { for (const usize i : revrep(0, 17)) { if (a < b) { std::swap(a, b); } if (get(b, i)) { b ^= a; } if (b == 0) { return a; } if (get(a, i)) { usize t = b; while (!get(t, i)) { t *= 2; } a ^= t; } } assert(false); }; usize g = 0; for (const auto e : a) { g = gcd(g, e); } const auto ok = [g, get](usize a) { for (const usize i : revrep(0, 17)) { if (get(a, i)) { usize t = g; while (!get(t, i)) { t *= 2; } a ^= t; } if (get(g, i)) { return a == 0; } } assert(false); }; const prime_sieve ps(am); std::vector rev(am); for (const auto e : a) { rev[e] += e; } ps.multiple_zeta(rev); const u64 sum = std::accumulate(a.cbegin(), a.cend(), static_cast(0)); u64 ans = std::numeric_limits::max(); for (const usize i : rep(1, am)) { if (ok(i)) { chmin(ans, sum - rev[i] + rev[i] / i); } } std::cout << ans << std::endl; } } // namespace n91 int main() { n91::main_(); return 0; }