#define LOCAL #include using namespace std; #pragma region Macros typedef long long ll; typedef __int128_t i128; typedef unsigned int uint; typedef unsigned long long ull; #define ALL(x) (x).begin(), (x).end() template istream& operator>>(istream& is, vector& v) { for (T& x : v) is >> x; return is; } template ostream& operator<<(ostream& os, const vector& v) { for (size_t i = 0; i < v.size(); i++) { os << v[i] << (i + 1 == v.size() ? "" : " "); } return os; } template ostream& operator<<(ostream& os, const pair& p) { os << '(' << p.first << ',' << p.second << ')'; return os; } template ostream& operator<<(ostream& os, const map& m) { os << '{'; for (auto itr = m.begin(); itr != m.end();) { os << '(' << itr->first << ',' << itr->second << ')'; if (++itr != m.end()) os << ','; } os << '}'; return os; } template ostream& operator<<(ostream& os, const unordered_map& m) { os << '{'; for (auto itr = m.begin(); itr != m.end();) { os << '(' << itr->first << ',' << itr->second << ')'; if (++itr != m.end()) os << ','; } os << '}'; return os; } template ostream& operator<<(ostream& os, const set& s) { os << '{'; for (auto itr = s.begin(); itr != s.end();) { os << *itr; if (++itr != s.end()) os << ','; } os << '}'; return os; } template ostream& operator<<(ostream& os, const multiset& s) { os << '{'; for (auto itr = s.begin(); itr != s.end();) { os << *itr; if (++itr != s.end()) os << ','; } os << '}'; return os; } template ostream& operator<<(ostream& os, const unordered_set& s) { os << '{'; for (auto itr = s.begin(); itr != s.end();) { os << *itr; if (++itr != s.end()) os << ','; } os << '}'; return os; } template ostream& operator<<(ostream& os, const deque& v) { for (size_t i = 0; i < v.size(); i++) { os << v[i] << (i + 1 == v.size() ? "" : " "); } return os; } template ostream& operator<<(ostream& os, const array& v) { for (size_t i = 0; i < N; i++) { os << v[i] << (i + 1 == N ? "" : " "); } return os; } template void print_tuple(ostream&, const T&) {} template void print_tuple(ostream& os, const T& t) { if (i) os << ','; os << get(t); print_tuple(os, t); } template ostream& operator<<(ostream& os, const tuple& t) { os << '{'; print_tuple<0, tuple, Args...>(os, t); return os << '}'; } void debug_out() { cerr << '\n'; } template void debug_out(Head&& head, Tail&&... tail) { cerr << head; if (sizeof...(Tail) > 0) cerr << ", "; debug_out(move(tail)...); } #ifdef LOCAL #define debug(...) \ cerr << " "; \ cerr << #__VA_ARGS__ << " :[" << __LINE__ << ":" << __FUNCTION__ << "]" << '\n'; \ cerr << " "; \ debug_out(__VA_ARGS__) #else #define debug(...) void(0) #endif template T gcd(T x, T y) { return y != 0 ? gcd(y, x % y) : x; } template T lcm(T x, T y) { return x / gcd(x, y) * y; } int topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); } int topbit(long long t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); } int botbit(signed a) { return a == 0 ? 32 : __builtin_ctz(a); } int botbit(long long a) { return a == 0 ? 64 : __builtin_ctzll(a); } int popcount(signed t) { return __builtin_popcount(t); } int popcount(long long t) { return __builtin_popcountll(t); } bool ispow2(int i) { return i && (i & -i) == i; } long long MSK(int n) { return (1LL << n) - 1; } template T ceil(T x, T y) { assert(y >= 1); return (x > 0 ? (x + y - 1) / y : x / y); } template T floor(T x, T y) { assert(y >= 1); return (x > 0 ? x / y : (x - y + 1) / y); } template inline bool chmin(T1& a, T2 b) { if (a > b) { a = b; return true; } return false; } template inline bool chmax(T1& a, T2 b) { if (a < b) { a = b; return true; } return false; } template void mkuni(vector& v) { sort(v.begin(), v.end()); v.erase(unique(v.begin(), v.end()), v.end()); } template int lwb(const vector& v, const T& x) { return lower_bound(v.begin(), v.end(), x) - v.begin(); } #pragma endregion #include #include #include struct UnionFind { UnionFind(int n) : n(n), num(n), data(n, -1) {} int find(int x) { assert(0 <= x && x < n); return data[x] < 0 ? x : data[x] = find(data[x]); } bool merge(int x, int y) { assert(0 <= x && x < n); assert(0 <= y && y < n); if ((x = find(x)) == (y = find(y))) return false; if (-data[x] < -data[y]) std::swap(x, y); data[x] += data[y]; data[y] = x; num--; return true; } bool same(int x, int y) { assert(0 <= x && x < n); assert(0 <= y && y < n); return find(x) == find(y); } int size(int x) { assert(0 <= x && x < n); return -data[find(x)]; } int count() const { return num; } std::vector> groups() { std::vector> res(n); for (int i = 0; i < n; i++) res[find(i)].emplace_back(i); res.erase(std::remove_if(res.begin(), res.end(), [&](const std::vector& v) { return v.empty(); })); return res; } int operator[](int x) { return find(x); } private: int n, num; // root node : -1 * component size // otherwise : parent std::vector data; }; #include #include namespace elementary_math { template std::vector divisor(T n) { std::vector res; for (T i = 1; i * i <= n; i++) { if (n % i == 0) { res.emplace_back(i); if (i * i != n) res.emplace_back(n / i); } } return res; } template std::vector> prime_factor(T n) { std::vector> res; for (T p = 2; p * p <= n; p++) { if (n % p == 0) { res.emplace_back(p, 0); while (n % p == 0) { res.back().second++; n /= p; } } } if (n > 1) res.emplace_back(n, 1); return res; } std::vector osa_k(int n) { std::vector min_factor(n + 1, 0); for (int i = 2; i <= n; i++) { if (min_factor[i]) continue; for (int j = i; j <= n; j += i) { if (!min_factor[j]) { min_factor[j] = i; } } } return min_factor; } std::vector prime_factor(const std::vector& min_factor, int n) { std::vector res; while (n > 1) { res.emplace_back(min_factor[n]); n /= min_factor[n]; } return res; } long long modpow(long long x, long long n, long long mod) { assert(0 <= n && 1 <= mod && mod < (1LL << 31)); if (mod == 1) return 0; x %= mod; long long res = 1; while (n > 0) { if (n & 1) res = res * x % mod; x = x * x % mod; n >>= 1; } return res; } long long extgcd(long long a, long long b, long long& x, long long& y) { long long d = a; if (b != 0) { d = extgcd(b, a % b, y, x); y -= (a / b) * x; } else x = 1, y = 0; return d; } long long inv_mod(long long a, long long mod) { assert(1 <= mod); long long x, y; if (extgcd(a, mod, x, y) != 1) return -1; return (mod + x % mod) % mod; } template T euler_phi(T n) { auto pf = prime_factor(n); T res = n; for (const auto& p : pf) { res /= p.first; res *= p.first - 1; } return res; } std::vector euler_phi_table(int n) { std::vector res(n + 1, 0); iota(res.begin(), res.end(), 0); for (int i = 2; i <= n; i++) { if (res[i] != i) continue; for (int j = i; j <= n; j += i) res[j] = res[j] / i * (i - 1); } return res; } // minimum i > 0 s.t. x^i \equiv 1 \pmod{m} template T order(T x, T m) { T n = euler_phi(m); auto cand = divisor(n); sort(cand.begin(), cand.end()); for (auto& i : cand) { if (modpow(x, i, m) == 1) { return i; } } return -1; } } // namespace elementary_math const int INF = 1e9; const long long IINF = 1e18; const int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1}; const char dir[4] = {'D', 'R', 'U', 'L'}; const long long MOD = 1000000007; // const long long MOD = 998244353; const int MAX_A = 100010; int main() { cin.tie(0); ios::sync_with_stdio(false); int N; cin >> N; vector A(N); cin >> A; vector cnt(MAX_A, 0); vector cand; for (int& x : A) cnt[x]++; ll ans = 0; for (int i = 1; i < MAX_A; i++) { if (cnt[i] == 0) continue; ans += 1LL * i * (cnt[i] - 1); cand.emplace_back(i); } int n = cand.size(); UnionFind UF(n); vector>> div(MAX_A); for (int i = 0; i < n; i++) { auto d = elementary_math::divisor(cand[i]); for (int& y : d) div[y].emplace_back(cand[i], i); } priority_queue> pq; for (int i = 1; i < MAX_A; i++) { if (div[i].size() < 2) continue; pq.emplace(-div[i][0].first * div[i][1].first / i, i); } auto UPDATE = [&](int x) { auto p = div[x].front(); div[x].pop_front(); while (!div[x].empty() and UF.same(div[x].front().second, p.second)) div[x].pop_front(); div[x].emplace_front(p); if (div[x].size() < 2) return; pq.emplace(-div[x][0].first * div[x][1].first / x, x); }; auto MERGE = [&](int x) { if (!UF.merge(div[x][0].second, div[x][1].second)) { UPDATE(x); return; } ans += div[x][0].first * div[x][1].first / x; auto p = div[x].front(); div[x].pop_front(); div[x].emplace_front(p); UPDATE(x); }; while (UF.count() > 1) { auto p = pq.top(); pq.pop(); MERGE(p.second); } cout << ans << '\n'; return 0; }