#include using namespace std; #define rep(i, n) for (int i = 0; i < n; i++) #define rep2(i, x, n) for (int i = x; i <= n; i++) #define rep3(i, x, n) for (int i = x; i >= n; i--) #define each(e, v) for (auto &e : v) #define pb push_back #define eb emplace_back #define all(x) x.begin(), x.end() #define rall(x) x.rbegin(), x.rend() #define sz(x) (int)x.size() using ll = long long; using pii = pair; using pil = pair; using pli = pair; using pll = pair; template bool chmax(T &x, const T &y) { return (x < y) ? (x = y, true) : false; } template bool chmin(T &x, const T &y) { return (x > y) ? (x = y, true) : false; } template int flg(T x, int i) { return (x >> i) & 1; } template void print(const vector &v, T x = 0) { int n = v.size(); for (int i = 0; i < n; i++) cout << v[i] + x << (i == n - 1 ? '\n' : ' '); if (v.empty()) cout << '\n'; } template void printn(const vector &v, T x = 0) { int n = v.size(); for (int i = 0; i < n; i++) cout << v[i] + x << '\n'; } template int lb(const vector &v, T x) { return lower_bound(begin(v), end(v), x) - begin(v); } template int ub(const vector &v, T x) { return upper_bound(begin(v), end(v), x) - begin(v); } template void rearrange(vector &v) { sort(begin(v), end(v)); v.erase(unique(begin(v), end(v)), end(v)); } template vector id_sort(const vector &v, bool greater = false) { int n = v.size(); vector ret(n); iota(begin(ret), end(ret), 0); sort(begin(ret), end(ret), [&](int i, int j) { return greater ? v[i] > v[j] : v[i] < v[j]; }); return ret; } template pair operator+(const pair &p, const pair &q) { return make_pair(p.first + q.first, p.second + q.second); } template pair operator-(const pair &p, const pair &q) { return make_pair(p.first - q.first, p.second - q.second); } template istream &operator>>(istream &is, pair &p) { S a; T b; is >> a >> b; p = make_pair(a, b); return is; } template ostream &operator<<(ostream &os, const pair &p) { return os << p.first << ' ' << p.second; } struct io_setup { io_setup() { ios_base::sync_with_stdio(false); cin.tie(NULL); cout << fixed << setprecision(15); } } io_setup; const int inf = (1 << 30) - 1; const ll INF = (1LL << 60) - 1; const int MOD = 1000000007; // const int MOD = 998244353; struct Union_Find_Tree { vector data; const int n; int cnt; Union_Find_Tree(int n) : data(n, -1), n(n), cnt(n) {} int root(int x) { if (data[x] < 0) return x; return data[x] = root(data[x]); } int operator[](int i) { return root(i); } bool unite(int x, int y) { x = root(x), y = root(y); if (x == y) return false; if (data[x] > data[y]) swap(x, y); data[x] += data[y], data[y] = x; cnt--; return true; } int size(int x) { return -data[root(x)]; } int count() { return cnt; }; bool same(int x, int y) { return root(x) == root(y); } void clear() { cnt = n; fill(begin(data), end(data), -1); } }; int main() { int N; cin >> N; int M = 100000; vector cnt(M + 1, 0); rep(i, N) { int x; cin >> x; cnt[x]++; } ll ans = 0; rep(i, M + 1) { if (cnt[i] > 1) { ans += 1LL * i * (cnt[i] - 1); N -= cnt[i] - 1; cnt[i] = 1; } } vector> ids(M + 1); vector> ds(M + 1); rep2(i, 1, M) { for (int j = i; j <= M; j += i) { if (cnt[j] > 0) { ds[j].eb(i, 0); ids[i].eb(j); } } } Union_Find_Tree uf(M + 1); vector tmp(M + 1, pli(INF, -1)); while (uf.count() > M - N + 2) { fill(all(tmp), pli(INF, -1)); rep(i, M + 1) { if (cnt[i] == 0) continue; int u = uf[i]; pli mi = pli(INF, -1); each(p, ds[i]) { int e = p.first; int &j = p.second; while (j < sz(ids[e]) && uf[ids[e][j]] == u) j++; if (j < sz(ids[e])) chmin(mi, pli(1LL * i * ids[e][j] / e, uf[ids[e][j]])); } chmin(tmp[u], mi); } vector> memo; rep(i, M + 1) { if (tmp[i].first < INF) { memo.eb(tmp[i].first, i, tmp[i].second); // cout << tmp[i].first << ' ' << i << ' ' << tmp[i].second << '\n'; } } sort(all(memo)); each(e, memo) { auto [c, u, v] = e; // cout << c << ' ' << u << ' ' << v << '\n'; if (uf.unite(u, v)) ans += c; } } cout << ans << '\n'; }