#include #include using namespace std; using namespace atcoder; istream &operator>>(istream &is, modint &a) { long long v; is >> v; a = v; return is; } ostream &operator<<(ostream &os, const modint &a) { return os << a.val(); } istream &operator>>(istream &is, modint998244353 &a) { long long v; is >> v; a = v; return is; } ostream &operator<<(ostream &os, const modint998244353 &a) { return os << a.val(); } istream &operator>>(istream &is, modint1000000007 &a) { long long v; is >> v; a = v; return is; } ostream &operator<<(ostream &os, const modint1000000007 &a) { return os << a.val(); } typedef long long ll; typedef vector> Graph; typedef pair pii; typedef pair pll; #define FOR(i,l,r) for (int i = l;i < (int)(r); i++) #define rep(i,n) for (int i = 0;i < (int)(n); i++) #define all(x) x.begin(), x.end() #define rall(x) x.rbegin(), x.rend() #define my_sort(x) sort(x.begin(), x.end()) #define my_max(x) *max_element(all(x)) #define my_min(x) *min_element(all(x)) template inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; } template inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; } const int INF = (1<<30) - 1; const ll LINF = (1LL<<62) - 1; const int MOD = 998244353; const int MOD2 = 1e9+7; const double PI = acos(-1); vector di = {1,0,-1,0}; vector dj = {0,1,0,-1}; #ifdef LOCAL # include # define debug(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__) #else # define debug(...) (static_cast(0)) #endif // https://qiita.com/drken/items/3beb679e54266f20ab63 struct Eratosthenes{ int N; vector isprime; vector minfactor, mobius; Eratosthenes(int N_max = 1e7){init(N_max);} //初期化 void init(int N_max = 1e7){ int N = N_max; isprime.assign(N+1,true); minfactor.assign(N+1,-1); mobius.assign(N+1,1); //Eratosthenes O(NloglogN) isprime[0] = false; isprime[1] = false; for(int p=2;p<=N;p++){ if (!isprime[p])continue; minfactor[p] = p; mobius[p] = -1; //pの倍数の処理 for(int q=2*p;q<=N;q+=p){ isprime[q] = false; if (minfactor[q] == -1){ minfactor[q] = p; } if ((q/p) % p == 0) mobius[q] = 0; else mobius[q] *= -1; } } } //素数判定,O(1) bool judge_prime(int num){ return isprime[num]; } //素数列挙,O(N) vector list_primes(int num = -1){ if (num == -1) num = N; vector primes; for(int p=0;p<=num;p++){ if (isprime[p]) primes.push_back(p); } return primes; } //高速素因数分解,O(logN),{(素因数,個数)...} vector factorize(int x){ vector ans; while(x > 1){ int p = minfactor[x]; int e = 0; while(minfactor[x] == p){ x /= p; e++; } ans.push_back(make_pair(p,e)); } return ans; } //高速約数列挙 O(240(N <= 1e6),1344(N <= 1e9)) vector divisors(int x){ vector ans; ans.push_back(1); vector facts = factorize(x); for(auto [p,e]:facts){ int s = ans.size(); for(int i=0;i mobius[n] = 0 //mobius[n] = pow(-1,Nの素数の種類) int my_mobius(int x){ return mobius[x]; } }; int main(){ cin.tie(0); ios_base::sync_with_stdio(false); int N; cin >> N; vector A(N); rep(i, N) cin >> A[i]; Eratosthenes er(200000); vector p = er.list_primes(200000); int M = p.size(); map mp; rep(i, M) mp[p[i]] = N + i; dsu uf(N + M); // [0, N), [N, N + M) rep(i, N){ vector pe = er.factorize(A[i]); for(auto &[p, _] : pe) uf.merge(i, mp[p]); } vector x; int cnt1 = 0; for(auto g : uf.groups()){ if((int)g.size() == 1) { if(g[0] < N) cnt1++; continue; } debug(g); int tmp = INF; for(auto v : g){ if(v < N) continue; chmin(tmp, p[v - N]); } x.push_back(tmp); } ll ans = LINF; chmin(ans, 2LL * ((ll)x.size() + cnt1)); chmin(ans, *min_element(all(x)) * ((ll)x.size() - 1LL + cnt1)); cout << ans << endl; }