#ifdef __LOCAL #include // プリコンパイル済みヘッダ ~/local/include/mytemplate.hpp.gch #else #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #endif using namespace std; #pragma GCC target "no-avx" // gcc12.2のバグ回避用。boost使用時はコメントアウトの事 // #include // using bint = boost::multiprecision::cpp_int; using int128 = __int128_t; using ll = long long; using vl = vector; using vvl = vector; using vb = vector; using vvb = vector; using vd = vector; using vvd = vector; using vc = vector; using vvc = vector; using pll = pair; #define REP1(i, n) REP3(i, 0, n, 1) #define REP2(i, s, n) REP3(i, s, n, 1) #define REP3(i, s, n, d) for(ll i = (ll)(s); i < (ll)(n); i += (d)) #define REP_OVERLOAD(e1, e2, e3, e4, NAME,...) NAME #define rep(...) REP_OVERLOAD(__VA_ARGS__, REP3, REP2, REP1)(__VA_ARGS__) #define DEP1(i, n) DEP3(i, n, -1, 1) #define DEP2(i, n, s) DEP3(i, n, s, 1) #define DEP3(i, n, s, d) for(ll i = (ll)(n); (ll)(s) < i; i -= (d)) #define DEP_OVERLOAD(e1, e2, e3, e4, NAME,...) NAME #define dep(...) DEP_OVERLOAD(__VA_ARGS__, DEP3, DEP2, DEP1)(__VA_ARGS__) #define fore(e, a) for (auto&& e: (a)) #define len(a) (ll)(a).size() #define all(a) (a).begin(), (a).end() #define rall(a) (a).rbegin(), (a).rend() #define pb push_back #define eb emplace_back #define fi first #define se second #define th third /********* C O N S T A N T **********/ constexpr ll INF = LONG_LONG_MAX / 2 - 10000LL; // 4,611,686,018,427,377,903 ~= 4.6e+18, 19桁 const double PI = acos(-1); /********* P A I R **********/ template inline pair& operator+=(pair& a, const pair b); template inline pair& operator-=(pair& a, const pair b); template inline pair& operator*=(pair& a, const pair b); template inline pair& operator/=(pair& a, const pair b); template inline pair& operator%=(pair& a, const pair b); template inline pair& operator+=(pair& a, const V b); template inline pair& operator-=(pair& a, const V b); template inline pair& operator*=(pair& a, const V b); template inline pair& operator/=(pair& a, const V b); template inline pair& operator%=(pair& a, const V b); template inline pair operator+(pair a, const V& b); template inline pair operator-(pair a, const V& b); template inline pair operator*(pair a, const V& b); template inline pair operator/(pair a, const V& b); template inline pair operator%(pair a, const V& b); template inline pair operator+(pair a); template inline pair operator-(pair a); template istream& operator >>(istream& stream, pair& a); template ostream& operator <<(ostream &stream, const pair& a); /********* V E C T O R **********/ template inline vector& operator+=(vector& a, const vector b); template inline vector& operator-=(vector& a, const vector b); template inline vector& operator*=(vector& a, const vector b); template inline vector& operator/=(vector& a, const vector b); template inline vector& operator%=(vector& a, const vector b); template inline vector& operator+=(vector& a, const U b); template inline vector& operator-=(vector& a, const U b); template inline vector& operator*=(vector& a, const U b); template inline vector& operator/=(vector& a, const U b); template inline vector& operator%=(vector& a, const U b); template inline vector operator+(vector a, const U& b); template inline vector operator-(vector a, const U& b); template inline vector operator*(vector a, const U& b); template inline vector operator/(vector a, const U& b); template inline vector operator%(vector a, const U& b); template inline vector operator+(vector a); template inline vector operator-(vector a); template istream& operator >>(istream& stream, vector& a); template ostream& operator <<(ostream& stream, const vector& v); template ostream& operator <<(ostream& stream, const vector>& vv); template inline T Sum(const vector& v) {return reduce(all(v));} // v.size() == 0 のとき T() を返す template inline T Max(const vector& v) {assert(v.size()); return *max_element(all(v));} template inline T Min(const vector& v) {assert(v.size()); return *min_element(all(v));} template inline ll Argmax(const vector& v) {assert(v.size()); return max_element(all(v)) - v.begin();} template inline ll Argmin(const vector& v) {assert(v.size()); return min_element(all(v)) - v.begin();} template inline bool Contains(const vector& v, const U& a) {return find(all(v), a) != v.end();} template inline void Unique(vector& v) {sort(all(v)); v.erase(unique(all(v)), v.end());} // ソートされたユニーク値のvectorに書き換える, O(NlogN). template vector make_vector(int n, U v) { return vector(n, v); } template auto make_vector(int n, Args... args) {auto val = make_vector(args...); return make_vector(n, move(val));} /********* S E T **********/ template istream& operator >>(istream& stream, set& st); template ostream& operator <<(ostream& stream, const set& st); template inline T Max(const set& st) {assert(st.size()); return *prev(st.end());} template inline T Min(const set& st) {assert(st.size()); return *st.begin();} /********* M U L T I S E T **********/ template istream& operator >>(istream& stream, multiset& st); template ostream& operator <<(ostream& stream, const multiset& st); template inline T Max(const multiset& st) {assert(st.size()); return *prev(st.end());} template inline T Min(const multiset& st) {assert(st.size()); return *st.begin();} template inline bool EraseOne(multiset& st, T x) {auto it=st.find(x); if (it!=st.end()) {st.erase(it); return true;} else return false;} // 要素xを1つ削除. 消せたらtrueを返す. /********* S T R I N G **********/ inline string ToUpper(const string& s) {string t; t.resize(s.size()); std::transform(all(s), t.begin(), ::toupper); return t; } inline string ToLower(const string& s) {string t; t.resize(s.size()); std::transform(all(s), t.begin(), ::tolower); return t; } inline char ToUpper(const char& c) {string s{c}, t; t.resize(s.size()); std::transform(all(s), t.begin(), ::toupper); return t[0]; } inline char ToLower(const char& c) {string s{c}, t; t.resize(s.size()); std::transform(all(s), t.begin(), ::tolower); return t[0]; } inline bool IsUpper(const char& c) {return isupper(c) > 0; } inline bool IsLower(const char& c) {return islower(c) > 0; } /********* T R I O **********/ template struct trio { T1 first; T2 second; T3 third; // コンストラクタ・代入演算子 trio() {first=T1(); second=T2(); third=T3();} trio(const T1& x) : first(x), second(x), third(x) {} trio(const T1& x, const T2& y, const T3& z) : first(x), second(y), third(z) {} trio(const trio& t) {first=t.first; second=t.second; third=t.third;} // コピーコンストラクタ trio& operator =(const trio& t) {first=t.first; second=t.second; third=t.third; return *this;} // 比較演算子 auto operator <=>(const trio&) const = default; // 単項演算子（+ -） trio operator +() const { return *this; } trio operator -() const { return (-1) * (*this); } // 複合代入演算子 trio& operator +=(const trio& t) {first += t.first; second += t.second; third += t.third; return *this;} trio& operator -=(const trio& t) {first -= t.first; second -= t.second; third -= t.third; return *this;} trio& operator *=(const trio& t) {first *= t.first; second *= t.second; third *= t.third; return *this;} trio& operator /=(const trio& t) {first /= t.first; second /= t.second; third /= t.third; return *this;} trio& operator %=(const trio& t) {first %= t.first; second %= t.second; third %= t.third; return *this;} // 算術演算子 friend trio operator +(const trio& lhs, const trio& rhs) {return trio(lhs) += rhs;} friend trio operator -(const trio& lhs, const trio& rhs) {return trio(lhs) -= rhs;} friend trio operator *(const trio& lhs, const trio& rhs) {return trio(lhs) *= rhs;} friend trio operator /(const trio& lhs, const trio& rhs) {return trio(lhs) /= rhs;} friend trio operator %(const trio& lhs, const trio& rhs) {return trio(lhs) %= rhs;} // 入出力 template friend istream& operator >>(istream&, trio&); template friend ostream& operator <<(ostream&, const trio&); operator tuple() {return tie(first, second, third);} }; using tll = trio; /********* R A N D O M **********/ struct Random { mt19937_64 rnd; Random() { random_device seed_gen; rnd.seed(seed_gen()); } Random(ll seed) { rnd.seed(seed); } ll randint(ll a, ll b) { // [a, b] uniform_int_distribution dist(a, b); return dist(rnd); } double randreal(double a, double b) { uniform_real_distribution dist(a, b); return dist(rnd); } char randchar(char a, char b) { // [a, b] uniform_int_distribution dist(a, b); return dist(rnd); } template void shuffle(vector& vec) { std::shuffle(all(vec), rnd); } }; /********* T I M E R **********/ struct Timer { int time_limit; int start_time; Timer(double time_limit_sec) { assert(time_limit_sec > 0); this->time_limit = time_limit_sec * CLOCKS_PER_SEC; this->start_time = clock(); } bool is_time_up() const { return clock() - this->start_time >= this->time_limit; } double get_elapsed_ratio() const { double ratio = 1.0 * (clock() - this->start_time) / (this->time_limit - this->start_time); return min(1.0, ratio); } }; /********* P R I N T **********/ template inline void print(const T& e); template inline void print(const H& h, const T&... t); template inline void End(const T&... t); /********* D E B U G **********/ #ifdef __LOCAL #define debug(...) if(DEBUG) do{cout << '[' << #__VA_ARGS__ << "] ";debug_(__VA_ARGS__);}while(0) #else #define debug(...) #endif void dbg_(const long long& e); template void dbg_(const T& e); template void dbg_(const pair& p); template void dbg_(const trio& t); template void debug_(const T& e); template void debug_(const vector& v); template void debug_(const vector>& vv); template void debug_(const map& mp); template void debug_(const vector>& vm); template void debug_(const set& st); template void debug_(const multiset& st); template void debug_(const vector>& vs); template void debug_(const vector>& vs); template void debug_(const H& h, const T&... t); /********* O T H E R S **********/ template inline bool chmin(T& a, U b) {if (a > b) {a = b; return true;} return false;} // bは値渡し! template inline bool chmax(T& a, U b) {if (a < b) {a = b; return true;} return false;} template inline auto Mod(const T& a, const U& m) {return (a % m + m) % m;} // 負もOK template inline auto Ceil(const T& x, const U& y) {return x < 0 ? x/y : (x + y - 1) / y;} // 負もOK template inline auto Floor(const T& x, const U& y) {return -(Ceil(-x, y)); } // 負もOK inline ll Isqrt(ll n) {assert(n >= 0); ll x = round(sqrt(n)); while(x * x > n) --x; return x;} inline ll Comb(ll n, ll r) {if (r < 0 || n < r) return 0; r = min(r, n - r); ll ret = 1; rep(i, r) {ret *= n - i; ret /= i + 1;} return ret;} // n=60, r=30までOK template inline T Pow(T x, ll n) {assert(n >= 0); T ret = 1; while(1) {if (n % 2) ret *= x; n /= 2; if(!n) return ret; x = x * x;}} // べき乗 mintもOK template inline T Aseries(T a, T d, ll n) {assert(n >= 0); return a * n + n * (n - 1) / 2 * d;} // 等差級数 mintもOK template inline T Gseries(T a, T r, ll n) {assert(n >= 0); if (r == 1) return a * n; else return a * (1 - Pow(r, n)) / (1 - r);} // 等比級数 mintもOK template using min_priority_queue = priority_queue, greater>; inline bool Bit(ll b, int i) {assert(0 <= i && i < 64); return (b >> i) & 1;} inline ll Popcount(ll b) {return __builtin_popcountll(b);} inline ll Mask(ll n) {assert(0 <= n && n < 63); return (1LL << n) - 1LL;} // [0, n)のbitが立った64bit整数を返す。 inline ll Mask(ll n, ll m) {assert(n >= m); return Mask(n) ^ Mask(m);} // [m, n)のbitが立った64bit整数を返す。 inline void PrintYesNo(bool b) {b ? print("Yes") : print("No");} /********* M O D **********/ #include // https://atcoder.github.io/ac-library/production/document_ja/ using namespace atcoder; // using mint = modint998244353; // modint1000000007; // istream& operator >>(istream& stream, mint& e) {ll n; stream >> n; e = n; return stream; } // ostream& operator <<(ostream& stream, const mint& e) { stream << e.val(); return stream; } // using vm = vector; // using vvm = vector; /***************************************/ constexpr bool DEBUG = true; // 線形篩　参考：https://atcoder.jp/contests/abc292/editorial/5912 struct LinearSieve { ll N; vl primes; // N以下の素数列 vl spf; // smallest prime factor (ex. spf[75] = 3) vl power; // iが含むspf[i]の個数 (ex. power[40] = 3) vl prev_divisor; // prev_divisor[i] = i / spf[i]^power[i]. LinearSieve(ll N) : N(N), spf(N + 1), power(N + 1), prev_divisor(N + 1) { rep(i, 2, N + 1) { if (spf[i] == 0) { primes.pb(i); spf[i] = i; power[i] = 1; prev_divisor[i] = 1; } fore(p, primes) { if (p * i > N) break; spf[p * i] = p; if (p == spf[i]) { prev_divisor[p * i] = prev_divisor[i]; power[p * i] = power[i] + 1; break; } prev_divisor[p * i] = i; power[p * i] = 1; } } } // 素因数分解結果を取得, O(mlogm) (m: nの素因数の種類数 ) map get(ll n) { assert(1 <= n && n <= N); map mp; while(n > 1) { mp[spf[n]] = power[n]; n = prev_divisor[n]; } return mp; } // 約数列挙（ソートなし）, O(M) (M: nの約数の個数) //参考: https://atcoder.jp/contests/abc170/submissions/14359259 vl divisor(ll n) { // 約数の個数を求め、配列を初期化 ll cnt = divisor_count(n); vl ret(cnt); ret[0] = 1; cnt = 1; // 計算した約数の個数 while(n > 1) { ll d = spf[n]; rep(k, 1, power[n] + 1) { rep(j, cnt) { ret[k * cnt + j] = ret[j] * d; } d *= spf[n]; } cnt *= power[n] + 1; n = prev_divisor[n]; } return ret; } // 約数の個数 ll divisor_count(ll n) { assert(1 <= n && n <= N); ll ret = 1; while(n > 1) { ret *= power[n] + 1; n = prev_divisor[n]; } return ret; } // オイラーのφ関数 ll phi(ll n) { assert(1 <= n && n <= N); ll ret = n; while(n > 1) { ll p = spf[n]; ret /= p; ret *= p - 1; n = prev_divisor[n]; } return ret; } }; // LinearSieve spf(100); // O(N) // auto mp = spf.get(12); // (2, 2), (3, 1). 素因数分解, O(mlogm) (m: 素因数の種類数) // vl vec = spf.divisor(12); // {1, 2, 4, 3, 6, 12}. 約数列挙（ソートなし）, O(M) (M: nの約数の個数) // ll n = spf.divisor_count(12); // 6. 約数の個数, O(m) // ll p = spf.phi(12); // p = 4. オイラーのφ関数. 12と互いに素: {1, 5, 7, 11} int main() { cin.tie(nullptr); cout << fixed << setprecision(10); ll N; cin >> N; vl A(N); cin >> A; auto spf = LinearSieve(201010); set st; ll n1 = 0; fore(a, A) { if (a == 1) { n1++; continue; } auto mp = spf.get(a); fore(p, mp) st.insert(p.fi); } if (n1 == N) End(N * 2); vl vec; // vec[i] = i番目の素数 fore(e, st) vec.pb(e); vl idx(201010, -1); // idx[素数] = 何番目か rep(i, len(vec)) { idx[vec[i]] = i; } ll N2 = N + len(vec); dsu uf(N2); rep(i, N) { ll a = A[i]; if (a == 1) continue; auto mp = spf.get(a); fore(p, mp) { ll v = idx[p.fi] + N; uf.merge(i, v); } } rep(i, N + 1, N2) { if (uf.same(N, i)) continue; n1++; uf.merge(N, i); } ll ans = min(2 * (n1 + 1), vec[0] * n1); print(ans); } /********* P A I R **********/ template inline pair& operator+=(pair& a, const pair b) {a.fi += b.fi; a.se += b.se; return a;} template inline pair& operator-=(pair& a, const pair b) {a.fi -= b.fi; a.se -= b.se; return a;} template inline pair& operator*=(pair& a, const pair b) {a.fi *= b.fi; a.se *= b.se; return a;} template inline pair& operator/=(pair& a, const pair b) {a.fi /= b.fi; a.se /= b.se; return a;} template inline pair& operator%=(pair& a, const pair b) {a.fi %= b.fi; a.se %= b.se; return a;} template inline pair& operator+=(pair& a, const V b) {a.fi += b; a.se += b; return a;} template inline pair& operator-=(pair& a, const V b) {a.fi -= b; a.se -= b; return a;} template inline pair& operator*=(pair& a, const V b) {a.fi *= b; a.se *= b; return a;} template inline pair& operator/=(pair& a, const V b) {a.fi /= b; a.se /= b; return a;} template inline pair& operator%=(pair& a, const V b) {a.fi %= b; a.se %= b; return a;} template inline pair operator+(pair a, const V& b) {a += b; return a;} template inline pair operator-(pair a, const V& b) {a -= b; return a;} template inline pair operator*(pair a, const V& b) {a *= b; return a;} template inline pair operator/(pair a, const V& b) {a /= b; return a;} template inline pair operator%(pair a, const V& b) {a %= b; return a;} template inline pair operator+(pair a) {return a;} template inline pair operator-(pair a) {return a * (-1);} template istream& operator >>(istream& stream, pair& a) {stream >> a.fi >> a.se; return stream;} template ostream& operator <<(ostream &stream, const pair& a) { stream << a.fi << " " << a.se; return stream; } /********* V E C T O R **********/ template inline vector& operator+=(vector& a, const vector b) {assert(a.size() == b.size()); rep(i, 0, a.size()) a[i] += b[i]; return a;} template inline vector& operator-=(vector& a, const vector b) {assert(a.size() == b.size()); rep(i, 0, a.size()) a[i] -= b[i]; return a;} template inline vector& operator*=(vector& a, const vector b) {assert(a.size() == b.size()); rep(i, 0, a.size()) a[i] *= b[i]; return a;} template inline vector& operator/=(vector& a, const vector b) {assert(a.size() == b.size()); rep(i, 0, a.size()) a[i] /= b[i]; return a;} template inline vector& operator%=(vector& a, const vector b) {assert(a.size() == b.size()); rep(i, 0, a.size()) a[i] %= b[i]; return a;} template inline vector& operator+=(vector& a, const U b) {fore(e, a) e += b; return a;} template inline vector& operator-=(vector& a, const U b) {fore(e, a) e -= b; return a;} template inline vector& operator*=(vector& a, const U b) {fore(e, a) e *= b; return a;} template inline vector& operator/=(vector& a, const U b) {fore(e, a) e /= b; return a;} template inline vector& operator%=(vector& a, const U b) {fore(e, a) e %= b; return a;} template inline vector operator+(vector a, const U& b) {a += b; return a;} template inline vector operator-(vector a, const U& b) {a -= b; return a;} template inline vector operator*(vector a, const U& b) {a *= b; return a;} template inline vector operator/(vector a, const U& b) {a /= b; return a;} template inline vector operator%(vector a, const U& b) {a %= b; return a;} template inline vector operator+(vector a) {return a;} template inline vector operator-(vector a) {return a * (-1);} template istream& operator >>(istream& stream, vector& a) {fore(e, a) stream >> e; return stream;} template ostream& operator <<(ostream& stream, const vector& v) {if(v.size()){stream << v[0]; rep(i, 1, v.size()) cout << " " << v[i];} return stream;} template ostream& operator <<(ostream& stream, const vector>& vv) {if(vv.size()){stream << vv[0]; rep(i, 1, vv.size()) cout << '\n' << vv[i];} return stream;} /********* S E T **********/ template istream& operator >>(istream& stream, set& st) {T e; stream >> e; st.insert(e); return stream;} template ostream& operator <<(ostream& stream, const set& st) {if(st.size()){auto it=st.begin(); stream << *it++; for(; it!=st.end(); it++) cout << " " << *it;} return stream;} /********* M U L T I S E T **********/ template istream& operator >>(istream& stream, multiset& st) {T e; stream >> e; st.insert(e); return stream;} template ostream& operator <<(ostream& stream, const multiset& st) {if(st.size()){auto it=st.begin(); stream << *it++; for(; it!=st.end(); it++) cout << " " << *it;} return stream;} /********* P R I N T **********/ template inline void print(const T& e) {cout << e << '\n';} template inline void print(const H& h, const T&... t) {cout << h << ' '; print(t...);} template inline void End(const T&... t) {print(t...); exit(0);} /********* D E B U G **********/ void dbg_(const long long& e) {if (e == INF) cout << "INF"; else if (e == -INF) cout << "-INF"; else cout << e;} template void dbg_(const T& e) {cout << e;} template void dbg_(const pair& p) {cout << '('; dbg_(p.first); cout << ' '; dbg_(p.second); cout << ')';} template void dbg_(const trio& t) {cout << '('; dbg_(t.first); cout << ' '; dbg_(t.second); cout << ' '; dbg_(t.third); cout << ')';} template void debug_(const T& e) {dbg_(e); cout << '\n';} template void debug_(const vector& v) {if (v.size()){auto it=v.begin(); dbg_(*it++); for(; it!=v.end(); ++it){cout << ' '; dbg_(*it);}} cout << '\n';} template void debug_(const vector>& vv) {cout << '\n'; ll cnt=0; for(auto&& v : vv){cout << cnt++ << ": "; debug_(v);}} template void debug_(const map& mp) {if (mp.size()) {auto it = mp.begin(); dbg_(*it++); for(; it != mp.end(); ++it) {cout << ' '; dbg_(*it);}} cout << '\n';} template void debug_(const vector>& vm){cout << '\n'; ll cnt=0; for(auto&& mp : vm){cout << cnt++ << ": "; debug_(mp);}} template void debug_(const set& st) {if(st.size()){auto it=st.begin(); dbg_(*it++); for(; it!=st.end(); ++it) {cout << ' '; dbg_(*it);}}cout << '\n';} template