This documentation is automatically generated by online-judge-tools/verification-helper
#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/problems/ALDS1_1_C"
#include <bits/stdc++.h>
#include "ugilib/base/constants.hpp"
#include "ugilib/base/definitions.hpp"
#include "ugilib/math/primes.hpp"
using namespace std;
// debug settings
// #define DEBUG
#ifdef DEBUG
// debug input
string _INPUT = R"(
5
1 2 3 4 5
)";
auto _cin = stringstream(_INPUT.substr(1)); // remove '\n' at _INPUT[0]
#else
// standard input
auto& _cin = cin;
#endif
// speed up
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
// reader
struct rd {
// T
template<typename T> static T i() { T x; _cin >> x; return x; } // T item
// vector<T>
template<typename T> static vector<T> v(int n) {vector<T> v(n); rep(i, n) _cin >> v[i]; return v;} // vector<T>
// vector<pair<T, T>>
template<typename T> static vector<pair<T, T>> vp(int n) {vector<pair<T, T>> v(n); rep(i, n) _cin >> v[i].first >> v[i].second; return v;} // vector<pair<T, T>>
// tuple
template<typename... Args> static tuple<Args...> t() {
tuple<Args...> values;
apply([](auto&... args) { ((_cin >> args), ...); }, values);
return values;
}
};
// debug print utility
namespace deb {
#include <cxxabi.h>
// demangle type name
string demangle(const char* name) {
int status = -4;
unique_ptr<char, void(*)(void*)> res{
abi::__cxa_demangle(name, NULL, NULL, &status),
free
};
return (status == 0) ? string(res.get()) : name ;
}
// meta functions for type traits
template<typename T>
constexpr bool isArithmeticContainer() { return is_arithmetic<typename T::value_type>::value; }
// for SFINAE
template<typename T, typename = void> struct has_key_and_mapped_type : false_type {};
template<typename T> struct has_key_and_mapped_type<T, void_t<typename T::key_type, typename T::mapped_type>> : true_type {};
// for map or unordered_map
template<typename T>
constexpr bool isMapLike() { return has_key_and_mapped_type<T>::value; }
// for values
template<typename T, typename enable_if<is_arithmetic<T>::value, nullptr_t>::type = nullptr>
void p(const T& x) { cout << x << " "; }
// for pairs
template <typename T, typename S>
void p(const pair<T, S>& _p){ p(_p.first); p(_p.second); cout << endl; }
// for containers
template<typename T, typename enable_if<!is_arithmetic<T>::value, nullptr_t>::type = nullptr>
void p(const T& container) {
// map and unordered_map
if constexpr (isMapLike<T>()) {
cout << demangle(typeid(T).name()) << ":" << endl;
for (const auto& kv : container) {
cout << "[" << kv.first << "] => ";
p(kv.second);
if constexpr (is_arithmetic_v<typename T::mapped_type>) cout << endl;
}
// vector or set or others
} else {
if constexpr (!isArithmeticContainer<T>()) cout << demangle(typeid(T).name()) << ":" << endl;
for (auto it = begin(container); it != end(container); ++it) {
p(*it);
}
if constexpr (isArithmeticContainer<T>()) cout << endl;
}
}
}; // namespace deb
int main() {
auto& cin = _cin;
// speed up io
cin.tie(nullptr);
ios::sync_with_stdio(false);
// code
int n = rd::i<int>();
vector<ll> queries = rd::v<ll>(n);
ll max = *max_element(queries.begin(), queries.end());
auto primes = ugilib::shieve(ll(sqrt(max))+2);
ll ans = 0;
unordered_set<ll> prime_set(primes.begin(), primes.end());
for (ll q : queries) {
if (prime_set.count(q)) ans++;
else {
bool is_prime = true;
for (ll p : primes) {
if (q % p == 0) {
is_prime = false;
break;
}
}
if (is_prime) ans++;
}
}
cout << ans << endl;
return 0;
}
#line 1 "tests/math/prime_enumerate.test.cpp"
#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/problems/ALDS1_1_C"
#include <bits/stdc++.h>
#line 2 "ugilib/base/definitions.hpp"
using ll = long long;
using ull = unsigned long long;
using ld = long double;
#define rep(i, n) for(size_t i = 0; i < n; i++) // rep macro
#define all(v) begin(v), end(v) // all iterator
#line 3 "ugilib/base/constants.hpp"
namespace ugilib::constants {
template<typename T>
inline constexpr T INF = std::numeric_limits<T>::max() / 2;
} // namespace ugilib::constants
const ll INF = ugilib::constants::INF<ll>;
#line 3 "ugilib/math/primes.hpp"
using namespace std;
namespace ugilib {
/**
* @brief エラトステネスの篩
* @tparam T 整数型
* @param n 素数の上限. nを含む
* @return vector<T> 素数リスト
* @note O(n log log n)
* @note jに代入される数の最大値はN^2なのでオーバーフローに注意
*/
template <typename T>
vector<T> shieve(const T &n) {
vector<bool> is_prime(n + 1, true);
vector<T> primes;
is_prime[0] = is_prime[1] = false;
for (T i = 2; i <= n; i++) {
if (!is_prime[i]) continue;
primes.push_back(i);
for (T j = i * i; 0 <= j && j <= n; j += i) { // オーバーフローに注意
is_prime[j] = false;
}
}
return primes;
}
/**
* @brief 素因数分解. 素数リストを用いる
* @tparam T 整数型
* @param n 素因数分解する数
* @param primes 素数リスト. shieveで取得したものを使う
* @return vector<pair<T, int>> 素因数とその個数
* @note O(sqrt(n)) より高速. shieveに時間がかかり,メモリをより消費する
*/
template <typename T>
vector<pair<T, int>> prime_factorization_with_shieve(T n, const vector<T>& primes) {
vector<pair<T, int>> factors; // 素因数とその個数
for (const T &p : primes) {
if (p * p > n) break;
if (n % p != 0) continue;
int count = 0;
while (n % p == 0) {
n /= p;
count++;
}
factors.push_back({p, count});
}
if (n != 1) factors.push_back({n, 1}); // nが素数の場合
return factors;
}
/**
* @brief 素因数分解
* @tparam T 整数型
* @param n 素因数分解する数
* @return vector<pair<T, int>> 素因数とその個数
* @note O(sqrt(n))
*/
template <typename T>
vector<pair<T, int>> prime_factorization(T n) {
vector<pair<T, int>> factors;
for (T i = 2; i * i <= n; i++) {
if (n % i != 0) continue;
int count = 0;
while (n % i == 0) {
n /= i;
count++;
}
factors.push_back({i, count});
}
if (n != 1) factors.push_back({n, 1}); // nが素数の場合
return factors;
}
} // namespace ugilib
#line 7 "tests/math/prime_enumerate.test.cpp"
using namespace std;
// debug settings
// #define DEBUG
#ifdef DEBUG
// debug input
string _INPUT = R"(
5
1 2 3 4 5
)";
auto _cin = stringstream(_INPUT.substr(1)); // remove '\n' at _INPUT[0]
#else
// standard input
auto& _cin = cin;
#endif
// speed up
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
// reader
struct rd {
// T
template<typename T> static T i() { T x; _cin >> x; return x; } // T item
// vector<T>
template<typename T> static vector<T> v(int n) {vector<T> v(n); rep(i, n) _cin >> v[i]; return v;} // vector<T>
// vector<pair<T, T>>
template<typename T> static vector<pair<T, T>> vp(int n) {vector<pair<T, T>> v(n); rep(i, n) _cin >> v[i].first >> v[i].second; return v;} // vector<pair<T, T>>
// tuple
template<typename... Args> static tuple<Args...> t() {
tuple<Args...> values;
apply([](auto&... args) { ((_cin >> args), ...); }, values);
return values;
}
};
// debug print utility
namespace deb {
#include <cxxabi.h>
// demangle type name
string demangle(const char* name) {
int status = -4;
unique_ptr<char, void(*)(void*)> res{
abi::__cxa_demangle(name, NULL, NULL, &status),
free
};
return (status == 0) ? string(res.get()) : name ;
}
// meta functions for type traits
template<typename T>
constexpr bool isArithmeticContainer() { return is_arithmetic<typename T::value_type>::value; }
// for SFINAE
template<typename T, typename = void> struct has_key_and_mapped_type : false_type {};
template<typename T> struct has_key_and_mapped_type<T, void_t<typename T::key_type, typename T::mapped_type>> : true_type {};
// for map or unordered_map
template<typename T>
constexpr bool isMapLike() { return has_key_and_mapped_type<T>::value; }
// for values
template<typename T, typename enable_if<is_arithmetic<T>::value, nullptr_t>::type = nullptr>
void p(const T& x) { cout << x << " "; }
// for pairs
template <typename T, typename S>
void p(const pair<T, S>& _p){ p(_p.first); p(_p.second); cout << endl; }
// for containers
template<typename T, typename enable_if<!is_arithmetic<T>::value, nullptr_t>::type = nullptr>
void p(const T& container) {
// map and unordered_map
if constexpr (isMapLike<T>()) {
cout << demangle(typeid(T).name()) << ":" << endl;
for (const auto& kv : container) {
cout << "[" << kv.first << "] => ";
p(kv.second);
if constexpr (is_arithmetic_v<typename T::mapped_type>) cout << endl;
}
// vector or set or others
} else {
if constexpr (!isArithmeticContainer<T>()) cout << demangle(typeid(T).name()) << ":" << endl;
for (auto it = begin(container); it != end(container); ++it) {
p(*it);
}
if constexpr (isArithmeticContainer<T>()) cout << endl;
}
}
}; // namespace deb
int main() {
auto& cin = _cin;
// speed up io
cin.tie(nullptr);
ios::sync_with_stdio(false);
// code
int n = rd::i<int>();
vector<ll> queries = rd::v<ll>(n);
ll max = *max_element(queries.begin(), queries.end());
auto primes = ugilib::shieve(ll(sqrt(max))+2);
ll ans = 0;
unordered_set<ll> prime_set(primes.begin(), primes.end());
for (ll q : queries) {
if (prime_set.count(q)) ans++;
else {
bool is_prime = true;
for (ll p : primes) {
if (q % p == 0) {
is_prime = false;
break;
}
}
if (is_prime) ans++;
}
}
cout << ans << endl;
return 0;
}