#763180 (C++17) No.1955 Not Prime

• 問題: No.1955 Not Prime
• ユーザー: suisen
• 提出日時: 2022-05-20 21:58:29
• 言語: C++17 (gcc 13.3.0 + boost 1.87.0)
• 結果: CE (最新)
  AC
  (最初)
• 実行時間: -
• コード長: 21,968 bytes
• コンパイル時間: 2,033 ms
• コンパイル使用メモリ: 199,104 KB
• 最終ジャッジ日時: 2025-01-29 10:35:05
• ジャッジサーバーID （参考情報）: judge1 / judge1

コンパイルメッセージ

main.cpp: In instantiation of ‘std::istream& operator>>(std::istream&, std::vector<_Tp>&) [with T = std::array<int, 2>; std::istream = std::basic_istream<char>]’:
main.cpp:197:26:   required from ‘void read(Args& ...) [with Args = {std::vector<std::array<int, 2>, std::allocator<std::array<int, 2> > >}]’
main.cpp:565:9:   required from here
main.cpp:186:55: error: no match for ‘operator>>’ (operand types are ‘std::istream’ {aka ‘std::basic_istream<char>’} and ‘std::array<int, 2>’)
  186 |     for (auto it = a.begin(); it != a.end(); ++it) in >> *it;
      |                                                    ~~~^~~~~~
In file included from /usr/include/c++/13/sstream:40,
                 from /usr/include/c++/13/complex:45,
                 from /usr/include/c++/13/ccomplex:39,
                 from /usr/include/x86_64-linux-gnu/c++/13/bits/stdc++.h:127,
                 from main.cpp:1:
/usr/include/c++/13/istream:325:7: note: candidate: ‘std::basic_istream<_CharT, _Traits>::__istream_type& std::basic_istream<_CharT, _Traits>::operator>>(void*&) [with _CharT = char; _Traits = std::char_traits<char>; __istream_type = std::basic_istream<char>]’
  325 |       operator>>(void*& __p)
      |       ^~~~~~~~
/usr/include/c++/13/istream:325:25: note:   no known conversion for argument 1 from ‘std::array<int, 2>’ to ‘void*&’
  325 |       operator>>(void*& __p)
      |                  ~~~~~~~^~~
/usr/include/c++/13/istream:224:7: note: candidate: ‘std::basic_istream<_CharT, _Traits>::__istream_type& std::basic_istream<_CharT, _Traits>::operator>>(long double&) [with _CharT = char; _Traits = std::char_traits<char>; __istream_type = std::basic_istream<char>]’
  224 |       operator>>(long double& __f)
      |       ^~~~~~~~
/usr/include/c++/13/istream:224:31: note:   no known conversion for argument 1 from ‘std::array<int, 2>’ to ‘long double&’
  224 |       operator>>(long double& __f)
      |                  ~~~~~~~~~~~~~^~~
/

ソースコード

#include <bits/stdc++.h>

#include <limits>
#include <type_traits>

namespace suisen {
// ! utility
template <typename ...Types>
using constraints_t = std::enable_if_t<std::conjunction_v<Types...>, std::nullptr_t>;
template <bool cond_v, typename Then, typename OrElse>
constexpr decltype(auto) constexpr_if(Then&& then, OrElse&& or_else) {
    if constexpr (cond_v) {
        return std::forward<Then>(then);
    } else {
        return std::forward<OrElse>(or_else);
    }
}

// ! function
template <typename ReturnType, typename Callable, typename ...Args>
using is_same_as_invoke_result = std::is_same<std::invoke_result_t<Callable, Args...>, ReturnType>;
template <typename F, typename T>
using is_uni_op = is_same_as_invoke_result<T, F, T>;
template <typename F, typename T>
using is_bin_op = is_same_as_invoke_result<T, F, T, T>;

template <typename Comparator, typename T>
using is_comparator = std::is_same<std::invoke_result_t<Comparator, T, T>, bool>;

// ! integral
template <typename T, typename = constraints_t<std::is_integral<T>>>
constexpr int bit_num = std::numeric_limits<std::make_unsigned_t<T>>::digits;
template <typename T, unsigned int n>
struct is_nbit { static constexpr bool value = bit_num<T> == n; };
template <typename T, unsigned int n>
static constexpr bool is_nbit_v = is_nbit<T, n>::value;

// ?
template <typename T>
struct safely_multipliable {};
template <>
struct safely_multipliable<int> { using type = long long; };
template <>
struct safely_multipliable<long long> { using type = __int128_t; };
template <>
struct safely_multipliable<unsigned int> { using type = unsigned long long; };
template <>
struct safely_multipliable<unsigned long int> { using type = __uint128_t; };
template <>
struct safely_multipliable<unsigned long long> { using type = __uint128_t; };
template <>
struct safely_multipliable<float> { using type = float; };
template <>
struct safely_multipliable<double> { using type = double; };
template <>
struct safely_multipliable<long double> { using type = long double; };
template <typename T>
using safely_multipliable_t = typename safely_multipliable<T>::type;

} // namespace suisen

// ! type aliases
using i128 = __int128_t;
using u128 = __uint128_t;

template <typename T>
using pq_greater = std::priority_queue<T, std::vector<T>, std::greater<T>>;
template <typename T, typename U>
using umap = std::unordered_map<T, U>;

// ! macros (capital: internal macro)
#define OVERLOAD2(_1,_2,name,...) name
#define OVERLOAD3(_1,_2,_3,name,...) name
#define OVERLOAD4(_1,_2,_3,_4,name,...) name

#define REP4(i,l,r,s)  for(std::remove_reference_t<std::remove_const_t<decltype(r)>>i=(l);i<(r);i+=(s))
#define REP3(i,l,r)    REP4(i,l,r,1)
#define REP2(i,n)      REP3(i,0,n)
#define REPINF3(i,l,s) for(std::remove_reference_t<std::remove_const_t<decltype(l)>>i=(l);;i+=(s))
#define REPINF2(i,l)   REPINF3(i,l,1)
#define REPINF1(i)     REPINF2(i,0)
#define RREP4(i,l,r,s) for(std::remove_reference_t<std::remove_const_t<decltype(r)>>i=(l)+fld((r)-(l)-1,s)*(s);i>=(l);i-=(s))
#define RREP3(i,l,r)   RREP4(i,l,r,1)
#define RREP2(i,n)     RREP3(i,0,n)

#define rep(...)    OVERLOAD4(__VA_ARGS__, REP4   , REP3   , REP2   )(__VA_ARGS__)
#define rrep(...)   OVERLOAD4(__VA_ARGS__, RREP4  , RREP3  , RREP2  )(__VA_ARGS__)
#define repinf(...) OVERLOAD3(__VA_ARGS__, REPINF3, REPINF2, REPINF1)(__VA_ARGS__)

#define CAT_I(a, b) a##b
#define CAT(a, b) CAT_I(a, b)
#define UNIQVAR(tag) CAT(tag, __LINE__)
#define loop(n) for (std::remove_reference_t<std::remove_const_t<decltype(n)>> UNIQVAR(loop_variable) = n; UNIQVAR(loop_variable) --> 0;)

#define all(iterable) std::begin(iterable), std::end(iterable)
#define input(type, ...) type __VA_ARGS__; read(__VA_ARGS__)

#ifdef LOCAL
#  define debug(...) debug_internal(#__VA_ARGS__, __VA_ARGS__)

template <class T, class... Args>
void debug_internal(const char* s, T&& first, Args&&... args) {
    constexpr const char* prefix = "[\033[32mDEBUG\033[m] ";
    constexpr const char* open_brakets = sizeof...(args) == 0 ? "" : "(";
    constexpr const char* close_brakets = sizeof...(args) == 0 ? "" : ")";
    std::cerr << prefix << open_brakets << s << close_brakets << ": " << open_brakets << std::forward<T>(first);
    ((std::cerr << ", " << std::forward<Args>(args)), ...);
    std::cerr << close_brakets << "\n";
}

#else
#  define debug(...) void(0)
#endif

// ! I/O utilities

// pair
template <typename T, typename U>
std::ostream& operator<<(std::ostream& out, const std::pair<T, U> &a) {
    return out << a.first << ' ' << a.second;
}
// tuple
template <unsigned int N = 0, typename ...Args>
std::ostream& operator<<(std::ostream& out, const std::tuple<Args...> &a) {
    if constexpr (N >= std::tuple_size_v<std::tuple<Args...>>) {
        return out;
    } else {
        out << std::get<N>(a);
        if constexpr (N + 1 < std::tuple_size_v<std::tuple<Args...>>) {
            out << ' ';
        }
        return operator<<<N + 1>(out, a);
    }
}
// vector
template <typename T>
std::ostream& operator<<(std::ostream& out, const std::vector<T> &a) {
    for (auto it = a.begin(); it != a.end();) {
        out << *it;
        if (++it != a.end()) out << ' ';
    }
    return out;
}
// array
template <typename T, size_t N>
std::ostream& operator<<(std::ostream& out, const std::array<T, N> &a) {
    for (auto it = a.begin(); it != a.end();) {
        out << *it;
        if (++it != a.end()) out << ' ';
    }
    return out;
}
inline void print() { std::cout << '\n'; }
template <typename Head, typename... Tail>
inline void print(const Head &head, const Tail &...tails) {
    std::cout << head;
    if (sizeof...(tails)) std::cout << ' ';
    print(tails...);
}
template <typename Iterable>
auto print_all(const Iterable& v, std::string sep = " ", std::string end = "\n") -> decltype(std::cout << *v.begin(), void()) {
    for (auto it = v.begin(); it != v.end();) {
        std::cout << *it;
        if (++it != v.end()) std::cout << sep;
    }
    std::cout << end;
}

// pair
template <typename T, typename U>
std::istream& operator>>(std::istream& in, std::pair<T, U> &a) {
    return in >> a.first >> a.second;
}
// tuple
template <unsigned int N = 0, typename ...Args>
std::istream& operator>>(std::istream& in, std::tuple<Args...> &a) {
    if constexpr (N >= std::tuple_size_v<std::tuple<Args...>>) {
        return in;
    } else {
        return operator>><N + 1>(in >> std::get<N>(a), a);
    }
}
// vector
template <typename T>
std::istream& operator>>(std::istream& in, std::vector<T> &a) {
    for (auto it = a.begin(); it != a.end(); ++it) in >> *it;
    return in;
}
// array
template <typename T, size_t N>
std::istream& operator>>(std::istream& in, std::array<T, N> &a) {
    for (auto it = a.begin(); it != a.end(); ++it) in >> *it;
    return in;
}
template <typename ...Args>
void read(Args &...args) {
    ( std::cin >> ... >> args );
}

// ! integral utilities

// Returns pow(-1, n)
template <typename T>
constexpr inline int pow_m1(T n) {
    return -(n & 1) | 1;
}
// Returns pow(-1, n)
template <>
constexpr inline int pow_m1<bool>(bool n) {
    return -int(n) | 1;
}

// Returns floor(x / y)
template <typename T>
constexpr inline T fld(const T x, const T y) {
    return (x ^ y) >= 0 ? x / y : (x - (y + pow_m1(y >= 0))) / y;
}
template <typename T>
constexpr inline T cld(const T x, const T y) {
    return (x ^ y) <= 0 ? x / y : (x + (y + pow_m1(y >= 0))) / y;
}

template <typename T, suisen::constraints_t<suisen::is_nbit<T, 16>> = nullptr>
constexpr inline int popcount(const T x) { return __builtin_popcount(x); }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 32>> = nullptr>
constexpr inline int popcount(const T x) { return __builtin_popcount(x); }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 64>> = nullptr>
constexpr inline int popcount(const T x) { return __builtin_popcountll(x); }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 16>> = nullptr>
constexpr inline int count_lz(const T x) { return x ? __builtin_clz(x)   : suisen::bit_num<T>; }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 32>> = nullptr>
constexpr inline int count_lz(const T x) { return x ? __builtin_clz(x)   : suisen::bit_num<T>; }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 64>> = nullptr>
constexpr inline int count_lz(const T x) { return x ? __builtin_clzll(x) : suisen::bit_num<T>; }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 16>> = nullptr>
constexpr inline int count_tz(const T x) { return x ? __builtin_ctz(x)   : suisen::bit_num<T>; }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 32>> = nullptr>
constexpr inline int count_tz(const T x) { return x ? __builtin_ctz(x)   : suisen::bit_num<T>; }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 64>> = nullptr>
constexpr inline int count_tz(const T x) { return x ? __builtin_ctzll(x) : suisen::bit_num<T>; }
template <typename T>
constexpr inline int floor_log2(const T x) { return suisen::bit_num<T> - 1 - count_lz(x); }
template <typename T>
constexpr inline int ceil_log2(const T x)  { return floor_log2(x) + ((x & -x) != x); }
template <typename T>
constexpr inline int kth_bit(const T x, const unsigned int k) { return (x >> k) & 1; }
template <typename T>
constexpr inline int parity(const T x) { return popcount(x) & 1; }

struct all_subset {
    struct all_subset_iter {
        const int s; int t;
        constexpr all_subset_iter(int s) : s(s), t(s + 1) {}
        constexpr auto operator*() const { return t; }
        constexpr auto operator++() {}
        constexpr auto operator!=(std::nullptr_t) { return t ? (--t &= s, true) : false; }
    };
    int s;
    constexpr all_subset(int s) : s(s) {}
    constexpr auto begin() { return all_subset_iter(s); }
    constexpr auto end()   { return nullptr; }
};

// ! container

template <typename T, typename Comparator, suisen::constraints_t<suisen::is_comparator<Comparator, T>> = nullptr>
auto priqueue_comp(const Comparator comparator) {
    return std::priority_queue<T, std::vector<T>, Comparator>(comparator);
}

template <typename Iterable>
auto isize(const Iterable &iterable) -> decltype(int(iterable.size())) {
    return iterable.size();
}

template <typename T, typename Gen, suisen::constraints_t<suisen::is_same_as_invoke_result<T, Gen, int>> = nullptr>
auto generate_vector(int n, Gen generator) {
    std::vector<T> v(n);
    for (int i = 0; i < n; ++i) v[i] = generator(i);
    return v;
}
template <typename T>
auto generate_range_vector(T l, T r) {
    return generate_vector(r - l, [l](int i) { return l + i; });
}
template <typename T>
auto generate_range_vector(T n) {
    return generate_range_vector(0, n);
}

template <typename T>
void sort_unique_erase(std::vector<T> &a) {
    std::sort(a.begin(), a.end());
    a.erase(std::unique(a.begin(), a.end()), a.end());
}

template <typename InputIterator, typename BiConsumer>
auto foreach_adjacent_values(InputIterator first, InputIterator last, BiConsumer f) -> decltype(f(*first++, *last), void()) {
    if (first != last) for (auto itr = first, itl = itr++; itr != last; itl = itr++) f(*itl, *itr);
}
template <typename Container, typename BiConsumer>
auto foreach_adjacent_values(Container c, BiConsumer f) -> decltype(c.begin(), c.end(), void()){
    foreach_adjacent_values(c.begin(), c.end(), f);
}

// ! other utilities

// x <- min(x, y). returns true iff `x` has chenged.
template <typename T>
inline bool chmin(T &x, const T &y) {
    if (y >= x) return false;
    x = y;
    return true;
}
// x <- max(x, y). returns true iff `x` has chenged.
template <typename T>
inline bool chmax(T &x, const T &y) {
    if (y <= x) return false;
    x = y;
    return true;
}

namespace suisen {}
using namespace suisen;
using namespace std;

struct io_setup {
    io_setup(int precision = 20) {
        std::ios::sync_with_stdio(false);
        std::cin.tie(nullptr);
        std::cout << std::fixed << std::setprecision(precision);
    }
} io_setup_ {};

// ! code from here

#include <cassert>
#include <cmath>
#include <vector>

#include <cstdint>

namespace suisen::internal::sieve {

constexpr std::uint8_t K = 8;
constexpr std::uint8_t PROD = 2 * 3 * 5;
constexpr std::uint8_t RM[K] = { 1,  7, 11, 13, 17, 19, 23, 29 };
constexpr std::uint8_t DR[K] = { 6,  4,  2,  4,  2,  4,  6,  2 };
constexpr std::uint8_t DF[K][K] = {
    { 0, 0, 0, 0, 0, 0, 0, 1 }, { 1, 1, 1, 0, 1, 1, 1, 1 },
    { 2, 2, 0, 2, 0, 2, 2, 1 }, { 3, 1, 1, 2, 1, 1, 3, 1 },
    { 3, 3, 1, 2, 1, 3, 3, 1 }, { 4, 2, 2, 2, 2, 2, 4, 1 },
    { 5, 3, 1, 4, 1, 3, 5, 1 }, { 6, 4, 2, 4, 2, 4, 6, 1 },
};
constexpr std::uint8_t DRP[K] = { 48, 32, 16, 32, 16, 32, 48, 16 };
constexpr std::uint8_t DFP[K][K] = {
    {  0,  0,  0,  0,  0,  0,  0,  8 }, {  8,  8,  8,  0,  8,  8,  8,  8 },
    { 16, 16,  0, 16,  0, 16, 16,  8 }, { 24,  8,  8, 16,  8,  8, 24,  8 },
    { 24, 24,  8, 16,  8, 24, 24,  8 }, { 32, 16, 16, 16, 16, 16, 32,  8 },
    { 40, 24,  8, 32,  8, 24, 40,  8 }, { 48, 32, 16, 32, 16, 32, 48,  8 },
};

constexpr std::uint8_t MASK[K][K] = {
    { 0x01, 0x02, 0x04, 0x08, 0x10, 0x20, 0x40, 0x80 }, { 0x02, 0x20, 0x10, 0x01, 0x80, 0x08, 0x04, 0x40 },
    { 0x04, 0x10, 0x01, 0x40, 0x02, 0x80, 0x08, 0x20 }, { 0x08, 0x01, 0x40, 0x20, 0x04, 0x02, 0x80, 0x10 },
    { 0x10, 0x80, 0x02, 0x04, 0x20, 0x40, 0x01, 0x08 }, { 0x20, 0x08, 0x80, 0x02, 0x40, 0x01, 0x10, 0x04 },
    { 0x40, 0x04, 0x08, 0x80, 0x01, 0x10, 0x20, 0x02 }, { 0x80, 0x40, 0x20, 0x10, 0x08, 0x04, 0x02, 0x01 },
};
constexpr std::uint8_t OFFSET[K][K] = {
    { 0, 1, 2, 3, 4, 5, 6, 7, },
    { 1, 5, 4, 0, 7, 3, 2, 6, },
    { 2, 4, 0, 6, 1, 7, 3, 5, },
    { 3, 0, 6, 5, 2, 1, 7, 4, },
    { 4, 7, 1, 2, 5, 6, 0, 3, },
    { 5, 3, 7, 1, 6, 0, 4, 2, },
    { 6, 2, 3, 7, 0, 4, 5, 1, },
    { 7, 6, 5, 4, 3, 2, 1, 0, },
};

constexpr std::uint8_t mask_to_index(const std::uint8_t bits) {
    switch (bits) {
        case 1 << 0: return 0;
        case 1 << 1: return 1;
        case 1 << 2: return 2;
        case 1 << 3: return 3;
        case 1 << 4: return 4;
        case 1 << 5: return 5;
        case 1 << 6: return 6;
        case 1 << 7: return 7;
        default: assert(false);
    }
}
} // namespace suisen::internal::sieve

namespace suisen {

template <unsigned int N>
class SimpleSieve {
    private:
        static constexpr unsigned int siz = N / internal::sieve::PROD + 1;
        static std::uint8_t flag[siz];
    public:
        SimpleSieve() {
            using namespace internal::sieve;
            flag[0] |= 1;
            unsigned int k_max = (unsigned int) std::sqrt(N + 2) / PROD;
            for (unsigned int kp = 0; kp <= k_max; ++kp) {
                for (std::uint8_t bits = ~flag[kp]; bits; bits &= bits - 1) {
                    const std::uint8_t mp = mask_to_index(bits & -bits), m = RM[mp];
                    unsigned int kr = kp * (PROD * kp + 2 * m) + m * m / PROD;
                    for (std::uint8_t mq = mp; kr < siz; kr += kp * DR[mq] + DF[mp][mq], ++mq &= 7) {
                        flag[kr] |= MASK[mp][mq];
                    }
                }
            }
        }
        std::vector<int> prime_list(unsigned int max_val = N) const {
            using namespace internal::sieve;
            std::vector<int> res { 2, 3, 5 };
            res.reserve(max_val / 25);
            for (unsigned int i = 0, offset = 0; i < siz and offset < max_val; ++i, offset += PROD) {
                for (uint8_t f = ~flag[i]; f;) {
                    uint8_t g = f & -f;
                    res.push_back(offset + RM[mask_to_index(g)]);
                    f ^= g;
                }
            }
            while (res.size() and (unsigned int) res.back() > max_val) res.pop_back();
            return res;
        }
        bool is_prime(const unsigned int p) const {
            using namespace internal::sieve;
            switch (p) {
                case 2: case 3: case 5: return true;
                default:
                    switch (p % PROD) {
                        case RM[0]: return ((flag[p / PROD] >> 0) & 1) == 0;
                        case RM[1]: return ((flag[p / PROD] >> 1) & 1) == 0;
                        case RM[2]: return ((flag[p / PROD] >> 2) & 1) == 0;
                        case RM[3]: return ((flag[p / PROD] >> 3) & 1) == 0;
                        case RM[4]: return ((flag[p / PROD] >> 4) & 1) == 0;
                        case RM[5]: return ((flag[p / PROD] >> 5) & 1) == 0;
                        case RM[6]: return ((flag[p / PROD] >> 6) & 1) == 0;
                        case RM[7]: return ((flag[p / PROD] >> 7) & 1) == 0;
                        default: return false;
                    }
            }
        }
};
template <unsigned int N>
std::uint8_t SimpleSieve<N>::flag[SimpleSieve<N>::siz];

template <unsigned int N>
class Sieve {
    private:
        static constexpr unsigned int base_max = (N + 1) * internal::sieve::K / internal::sieve::PROD;
        static unsigned int pf[base_max + internal::sieve::K];

    public:
        Sieve() {
            using namespace internal::sieve;
            pf[0] = 1;
            unsigned int k_max = ((unsigned int) std::sqrt(N + 1) - 1) / PROD;
            for (unsigned int kp = 0; kp <= k_max; ++kp) {
                const int base_i = kp * K, base_act_i = kp * PROD;
                for (int mp = 0; mp < K; ++mp) {
                    const int m = RM[mp], i = base_i + mp;
                    if (pf[i] == 0) {
                        unsigned int act_i = base_act_i + m;
                        unsigned int base_k = (kp * (PROD * kp + 2 * m) + m * m / PROD) * K;
                        for (std::uint8_t mq = mp; base_k <= base_max; base_k += kp * DRP[mq] + DFP[mp][mq], ++mq &= 7) {
                            pf[base_k + OFFSET[mp][mq]] = act_i;
                        }
                    }
                }
            }
        }
        bool is_prime(const unsigned int p) const {
            using namespace internal::sieve;
            switch (p) {
                case 2: case 3: case 5: return true;
                default:
                    switch (p % PROD) {
                        case RM[0]: return pf[p / PROD * K + 0] == 0;
                        case RM[1]: return pf[p / PROD * K + 1] == 0;
                        case RM[2]: return pf[p / PROD * K + 2] == 0;
                        case RM[3]: return pf[p / PROD * K + 3] == 0;
                        case RM[4]: return pf[p / PROD * K + 4] == 0;
                        case RM[5]: return pf[p / PROD * K + 5] == 0;
                        case RM[6]: return pf[p / PROD * K + 6] == 0;
                        case RM[7]: return pf[p / PROD * K + 7] == 0;
                        default: return false;
                    }
            }
        }
        int prime_factor(const unsigned int p) const {
            using namespace internal::sieve;
            switch (p % PROD) {
                case  0: case  2: case  4: case  6: case  8:
                case 10: case 12: case 14: case 16: case 18:
                case 20: case 22: case 24: case 26: case 28: return 2;
                case  3: case  9: case 15: case 21: case 27: return 3;
                case  5: case 25: return 5;
                case RM[0]: return pf[p / PROD * K + 0] ? pf[p / PROD * K + 0] : p;
                case RM[1]: return pf[p / PROD * K + 1] ? pf[p / PROD * K + 1] : p;
                case RM[2]: return pf[p / PROD * K + 2] ? pf[p / PROD * K + 2] : p;
                case RM[3]: return pf[p / PROD * K + 3] ? pf[p / PROD * K + 3] : p;
                case RM[4]: return pf[p / PROD * K + 4] ? pf[p / PROD * K + 4] : p;
                case RM[5]: return pf[p / PROD * K + 5] ? pf[p / PROD * K + 5] : p;
                case RM[6]: return pf[p / PROD * K + 6] ? pf[p / PROD * K + 6] : p;
                case RM[7]: return pf[p / PROD * K + 7] ? pf[p / PROD * K + 7] : p;
                default: assert(false);
            }
        }
        /**
         * Returns a vector of `{ prime, index }`.
         */
        std::vector<std::pair<int, int>> factorize(unsigned int n) const {
            assert(0 < n and n <= N);
            std::vector<std::pair<int, int>> prime_powers;
            while (n > 1) {
                int p = prime_factor(n), c = 0;
                do { n /= p, ++c; } while (n % p == 0);
                prime_powers.emplace_back(p, c);
            }
            return prime_powers;
        }
        /**
         * Returns the divisors of `n`.
         * It is NOT guaranteed that the returned vector is sorted.
         */
        std::vector<int> divisors(unsigned int n) const {
            assert(0 < n and n <= N);
            std::vector<int> divs { 1 };
            for (auto [prime, index] : factorize(n)) {
                int sz = divs.size();
                for (int i = 0; i < sz; ++i) {
                    int d = divs[i];
                    for (int j = 0; j < index; ++j) {
                        divs.push_back(d *= prime);
                    }
                }
            }
            return divs;
        }
};
template <unsigned int N>
unsigned int Sieve<N>::pf[Sieve<N>::base_max + internal::sieve::K];
} // namespace suisen

Sieve<1000000> sieve;

int dlen(int n) {
    if (n < 10) return 1;
    if (n < 100) return 2;
    return 3;
}

#include <atcoder/twosat>

int main() {
    input(int, n);

    vector<array<int, 2>> ps(n);
    read(ps);

    array<int, 4> pows { 1, 10, 100, 1000 };

    vector<array<int, 2>> ls(n);
    rep(i, n) {
        ls[i][0] = dlen(ps[i][0]);
        ls[i][1] = dlen(ps[i][1]);
    }

    atcoder::two_sat sat(n);
    rep(i, n) rep(x, 2) {
        rep(j, n) rep(y, 2) {
            debug(i, x, j, y, ps[i][x] * pows[ls[j][y]] + ps[j][y]);
            if (sieve.is_prime(ps[i][x] * pows[ls[j][y]] + ps[j][y])) {
                sat.add_clause(i, not x, j, y);
            }
        }
    }
    print(sat.satisfiable() ? "Yes" : "No");

    return 0;
}