結果

問題 No.1529 Constant Lcm
ユーザー jell
提出日時 2021-06-04 22:44:25
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 15 ms / 3,000 ms
コード長 35,775 bytes
コンパイル時間 3,827 ms
コンパイル使用メモリ 258,096 KB
最終ジャッジ日時 2025-01-22 02:26:51
ジャッジサーバーID
（参考情報） 		judge5 / judge3
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ファイルパターン 結果
sample AC * 2
other AC * 24
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#line 1 "other-workspace\\yuki2.cc"
// #undef _GLIBCXX_DEBUG
// #define NDEBUG
#include <bits/extc++.h>
#line 2 "Library\\lib\\alias"
/**
 * @file alias
 * @brief Alias
 */
#line 10 "Library\\lib\\alias"
#line 2 "Library\\lib\\bit"
#if __cplusplus > 201703L
#include <bit>
#elif __cplusplus > 201402L
#ifndef _GLIBCXX_BIT
#define _GLIBCXX_BIT 1
#include <limits>
#include <type_traits>
namespace std {
template <typename _Tp> constexpr int __countl_zero(_Tp __x) noexcept {
  constexpr auto _Nd = numeric_limits<_Tp>::digits;
  if (__x == 0) return _Nd;
  constexpr auto _Nd_ull = numeric_limits<unsigned long long>::digits;
  constexpr auto _Nd_ul = numeric_limits<unsigned long>::digits;
  constexpr auto _Nd_u = numeric_limits<unsigned>::digits;
  if _GLIBCXX17_CONSTEXPR (_Nd <= _Nd_u) {
    constexpr int __diff = _Nd_u - _Nd;
    return __builtin_clz(__x) - __diff;
  } else if _GLIBCXX17_CONSTEXPR (_Nd <= _Nd_ul) {
    constexpr int __diff = _Nd_ul - _Nd;
    return __builtin_clzl(__x) - __diff;
  } else if _GLIBCXX17_CONSTEXPR (_Nd <= _Nd_ull) {
    constexpr int __diff = _Nd_ull - _Nd;
    return __builtin_clzll(__x) - __diff;
  } else  // (_Nd > _Nd_ull)
  {
    static_assert(_Nd <= (2 * _Nd_ull),
                  "Maximum supported integer size is 128-bit");
    unsigned long long __high = __x >> _Nd_ull;
    if (__high != 0) {
      constexpr int __diff = (2 * _Nd_ull) - _Nd;
      return __builtin_clzll(__high) - __diff;
    }
    constexpr auto __max_ull = numeric_limits<unsigned long long>::max();
    unsigned long long __low = __x & __max_ull;
    return (_Nd - _Nd_ull) + __builtin_clzll(__low);
  }
}
template <typename _Tp> constexpr int __countr_zero(_Tp __x) noexcept {
  constexpr auto _Nd = numeric_limits<_Tp>::digits;
  if (__x == 0) return _Nd;
  constexpr auto _Nd_ull = numeric_limits<unsigned long long>::digits;
  constexpr auto _Nd_ul = numeric_limits<unsigned long>::digits;
  constexpr auto _Nd_u = numeric_limits<unsigned>::digits;
  if _GLIBCXX17_CONSTEXPR (_Nd <= _Nd_u)
    return __builtin_ctz(__x);
  else if _GLIBCXX17_CONSTEXPR (_Nd <= _Nd_ul)
    return __builtin_ctzl(__x);
  else if _GLIBCXX17_CONSTEXPR (_Nd <= _Nd_ull)
    return __builtin_ctzll(__x);
  else  // (_Nd > _Nd_ull)
  {
    static_assert(_Nd <= (2 * _Nd_ull),
                  "Maximum supported integer size is 128-bit");
    constexpr auto __max_ull = numeric_limits<unsigned long long>::max();
    unsigned long long __low = __x & __max_ull;
    if (__low != 0) return __builtin_ctzll(__low);
    unsigned long long __high = __x >> _Nd_ull;
    return __builtin_ctzll(__high) + _Nd_ull;
  }
}
template <typename _Tp> constexpr int __popcount(_Tp __x) noexcept {
  constexpr auto _Nd = numeric_limits<_Tp>::digits;
  if (__x == 0) return 0;
  constexpr auto _Nd_ull = numeric_limits<unsigned long long>::digits;
  constexpr auto _Nd_ul = numeric_limits<unsigned long>::digits;
  constexpr auto _Nd_u = numeric_limits<unsigned>::digits;
  if _GLIBCXX17_CONSTEXPR (_Nd <= _Nd_u)
    return __builtin_popcount(__x);
  else if _GLIBCXX17_CONSTEXPR (_Nd <= _Nd_ul)
    return __builtin_popcountl(__x);
  else if _GLIBCXX17_CONSTEXPR (_Nd <= _Nd_ull)
    return __builtin_popcountll(__x);
  else  // (_Nd > _Nd_ull)
  {
    static_assert(_Nd <= (2 * _Nd_ull),
                  "Maximum supported integer size is 128-bit");
    constexpr auto __max_ull = numeric_limits<unsigned long long>::max();
    unsigned long long __low = __x & __max_ull;
    unsigned long long __high = __x >> _Nd_ull;
    return __builtin_popcountll(__low) + __builtin_popcountll(__high);
  }
}
template <typename _Tp> constexpr _Tp __bit_ceil(_Tp __x) noexcept {
  constexpr auto _Nd = numeric_limits<_Tp>::digits;
  if (__x == 0 || __x == 1) return 1;
  auto __shift_exponent = _Nd - __countl_zero((_Tp)(__x - 1u));
#ifdef _GLIBCXX_HAVE_BUILTIN_IS_CONSTANT_EVALUATED
  if (!__builtin_is_constant_evaluated()) {
    __glibcxx_assert(__shift_exponent != numeric_limits<_Tp>::digits);
  }
#endif
  using __promoted_type = decltype(__x << 1);
  if _GLIBCXX17_CONSTEXPR (!is_same<__promoted_type, _Tp>::value) {
    const int __extra_exp = sizeof(__promoted_type) / sizeof(_Tp) / 2;
    __shift_exponent |= (__shift_exponent & _Nd) << __extra_exp;
  }
  return (_Tp)1u << __shift_exponent;
}
template <typename _Tp> constexpr _Tp __bit_floor(_Tp __x) noexcept {
  constexpr auto _Nd = numeric_limits<_Tp>::digits;
  if (__x == 0) return 0;
  return (_Tp)1u << (_Nd - __countl_zero((_Tp)(__x >> 1)));
}
template <typename _Tp> constexpr _Tp __bit_width(_Tp __x) noexcept {
  constexpr auto _Nd = numeric_limits<_Tp>::digits;
  return _Nd - __countl_zero(__x);
}
}  // namespace std
#endif
#endif
#line 2 "Library\\lib\\limits"
#line 4 "Library\\lib\\limits"
namespace workspace {
template <class _Tp> struct numeric_limits : std::numeric_limits<_Tp> {};
#ifdef __SIZEOF_INT128__
template <> struct numeric_limits<__uint128_t> {
  constexpr static __uint128_t max() { return ~__uint128_t(0); }
  constexpr static __uint128_t min() { return 0; }
};
template <> struct numeric_limits<__int128_t> {
  constexpr static __int128_t max() {
    return numeric_limits<__uint128_t>::max() >> 1;
  }
  constexpr static __int128_t min() { return -max() - 1; }
};
#endif
}  // namespace workspace
#line 13 "Library\\lib\\alias"
namespace workspace {
constexpr static char eol = '\n';
using namespace std;
using i32 = int_least32_t;
using u32 = uint_least32_t;
using i64 = int_least64_t;
using u64 = uint_least64_t;
#ifdef __SIZEOF_INT128__
using i128 = __int128_t;
using u128 = __uint128_t;
#else
#warning 128-bit integer is not available.
#endif
template <class _T1, class _T2,
          typename = decltype(std::declval<const _T2 &>() <
                              std::declval<const _T1 &>())>
constexpr
    typename std::conditional<std::is_same<_T1, _T2>::value, const _T1 &,
                              typename std::common_type<_T1, _T2>::type>::type
    min(const _T1 &__x, const _T2 &__y) noexcept {
  return __y < __x ? __y : __x;
}
template <class _T1, class _T2, class _Compare,
          typename = decltype(std::declval<_Compare>()(
              std::declval<const _T2 &>(), std::declval<const _T1 &>()))>
constexpr
    typename std::conditional<std::is_same<_T1, _T2>::value, const _T1 &,
                              typename std::common_type<_T1, _T2>::type>::type
    min(const _T1 &__x, const _T2 &__y, _Compare __comp) noexcept {
  return __comp(__y, __x) ? __y : __x;
}
template <class _Tp, typename = decltype(std::declval<const _Tp &>() <
                                         std::declval<const _Tp &>())>
constexpr _Tp min(std::initializer_list<_Tp> __x) noexcept {
  return *std::min_element(__x.begin(), __x.end());
}
template <class _Tp, class _Compare,
          typename = decltype(std::declval<_Compare>()(
              std::declval<const _Tp &>(), std::declval<const _Tp &>()))>
constexpr _Tp min(std::initializer_list<_Tp> __x, _Compare __comp) noexcept {
  return *std::min_element(__x.begin(), __x.end(), __comp);
}
template <class _T1, class _T2,
          typename = decltype(std::declval<const _T1 &>() <
                              std::declval<const _T2 &>())>
constexpr
    typename std::conditional<std::is_same<_T1, _T2>::value, const _T1 &,
                              typename std::common_type<_T1, _T2>::type>::type
    max(const _T1 &__x, const _T2 &__y) noexcept {
  return __x < __y ? __y : __x;
}
template <class _T1, class _T2, class _Compare,
          typename = decltype(std::declval<_Compare>()(
              std::declval<const _T1 &>(), std::declval<const _T2 &>()))>
constexpr
    typename std::conditional<std::is_same<_T1, _T2>::value, const _T1 &,
                              typename std::common_type<_T1, _T2>::type>::type
    max(const _T1 &__x, const _T2 &__y, _Compare __comp) noexcept {
  return __comp(__x, __y) ? __y : __x;
}
template <class _Tp, typename = decltype(std::declval<const _Tp &>() <
                                         std::declval<const _Tp &>())>
constexpr _Tp max(std::initializer_list<_Tp> __x) noexcept {
  return *std::max_element(__x.begin(), __x.end());
}
template <class _Tp, class _Compare,
          typename = decltype(std::declval<_Compare>()(
              std::declval<const _Tp &>(), std::declval<const _Tp &>()))>
constexpr _Tp max(std::initializer_list<_Tp> __x, _Compare __comp) noexcept {
  return *std::max_element(__x.begin(), __x.end(), __comp);
}
#ifdef _GLIBCXX_BIT
template <typename _Tp> constexpr _Tp __bsf(_Tp __x) noexcept {
  return std::__countr_zero(__x);
}
template <typename _Tp> constexpr _Tp __bsr(_Tp __x) noexcept {
  return std::__bit_width(__x) - 1;
}
#endif
}  // namespace workspace
#line 6 "other-workspace\\yuki2.cc"
// #include "lib/cxx20"
#line 1 "Library\\lib\\direct"
#ifdef ONLINE_JUDGE
#pragma GCC optimize("O3")
#pragma GCC target("avx,avx2")
#pragma GCC optimize("unroll-loops")
#endif
#line 8 "other-workspace\\yuki2.cc"
// #include "lib/opt"
#line 2 "Library\\src\\sys\\call_once.hpp"
/**
 * @file call_once.hpp
 * @brief Call Once
 */
#line 9 "Library\\src\\sys\\call_once.hpp"
namespace workspace {
/**
 * @brief Call once.
 */
template <class _F> void call_once(_F &&__f) {
  static std::unordered_set<void *> __called;
  if (__called.count(std::addressof(__f))) return;
  __called.emplace(std::addressof(__f));
  __f();
}
}  // namespace workspace
#line 2 "Library\\src\\sys\\clock.hpp"
/*
 * @fn clock.hpp
 * @brief Clock
 */
#line 9 "Library\\src\\sys\\clock.hpp"
namespace workspace {
using namespace std::chrono;
namespace internal {
// The start time of the program.
const auto start_time{system_clock::now()};
}  // namespace internal
/*
 * @fn elapsed
 * @return elapsed time of the program
 */
int64_t elapsed() {
  const auto end_time{system_clock::now()};
  return duration_cast<milliseconds>(end_time - internal::start_time).count();
}
}  // namespace workspace
#line 2 "Library\\src\\sys\\ejection.hpp"
/**
 * @file ejection.hpp
 * @brief Ejection
 */
#line 9 "Library\\src\\sys\\ejection.hpp"
namespace workspace {
namespace internal {
struct ejection {
  bool exit = 0;
};
}  // namespace internal
/**
 * @brief eject from a try block, throw nullptr
 * @param arg output
 */
template <class Tp> void eject(Tp const &arg) {
  std::cout << arg << "\n";
  throw internal::ejection{};
}
void exit() { throw internal::ejection{true}; }
}  // namespace workspace
#line 2 "Library\\src\\sys\\iteration.hpp"
/**
 * @file iteration.hpp
 * @brief Case Iteration
 */
#line 9 "Library\\src\\sys\\iteration.hpp"
#line 11 "Library\\src\\sys\\iteration.hpp"
namespace workspace {
void main();
struct {
  // 1-indexed
  unsigned current{0};
  unsigned total{1};
  void read() { (std::cin >> total).ignore(); }
  int iterate() {
    static bool once = false;
    assert(!once);
    once = true;
    while (current++ < total) {
      try {
        main();
      } catch (internal::ejection const& status) {
        if (status.exit) break;
      }
    }
    return 0;
  }
} case_info;
}  // namespace workspace
#line 2 "Library\\lib\\utils"
// #include "src/utils/cached.hpp"
// #include "src/utils/cat.hpp"
// #include "src/utils/chval.hpp"
// #include "src/utils/compare.hpp"
// #include "src/utils/fixed_point.hpp"
// #include "src/utils/hash.hpp"
// #include "src/utils/io/istream.hpp"
// #include "src/utils/io/ostream.hpp"
// #include "src/utils/io/read.hpp"
// #include "src/utils/grid/motion.hpp"
#line 2 "Library\\src\\utils\\io\\setup.hpp"
/**
 * @file setup.hpp
 * @brief I/O Setup
 */
#line 10 "Library\\src\\utils\\io\\setup.hpp"
namespace workspace {
/**
 * @brief Setup I/O.
 * @param __n Standard output precision
 */
void io_setup(int __n) {
  std::cin.tie(0)->sync_with_stdio(0);
  std::cout << std::fixed << std::setprecision(__n);
#ifdef _buffer_check
  atexit([] {
    char bufc;
    if (std::cin >> bufc)
      std::cerr << "\n\033[43m\033[30mwarning: buffer not empty.\033[0m\n\n";
  });
#endif
}
}  // namespace workspace
#line 2 "Library\\src\\utils\\iterator\\category.hpp"
/*
 * @file category.hpp
 * @brief Iterator Category
 */
#line 10 "Library\\src\\utils\\iterator\\category.hpp"
namespace workspace {
/*
 * @tparam Tuple Tuple of iterator types
 */
template <class Tuple, size_t N = std::tuple_size<Tuple>::value - 1>
struct common_iterator_category {
  using type = typename std::common_type<
      typename common_iterator_category<Tuple, N - 1>::type,
      typename std::iterator_traits<typename std::tuple_element<
          N, Tuple>::type>::iterator_category>::type;
};
template <class Tuple> struct common_iterator_category<Tuple, 0> {
  using type = typename std::iterator_traits<
      typename std::tuple_element<0, Tuple>::type>::iterator_category;
};
}  // namespace workspace
#line 2 "Library\\src\\utils\\iterator\\reverse.hpp"
/*
 * @file reverse_iterator.hpp
 * @brief Reverse Iterator
 */
#if __cplusplus >= 201703L
#include <iterator>
#include <optional>
namespace workspace {
/*
 * @class reverse_iterator
 * @brief Wrapper class for `std::reverse_iterator`.
 * @see http://gcc.gnu.org/PR51823
 */
template <class Iterator>
class reverse_iterator : public std::reverse_iterator<Iterator> {
  using base_std = std::reverse_iterator<Iterator>;
  std::optional<typename base_std::value_type> deref;
 public:
  using base_std::reverse_iterator;
  constexpr typename base_std::reference operator*() noexcept {
    if (!deref) {
      Iterator tmp = base_std::current;
      deref = *--tmp;
    }
    return deref.value();
  }
  constexpr reverse_iterator &operator++() noexcept {
    base_std::operator++();
    deref.reset();
    return *this;
  }
  constexpr reverse_iterator &operator--() noexcept {
    base_std::operator++();
    deref.reset();
    return *this;
  }
  constexpr reverse_iterator operator++(int) noexcept {
    base_std::operator++();
    deref.reset();
    return *this;
  }
  constexpr reverse_iterator operator--(int) noexcept {
    base_std::operator++();
    deref.reset();
    return *this;
  }
};
}  // namespace workspace
#endif
#line 15 "Library\\lib\\utils"
// #include "src/utils/make_vector.hpp"
// #include "src/utils/py-like/enumerate.hpp"
#line 2 "Library\\src\\utils\\py-like\\range.hpp"
/**
 * @file range.hpp
 * @brief Range
 */
#line 9 "Library\\src\\utils\\py-like\\range.hpp"
#line 2 "Library\\src\\utils\\py-like\\reversed.hpp"
/**
 * @file reversed.hpp
 * @brief Reversed
 */
#include <initializer_list>
#line 10 "Library\\src\\utils\\py-like\\reversed.hpp"
namespace workspace {
namespace _reversed_impl {
template <class _Container> class reversed {
  _Container __cont;
 public:
  constexpr reversed(_Container &&__cont) noexcept : __cont(__cont) {}
  constexpr decltype(auto) begin() noexcept { return std::rbegin(__cont); }
  constexpr decltype(auto) begin() const noexcept {
    return std::rbegin(__cont);
  }
  constexpr decltype(auto) end() noexcept { return std::rend(__cont); }
  constexpr decltype(auto) end() const noexcept { return std::rend(__cont); }
  constexpr decltype(auto) size() const noexcept {
    return
#if __cplusplus < 201703L
        __cont.size();
#else
        std::size(__cont);
#endif
  }
};
}  // namespace _reversed_impl
template <class _Container>
constexpr decltype(auto) reversed(_Container &&__cont) noexcept {
  return _reversed_impl::reversed<_Container>{std::forward<_Container>(__cont)};
}
template <class _Tp>
constexpr decltype(auto) reversed(
    std::initializer_list<_Tp> &&__cont) noexcept {
  return _reversed_impl::reversed<std::initializer_list<_Tp>>{
      std::forward<std::initializer_list<_Tp>>(__cont)};
}
}  // namespace workspace
#line 12 "Library\\src\\utils\\py-like\\range.hpp"
#if __cplusplus >= 201703L
namespace workspace {
template <class _Index> class range {
  _Index __first, __last;
 public:
  class iterator {
    _Index current;
   public:
    using difference_type = std::ptrdiff_t;
    using value_type = _Index;
    using reference = typename std::add_const<_Index>::type &;
    using pointer = iterator;
    using iterator_category = std::random_access_iterator_tag;
    constexpr iterator(const _Index &__i = _Index()) noexcept : current(__i) {}
    constexpr bool operator==(const iterator &__x) const noexcept {
      return current == __x.current;
    }
    constexpr bool operator!=(const iterator &__x) const noexcept {
      return current != __x.current;
    }
    constexpr bool operator<(const iterator &__x) const noexcept {
      return current < __x.current;
    }
    constexpr bool operator<=(const iterator &__x) const noexcept {
      return current <= __x.current;
    }
    constexpr bool operator>(const iterator &__x) const noexcept {
      return current > __x.current;
    }
    constexpr bool operator>=(const iterator &__x) const noexcept {
      return current >= __x.current;
    }
    constexpr iterator &operator++() noexcept {
      ++current;
      return *this;
    }
    constexpr iterator &operator++(int) noexcept {
      auto __tmp = *this;
      ++current;
      return __tmp;
    }
    constexpr iterator &operator--() noexcept {
      --current;
      return *this;
    }
    constexpr iterator &operator--(int) noexcept {
      auto __tmp = *this;
      --current;
      return __tmp;
    }
    constexpr difference_type operator-(const iterator &__x) const noexcept {
      return current - __x.current;
    }
    constexpr iterator &operator+=(difference_type __x) noexcept {
      current += __x;
      return *this;
    }
    constexpr iterator operator+(difference_type __x) const noexcept {
      return iterator(*this) += __x;
    }
    constexpr iterator &operator-=(difference_type __x) noexcept {
      current -= __x;
      return *this;
    }
    constexpr iterator operator-(difference_type __x) const noexcept {
      return iterator(*this) -= __x;
    }
    constexpr reference operator*() const noexcept { return current; }
  };
  constexpr range(_Index __first, _Index __last) noexcept
      : __first(__first), __last(__last) {}
  constexpr range(_Index __last) noexcept : __first(), __last(__last) {}
  constexpr iterator begin() const noexcept { return iterator{__first}; }
  constexpr iterator end() const noexcept { return iterator{__last}; }
  constexpr reverse_iterator<iterator> rbegin() const noexcept {
    return reverse_iterator<iterator>(end());
  }
  constexpr reverse_iterator<iterator> rend() const noexcept {
    return reverse_iterator<iterator>(begin());
  }
  constexpr size_t size() const noexcept {
    return std::distance(__first, __last);
  }
};
template <class... _Args>
constexpr decltype(auto) rrange(_Args &&...__args) noexcept {
  return reversed(range(std::forward<_Args>(__args)...));
}
template <class _Container>
constexpr decltype(auto) iterate(_Container &&__cont) noexcept {
  return range(std::begin(__cont), std::end(__cont));
}
template <class _Container>
constexpr decltype(auto) riterate(_Container &&__cont) noexcept {
  return range(std::rbegin(__cont), std::rend(__cont));
}
}  // namespace workspace
#endif
#line 18 "Library\\lib\\utils"
// #include "src/utils/py-like/reversed.hpp"
// #include "src/utils/py-like/zip.hpp"
// #include "src/utils/rand/rng.hpp"
// #include "src/utils/rand/shuffle.hpp"
// #include "src/utils/round_div.hpp"
// #include "src\utils\rand\tree.hpp"
// #include "src\utils\reference_list.hpp"
#line 11 "other-workspace\\yuki2.cc"
signed main() {
  using namespace workspace;
  io_setup(15);
  /* given
    case_info.read();  //*/
  /* unspecified
    case_info.total = -1;  //*/
  return case_info.iterate();
}
#line 2 "Library\\src\\modular\\modint.hpp"
/**
 * @file modint.hpp
 *
 * @brief Modular Arithmetic
 */
#line 12 "Library\\src\\modular\\modint.hpp"
#line 2 "Library\\src\\number_theory\\sqrt_mod.hpp"
/**
 * @file sqrt_mod.hpp
 * @brief Tonelli-Shanks Algorithm
 */
#line 2 "Library\\src\\number_theory\\pow_mod.hpp"
/**
 * @file mod_pow.hpp
 * @brief Modular Exponentiation
 */
#line 9 "Library\\src\\number_theory\\pow_mod.hpp"
#line 2 "Library\\src\\utils\\sfinae.hpp"
/**
 * @file sfinae.hpp
 * @brief SFINAE
 */
#line 10 "Library\\src\\utils\\sfinae.hpp"
#include <type_traits>
#ifndef __INT128_DEFINED__
#ifdef __SIZEOF_INT128__
#define __INT128_DEFINED__ 1
#else
#define __INT128_DEFINED__ 0
#endif
#endif
namespace std {
#if __INT128_DEFINED__
template <> struct make_signed<__uint128_t> { using type = __int128_t; };
template <> struct make_signed<__int128_t> { using type = __int128_t; };
template <> struct make_unsigned<__uint128_t> { using type = __uint128_t; };
template <> struct make_unsigned<__int128_t> { using type = __uint128_t; };
template <> struct is_signed<__uint128_t> : std::false_type {};
template <> struct is_signed<__int128_t> : std::true_type {};
template <> struct is_unsigned<__uint128_t> : std::true_type {};
template <> struct is_unsigned<__int128_t> : std::false_type {};
#endif
}  // namespace std
namespace workspace {
template <class Tp, class... Args> struct variadic_front { using type = Tp; };
template <class... Args> struct variadic_back;
template <class Tp> struct variadic_back<Tp> { using type = Tp; };
template <class Tp, class... Args> struct variadic_back<Tp, Args...> {
  using type = typename variadic_back<Args...>::type;
};
template <class type, template <class> class trait>
using enable_if_trait_type = typename std::enable_if<trait<type>::value>::type;
/**
 * @brief Return type of subscripting ( @c [] ) access.
 */
template <class _Tp>
using subscripted_type =
    typename std::decay<decltype(std::declval<_Tp&>()[0])>::type;
template <class Container>
using element_type = typename std::decay<decltype(
    *std::begin(std::declval<Container&>()))>::type;
template <class _Tp, class = std::nullptr_t>
struct has_begin : std::false_type {};
template <class _Tp>
struct has_begin<_Tp, decltype(std::begin(std::declval<_Tp>()), nullptr)>
    : std::true_type {};
template <class _Tp, class = void> struct has_mod : std::false_type {};
template <class _Tp>
struct has_mod<_Tp, std::__void_t<decltype(_Tp::mod)>> : std::true_type {};
template <class _Tp, class = void> struct is_integral_ext : std::false_type {};
template <class _Tp>
struct is_integral_ext<
    _Tp, typename std::enable_if<std::is_integral<_Tp>::value>::type>
    : std::true_type {};
#if __INT128_DEFINED__
template <> struct is_integral_ext<__int128_t> : std::true_type {};
template <> struct is_integral_ext<__uint128_t> : std::true_type {};
#endif
#if __cplusplus >= 201402
template <class _Tp>
constexpr static bool is_integral_ext_v = is_integral_ext<_Tp>::value;
#endif
template <typename _Tp, typename = void> struct multiplicable_uint {
  using type = uint_least32_t;
};
template <typename _Tp>
struct multiplicable_uint<
    _Tp,
    typename std::enable_if<(2 < sizeof(_Tp)) &&
                            (!__INT128_DEFINED__ || sizeof(_Tp) <= 4)>::type> {
  using type = uint_least64_t;
};
#if __INT128_DEFINED__
template <typename _Tp>
struct multiplicable_uint<_Tp,
                          typename std::enable_if<(4 < sizeof(_Tp))>::type> {
  using type = __uint128_t;
};
#endif
template <typename _Tp> struct multiplicable_int {
  using type =
      typename std::make_signed<typename multiplicable_uint<_Tp>::type>::type;
};
template <typename _Tp> struct multiplicable {
  using type = std::conditional_t<
      is_integral_ext<_Tp>::value,
      std::conditional_t<std::is_signed<_Tp>::value,
                         typename multiplicable_int<_Tp>::type,
                         typename multiplicable_uint<_Tp>::type>,
      _Tp>;
};
template <class> struct first_arg { using type = void; };
template <class _R, class _Tp, class... _Args>
struct first_arg<_R(_Tp, _Args...)> {
  using type = _Tp;
};
template <class _R, class _Tp, class... _Args>
struct first_arg<_R (*)(_Tp, _Args...)> {
  using type = _Tp;
};
template <class _G, class _R, class _Tp, class... _Args>
struct first_arg<_R (_G::*)(_Tp, _Args...)> {
  using type = _Tp;
};
template <class _G, class _R, class _Tp, class... _Args>
struct first_arg<_R (_G::*)(_Tp, _Args...) const> {
  using type = _Tp;
};
template <class _Tp, class = void> struct parse_compare : first_arg<_Tp> {};
template <class _Tp>
struct parse_compare<_Tp, std::__void_t<decltype(&_Tp::operator())>>
    : first_arg<decltype(&_Tp::operator())> {};
}  // namespace workspace
#line 11 "Library\\src\\number_theory\\pow_mod.hpp"
namespace workspace {
/**
 * @brief Compile time modular exponentiation.
 *
 * @param __x
 * @param __n Exponent
 * @param __mod Modulus
 * @return
 */
template <class _Tp>
constexpr std::enable_if_t<(is_integral_ext<_Tp>::value), _Tp> pow_mod(
    _Tp __x, _Tp __n, _Tp __mod) noexcept {
  assert(__mod > 0);
  using mul_type = typename multiplicable_uint<_Tp>::type;
  if ((__x %= __mod) < 0) __x += __mod;
  mul_type __y{1};
  while (__n) {
    if (__n & 1) (__y *= __x) %= __mod;
    __x = (mul_type)__x * __x % __mod;
    __n >>= 1;
  }
  return __y;
};
}  // namespace workspace
#line 10 "Library\\src\\number_theory\\sqrt_mod.hpp"
namespace workspace {
/**
 * @brief Compile time modular square root.
 *
 * @param __x
 * @param __mod Modulus
 * @return One if it exists. Otherwise -1.
 */
template <class _Tp>
constexpr std::enable_if_t<(is_integral_ext<_Tp>::value), _Tp> sqrt_mod(
    _Tp __x, _Tp __mod) noexcept {
  assert(__mod > 0);
  using mul_type = typename multiplicable_uint<_Tp>::type;
  if ((__x %= __mod) < 0) __x += __mod;
  if (!__x) return 0;
  if (__mod == 2) return __x;
  if (pow_mod(__x, __mod >> 1, __mod) != 1) return -1;
  _Tp __z = __builtin_ctz(__mod - 1), __q = __mod >> __z;
  mul_type __a = pow_mod(__x, (__q + 1) >> 1, __mod), __b = 2;
  while (pow_mod<_Tp>(__b, __mod >> 1, __mod) == 1) ++__b;
  __b = pow_mod<_Tp>(__b, __q, __mod);
  _Tp __shift = 0;
  for (auto __r = __a * __a % __mod * pow_mod(__x, __mod - 2, __mod) % __mod;
       __r != 1; (__r *= (__b *= __b) %= __mod) %= __mod) {
    auto __bsf = __z;
    for (auto __e = __r; __e != 1; --__bsf) (__e *= __e) %= __mod;
    while (++__shift != __bsf) (__b *= __b) %= __mod;
    (__a *= __b) %= __mod;
  }
  return __a;
};
}  // namespace workspace
#line 15 "Library\\src\\modular\\modint.hpp"
namespace workspace {
namespace _modint_impl {
template <auto _Mod, unsigned _Storage> struct modint {
  static_assert(is_integral_ext<decltype(_Mod)>::value,
                "_Mod must be integral type.");
  using mod_type = std::make_signed_t<typename std::conditional<
      0 < _Mod, std::add_const_t<decltype(_Mod)>, decltype(_Mod)>::type>;
  using value_type = std::decay_t<mod_type>;
  using mul_type = typename multiplicable_uint<value_type>::type;
  // Modulus
  static mod_type mod;
  static unsigned storage;
 private:
  value_type value = 0;
  struct direct_ctor_t {};
  constexpr static direct_ctor_t direct_ctor_tag{};
  // Direct constructor
  template <class _Tp>
  constexpr modint(_Tp __n, direct_ctor_t) noexcept : value(__n) {}
 public:
  constexpr modint() noexcept = default;
  template <class _Tp, typename = std::enable_if_t<is_integral_ext<_Tp>::value>>
  constexpr modint(_Tp __n) noexcept
      : value((__n %= mod) < 0 ? __n += mod : __n) {}
  constexpr modint(bool __n) noexcept : value(__n) {}
  constexpr operator value_type() const noexcept { return value; }
  // unary operators {{
  constexpr modint operator++(int) noexcept {
    modint __t{*this};
    operator++();
    return __t;
  }
  constexpr modint operator--(int) noexcept {
    modint __t{*this};
    operator--();
    return __t;
  }
  constexpr modint &operator++() noexcept {
    if (++value == mod) value = 0;
    return *this;
  }
  constexpr modint &operator--() noexcept {
    if (!value)
      value = mod - 1;
    else
      --value;
    return *this;
  }
  constexpr modint operator+() const noexcept { return *this; }
  constexpr modint operator-() const noexcept {
    return {value ? mod - value : 0, direct_ctor_tag};
  }
  // }} unary operators
  // operator+= {{
  constexpr modint &operator+=(const modint &__x) noexcept {
    if ((value += __x.value) >= mod) value -= mod;
    return *this;
  }
  template <class _Tp>
  constexpr std::enable_if_t<is_integral_ext<_Tp>::value, modint> &operator+=(
      _Tp const &__x) noexcept {
    if (((value += __x) %= mod) < 0) value += mod;
    return *this;
  }
  // }} operator+=
  // operator+ {{
  template <class _Tp>
  constexpr std::enable_if_t<is_integral_ext<_Tp>::value, modint> operator+(
      _Tp const &__x) const noexcept {
    return modint{*this} += __x;
  }
  constexpr modint operator+(modint __x) const noexcept { return __x += *this; }
  template <class _Tp>
  constexpr friend std::enable_if_t<is_integral_ext<_Tp>::value, modint>
  operator+(_Tp const &__x, modint __y) noexcept {
    return __y += __x;
  }
  // }} operator+
  // operator-= {{
  constexpr modint &operator-=(const modint &__x) noexcept {
    if ((value -= __x.value) < 0) value += mod;
    return *this;
  }
  template <class _Tp>
  constexpr std::enable_if_t<is_integral_ext<_Tp>::value, modint> &operator-=(
      _Tp __x) noexcept {
    if (((value -= __x) %= mod) < 0) value += mod;
    return *this;
  }
  // }} operator-=
  // operator- {{
  template <class _Tp>
  constexpr std::enable_if_t<is_integral_ext<_Tp>::value, modint> operator-(
      _Tp const &__x) const noexcept {
    return modint{*this} -= __x;
  }
  constexpr modint operator-(const modint &__x) const noexcept {
    return modint{*this} -= __x;
  }
  template <class _Tp>
  constexpr friend std::enable_if_t<is_integral_ext<_Tp>::value, modint>
  operator-(_Tp __x, const modint &__y) noexcept {
    if (((__x -= __y.value) %= mod) < 0) __x += mod;
    return {__x, direct_ctor_tag};
  }
  // }} operator-
  // operator*= {{
  constexpr modint &operator*=(const modint &__x) noexcept {
    value =
        static_cast<value_type>(value * static_cast<mul_type>(__x.value) % mod);
    return *this;
  }
  template <class _Tp>
  constexpr std::enable_if_t<is_integral_ext<_Tp>::value, modint> &operator*=(
      _Tp __x) noexcept {
    value = static_cast<value_type>(
        value * mul_type((__x %= mod) < 0 ? __x + mod : __x) % mod);
    return *this;
  }
  // }} operator*=
  // operator* {{
  constexpr modint operator*(const modint &__x) const noexcept {
    return {static_cast<mul_type>(value) * __x.value % mod, direct_ctor_tag};
  }
  template <class _Tp>
  constexpr std::enable_if_t<is_integral_ext<_Tp>::value, modint> operator*(
      _Tp __x) const noexcept {
    __x %= mod;
    if (__x < 0) __x += mod;
    return {static_cast<mul_type>(value) * __x % mod, direct_ctor_tag};
  }
  template <class _Tp>
  constexpr friend std::enable_if_t<is_integral_ext<_Tp>::value, modint>
  operator*(_Tp __x, const modint &__y) noexcept {
    __x %= mod;
    if (__x < 0) __x += mod;
    return {static_cast<mul_type>(__x) * __y.value % mod, direct_ctor_tag};
  }
  // }} operator*
 protected:
  static value_type _mem(value_type __x) {
    static std::vector<value_type> __m{0, 1};
    static value_type __i = (__m.reserve(storage), 1);
    while (__i < __x) {
      ++__i;
      __m.emplace_back(mod - mul_type(mod / __i) * __m[mod % __i] % mod);
    }
    return __m[__x];
  }
  static value_type _div(mul_type __r, value_type __x) noexcept {
    assert(__x != value_type(0));
    if (!__r) return 0;
    std::make_signed_t<value_type> __v{};
    bool __neg = __x < 0 ? __x = -__x, true : false;
    if (static_cast<decltype(storage)>(__x) < storage)
      __v = _mem(__x);
    else {
      value_type __y{mod}, __u{1}, __t;
      while (__x)
        __t = __y / __x, __y ^= __x ^= (__y -= __t * __x) ^= __x,
        __v ^= __u ^= (__v -= __t * __u) ^= __u;
      if (__y < 0) __neg ^= 1;
    }
    if (__neg)
      __v = 0 < __v ? mod - __v : -__v;
    else if (__v < 0)
      __v += mod;
    return __r == mul_type(1) ? static_cast<value_type>(__v)
                              : static_cast<value_type>(__r * __v % mod);
  }
 public:
  // operator/= {{
  constexpr modint &operator/=(const modint &__x) noexcept {
    if (value) value = _div(value, __x.value);
    return *this;
  }
  template <class _Tp>
  constexpr std::enable_if_t<is_integral_ext<_Tp>::value, modint> &operator/=(
      _Tp __x) noexcept {
    if (value) value = _div(value, __x %= mod);
    return *this;
  }
  // }} operator/=
  // operator/ {{
  constexpr modint operator/(const modint &__x) const noexcept {
    if (!value) return {};
    return {_div(value, __x.value), direct_ctor_tag};
  }
  template <class _Tp>
  constexpr std::enable_if_t<is_integral_ext<_Tp>::value, modint> operator/(
      _Tp __x) const noexcept {
    if (!value) return {};
    return {_div(value, __x %= mod), direct_ctor_tag};
  }
  template <class _Tp>
  constexpr friend std::enable_if_t<is_integral_ext<_Tp>::value, modint>
  operator/(_Tp __x, const modint &__y) noexcept {
    if (!__x) return {};
    if ((__x %= mod) < 0) __x += mod;
    return {_div(__x, __y.value), direct_ctor_tag};
  }
  // }} operator/
  constexpr modint inv() const noexcept { return _div(1, value); }
  template <class _Tp>
  constexpr std::enable_if_t<is_integral_ext<_Tp>::value, modint> pow(
      _Tp __e) const noexcept {
    modint __r{1, direct_ctor_tag};
    for (modint __b{__e < 0 ? __e = -__e, _div(1, value) : value,
                              direct_ctor_tag};
         __e; __e >>= 1, __b *= __b)
      if (__e & 1) __r *= __b;
    return __r;
  }
  template <class _Tp>
  constexpr friend std::enable_if_t<is_integral_ext<_Tp>::value, modint> pow(
      modint __b, _Tp __e) noexcept {
    if (__e < 0) {
      __e = -__e;
      __b.value = _div(1, __b.value);
    }
    modint __r{1, direct_ctor_tag};
    for (; __e; __e >>= 1, __b *= __b)
      if (__e & 1) __r *= __b;
    return __r;
  }
  constexpr modint sqrt() const noexcept {
    return {sqrt_mod(value, mod), direct_ctor_tag};
  }
  friend constexpr modint sqrt(const modint &__x) noexcept {
    return {sqrt_mod(__x.value, mod), direct_ctor_tag};
  }
  template <class _Os>
  friend _Os &operator<<(_Os &__os, const modint &__x) noexcept {
    return __os << __x.value;
  }
  friend std::istream &operator>>(std::istream &__is, modint &__x) noexcept {
    std::string __s;
    __is >> __s;
    bool __neg = false;
    if (__s.front() == '-') {
      __neg = true;
      __s.erase(__s.begin());
    }
    __x = 0;
    for (char __c : __s) __x = __x * 10 + (__c - '0');
    if (__neg) __x = -__x;
    return __is;
  }
};
template <auto _Mod, unsigned _Storage>
typename modint<_Mod, _Storage>::mod_type modint<_Mod, _Storage>::mod =
    _Mod > 0 ? _Mod : 0;
template <auto _Mod, unsigned _Storage>
unsigned modint<_Mod, _Storage>::storage = _Storage;
}  // namespace _modint_impl
template <auto _Mod, unsigned _Storage = 0,
          typename = std::enable_if_t<(_Mod > 0)>>
using modint = _modint_impl::modint<_Mod, _Storage>;
template <unsigned _Id = 0>
using modint_runtime = _modint_impl::modint<-(signed)_Id, 0>;
}  // namespace workspace
#line 27 "other-workspace\\yuki2.cc"
namespace workspace {
using mint = modint<998244353>;
void main() {
  // start here!
  int n;
  cin >> n;
  mint ans{1};
  vector<int> a(n);
  for (auto d : range(2, n)) {
    if (a[d]) continue;
    for (auto x : range((n - 1) / d + 1)) {
      a[x * d] = 1;
    }
    i64 m = 1;
    while (m * d < n) m *= d;
    ans *= m;
    m = n;
    while (m % d == 0) {
      ans *= d;
      m /= d;
    }
    if (m == 1) ans /= d;
  }
  cout << ans << "\n";
}
}  // namespace workspace
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