#line 1 "other/1255.cpp" #include #if __has_include() #include #endif #line 7 "Library/alias.hpp" namespace workspace { constexpr char eol = '\n'; using namespace std; using i32 = int_least32_t; using i64 = int_least64_t; using i128 = __int128_t; using u32 = uint_least32_t; using u64 = uint_least64_t; using u128 = __uint128_t; template > using priority_queue = std::priority_queue, Comp>; template using stack = std::stack>; } // namespace workspace #line 5 "Library/config.hpp" namespace config { const auto start_time{std::chrono::system_clock::now()}; int64_t elapsed() { using namespace std::chrono; const auto end_time{system_clock::now()}; return duration_cast(end_time - start_time).count(); } __attribute__((constructor)) void setup() { using namespace std; ios::sync_with_stdio(false); cin.tie(nullptr); cout << fixed << setprecision(15); #ifdef _buffer_check atexit([] { char bufc; if (cin >> bufc) cerr << "\n\033[43m\033[30mwarning: buffer not empty.\033[0m\n\n"; }); #endif } unsigned cases(), caseid = 1; template void loop(F main) { for (const unsigned total = cases(); caseid <= total; ++caseid) main(); } } // namespace config #line 2 "Library/option.hpp" #ifdef ONLINE_JUDGE #pragma GCC optimize("O3") #pragma GCC target("avx,avx2") #pragma GCC optimize("unroll-loops") #endif #line 2 "Library/utils/binary_search.hpp" #if __cplusplus >= 201703L #include #include #include namespace workspace { // binary search on a discrete range. template std::enable_if_t< std::is_convertible_v, bool>, iter_type> binary_search(iter_type ok, iter_type ng, pred_type pred) { assert(ok != ng); std::make_signed_t dist(ng - ok); while (1 < dist || dist < -1) { iter_type mid(ok + dist / 2); if (pred(mid)) ok = mid, dist -= dist / 2; else ng = mid, dist /= 2; } return ok; } // parallel binary search on each discrete range. template std::enable_if_t>, std::vector>, std::vector> binary_search(std::vector> ends, pred_type pred) { std::vector mids(ends.size()); for (;;) { bool all_found = true; for (size_t i{}; i != ends.size(); ++i) { auto [ok, ng] = ends[i]; iter_type mid(ok + (ng - ok) / 2); if (mids[i] != mid) { all_found = false; mids[i] = mid; } } if (all_found) break; auto res = pred(mids); for (size_t i{}; i != ends.size(); ++i) { (res[i] ? ends[i].first : ends[i].second) = mids[i]; } } return mids; } // binary search on a real number interval. template std::enable_if_t< std::is_convertible_v, bool>, real_type> binary_search(real_type ok, real_type ng, const real_type eps, pred_type pred) { assert(ok != ng); for (auto loops = 0; loops != std::numeric_limits::digits && (ok + eps < ng || ng + eps < ok); ++loops) { real_type mid{(ok + ng) / 2}; (pred(mid) ? ok : ng) = mid; } return ok; } // parallel binary search on each real interval. template std::enable_if_t>, std::vector>, std::vector> binary_search(std::vector> ends, const real_type eps, pred_type pred) { std::vector mids(ends.size()); for (auto loops = 0; loops != std::numeric_limits::digits; ++loops) { bool all_found = true; for (size_t i{}; i != ends.size(); ++i) { auto [ok, ng] = ends[i]; if (ok + eps < ng || ng + eps < ok) { all_found = false; mids[i] = (ok + ng) / 2; } } if (all_found) break; auto res = pred(mids); for (size_t i{}; i != ends.size(); ++i) { (res[i] ? ends[i].first : ends[i].second) = mids[i]; } } return mids; } } // namespace workspace #endif #line 3 "Library/utils/casefmt.hpp" namespace workspace { std::ostream &casefmt(std::ostream& os) { return os << "Case #" << config::caseid << ": "; } } // namespace workspace #line 3 "Library/utils/chval.hpp" namespace workspace { template > bool chle(T &x, const T &y, Comp comp = Comp()) { return comp(y, x) ? x = y, true : false; } template > bool chge(T &x, const T &y, Comp comp = Comp()) { return comp(x, y) ? x = y, true : false; } } // namespace workspace #line 5 "Library/utils/coordinate_compression.hpp" template class coordinate_compression { std::vector uniquely; std::vector compressed; public: coordinate_compression(const std::vector &raw) : uniquely(raw), compressed(raw.size()) { std::sort(uniquely.begin(), uniquely.end()); uniquely.erase(std::unique(uniquely.begin(), uniquely.end()), uniquely.end()); for (size_t i = 0; i != size(); ++i) compressed[i] = std::lower_bound(uniquely.begin(), uniquely.end(), raw[i]) - uniquely.begin(); } size_t operator[](const size_t idx) const { assert(idx < size()); return compressed[idx]; } size_t size() const { return compressed.size(); } size_t count() const { return uniquely.size(); } T value(const size_t ord) const { assert(ord < count()); return uniquely[ord]; } size_t order(const T &value) const { return std::lower_bound(uniquely.begin(), uniquely.end(), value) - uniquely.begin(); } auto begin() { return compressed.begin(); } auto end() { return compressed.end(); } auto rbegin() { return compressed.rbegin(); } auto rend() { return compressed.rend(); } }; #line 3 "Library/utils/fixed_point.hpp" namespace workspace { // specify the return type of lambda. template class fixed_point { lambda_type func; public: fixed_point(lambda_type &&f) : func(std::move(f)) {} template auto operator()(Args &&... args) const { return func(*this, std::forward(args)...); } }; } // namespace workspace #line 6 "Library/utils/hash.hpp" #line 3 "Library/utils/sfinae.hpp" #include template class trait> using enable_if_trait_type = typename std::enable_if::value>::type; template using element_type = typename std::decay()))>::type; template struct mapped_of { using type = element_type; }; template struct mapped_of::first_type> { using type = typename T::mapped_type; }; template using mapped_type = typename mapped_of::type; template struct is_integral_ext : std::false_type {}; template struct is_integral_ext< T, typename std::enable_if::value>::type> : std::true_type {}; template <> struct is_integral_ext<__int128_t> : std::true_type {}; template <> struct is_integral_ext<__uint128_t> : std::true_type {}; #if __cplusplus >= 201402 template constexpr static bool is_integral_ext_v = is_integral_ext::value; #endif template struct multiplicable_uint { using type = uint_least32_t; }; template struct multiplicable_uint::type> { using type = uint_least64_t; }; template struct multiplicable_uint::type> { using type = __uint128_t; }; #line 8 "Library/utils/hash.hpp" namespace workspace { template struct hash : std::hash {}; #if __cplusplus >= 201703L template struct hash> { size_t operator()(uint64_t x) const { static const uint64_t m = std::random_device{}(); x ^= x >> 23; x ^= m; x ^= x >> 47; return x - (x >> 32); } }; #endif template size_t hash_combine(const size_t &seed, const Key &key) { return seed ^ (hash()(key) + 0x9e3779b9 /* + (seed << 6) + (seed >> 2) */); } template struct hash> { size_t operator()(const std::pair &pair) const { return hash_combine(hash()(pair.first), pair.second); } }; template class hash> { template ::value - 1> struct tuple_hash { static uint64_t apply(const Tuple &t) { return hash_combine(tuple_hash::apply(t), std::get(t)); } }; template struct tuple_hash { static uint64_t apply(const Tuple &t) { return 0; } }; public: uint64_t operator()(const std::tuple &t) const { return tuple_hash>::apply(t); } }; template struct hash_table_wrapper : hash_table { using key_type = typename hash_table::key_type; size_t count(const key_type &key) const { return hash_table::find(key) != hash_table::end(); } template auto emplace(Args &&... args) { return hash_table::insert(typename hash_table::value_type(args...)); } }; template using cc_hash_table = hash_table_wrapper<__gnu_pbds::cc_hash_table>>; template using gp_hash_table = hash_table_wrapper<__gnu_pbds::gp_hash_table>>; template using unordered_map = std::unordered_map>; template using unordered_set = std::unordered_set>; } // namespace workspace #line 2 "Library/utils/make_vector.hpp" #if __cplusplus >= 201703L #include namespace workspace { template constexpr auto make_vector(size_t* sizes, T const& init = T()) { if constexpr (N) return std::vector(*sizes, make_vector(std::next(sizes), init)); else return init; } template constexpr auto make_vector(const size_t (&sizes)[N], T const& init = T()) { return make_vector((size_t*)sizes, init); } } // namespace workspace #endif #line 3 "Library/utils/random_number_generator.hpp" template class random_number_generator { typename std::conditional::value, std::uniform_int_distribution, std::uniform_real_distribution>::type unif; std::mt19937 engine; public: random_number_generator(num_type min = std::numeric_limits::min(), num_type max = std::numeric_limits::max()) : unif(min, max), engine(std::random_device{}()) {} num_type min() const { return unif.min(); } num_type max() const { return unif.max(); } // generate a random number in [min(), max()]. num_type operator()() { return unif(engine); } }; #line 3 "Library/utils/read.hpp" namespace workspace { // read with std::cin. template struct read { typename std::remove_const::type value; template read(types... args) : value(args...) { std::cin >> value; } operator T() const { return value; } }; template <> struct read { template operator T() const { T value; std::cin >> value; return value; } }; } // namespace workspace #line 4 "Library/utils/stream.hpp" #line 6 "Library/utils/stream.hpp" namespace std { template istream &operator>>(istream &is, pair &p) { return is >> p.first >> p.second; } template ostream &operator<<(ostream &os, const pair &p) { return os << p.first << ' ' << p.second; } template struct tuple_is { static istream &apply(istream &is, tuple_t &t) { tuple_is::apply(is, t); return is >> get(t); } }; template struct tuple_is { static istream &apply(istream &is, tuple_t &t) { return is; } }; template istream &operator>>(istream &is, tuple &t) { return tuple_is, tuple_size>::value - 1>::apply(is, t); } template struct tuple_os { static ostream &apply(ostream &os, const tuple_t &t) { tuple_os::apply(os, t); return os << ' ' << get(t); } }; template struct tuple_os { static ostream &apply(ostream &os, const tuple_t &t) { return os << get<0>(t); } }; template struct tuple_os { static ostream &apply(ostream &os, const tuple_t &t) { return os; } }; template ostream &operator<<(ostream &os, const tuple &t) { return tuple_os, tuple_size>::value - 1>::apply(os, t); } template > typename enable_if::type, string>::value && !is_same::type, char *>::value, istream &>::type operator>>(istream &is, Container &cont) { for (auto &&e : cont) is >> e; return is; } template > typename enable_if::type, string>::value && !is_same::type, char *>::value, ostream &>::type operator<<(ostream &os, const Container &cont) { bool head = true; for (auto &&e : cont) head ? head = 0 : (os << ' ', 0), os << e; return os; } } // namespace std #line 4 "Library/utils/trinary_search.hpp" // trinary search on discrete range. template iter_type trinary(iter_type first, iter_type last, comp_type comp) { assert(first < last); intmax_t dist(last - first); while(dist > 2) { iter_type left(first + dist / 3), right(first + dist * 2 / 3); if(comp(left, right)) last = right, dist = dist * 2 / 3; else first = left, dist -= dist / 3; } if(dist > 1 && comp(first + 1, first)) ++first; return first; } // trinary search on real numbers. template long double trinary(long double first, long double last, const long double eps, comp_type comp) { assert(first < last); while(last - first > eps) { long double left{(first * 2 + last) / 3}, right{(first + last * 2) / 3}; if(comp(left, right)) last = right; else first = left; } return first; } #line 2 "Library/utils/wrapper.hpp" template class reversed { Container &ref, copy; public: constexpr reversed(Container &ref) : ref(ref) {} constexpr reversed(Container &&ref = Container()) : ref(copy), copy(ref) {} constexpr auto begin() const { return ref.rbegin(); } constexpr auto end() const { return ref.rend(); } constexpr operator Container() const { return ref; } }; #line 9 "other/1255.cpp" namespace workspace { void main(); } int main() { config::loop(workspace::main); } unsigned config::cases() { // return -1; // unspecified int t; std::cin >> t; return t; // given return 1; } #line 4 "Library/modulus/modint.hpp" #line 6 "Library/modulus/modint.hpp" // A non-positive Mod corresponds a runtime type of modint. template struct modint { static_assert(is_integral_ext::value, "Mod must be integral type."); using mod_type = typename std::conditional< 0 < Mod, typename std::add_const::type, Mod_type>::type; static mod_type mod; using value_type = typename std::decay::type; constexpr operator value_type() const noexcept { return value; } constexpr static modint one() noexcept { return 1; } constexpr modint() noexcept = default; template ::value>::type * = nullptr> constexpr modint(int_type n) noexcept : value((n %= mod) < 0 ? mod + n : n) {} constexpr modint(bool n) noexcept : modint(int(n)) {} constexpr modint operator++(int) noexcept { modint t{*this}; return operator+=(1), t; } constexpr modint operator--(int) noexcept { modint t{*this}; return operator-=(1), t; } constexpr modint &operator++() noexcept { return operator+=(1); } constexpr modint &operator--() noexcept { return operator-=(1); } constexpr modint operator-() const noexcept { return value ? mod - value : 0; } constexpr modint &operator+=(const modint &rhs) noexcept { return (value += rhs.value) < mod ? 0 : value -= mod, *this; } constexpr modint &operator-=(const modint &rhs) noexcept { return (value += mod - rhs.value) < mod ? 0 : value -= mod, *this; } constexpr modint &operator*=(const modint &rhs) noexcept { return value = (typename multiplicable_uint::type)value * rhs.value % mod, *this; } constexpr modint &operator/=(const modint &rhs) noexcept { return operator*=(rhs.inverse()); } template constexpr typename std::enable_if::value, modint>::type operator+(const int_type &rhs) const noexcept { return modint{*this} += rhs; } constexpr modint operator+(const modint &rhs) const noexcept { return modint{*this} += rhs; } template constexpr typename std::enable_if::value, modint>::type operator-(const int_type &rhs) const noexcept { return modint{*this} -= rhs; } constexpr modint operator-(const modint &rhs) const noexcept { return modint{*this} -= rhs; } template constexpr typename std::enable_if::value, modint>::type operator*(const int_type &rhs) const noexcept { return modint{*this} *= rhs; } constexpr modint operator*(const modint &rhs) const noexcept { return modint{*this} *= rhs; } template constexpr typename std::enable_if::value, modint>::type operator/(const int_type &rhs) const noexcept { return modint{*this} /= rhs; } constexpr modint operator/(const modint &rhs) const noexcept { return modint{*this} /= rhs; } template constexpr friend typename std::enable_if::value, modint>::type operator+(const int_type &lhs, const modint &rhs) noexcept { return modint(lhs) + rhs; } template constexpr friend typename std::enable_if::value, modint>::type operator-(const int_type &lhs, const modint &rhs) noexcept { return modint(lhs) - rhs; } template constexpr friend typename std::enable_if::value, modint>::type operator*(const int_type &lhs, const modint &rhs) noexcept { return modint(lhs) * rhs; } template constexpr friend typename std::enable_if::value, modint>::type operator/(const int_type &lhs, const modint &rhs) noexcept { return modint(lhs) / rhs; } constexpr modint inverse() const noexcept { assert(value); value_type a{mod}, b{value}, u{}, v{1}, t{}; while (b) t = a / b, a ^= b ^= (a -= t * b) ^= b, u ^= v ^= (u -= t * v) ^= v; return {u}; } template constexpr typename std::enable_if::value, modint>::type power(int_type e) noexcept { if (e < 0) e = e % (mod - 1) + mod - 1; modint res{1}; for (modint p{value}; e; e >>= 1, p *= p) { if (e & 1) res *= p; } return res; } template friend constexpr typename std::enable_if::value, modint>::type pow(modint b, int_type e) noexcept { modint res{1}; for ((e %= mod - 1) < 0 ? e += mod - 1 : 0; e; e >>= 1, b *= b) if (e & 1) res *= b; return res; } friend std::ostream &operator<<(std::ostream &os, const modint &rhs) noexcept { return os << rhs.value; } friend std::istream &operator>>(std::istream &is, modint &rhs) noexcept { intmax_t value; rhs = (is >> value, value); return is; } protected: value_type value = 0; }; template typename modint::mod_type modint::mod = Mod; template using modint_runtime = modint<-(signed)type_id>; // #define modint_newtype modint<-__COUNTER__> #line 3 "Library/number_theory/ext_gcd.hpp" #line 5 "Library/number_theory/ext_gcd.hpp" template constexpr typename std::enable_if::value, std::pair>::type ext_gcd(int_type a, int_type b) { int_type p{1}, q{}, r{}, s{1}, t{}; if (a < 0) { std::tie(p, q) = ext_gcd(-a, b); p = -p; } else if (b < 0) { std::tie(p, q) = ext_gcd(a, -b); q = -q; } else { while (b) { r ^= p ^= r ^= p -= (t = a / b) * r; s ^= q ^= s ^= q -= t * s; b ^= a ^= b ^= a %= b; } } return {p, q}; } #line 25 "other/1255.cpp" namespace workspace { using mint = modint_runtime<>; void main() { // start here! i64 n; cin >> n; mint::mod = n * 2 - 1; i64 phi = mint::mod; { i64 m = mint::mod; for (i64 p = 2; p * p <= m; p++) { if (m % p) continue; phi /= p; phi *= p - 1; while (1) { m /= p; if (m % p) break; } } if (m > 1) phi /= m, phi *= m - 1; } i64 ord = phi; for (i64 d = 1; d * d <= phi; d++) { for (auto &&e : {d, phi / d}) { if (pow(mint(2), e) == 1) { chle(ord, e); } } } cout << lcm(ord, 2) << eol; } }