#line 2 "/Users/noya2/Desktop/Noya2_library/template/template.hpp" using namespace std; #include<bits/stdc++.h> #line 1 "/Users/noya2/Desktop/Noya2_library/template/inout_old.hpp" namespace noya2 { template <typename T, typename U> ostream &operator<<(ostream &os, const pair<T, U> &p){ os << p.first << " " << p.second; return os; } template <typename T, typename U> istream &operator>>(istream &is, pair<T, U> &p){ is >> p.first >> p.second; return is; } template <typename T> ostream &operator<<(ostream &os, const vector<T> &v){ int s = (int)v.size(); for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i]; return os; } template <typename T> istream &operator>>(istream &is, vector<T> &v){ for (auto &x : v) is >> x; return is; } void in() {} template <typename T, class... U> void in(T &t, U &...u){ cin >> t; in(u...); } void out() { cout << "\n"; } template <typename T, class... U, char sep = ' '> void out(const T &t, const U &...u){ cout << t; if (sizeof...(u)) cout << sep; out(u...); } template<typename T> void out(const vector<vector<T>> &vv){ int s = (int)vv.size(); for (int i = 0; i < s; i++) out(vv[i]); } struct IoSetup { IoSetup(){ cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); cerr << fixed << setprecision(7); } } iosetup_noya2; } // namespace noya2 #line 1 "/Users/noya2/Desktop/Noya2_library/template/const.hpp" namespace noya2{ const int iinf = 1'000'000'007; const long long linf = 2'000'000'000'000'000'000LL; const long long mod998 = 998244353; const long long mod107 = 1000000007; const long double pi = 3.14159265358979323; const vector<int> dx = {0,1,0,-1,1,1,-1,-1}; const vector<int> dy = {1,0,-1,0,1,-1,-1,1}; const string ALP = "ABCDEFGHIJKLMNOPQRSTUVWXYZ"; const string alp = "abcdefghijklmnopqrstuvwxyz"; const string NUM = "0123456789"; void yes(){ cout << "Yes\n"; } void no(){ cout << "No\n"; } void YES(){ cout << "YES\n"; } void NO(){ cout << "NO\n"; } void yn(bool t){ t ? yes() : no(); } void YN(bool t){ t ? YES() : NO(); } } // namespace noya2 #line 2 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp" #line 6 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp" namespace noya2{ unsigned long long inner_binary_gcd(unsigned long long a, unsigned long long b){ if (a == 0 || b == 0) return a + b; int n = __builtin_ctzll(a); a >>= n; int m = __builtin_ctzll(b); b >>= m; while (a != b) { int mm = __builtin_ctzll(a - b); bool f = a > b; unsigned long long c = f ? a : b; b = f ? b : a; a = (c - b) >> mm; } return a << std::min(n, m); } template<typename T> T gcd_fast(T a, T b){ return static_cast<T>(inner_binary_gcd(std::abs(a),std::abs(b))); } long long sqrt_fast(long long n) { if (n <= 0) return 0; long long x = sqrt(n); while ((x + 1) * (x + 1) <= n) x++; while (x * x > n) x--; return x; } template<typename T> T floor_div(const T n, const T d) { assert(d != 0); return n / d - static_cast<T>((n ^ d) < 0 && n % d != 0); } template<typename T> T ceil_div(const T n, const T d) { assert(d != 0); return n / d + static_cast<T>((n ^ d) >= 0 && n % d != 0); } template<typename T> void uniq(std::vector<T> &v){ std::sort(v.begin(),v.end()); v.erase(unique(v.begin(),v.end()),v.end()); } template <typename T, typename U> inline bool chmin(T &x, U y) { return (y < x) ? (x = y, true) : false; } template <typename T, typename U> inline bool chmax(T &x, U y) { return (x < y) ? (x = y, true) : false; } template<typename T> inline bool range(T l, T x, T r){ return l <= x && x < r; } } // namespace noya2 #line 8 "/Users/noya2/Desktop/Noya2_library/template/template.hpp" #define rep(i,n) for (int i = 0; i < (int)(n); i++) #define repp(i,m,n) for (int i = (m); i < (int)(n); i++) #define reb(i,n) for (int i = (int)(n-1); i >= 0; i--) #define all(v) (v).begin(),(v).end() using ll = long long; using ld = long double; using uint = unsigned int; using ull = unsigned long long; using pii = pair<int,int>; using pll = pair<ll,ll>; using pil = pair<int,ll>; using pli = pair<ll,int>; namespace noya2{ /* ~ (. _________ . /) */ } using namespace noya2; #line 2 "c.cpp" #line 2 "/Users/noya2/Desktop/Noya2_library/utility/modint.hpp" #line 4 "/Users/noya2/Desktop/Noya2_library/utility/modint.hpp" #line 2 "/Users/noya2/Desktop/Noya2_library/math/prime.hpp" #line 4 "/Users/noya2/Desktop/Noya2_library/math/prime.hpp" namespace noya2 { constexpr long long safe_mod(long long x, long long m) { x %= m; if (x < 0) x += m; return x; } constexpr long long pow_mod_constexpr(long long x, long long n, int m) { if (m == 1) return 0; unsigned int _m = (unsigned int)(m); unsigned long long r = 1; unsigned long long y = safe_mod(x, m); while (n) { if (n & 1) r = (r * y) % _m; y = (y * y) % _m; n >>= 1; } return r; } constexpr bool is_prime_constexpr(int n) { if (n <= 1) return false; if (n == 2 || n == 7 || n == 61) return true; if (n % 2 == 0) return false; long long d = n - 1; while (d % 2 == 0) d /= 2; constexpr long long bases[3] = {2, 7, 61}; for (long long a : bases) { long long t = d; long long y = pow_mod_constexpr(a, t, n); while (t != n - 1 && y != 1 && y != n - 1) { y = y * y % n; t <<= 1; } if (y != n - 1 && t % 2 == 0) { return false; } } return true; } template <int n> constexpr bool is_prime_flag = is_prime_constexpr(n); // {gcd(a, b), a^{-1} mod b} constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) { a = safe_mod(a, b); if (a == 0) return {b, 0}; long long s = b, t = a; long long m0 = 0, m1 = 1; while (t) { long long u = s / t; s -= t * u; m0 -= m1 * u; auto tmp = s; s = t; t = tmp; tmp = m0; m0 = m1; m1 = tmp; } if (m0 < 0) m0 += b / s; return {s, m0}; } constexpr int primitive_root_constexpr(int m) { if (m == 2) return 1; if (m == 167772161) return 3; if (m == 469762049) return 3; if (m == 754974721) return 11; if (m == 998244353) return 3; int divs[20] = {}; divs[0] = 2; int cnt = 1; int x = (m - 1) / 2; while (x % 2 == 0) x /= 2; for (int i = 3; (long long)(i)*i <= x; i += 2) { if (x % i == 0) { divs[cnt++] = i; while (x % i == 0) { x /= i; } } } if (x > 1) { divs[cnt++] = x; } for (int g = 2;; g++) { bool ok = true; for (int i = 0; i < cnt; i++) { if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) { ok = false; break; } } if (ok) return g; } } template <int m> constexpr int primitive_root_flag = primitive_root_constexpr(m); // constexpr long long primitive_root_constexpr(long long m){ // if (m == (1LL << 47) - (1LL << 24) + 1) return 3; // return primitive_root_constexpr(static_cast<int>(m)); // } } // namespace noya2 #line 6 "/Users/noya2/Desktop/Noya2_library/utility/modint.hpp" namespace noya2{ struct barrett { unsigned int _m; unsigned long long im; explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {} unsigned int umod() const { return _m; } unsigned int mul(unsigned int a, unsigned int b) const { unsigned long long z = a; z *= b; unsigned long long x = (unsigned long long)((__uint128_t(z) * im) >> 64); unsigned int v = (unsigned int)(z - x * _m); if (_m <= v) v += _m; return v; } }; template <int m> struct static_modint { using mint = static_modint; public: static constexpr int mod() { return m; } static mint raw(int v) { mint x; x._v = v; return x; } constexpr static_modint() : _v(0) {} template<std::signed_integral T> constexpr static_modint(T v){ long long x = (long long)(v % (long long)(umod())); if (x < 0) x += umod(); _v = (unsigned int)(x); } template<std::unsigned_integral T> constexpr static_modint(T v){ _v = (unsigned int)(v % umod()); } constexpr unsigned int val() const { return _v; } mint& operator++() { _v++; if (_v == umod()) _v = 0; return *this; } mint& operator--() { if (_v == 0) _v = umod(); _v--; return *this; } mint operator++(int) { mint result = *this; ++*this; return result; } mint operator--(int) { mint result = *this; --*this; return result; } constexpr mint& operator+=(const mint& rhs) { _v += rhs._v; if (_v >= umod()) _v -= umod(); return *this; } constexpr mint& operator-=(const mint& rhs) { _v -= rhs._v; if (_v >= umod()) _v += umod(); return *this; } constexpr mint& operator*=(const mint& rhs) { unsigned long long z = _v; z *= rhs._v; _v = (unsigned int)(z % umod()); return *this; } constexpr mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); } constexpr mint operator+() const { return *this; } constexpr mint operator-() const { return mint() - *this; } constexpr mint pow(long long n) const { assert(0 <= n); mint x = *this, r = 1; while (n) { if (n & 1) r *= x; x *= x; n >>= 1; } return r; } constexpr mint inv() const { if (prime) { assert(_v); return pow(umod() - 2); } else { auto eg = inv_gcd(_v, m); assert(eg.first == 1); return eg.second; } } friend constexpr mint operator+(const mint& lhs, const mint& rhs) { return mint(lhs) += rhs; } friend constexpr mint operator-(const mint& lhs, const mint& rhs) { return mint(lhs) -= rhs; } friend constexpr mint operator*(const mint& lhs, const mint& rhs) { return mint(lhs) *= rhs; } friend constexpr mint operator/(const mint& lhs, const mint& rhs) { return mint(lhs) /= rhs; } friend constexpr bool operator==(const mint& lhs, const mint& rhs) { return lhs._v == rhs._v; } friend constexpr bool operator!=(const mint& lhs, const mint& rhs) { return lhs._v != rhs._v; } friend std::ostream &operator<<(std::ostream &os, const mint& p) { return os << p.val(); } friend std::istream &operator>>(std::istream &is, mint &a) { long long t; is >> t; a = mint(t); return (is); } private: unsigned int _v; static constexpr unsigned int umod() { return m; } static constexpr bool prime = is_prime_flag<m>; }; template <int id> struct dynamic_modint { using mint = dynamic_modint; public: static int mod() { return (int)(bt.umod()); } static void set_mod(int m) { assert(1 <= m); bt = barrett(m); } static mint raw(int v) { mint x; x._v = v; return x; } dynamic_modint() : _v(0) {} template<std::signed_integral T> dynamic_modint(T v){ long long x = (long long)(v % (long long)(umod())); if (x < 0) x += umod(); _v = (unsigned int)(x); } template<std::unsigned_integral T> dynamic_modint(T v){ _v = (unsigned int)(v % umod()); } unsigned int val() const { return _v; } mint& operator++() { _v++; if (_v == umod()) _v = 0; return *this; } mint& operator--() { if (_v == 0) _v = umod(); _v--; return *this; } mint operator++(int) { mint result = *this; ++*this; return result; } mint operator--(int) { mint result = *this; --*this; return result; } mint& operator+=(const mint& rhs) { _v += rhs._v; if (_v >= umod()) _v -= umod(); return *this; } mint& operator-=(const mint& rhs) { _v += mod() - rhs._v; if (_v >= umod()) _v -= umod(); return *this; } mint& operator*=(const mint& rhs) { _v = bt.mul(_v, rhs._v); return *this; } mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); } mint operator+() const { return *this; } mint operator-() const { return mint() - *this; } mint pow(long long n) const { assert(0 <= n); mint x = *this, r = 1; while (n) { if (n & 1) r *= x; x *= x; n >>= 1; } return r; } mint inv() const { auto eg = noya2::inv_gcd(_v, mod()); assert(eg.first == 1); return eg.second; } friend mint operator+(const mint& lhs, const mint& rhs) { return mint(lhs) += rhs; } friend mint operator-(const mint& lhs, const mint& rhs) { return mint(lhs) -= rhs; } friend mint operator*(const mint& lhs, const mint& rhs) { return mint(lhs) *= rhs; } friend mint operator/(const mint& lhs, const mint& rhs) { return mint(lhs) /= rhs; } friend bool operator==(const mint& lhs, const mint& rhs) { return lhs._v == rhs._v; } friend bool operator!=(const mint& lhs, const mint& rhs) { return lhs._v != rhs._v; } friend std::ostream &operator<<(std::ostream &os, const mint& p) { return os << p.val(); } friend std::istream &operator>>(std::istream &is, mint &a) { long long t; is >> t; a = mint(t); return (is); } private: unsigned int _v; static barrett bt; static unsigned int umod() { return bt.umod(); } }; template <int id> noya2::barrett dynamic_modint<id>::bt(998244353); using modint998244353 = static_modint<998244353>; using modint1000000007 = static_modint<1000000007>; using modint = dynamic_modint<-1>; template<typename T> concept Modint = requires (T &a){ T::mod(); a.inv(); a.val(); a.pow(declval<int>()); }; } // namespace noya2 #line 4 "c.cpp" using mint = modint998244353; #line 2 "/Users/noya2/Desktop/Noya2_library/math/factorize.hpp" #line 6 "/Users/noya2/Desktop/Noya2_library/math/factorize.hpp" #include <initializer_list> #line 10 "/Users/noya2/Desktop/Noya2_library/math/factorize.hpp" namespace fast_factorize { /* See : https://judge.yosupo.jp/submission/189742 */ // ---- gcd ---- uint64_t gcd_stein_impl( uint64_t x, uint64_t y ) { if( x == y ) { return x; } const uint64_t a = y - x; const uint64_t b = x - y; const int n = __builtin_ctzll( b ); const uint64_t s = x < y ? a : b; const uint64_t t = x < y ? x : y; return gcd_stein_impl( s >> n, t ); } uint64_t gcd_stein( uint64_t x, uint64_t y ) { if( x == 0 ) { return y; } if( y == 0 ) { return x; } const int n = __builtin_ctzll( x ); const int m = __builtin_ctzll( y ); return gcd_stein_impl( x >> n, y >> m ) << ( n < m ? n : m ); } // ---- is_prime ---- uint64_t mod_pow( uint64_t x, uint64_t y, uint64_t mod ) { uint64_t ret = 1; uint64_t acc = x; for( ; y; y >>= 1 ) { if( y & 1 ) { ret = __uint128_t(ret) * acc % mod; } acc = __uint128_t(acc) * acc % mod; } return ret; } bool miller_rabin( uint64_t n, const std::initializer_list<uint64_t>& as ) { return std::all_of( as.begin(), as.end(), [n]( uint64_t a ) { if( n <= a ) { return true; } int e = __builtin_ctzll( n - 1 ); uint64_t z = mod_pow( a, ( n - 1 ) >> e, n ); if( z == 1 || z == n - 1 ) { return true; } while( --e ) { z = __uint128_t(z) * z % n; if( z == 1 ) { return false; } if( z == n - 1 ) { return true; } } return false; }); } bool is_prime( uint64_t n ) { if( n == 2 ) { return true; } if( n % 2 == 0 ) { return false; } if( n < 4759123141 ) { return miller_rabin( n, { 2, 7, 61 } ); } return miller_rabin( n, { 2, 325, 9375, 28178, 450775, 9780504, 1795265022 } ); } // ---- Montgomery ---- class Montgomery { uint64_t mod; uint64_t R; public: Montgomery( uint64_t n ) : mod(n), R(n) { for( size_t i = 0; i < 5; ++i ) { R *= 2 - mod * R; } } uint64_t fma( uint64_t a, uint64_t b, uint64_t c ) const { const __uint128_t d = __uint128_t(a) * b; const uint64_t e = c + mod + ( d >> 64 ); const uint64_t f = uint64_t(d) * R; const uint64_t g = ( __uint128_t(f) * mod ) >> 64; return e - g; } uint64_t mul( uint64_t a, uint64_t b ) const { return fma( a, b, 0 ); } }; // ---- Pollard's rho algorithm ---- uint64_t pollard_rho( uint64_t n ) { if( n % 2 == 0 ) { return 2; } const Montgomery m( n ); constexpr uint64_t C1 = 1; constexpr uint64_t C2 = 2; constexpr uint64_t M = 512; uint64_t Z1 = 1; uint64_t Z2 = 2; retry: uint64_t z1 = Z1; uint64_t z2 = Z2; for( size_t k = M; ; k *= 2 ) { const uint64_t x1 = z1 + n; const uint64_t x2 = z2 + n; for( size_t j = 0; j < k; j += M ) { const uint64_t y1 = z1; const uint64_t y2 = z2; uint64_t q1 = 1; uint64_t q2 = 2; z1 = m.fma( z1, z1, C1 ); z2 = m.fma( z2, z2, C2 ); for( size_t i = 0; i < M; ++i ) { const uint64_t t1 = x1 - z1; const uint64_t t2 = x2 - z2; z1 = m.fma( z1, z1, C1 ); z2 = m.fma( z2, z2, C2 ); q1 = m.mul( q1, t1 ); q2 = m.mul( q2, t2 ); } q1 = m.mul( q1, x1 - z1 ); q2 = m.mul( q2, x2 - z2 ); const uint64_t q3 = m.mul( q1, q2 ); const uint64_t g3 = gcd_stein( n, q3 ); if( g3 == 1 ) { continue; } if( g3 != n ) { return g3; } const uint64_t g1 = gcd_stein( n, q1 ); const uint64_t g2 = gcd_stein( n, q2 ); const uint64_t C = g1 != 1 ? C1 : C2; const uint64_t x = g1 != 1 ? x1 : x2; uint64_t z = g1 != 1 ? y1 : y2; uint64_t g = g1 != 1 ? g1 : g2; if( g == n ) { do { z = m.fma( z, z, C ); g = gcd_stein( n, x - z ); } while( g == 1 ); } if( g != n ) { return g; } Z1 += 2; Z2 += 2; goto retry; } } } void factorize_impl( uint64_t n, std::vector<uint64_t>& ret ) { if( n <= 1 ) { return; } if( is_prime( n ) ) { ret.push_back( n ); return; } const uint64_t p = pollard_rho( n ); factorize_impl( p, ret ); factorize_impl( n / p, ret ); } std::vector<uint64_t> factorize( uint64_t n ) { std::vector<uint64_t> ret; factorize_impl( n, ret ); std::sort( ret.begin(), ret.end() ); return ret; } } // namespace fast_factorize namespace noya2 { std::vector<std::pair<long long, int>> factorize(long long n){ std::vector<std::pair<long long, int>> ans; auto ps = fast_factorize::factorize(n); int sz = ps.size(); for (int l = 0, r = 0; l < sz; l = r){ while (r < sz && ps[l] == ps[r]) r++; ans.emplace_back(ps[l], r-l); } return ans; } std::vector<long long> divisors(long long n){ auto ps = fast_factorize::factorize(n); int sz = ps.size(); std::vector<long long> ans = {1}; for (int l = 0, r = 0; l < sz; l = r){ while (r < sz && ps[l] == ps[r]) r++; int e = r - l; int len = ans.size(); ans.reserve(len*(e+1)); long long mul = ps[l]; while (true){ for (int i = 0; i < len; i++){ ans.emplace_back(ans[i]*mul); } if (--e == 0) break; mul *= ps[l]; } } return ans; } std::vector<long long> divisors(const std::vector<std::pair<long long, int>> &pes){ std::vector<long long> ans = {1}; for (auto [p, e] : pes){ int len = ans.size(); ans.reserve(len*(e+1)); long long mul = p; while (true){ for (int i = 0; i < len; i++){ ans.emplace_back(ans[i]*mul); } if (--e == 0) break; mul *= p; } } return ans; } } // namespace noya2 #line 6 "c.cpp" void solve(){ ll n; in(n); auto ds = divisors(n); sort(all(ds)); unordered_map<ll,mint> dp; dp[1] = 1; for (ll x : ds){ if (x == n) break; mint add = dp[x]; ll pre = -1; int cnt = 0; for (ll a : ds){ if (x % a == 0) continue; ll to = x / gcd_fast(x, a) * a; if (pre == to){ cnt++; } else { if (pre != -1){ dp[pre] += add * cnt; } pre = to; cnt = 1; } } if (pre != -1){ dp[pre] += add * cnt; } } out(dp[n]); } int main(){ int t = 1; //in(t); while (t--) { solve(); } }