#include using namespace std; using ll = long long; 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& 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& 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 factorize( uint64_t n ) { std::vector ret; factorize_impl( n, ret ); std::sort( ret.begin(), ret.end() ); return ret; } } // namespace fast_factorize std::vector> factorize(long long n){ std::vector> 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; } int main(){ const int mx = 61; vector partition_numbers(mx,0); partition_numbers[0] = 1; for (int n = 1; n < mx; n++){ for (int k = 1; k*(3*k-1)/2 <= n; k++){ partition_numbers[n] += partition_numbers[n-k*(3*k-1)/2] * (k % 2 == 0 ? -1 : 1); } for (int k = -1; k*(3*k-1)/2 <= n; k--){ partition_numbers[n] += partition_numbers[n-k*(3*k-1)/2] * (k % 2 == 0 ? -1 : 1); } } ll n; cin >> n; ll ans = 1; for (auto [p, e] : factorize(n)){ ans *= partition_numbers[e]; } cout << ans << endl; }