#595204 (C++17) No.1322 Totient Bound

• 問題: No.1322 Totient Bound
• ユーザー: NyaanNyaan
• 提出日時: 2020-12-19 02:51:15
• 言語: C++17 (gcc 12.3.0 + boost 1.83.0)
• 結果: TLE (最新)
  AC
  (最初)
• 実行時間: -
• コード長: 22,125 bytes
• コンパイル時間: 4,198 ms
• コンパイル使用メモリ: 299,596 KB
• 実行使用メモリ: 6,944 KB
• 最終ジャッジ日時: 2024-09-21 09:57:50
• 合計ジャッジ時間: 80,918 ms
• ジャッジサーバーID （参考情報）: judge5 / judge3

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	1 ms; 5,248 KB
testcase_01	AC	2 ms; 5,376 KB
testcase_02	AC	1 ms; 5,376 KB
testcase_03	AC	2 ms; 5,376 KB
testcase_04	AC	2 ms; 5,376 KB
testcase_05	AC	2 ms; 5,376 KB
testcase_06	AC	2 ms; 5,376 KB
testcase_07	AC	2 ms; 5,376 KB
testcase_08	AC	2 ms; 5,376 KB
testcase_09	AC	1 ms; 5,376 KB
testcase_10	AC	2 ms; 5,376 KB
testcase_11	AC	1 ms; 5,376 KB
testcase_12	AC	2 ms; 5,376 KB
testcase_13	AC	3 ms; 5,376 KB
testcase_14	AC	3 ms; 5,376 KB
testcase_15	AC	2 ms; 5,376 KB
testcase_16	AC	2 ms; 5,376 KB
testcase_17	AC	3 ms; 5,376 KB
testcase_18	AC	505 ms; 5,376 KB
testcase_19	AC	919 ms; 5,376 KB
testcase_20	AC	3,311 ms; 6,588 KB
testcase_21	AC	3,770 ms; 6,464 KB
testcase_22	AC	3,870 ms; 6,592 KB
testcase_23	AC	4,889 ms; 6,920 KB
testcase_24	AC	4,921 ms; 6,796 KB
testcase_25	AC	4,931 ms; 6,924 KB
testcase_26	AC	4,997 ms; 6,800 KB
testcase_27	AC	4,947 ms; 6,796 KB
testcase_28	AC	4,981 ms; 6,796 KB
testcase_29	AC	4,904 ms; 6,800 KB
testcase_30	AC	2 ms; 5,376 KB
testcase_31	AC	2 ms; 5,376 KB
testcase_32	AC	2 ms; 5,376 KB
testcase_33	AC	4,875 ms; 6,792 KB
testcase_34	TLE	-
testcase_35	AC	4,950 ms; 6,796 KB
testcase_36	AC	4,865 ms; 6,912 KB
testcase_37	AC	4,801 ms; 6,908 KB
testcase_38	AC	4,861 ms; 6,924 KB

ソースコード

/**
 *  date : 2020-12-19 02:50:56
 */

#define NDEBUG
using namespace std;

// intrinstic
#include <immintrin.h>

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <csetjmp>
#include <csignal>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>
#include <deque>
#include <exception>
#include <forward_list>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iosfwd>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <locale>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <ratio>
#include <regex>
#include <set>
#include <sstream>
#include <stack>
#include <stdexcept>
#include <streambuf>
#include <string>
#include <system_error>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <valarray>
#include <vector>

// utility
namespace Nyaan {
using ll = long long;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;

template <typename T>
using V = vector<T>;
template <typename T>
using VV = vector<vector<T>>;
using vi = vector<int>;
using vl = vector<long long>;
using vd = V<double>;
using vs = V<string>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<long long>>;

template <typename T, typename U>
struct P : pair<T, U> {
  template <typename... Args>
  P(Args... args) : pair<T, U>(args...) {}

  using pair<T, U>::first;
  using pair<T, U>::second;

  T &x() { return first; }
  const T &x() const { return first; }
  U &y() { return second; }
  const U &y() const { return second; }

  P &operator+=(const P &r) {
    first += r.first;
    second += r.second;
    return *this;
  }
  P &operator-=(const P &r) {
    first -= r.first;
    second -= r.second;
    return *this;
  }
  P &operator*=(const P &r) {
    first *= r.first;
    second *= r.second;
    return *this;
  }
  P operator+(const P &r) const { return P(*this) += r; }
  P operator-(const P &r) const { return P(*this) -= r; }
  P operator*(const P &r) const { return P(*this) *= r; }
};

using pl = P<ll, ll>;
using pi = P<int, int>;
using vp = V<pl>;

constexpr int inf = 1001001001;
constexpr long long infLL = 4004004004004004004LL;

template <typename T>
int sz(const T &t) {
  return t.size();
}
template <typename T, size_t N>
void mem(T (&a)[N], int c) {
  memset(a, c, sizeof(T) * N);
}

template <typename T, typename U>
inline bool amin(T &x, U y) {
  return (y < x) ? (x = y, true) : false;
}
template <typename T, typename U>
inline bool amax(T &x, U y) {
  return (x < y) ? (x = y, true) : false;
}

template <typename T>
int lb(const vector<T> &v, const T &a) {
  return lower_bound(begin(v), end(v), a) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, const T &a) {
  return upper_bound(begin(v), end(v), a) - begin(v);
}

constexpr long long TEN(int n) {
  long long ret = 1, x = 10;
  for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1);
  return ret;
}

template <typename T, typename U>
pair<T, U> mkp(const T &t, const U &u) {
  return make_pair(t, u);
}

template <typename T>
vector<T> mkrui(const vector<T> &v, bool rev = false) {
  vector<T> ret(v.size() + 1);
  if (rev) {
    for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1];
  } else {
    for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i];
  }
  return ret;
};

template <typename T>
vector<T> mkuni(const vector<T> &v) {
  vector<T> ret(v);
  sort(ret.begin(), ret.end());
  ret.erase(unique(ret.begin(), ret.end()), ret.end());
  return ret;
}

template <typename F>
vector<int> mkord(int N, F f) {
  vector<int> ord(N);
  iota(begin(ord), end(ord), 0);
  sort(begin(ord), end(ord), f);
  return ord;
}

template <typename T>
vector<T> reord(const vector<T> &v, const vector<T> &ord) {
  int N = v.size();
  vector<T> ret(N);
  for (int i = 0; i < N; i++) ret[i] = v[ord[i]];
  return ret;
};

template <typename T = int>
vector<T> mkiota(int N) {
  vector<T> ret(N);
  iota(begin(ret), end(ret), 0);
  return ret;
}

template <typename T>
vector<int> mkinv(vector<T> &v, int max_val = -1) {
  if (max_val < (int)v.size()) max_val = v.size() - 1;
  vector<int> inv(max_val + 1, -1);
  for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;
  return inv;
}

}  // namespace Nyaan

// bit operation
namespace Nyaan {

__attribute__((target("popcnt"))) inline int popcnt(const u64 &a) {
  return _mm_popcnt_u64(a);
}

__attribute__((target("bmi"))) inline int lsb(const u64 &a) {
  return _tzcnt_u64(a);
}
__attribute__((target("bmi"))) inline int ctz(const u64 &a) {
  return _tzcnt_u64(a);
}

__attribute__((target("lzcnt"))) inline int msb(const u64 &a) {
  return 63 - _lzcnt_u64(a);
}
__attribute__((target("lzcnt"))) inline int clz64(const u64 &a) {
  return _lzcnt_u64(a);
}

template <typename T>
inline int gbit(const T &a, int i) {
  return (a >> i) & 1;
}
template <typename T>
inline void sbit(T &a, int i, bool b) {
  a ^= (gbit(a, i) == b ? 0 : (T(b) << i));
}

constexpr long long PW(int n) { return 1LL << n; }

constexpr long long MSK(int n) { return (1LL << n) - 1; }

}  // namespace Nyaan

// inout
namespace Nyaan {

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...);
}

void outr() {}
template <typename T, class... U, char sep = ' '>
void outr(const T &t, const U &... u) {
  cout << t;
  outr(u...);
}

struct IoSetupNya {
  IoSetupNya() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(15);
    cerr << fixed << setprecision(7);
  }
} iosetupnya;

}  // namespace Nyaan

// debug
namespace DebugImpl {

template <typename U, typename = void>
struct is_specialize : false_type {};
template <typename U>
struct is_specialize<
    U, typename conditional<false, typename U::iterator, void>::type>
    : true_type {};
template <typename U>
struct is_specialize<
    U, typename conditional<false, decltype(U::first), void>::type>
    : true_type {};
template <typename U>
struct is_specialize<U, enable_if_t<is_integral<U>::value, void>> : true_type {
};

void dump(const char& t) { cerr << t; }

void dump(const string& t) { cerr << t; }

template <typename U,
          enable_if_t<!is_specialize<U>::value, nullptr_t> = nullptr>
void dump(const U& t) {
  cerr << t;
}

template <typename T>
void dump(const T& t, enable_if_t<is_integral<T>::value>* = nullptr) {
  string res;
  if (t == Nyaan::inf) res = "inf";
  if (is_signed<T>::value)
    if (t == -Nyaan::inf) res = "-inf";
  if (sizeof(T) == 8) {
    if (t == Nyaan::infLL) res = "inf";
    if (is_signed<T>::value)
      if (t == -Nyaan::infLL) res = "-inf";
  }
  if (res.empty()) res = to_string(t);
  cerr << res;
}

template <typename T, typename U>
void dump(const pair<T, U>&);
template <typename T>
void dump(const pair<T*, int>&);

template <typename T>
void dump(const T& t,
          enable_if_t<!is_void<typename T::iterator>::value>* = nullptr) {
  cerr << "[ ";
  for (auto it = t.begin(); it != t.end();) {
    dump(*it);
    cerr << (++it == t.end() ? "" : ", ");
  }
  cerr << " ]";
}

template <typename T, typename U>
void dump(const pair<T, U>& t) {
  cerr << "( ";
  dump(t.first);
  cerr << ", ";
  dump(t.second);
  cerr << " )";
}

template <typename T>
void dump(const pair<T*, int>& t) {
  cerr << "[ ";
  for (int i = 0; i < t.second; i++) {
    dump(t.first[i]);
    cerr << (i == t.second - 1 ? "" : ", ");
  }
  cerr << " ]";
}

void trace() { cerr << endl; }
template <typename Head, typename... Tail>
void trace(Head&& head, Tail&&... tail) {
  cerr << " ";
  dump(head);
  if (sizeof...(tail) != 0) cerr << ",";
  trace(forward<Tail>(tail)...);
}

}  // namespace DebugImpl

#ifdef NyaanDebug
#define trc(...)                            \
  do {                                      \
    cerr << "## " << #__VA_ARGS__ << " = "; \
    DebugImpl::trace(__VA_ARGS__);          \
  } while (0)
#else
#define trc(...)
#endif

// macro
#define each(x, v) for (auto&& x : v)
#define each2(x, y, v) for (auto&& [x, y] : v)
#define all(v) (v).begin(), (v).end()
#define rep(i, N) for (long long i = 0; i < (long long)(N); i++)
#define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--)
#define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++)
#define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--)
#define reg(i, a, b) for (long long i = (a); i < (b); i++)
#define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--)
#define repc(i, a, cond) for (long long i = (a); (cond); i++)
#define enm(i, val, vec)                                  \
  for (long long i = 0; i < (long long)(vec).size(); i++) \
    if (auto& val = vec[i]; false)                        \
      ;                                                   \
    else

#define ini(...)   \
  int __VA_ARGS__; \
  in(__VA_ARGS__)
#define inl(...)         \
  long long __VA_ARGS__; \
  in(__VA_ARGS__)
#define ins(...)      \
  string __VA_ARGS__; \
  in(__VA_ARGS__)
#define inc(...)    \
  char __VA_ARGS__; \
  in(__VA_ARGS__)
#define in2(s, t)                           \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i]);                         \
  }
#define in3(s, t, u)                        \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i], u[i]);                   \
  }
#define in4(s, t, u, v)                     \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i], u[i], v[i]);             \
  }

#define die(...)             \
  do {                       \
    Nyaan::out(__VA_ARGS__); \
    return;                  \
  } while (0)

namespace Nyaan {
void solve();
}
int main() { Nyaan::solve(); }


using namespace Nyaan;



namespace inner {

using i32 = int32_t;
using u32 = uint32_t;
using i64 = int64_t;
using u64 = uint64_t;

template <typename T>
T gcd(T a, T b) {
  while (b) swap(a %= b, b);
  return a;
}

template <typename T>
T inv(T a, T p) {
  T b = p, x = 1, y = 0;
  while (a) {
    T q = b / a;
    swap(a, b %= a);
    swap(x, y -= q * x);
  }
  assert(b == 1);
  return y < 0 ? y + p : y;
}

template <typename T, typename U>
T modpow(T a, U n, T p) {
  T ret = 1 % p;
  for (; n; n >>= 1, a = U(a) * a % p)
    if (n & 1) ret = U(ret) * a % p;
  return ret;
}

}  // namespace inner

namespace my_rand {

// [0, 2^64 - 1)
uint64_t rng() {
  static uint64_t x_ =
      uint64_t(chrono::duration_cast<chrono::nanoseconds>(
                   chrono::high_resolution_clock::now().time_since_epoch())
                   .count()) *
      10150724397891781847ULL;
  x_ ^= x_ << 7;
  return x_ ^= x_ >> 9;
}

// [l, r)
int64_t randint(int64_t l, int64_t r) {
  assert(l < r);
  return l + rng() % (r - l);
}

// choose n numbers from [l, r) without overlapping
vector<int64_t> randset(int64_t l, int64_t r, int64_t n) {
  assert(l <= r && n <= r - l);
  unordered_set<int64_t> s;
  for (int64_t i = n; i; --i) {
    int64_t m = randint(l, r + 1 - i);
    if (s.find(m) != s.end()) m = r - i;
    s.insert(m);
  }
  vector<int64_t> ret;
  for (auto& x : s) ret.push_back(x);
  return ret;
}

// [0.0, 1.0)
double rnd() {
  union raw_cast {
    double t;
    uint64_t u;
  };
  constexpr uint64_t p = uint64_t(1023 - 64) << 52;
  return rng() * ((raw_cast*)(&p))->t;
}

template <typename T>
void randshf(vector<T>& v) {
  int n = v.size();
  for (int loop = 0; loop < 2; loop++)
    for (int i = 0; i < n; i++) swap(v[i], v[randint(0, n)]);
}

}  // namespace my_rand

using my_rand::randint;
using my_rand::randset;
using my_rand::randshf;
using my_rand::rnd;
using my_rand::rng;



struct ArbitraryLazyMontgomeryModInt {
  using mint = ArbitraryLazyMontgomeryModInt;
  using i32 = int32_t;
  using u32 = uint32_t;
  using u64 = uint64_t;

  static u32 mod;
  static u32 r;
  static u32 n2;

  static u32 get_r() {
    u32 ret = mod;
    for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret;
    return ret;
  }

  static void set_mod(u32 m) {
    assert(m < (1 << 30));
    assert((m & 1) == 1);
    mod = m;
    n2 = -u64(m) % m;
    r = get_r();
    assert(r * mod == 1);
  }

  u32 a;

  ArbitraryLazyMontgomeryModInt() : a(0) {}
  ArbitraryLazyMontgomeryModInt(const int64_t &b)
      : a(reduce(u64(b % mod + mod) * n2)){};

  static u32 reduce(const u64 &b) {
    return (b + u64(u32(b) * u32(-r)) * mod) >> 32;
  }

  mint &operator+=(const mint &b) {
    if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;
    return *this;
  }

  mint &operator-=(const mint &b) {
    if (i32(a -= b.a) < 0) a += 2 * mod;
    return *this;
  }

  mint &operator*=(const mint &b) {
    a = reduce(u64(a) * b.a);
    return *this;
  }

  mint &operator/=(const mint &b) {
    *this *= b.inverse();
    return *this;
  }

  mint operator+(const mint &b) const { return mint(*this) += b; }
  mint operator-(const mint &b) const { return mint(*this) -= b; }
  mint operator*(const mint &b) const { return mint(*this) *= b; }
  mint operator/(const mint &b) const { return mint(*this) /= b; }
  bool operator==(const mint &b) const {
    return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
  }
  bool operator!=(const mint &b) const {
    return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
  }
  mint operator-() const { return mint() - mint(*this); }

  mint pow(u64 n) const {
    mint ret(1), mul(*this);
    while (n > 0) {
      if (n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }

  friend ostream &operator<<(ostream &os, const mint &b) {
    return os << b.get();
  }

  friend istream &operator>>(istream &is, mint &b) {
    int64_t t;
    is >> t;
    b = ArbitraryLazyMontgomeryModInt(t);
    return (is);
  }

  mint inverse() const { return pow(mod - 2); }

  u32 get() const {
    u32 ret = reduce(a);
    return ret >= mod ? ret - mod : ret;
  }

  static u32 get_mod() { return mod; }
};
typename ArbitraryLazyMontgomeryModInt::u32 ArbitraryLazyMontgomeryModInt::mod;
typename ArbitraryLazyMontgomeryModInt::u32 ArbitraryLazyMontgomeryModInt::r;
typename ArbitraryLazyMontgomeryModInt::u32 ArbitraryLazyMontgomeryModInt::n2;



struct montgomery64 {
  using mint = montgomery64;
  using i64 = int64_t;
  using u64 = uint64_t;
  using u128 = __uint128_t;

  static u64 mod;
  static u64 r;
  static u64 n2;

  static u64 get_r() {
    u64 ret = mod;
    for (i64 i = 0; i < 5; ++i) ret *= 2 - mod * ret;
    return ret;
  }

  static void set_mod(u64 m) {
    assert(m < (1LL << 62));
    assert((m & 1) == 1);
    mod = m;
    n2 = -u128(m) % m;
    r = get_r();
    assert(r * mod == 1);
  }

  u64 a;

  montgomery64() : a(0) {}
  montgomery64(const int64_t &b) : a(reduce((u128(b) + mod) * n2)){};

  static u64 reduce(const u128 &b) {
    return (b + u128(u64(b) * u64(-r)) * mod) >> 64;
  }

  mint &operator+=(const mint &b) {
    if (i64(a += b.a - 2 * mod) < 0) a += 2 * mod;
    return *this;
  }

  mint &operator-=(const mint &b) {
    if (i64(a -= b.a) < 0) a += 2 * mod;
    return *this;
  }

  mint &operator*=(const mint &b) {
    a = reduce(u128(a) * b.a);
    return *this;
  }

  mint &operator/=(const mint &b) {
    *this *= b.inverse();
    return *this;
  }

  mint operator+(const mint &b) const { return mint(*this) += b; }
  mint operator-(const mint &b) const { return mint(*this) -= b; }
  mint operator*(const mint &b) const { return mint(*this) *= b; }
  mint operator/(const mint &b) const { return mint(*this) /= b; }
  bool operator==(const mint &b) const {
    return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
  }
  bool operator!=(const mint &b) const {
    return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
  }
  mint operator-() const { return mint() - mint(*this); }

  mint pow(u128 n) const {
    mint ret(1), mul(*this);
    while (n > 0) {
      if (n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }

  friend ostream &operator<<(ostream &os, const mint &b) {
    return os << b.get();
  }

  friend istream &operator>>(istream &is, mint &b) {
    int64_t t;
    is >> t;
    b = montgomery64(t);
    return (is);
  }

  mint inverse() const { return pow(mod - 2); }

  u64 get() const {
    u64 ret = reduce(a);
    return ret >= mod ? ret - mod : ret;
  }

  static u64 get_mod() { return mod; }
};
typename montgomery64::u64 montgomery64::mod, montgomery64::r, montgomery64::n2;

namespace fast_factorize {
using u64 = uint64_t;

template <typename mint>
bool miller_rabin(u64 n, vector<u64> as) {
  if (mint::get_mod() != n) mint::set_mod(n);
  u64 d = n - 1;
  while (~d & 1) d >>= 1;
  mint e{1}, rev{int64_t(n - 1)};
  for (u64 a : as) {
    if (n <= a) break;
    u64 t = d;
    mint y = mint(a).pow(t);
    while (t != n - 1 && y != e && y != rev) {
      y *= y;
      t *= 2;
    }
    if (y != rev && t % 2 == 0) return false;
  }
  return true;
}

bool is_prime(u64 n) {
  if (~n & 1) return n == 2;
  if (n <= 1) return false;
  if (n < (1LL << 30))
    return miller_rabin<ArbitraryLazyMontgomeryModInt>(n, {2, 7, 61});
  else
    return miller_rabin<montgomery64>(
        n, {2, 325, 9375, 28178, 450775, 9780504, 1795265022});
}

template <typename mint, typename T>
T pollard_rho(T n) {
  if (~n & 1) return 2;
  if (is_prime(n)) return n;
  if (mint::get_mod() != n) mint::set_mod(n);
  mint R, one = 1;
  auto f = [&](mint x) { return x * x + R; };
  auto rnd_ = [&]() { return rng() % (n - 2) + 2; };
  while (1) {
    mint x, y, ys, q = one;
    R = rnd_(), y = rnd_();
    T g = 1;
    constexpr int m = 128;
    for (int r = 1; g == 1; r <<= 1) {
      x = y;
      for (int i = 0; i < r; ++i) y = f(y);
      for (int k = 0; g == 1 && k < r; k += m) {
        ys = y;
        for (int i = 0; i < m && i < r - k; ++i) q *= x - (y = f(y));
        g = inner::gcd<T>(q.get(), n);
      }
    }
    if (g == n) do
        g = inner::gcd<T>((x - (ys = f(ys))).get(), n);
      while (g == 1);
    if (g != n) return g;
  }
  exit(1);
}

vector<u64> inner_factorize(u64 n) {
  if (n <= 1) return {};
  u64 p;
  if (n <= (1LL << 30))
    p = pollard_rho<ArbitraryLazyMontgomeryModInt, uint32_t>(n);
  else
    p = pollard_rho<montgomery64, uint64_t>(n);
  if (p == n) return {p};
  auto l = inner_factorize(p);
  auto r = inner_factorize(n / p);
  copy(begin(r), end(r), back_inserter(l));
  return l;
}

vector<u64> factorize(u64 n) {
  auto ret = inner_factorize(n);
  sort(begin(ret), end(ret));
  return ret;
}

using i64 = int64_t;

map<u64, i64> factor_count(u64 n) {
  map<u64, i64> mp;
  for (auto &x : factorize(n)) mp[x]++;
  return mp;
}

vector<u64> divisors(u64 n) {
  if (n == 0) return {};
  vector<pair<u64, i64>> v;
  for (auto &p : factor_count(n)) v.push_back(p);
  vector<u64> ret;
  auto f = [&](auto rec, int i, u64 x) -> void {
    if (i == (int)v.size()) {
      ret.push_back(x);
      return;
    }
    for (int j = v[i].second;; --j) {
      rec(rec, i + 1, x);
      if (j == 0) break;
      x *= v[i].first;
    }
  };
  f(f, 0, 1);
  sort(begin(ret), end(ret));
  return ret;
}

}  // namespace fast_factorize

using fast_factorize::divisors;
using fast_factorize::factor_count;
using fast_factorize::factorize;
using fast_factorize::is_prime;

/**
 * @brief 高速素因数分解(Miller Rabin/Pollard's Rho)
 * @docs docs/prime/fast-factorize.md
 */


inline long long fast_div(long long a, long long b) { return double(a) / b; }

void Nyaan::solve() {
  /**/
  // さっきの提出に「N / (log N)^2」と書いたけどN / (log
  // N)の間違いでした…(ゴメンナサイ)

  inl(N);
  vector<ll> ns{0}, kouho;
  for (ll i = N; i > 0; i = N / (N / i + 1)) {
    ns.push_back(i);
    kouho.push_back(i + 1);
  }
  {
    vl buf;
    each(x, kouho) if (is_prime(x)) buf.push_back(x);
    sort(all(buf));
    swap(buf, kouho);
  }
  vector<ll> h(ns);
  int sq = sqrt(N);

  auto idx = [&](ll x) { return x ? x <= sq ? sz(h) - x : fast_div(N, x) : 0; };
  each(p, kouho) {
    ll bound = min<__int128_t>(1e11, __int128_t(p) * (p - 1));
    for (int i = 1; i < sz(h); i++) {
      if (p - 1 > ns[i]) break;
      ll d1 = fast_div(ns[i], p);
      if (ns[i] > bound) {
        ll d2 = fast_div(ns[i], (p - 1));
        h[i] += h[idx(d2)] - h[idx(d1)];
      } else if ((d1 + 1) * (p - 1) <= ns[i]) {
        ll d2 = d1 + 1;
        h[i] += h[idx(d2)] - h[idx(d1)];
      }
    }
  }
  out(h[1]);
  //*/

  /**
  #include "multiplicative-function/mf-famous-series.hpp"
  auto tot = totient<int>(10000);
  // trc(tot);
  int n = 50;
  vi cnt(n + 1);
  rep(i, 10001) if (i and tot[i] <= n) cnt[tot[i]]++;
  trc(cnt);
  auto dirichlet = [](vi a, vi b) {
    int n_ = sz(a) - 1;
    vi c(n_ + 1);
    rep1(i, n_) {
      rep1(j, n_) {
        if (i * j > n_) break;
        c[i * j] += a[i] * b[j];
      }
    }
    return c;
  };

  vi a(n + 1, 1);
  a[0] = 0;
  for (auto p : vi{2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47}) {
    vi b(n + 1);
    b[1]++, b[p - 1]++, b[p]--;
    a = dirichlet(a, b);
    trc(p, a);
    trc(accumulate(all(a),0));
  }
  trc(a);
  //*/
}