#define PROBLEM "https://judge.yosupo.jp/problem/counting_primes"
#include "../../cpp/template/template.cpp"
#include "../../cpp/math/meissel-lehhmer.cpp"
int main(){
long long n;;cin>>n;
MeisselLehmer P(n);
cout << P.count() << endl;
}
#line 1 "cpp/z_test/yosupo-counting_primes.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/counting_primes"
#line 2 "cpp/template/template.cpp"
//yukicoder@cpp17
#include <iostream>
#include <iomanip>
#include <algorithm>
#include <cmath>
#include <cctype>
#include <climits>
#include <cassert>
#include <string>
#include <vector>
#include <set>
#include <stack>
#include <queue>
#include <map>
#include <random>
#include <bitset>
#include <complex>
#include <utility>
#include <numeric>
#include <functional>
using namespace std;
using ll = long long;
using P = pair<ll,ll>;
const ll MOD = 998244353;
const ll MODx = 1000000007;
const int INF = (1<<30)-1;
const ll LINF = (1LL<<62LL)-1;
const double EPS = (1e-10);
P ar4[4] = {{0,1},{0,-1},{1,0},{-1,0}};
P ar8[8] = {{-1,-1},{-1,0},{-1,1},{0,-1},{0,1},{1,-1},{1,0},{1,1}};
template <typename T> vector<T> make_vector(size_t a, T b) { return vector<T>(a, b); }
template <typename... Ts> auto make_vector(size_t a, Ts... ts) { return vector<decltype(make_vector(ts...))>(a, make_vector(ts...)); }
/*
確認ポイント
cout << fixed << setprecision(n) << 小数計算//n桁の小数表記になる
計算量は変わらないが楽できるシリーズ
min(max)_element(iter,iter)で一番小さい(大きい)値のポインタが帰ってくる
count(iter,iter,int)でintがiterからiterの間にいくつあったかを取得できる
*/
/* comment outed because can cause bugs
__attribute__((constructor))
void initial() {
cin.tie(0);
ios::sync_with_stdio(false);
}
*/
#line 4 "cpp/z_test/yosupo-counting_primes.cpp"
#line 1 "cpp/data-structure/binary-indexed-tree.cpp"
template<typename T>
struct BIT{//1_Indexed
int n;
vector<T> bit;
BIT(){}
BIT(int n_):n(n_+1),bit(n,0){}
void set(int n_){
n = n_;
bit.assign(n,0);
}
T sum(int a){
T ret = 0;
for(int i = a; i > 0; i -= i & -i) ret += bit[i];
return ret;
}
void add(int a,T w){
for(int i = a; i <= n; i += i & -i)bit[i] += w;
}
T query(int r,int l){
return sum(l-1)-sum(r-1);
}
int lower_bound(T x){
if(x <= 0){
return 0;
}
x--;
int t = 1;
while(t < n)t <<= 1;
int st = 0;
int base = 0;
for(; t; t/=2){
if(st+t <= n && base+bit[st+t] <= x){
base += bit[st+t];
st += t;
}
}
return st+1;
}
};
#line 1 "cpp/math/sieve-of-eratosthenes.cpp"
struct SieveEratos{
int N;
vector<int> minp;
vector<bool> t;
vector<int> primes;
map<int,int> invprimes;
SieveEratos(){}
SieveEratos(int n):N(n+1){
generate();
}
void set(int n){
N = n+1;
generate();
}
void generate(){
t.assign(N, true);
t[0] = t[1] = false;
for(int i = 2; N > i; i++){
if(t[i]){
primes.emplace_back(i);
for(int j = i+i; N > j; j+=i){
t[j] = false;
}
}
}
}
void generate_invprime(){
for(size_t i = 0; primes.size() > i; i++){
invprimes[primes[i]] = i+1;
}
}
void generate_minfactor(){
minp.assign(N, N+2);
minp[0] = minp[1] = -1;
for(int i = 2; N > i; i++){
if(minp[i] == N+2){
minp[i] = i;
for(int j = i+i; N > j; j+=i){
minp[j] = min(i, minp[j]);
}
}
}
}
bool operator[](int x){return t[x] == x;}
};
#line 1 "cpp/math/exactsqrt.cpp"
// 整数型を取得することを想定
template <typename T>
T CeilExactSqrt(int c, T x){
T mn = 0;
T mx = x;
while(mx-mn > 1){
T ce = (mn+mx)/2;
T nw = 1;
for(int i = 0; c > i; i++){
if(x/ce < nw){
mx = ce;
break;
}
nw *= ce;
if(i+1 == c && x == nw){
mx = ce;
}
}
if(mx != ce)mn = ce;
}
return mx;
}
template <typename T>
T FloorExactSqrt(int c, T x){
T mn = 0;
T mx = x;
while(mx-mn > 1){
T ce = (mn+mx)/2;
T nw = 1;
for(int i = 0; c > i; i++){
if(x/ce < nw){
mx = ce;
break;
}
nw *= ce;
}
if(mx != ce)mn = ce;
}
return mn;
}
#line 4 "cpp/math/meissel-lehhmer.cpp"
struct MeisselLehmer{
long long N;
long long alpha;
SieveEratos sieve;
BIT<int> varphiTable;
struct d{
long long m,b;
int cof;
bool operator<(const d x)const{
if(m == x.m) return b < x.b;
return m < x.m;
}
};
vector<d> varphiQueue;
MeisselLehmer(long long n): N(n){
alpha = ceil(pow(N, 0.34));
sieve.set(N/alpha+10);
sieve.generate_invprime();
sieve.generate_minfactor();
}
long long varphiLoop(long long n, long long a, int cof = 1){
if(a == 0){
return n;
}else{
if(n/sieve.primes[a-1] <= N/alpha){
if(n/sieve.primes[a-1] >= 2){
varphiQueue.push_back({n/sieve.primes[a-1], a-1, cof*-1});
return varphiLoop(n, a-1, cof);
}else{
return varphiLoop(n, a-1, cof) - varphiLoop(n/sieve.primes[a-1], a-1, cof*-1);
}
}else{
return varphiLoop(n, a-1, cof) - varphiLoop(n/sieve.primes[a-1], a-1, cof*-1);
}
}
}
long long varphi(long long n, long long a){
varphiTable.set(N/alpha+1);
long long val = varphiLoop(n,a);
sort(varphiQueue.begin(), varphiQueue.end());
int cur = 0;
for(int i = 2; N/alpha >= i; i++){
varphiTable.add(sieve.invprimes[sieve.minp[i]], 1);
while(cur < varphiQueue.size() && varphiQueue[cur].m == i){
val += varphiQueue[cur].cof * (varphiQueue[cur].m - varphiTable.query(1, varphiQueue[cur].b+1));
cur++;
}
}
varphiQueue.clear();
return val;
}
long long P2(long long n, long long a){
long long val = 0;
int cur = sieve.primes.size()-1;
for(int i = a; n/sieve.primes[a-1] > sieve.primes[i]; i++){
while((sieve.primes[cur] > n / sieve.primes[i] || (n%sieve.primes[i] == 0 && sieve.primes[cur] == n/sieve.primes[i]))){
cur--;
}
if(cur < i)break;
val += cur-i+1;
}
return val;
}
long long count(long long n = -1){
if(n == -1)n = N;
long long prevN = N;
N = n;
alpha = ceil(pow(N, 0.34));
if(N < 2)return 0;
else if(N < 3)return 1;
long long val = varphi(N, alpha) + alpha-1 - P2(N, alpha);
N = prevN;
return val;
}
};
#line 6 "cpp/z_test/yosupo-counting_primes.cpp"
int main(){
long long n;;cin>>n;
MeisselLehmer P(n);
cout << P.count() << endl;
}
cpp/z_test/yosupo-counting_primes.cpp
cpp/geometry/two-points-distance.cpp