#[allow(unused_imports)] use std::cmp::*; #[allow(unused_imports)] use std::collections::*; use std::io::{Write, BufWriter}; // https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 macro_rules! input { ($($r:tt)*) => { let stdin = std::io::stdin(); let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock())); let mut next = move || -> String{ bytes.by_ref().map(|r|r.unwrap() as char) .skip_while(|c|c.is_whitespace()) .take_while(|c|!c.is_whitespace()) .collect() }; input_inner!{next, $($r)*} }; } macro_rules! input_inner { ($next:expr) => {}; ($next:expr, ) => {}; ($next:expr, $var:ident : $t:tt $($r:tt)*) => { let $var = read_value!($next, $t); input_inner!{$next $($r)*} }; } macro_rules! read_value { ($next:expr, [graph1; $len:expr]) => {{ let mut g = vec![vec![]; $len]; let ab = read_value!($next, [(usize1, usize1)]); for (a, b) in ab { g[a].push(b); g[b].push(a); } g }}; ($next:expr, ( $($t:tt),* )) => { ( $(read_value!($next, $t)),* ) }; ($next:expr, [ $t:tt ; $len:expr ]) => { (0..$len).map(|_| read_value!($next, $t)).collect::>() }; ($next:expr, chars) => { read_value!($next, String).chars().collect::>() }; ($next:expr, usize1) => (read_value!($next, usize) - 1); ($next:expr, [ $t:tt ]) => {{ let len = read_value!($next, usize); read_value!($next, [$t; len]) }}; ($next:expr, $t:ty) => ($next().parse::<$t>().expect("Parse error")); } trait Change { fn chmax(&mut self, x: Self); fn chmin(&mut self, x: Self); } impl Change for T { fn chmax(&mut self, x: T) { if *self < x { *self = x; } } fn chmin(&mut self, x: T) { if *self > x { *self = x; } } } #[allow(unused)] macro_rules! debug { ($($format:tt)*) => (write!(std::io::stderr(), $($format)*).unwrap()); } #[allow(unused)] macro_rules! debugln { ($($format:tt)*) => (writeln!(std::io::stderr(), $($format)*).unwrap()); } struct DivDP { // stores dp[n], dp[n/2], ..., dp[n/b]. dp_big: Vec, dp: Vec, n: i64, b: i64, } impl DivDP { fn new(n: i64, b: i64) -> Self { let dp_big = vec![0; b as usize + 1]; let dp = vec![0; (n / b) as usize]; DivDP { dp_big: dp_big, dp: dp, n: n, b: b, } } // pos should be of form floor(n / ???). fn upd(&mut self, pos: i64, f: F) where F: Fn(i64) -> i64 { if pos >= self.n / self.b { let idx = self.n / pos; debug_assert_eq!(pos, self.n / idx); self.dp_big[idx as usize] = f(self.dp_big[idx as usize]); return; } let idx = pos as usize; self.dp[idx] = f(self.dp[idx]); } fn get(&self, pos: i64) -> i64 { if pos >= self.n / self.b { let idx = self.n / pos; debug_assert_eq!(pos, self.n / idx); return self.dp_big[idx as usize]; } let idx = pos as usize; self.dp[idx] } fn init(&mut self, f: F) where F: Fn(i64) -> i64 { for i in 0..self.dp.len() { self.dp[i] = f(i as i64); } for i in (1..self.dp_big.len()).rev() { self.dp_big[i] = f(self.n / i as i64); } } fn upd_all(&mut self, f: F) where F: Fn(i64, i64) -> i64 { for i in 0..self.dp.len() { self.dp[i] = f(i as i64, self.dp[i]); } for i in (1..self.dp_big.len()).rev() { self.dp_big[i] = f(self.n / i as i64, self.dp_big[i]); } } } impl std::fmt::Debug for DivDP { fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result { for i in 0..self.dp.len() { writeln!(f, "{}: {}", i, self.dp[i])?; } for i in (1..self.dp_big.len()).rev() { writeln!(f, "{}: {}", self.n / i as i64, self.dp_big[i])?; } Ok(()) } } fn primes(v: usize) -> Vec { let mut pr = vec![true; v + 1]; pr[0] = false; pr[1] = false; for i in 2..v + 1 { if !pr[i] { continue; } for j in 2..v / i + 1 { pr[i * j] = false; } } let prs: Vec<_> = (0..v + 1).filter(|&i| pr[i]).collect(); prs } fn is_prime(x: i64) -> bool { if x <= 1 { return false; } let mut i = 2; while i * i <= x { if x % i == 0 { return false; } i += 1; } true } // Tags: sieve, prime-sieve, Lucy's-sieve fn solve() { let out = std::io::stdout(); let mut out = BufWriter::new(out.lock()); macro_rules! puts { ($($format:tt)*) => (let _ = write!(out,$($format)*);); } #[allow(unused)] macro_rules! putvec { ($v:expr) => { for i in 0..$v.len() { puts!("{}{}", $v[i], if i + 1 == $v.len() {"\n"} else {" "}); } } } input! { n: i64, } let mut sqn = 0; while sqn * sqn <= n { sqn += 1; } sqn -= 1; let prs = primes(sqn as usize + 1); let mut dp = DivDP::new(n, sqn); dp.init(|x| max(0, x - 1)); for &p in &prs { let p = p as i64; for i in 1..=min(sqn, n / p / p) { let val = dp.get(n / i / p); let val = val - dp.get(p - 1); dp.upd(n / i, |x| x - val); } for i in (p * p..n / sqn).rev() { let val = dp.get(i / p); let val = val - dp.get(p - 1); dp.upd(i, |x| x - val); } } // dp[j] = #{x <= j | x is prime} // eprintln!("dp:\n{:?}", dp); // dp[j] = #{x <= j + 1 | x is prime} dp.upd_all(|idx, val| val + if is_prime(idx + 1) { 1 } else { 0 }); // eprintln!("dp:\n{:?}", dp); for &p in prs.iter().rev() { let p = p as i64; for i in 1..=min(sqn, n / p / (p - 1)) { let mut cur = p - 1; let mut val = 0; while cur * p <= n && n / i >= cur * p { val += dp.get(n / i / cur); val -= dp.get(p - 1); cur *= p; val += 1; // for cur * p } dp.upd(n / i, |x| x + val); } for i in (p * (p - 1)..n / sqn).rev() { let mut cur = p - 1; let mut val = 0; while cur * p <= n && i >= cur * p { val += dp.get(i / cur); val -= dp.get(p - 1); cur *= p; val += 1; // for cur * p } dp.upd(i, |x| x + val); } // eprintln!("p = {}, dp = {:?}", p, dp); } // dp[j] = #{x | phi(x) <= j} // eprintln!("dp = {:?}", dp); puts!("{}\n", dp.get(n) + 1); } fn main() { // In order to avoid potential stack overflow, spawn a new thread. let stack_size = 104_857_600; // 100 MB let thd = std::thread::Builder::new().stack_size(stack_size); thd.spawn(|| solve()).unwrap().join().unwrap(); }