fn main() { input! { n: usize, p: [usize1; n], } let mut dp = vec![0; n + 1]; let mut used = vec![false; n]; for i in 0..n { if used[i] { continue; } let mut pos = i; let mut g = 0; let mut len = 0; while !used[pos] { g = gcd(g, pos - i); used[pos] = true; pos = p[pos]; len += 1; } dp[g] += len - 1 } enumerate_prime(n, |p| { for j in (1..=(n / p)).rev() { dp[j] += dp[j * p]; } }); use util::*; println!("{}", dp[1..n].iter().join("\n")); } fn gcd(a: usize, b: usize) -> usize { if b == 0 { a } else { gcd(b, a % b) } } // ---------- begin input macro ---------- // reference: https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 #[macro_export] macro_rules! input { (source = $s:expr, $($r:tt)*) => { let mut iter = $s.split_whitespace(); input_inner!{iter, $($r)*} }; ($($r:tt)*) => { let s = { use std::io::Read; let mut s = String::new(); std::io::stdin().read_to_string(&mut s).unwrap(); s }; let mut iter = s.split_whitespace(); input_inner!{iter, $($r)*} }; } #[macro_export] macro_rules! input_inner { ($iter:expr) => {}; ($iter:expr, ) => {}; ($iter:expr, $var:ident : $t:tt $($r:tt)*) => { let $var = read_value!($iter, $t); input_inner!{$iter $($r)*} }; } #[macro_export] macro_rules! read_value { ($iter:expr, ( $($t:tt),* )) => { ( $(read_value!($iter, $t)),* ) }; ($iter:expr, [ $t:tt ; $len:expr ]) => { (0..$len).map(|_| read_value!($iter, $t)).collect::>() }; ($iter:expr, chars) => { read_value!($iter, String).chars().collect::>() }; ($iter:expr, bytes) => { read_value!($iter, String).bytes().collect::>() }; ($iter:expr, usize1) => { read_value!($iter, usize) - 1 }; ($iter:expr, $t:ty) => { $iter.next().unwrap().parse::<$t>().expect("Parse error") }; } // ---------- end input macro ---------- // --------- end sieve ---------- pub struct Sieve { size: usize, factor: Vec, } impl Sieve { pub fn new(size: usize) -> Sieve { let mut factor = (0..(size + 1)).collect::>(); for i in (2..).take_while(|p| p * p <= size) { if i == factor[i] { for j in i..(size / i + 1) { factor[j * i] = i; } } } Sieve { size: size, factor: factor, } } pub fn factor(&self, n: usize) -> Option { assert!(n <= self.size); if n == 1 { None } else { Some(self.factor[n]) } } pub fn factorize(&self, mut n: usize, res: &mut Vec) { assert!(n <= self.size); res.clear(); res.push(1); while let Some(p) = self.factor(n) { let len = res.len(); while n % p == 0 { n /= p; for _ in 0..len { let v = res[res.len() - len] * p; res.push(v); } } } } } // --------- end sieve ---------- // ---------- begin enumerate prime ---------- fn enumerate_prime(n: usize, mut f: F) where F: FnMut(usize), { assert!(1 <= n && n <= 5 * 10usize.pow(8)); let batch = (n as f64).sqrt().ceil() as usize; let mut is_prime = vec![true; batch + 1]; for i in (2..).take_while(|p| p * p <= batch) { if is_prime[i] { let mut j = i * i; while let Some(p) = is_prime.get_mut(j) { *p = false; j += i; } } } let mut prime = vec![]; for (i, p) in is_prime.iter().enumerate().skip(2) { if *p && i <= n { f(i); prime.push(i); } } let mut l = batch + 1; while l <= n { let r = std::cmp::min(l + batch, n + 1); is_prime.clear(); is_prime.resize(r - l, true); for &p in prime.iter() { let mut j = (l + p - 1) / p * p - l; while let Some(is_prime) = is_prime.get_mut(j) { *is_prime = false; j += p; } } for (i, _) in is_prime.iter().enumerate().filter(|p| *p.1) { f(i + l); } l += batch; } } // ---------- end enumerate prime ---------- mod util { pub trait Join { fn join(self, sep: &str) -> String; } impl Join for I where I: Iterator, T: std::fmt::Display, { fn join(self, sep: &str) -> String { let mut s = String::new(); use std::fmt::*; for (i, v) in self.enumerate() { if i > 0 { write!(&mut s, "{}", sep).ok(); } write!(&mut s, "{}", v).ok(); } s } } }