Problem:
Score : 600 points

Problem Statement

Takahashi has N cards. The i-th of these cards has an integer A_i written on it.

Takahashi will choose an integer K, and then repeat the following operation some number of times:

Choose exactly K cards such that the integers written on them are all different, and eat those cards. (The eaten cards disappear.)

For each K = 1,2, \ldots, N, find the maximum number of times Takahashi can do the operation.

Constraints

1 \le N \le 3 \times 10^5

1 \le A_i \le N

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 \ldots A_N

Output

Print N integers.
The t-th (1 \le t \le N) of them should be the answer for the case K=t.

Sample Input 1

3
2 1 2

Sample Output 1

3
1
0

For K = 1, we can do the operation as follows:

Choose the first card to eat.

Choose the second card to eat.

Choose the third card to eat.

For K = 2, we can do the operation as follows:

Choose the first and second cards to eat.

For K = 3, we cannot do the operation at all. Note that we cannot choose the first and third cards at the same time.

Sample Input 2

5
1 2 3 4 5

Sample Output 2

5
2
1
1
1

Sample Input 3

4
1 3 3 3

Sample Output 3

4
1
0
0

Solution in Rust (1.15.1) (judge verdict: Time Limit Exceeded)

#![allow(unused_imports, unused_macros, dead_code)]

macro_rules! min {
    (.. $x:expr) => {{
        let mut it = $x.iter();
        it.next().map(|z| it.fold(z, |x, y| min!(x, y)))
    }};
    ($x:expr) => ($x);
    ($x:expr, $($ys:expr),*) => {{
        let t = min!($($ys),*);
        if $x < t { $x } else { t }
    }}
}
macro_rules! max {
    (.. $x:expr) => {{
        let mut it = $x.iter();
        it.next().map(|z| it.fold(z, |x, y| max!(x, y)))
    }};
    ($x:expr) => ($x);
    ($x:expr, $($ys:expr),*) => {{
        let t = max!($($ys),*);
        if $x > t { $x } else { t }
    }}
}


macro_rules! ewriteln {
    ($($args:expr),*) => { let _ = writeln!(&mut std::io::stderr(), $($args),*); };
}
macro_rules! trace {
    ($x:expr) => { ewriteln!(">>> {} = {:?}", stringify!($x), $x) };
    ($($xs:expr),*) => { trace!(($($xs),*)) }
}
macro_rules! put {
    (.. $x:expr) => {{
        let mut it = $x.iter();
        if let Some(x) = it.next() { print!("{}", x); }
        for x in it { print!(" {}", x); }
        println!("");
    }};
    ($x:expr) => { println!("{}", $x) };
    ($x:expr, $($xs:expr),*) => { print!("{} ", $x); put!($($xs),*) }
}

const M: i64 = 1_000_000_007;

fn runlength<A: Copy + PartialEq>(xs: &Vec<A>) -> Vec<usize> {
    let m = xs.len();
    if m == 0 { return vec![]; }
    let mut count = 1;
    let mut result = vec![];
    for i in 0..m {
        if i > 0 {
            if xs[i - 1] == xs[i] {
                count += 1;
            } else {
                count = 1;
            }
        }
        if i == m - 1 || xs[i] != xs[i + 1] {
            result.push(count);
        }
    }
    result
}

/// Returns: cs.iter().map(|&c| min!(c, mid)).sum::<usize>()
fn min_sum(cs: &Vec<usize>, cs_acc: &Vec<usize>, m: usize, sum: usize) -> usize {
    let n = cs.len();
    if cs[n - 1] <= m { return sum }
    if cs[0] > m { return n * m }
    let mut left = 0; // cs[left] <= m
    let mut right = n - 1; // cs[right] > m
    for _ in 0..30 {
        let mid = (left + right) / 2;
        if cs[mid] <= m {
            left = mid;
        } else {
            right = mid;
        }
    }
    cs_acc[right] + (n - right) * m
}

fn solve(cs: &Vec<usize>, cs_acc: &Vec<usize>, k: usize, sum: usize) -> usize {
    if cs.len() < k { return 0 }
    let mut left = 1; // ok
    let mut right = cs.iter().sum::<usize>() + 100;
    for _ in 0..30 {
        let mid = (left + right) / 2;
        if min_sum(&cs, &cs_acc, mid, sum) >= mid * k {
            left = mid;
        } else {
            right = mid;
        }
    }
    left
}

fn main() {
    let mut sc = Scanner::new();
    let n: usize = sc.cin();
    let mut xs: Vec<usize> = sc.vec(n);
    xs.sort();
    let mut cs = runlength(&xs);
    cs.sort();
    let mut cs_acc = vec![0; cs.len() + 1];
    {
        for i in 0..cs.len() {
            cs_acc[i + 1] = cs_acc[i] + cs[i];
        }
    } // cs_acc[i] = sum cs[0..i)
    for k in 1..n+1 {
        put!(solve(&cs, &cs_acc, k, n));
    }
}

use std::io::{self, Write};
use std::str::FromStr;
use std::collections::VecDeque;

struct Scanner { stdin: io::Stdin, buffer: VecDeque<String>, }
impl Scanner {
    fn new() -> Self { Scanner { stdin: io::stdin(), buffer: VecDeque::new() } }
    fn cin<T: FromStr>(&mut self) -> T {
        while self.buffer.len() == 0 {
            let mut line = String::new();
            let _ = self.stdin.read_line(&mut line);
            for w in line.split_whitespace() {
                self.buffer.push_back(String::from(w));
            }
        }
        self.buffer.pop_front().unwrap().parse::<T>().ok().unwrap()
    }
    fn chars(&mut self) -> Vec<char> { self.cin::<String>().chars().collect() }
    fn vec<T: FromStr>(&mut self, n: usize) -> Vec<T> { (0..n).map(|_| self.cin()).collect() }
}