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: Accepted)

#![allow(unused_imports)]
#![allow(non_snake_case)]
use std::cmp::*;
use std::collections::*;
use std::io::Write;

#[allow(unused_macros)]
macro_rules! debug {
    ($($e:expr),*) => {
        #[cfg(debug_assertions)]
        $({
            let (e, mut err) = (stringify!($e), std::io::stderr());
            writeln!(err, "{} = {:?}", e, $e).unwrap()
        })*
    };
}

fn main() {
    let n = read::<usize>();
    let a = read_vec::<usize>();
    let mut counts = vec![0; n + 1];
    for num in a {
        counts[num] += 1;
    }

    let mut a = vec![];
    for count in counts {
        if count != 0 {
            a.push(count);
        }
    }
    a.sort();

    let mut sum = vec![0; a.len() + 1];
    sum[0] = 0;
    for i in 1..a.len() + 1 {
        sum[i] = a[i - 1] + sum[i - 1];
    }

    for k in 1..n + 1 {
        let criterion = |mid: usize| -> bool {
            let idx = a.lower_bound(&mid);
            (a.len() - idx) * mid + sum[idx] >= mid * k
        };
        let (ok, _) = binary_search(0, n + 1, criterion);
        println!("{}", ok);
    }
}

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}

fn binary_search<F>(lb: usize, ub: usize, criterion: F) -> (usize, usize)
where
    F: Fn(usize) -> bool,
{
    let mut ok = lb;
    let mut ng = ub;
    while ng - ok > 1 {
        let mid = (ng + ok) / 2;
        if criterion(mid) {
            ok = mid;
        } else {
            ng = mid;
        }
    }
    (ok, ng)
}

pub trait BinarySearch<T> {
    fn lower_bound(&self, x: &T) -> usize;
}

impl<T: Ord> BinarySearch<T> for [T] {
    fn lower_bound(&self, x: &T) -> usize {
        let mut low = 0;
        let mut high = self.len();

        while low != high {
            let mid = (low + high) / 2;
            match self[mid].cmp(x) {
                Ordering::Less => {
                    low = mid + 1;
                }
                Ordering::Equal | Ordering::Greater => {
                    high = mid;
                }
            }
        }
        low
    }
}