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)

use std::cmp;

fn main() {
    let s = std::io::stdin();
    let mut sc = Scanner { stdin: s.lock() };
    let n: usize = sc.read();
    let mut count: Vec<usize> = vec![0; n];
    for _ in 0..n {
        let a = sc.read::<usize>() - 1;
        count[a] += 1;
    }

    let mut count_count = vec![0; n + 1];
    for count in count.into_iter() {
        count_count[count] += 1;
    }

    let mut rows = count_count
        .into_iter()
        .enumerate()
        .filter(|&(count, num)| count > 0 && num > 0)
        .collect::<Vec<_>>();
    rows.sort();
    let mut ans = vec![0; n + 1];
    let mut sum = rows.iter().map(|&(count, num)| count * num).sum::<usize>();
    let mut popped = 0;
    for height in (1..(n + 1)).rev() {
        while let Some((max, num)) = rows.pop() {
            if max >= height {
                sum -= max * num;
                popped += num;
            } else {
                rows.push((max, num));
                break;
            }
        }

        let columns = sum / height + popped;
        ans[columns] = cmp::max(ans[columns], height);
    }
    for k in (0..n).rev() {
        ans[k] = cmp::max(ans[k], ans[k + 1]);
    }

    for k in 1..(n + 1) {
        println!("{}", ans[k]);
    }
}

pub struct Scanner<R> {
    stdin: R,
}

impl<R: std::io::Read> Scanner<R> {
    pub fn read<T: std::str::FromStr>(&mut self) -> T {
        use std::io::Read;
        let buf = self
            .stdin
            .by_ref()
            .bytes()
            .map(|b| b.unwrap())
            .skip_while(|&b| b == b' ' || b == b'\n')
            .take_while(|&b| b != b' ' && b != b'\n')
            .collect::<Vec<_>>();
        unsafe { std::str::from_utf8_unchecked(&buf) }
            .parse()
            .ok()
            .expect("Parse error.")
    }
    pub fn vec<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read()).collect()
    }
    pub fn chars(&mut self) -> Vec<char> {
        self.read::<String>().chars().collect()
    }
}