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: Wrong Answer)

use std::cmp;
use std::collections::{BTreeMap, BinaryHeap};

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 nums = vec![0; n + 1];
    let mut rows = vec![];
    for count in count.into_iter() {
        if count > 0 {
            nums[count] += 1;
            rows.push(count);
        }
    }
    rows.sort();

    // num_map[count] = num;
    let num_map = nums
        .into_iter()
        .enumerate()
        .filter(|&(count, num)| count > 0)
        .collect::<BTreeMap<_, _>>();

    let mut ans_map = BTreeMap::new();
    for k in (1..(n + 1)).rev() {
        let round = n / k;
        if ans_map.contains_key(&round) {
            continue;
        }

        let mut remain = n;
        let mut cur_remain = round;
        let mut ans = 0;
        for (&row, &num) in num_map.iter().rev() {
            if row >= round {
                ans += num;
            } else {
                let sum = row * num;
                if sum >= cur_remain {
                    let sum = sum - cur_remain;
                    ans += 1;
                    ans += sum / round;
                    cur_remain = round - (sum % round);
                } else {
                    cur_remain -= sum;
                }
            }
        }

        ans_map.insert(round, ans);
    }

    let mut ans = vec![0; n + 1];
    for (round, c) in ans_map.into_iter() {
        ans[c] = round;
    }
    for i in (1..ans.len()).rev() {
        ans[i - 1] = cmp::max(ans[i], ans[i - 1]);
    }
    for i in 1..(n + 1) {
        println!("{}", ans[i]);
    }
}

fn remove(v: usize, map: &mut BTreeMap<usize, usize>) {
    let cur = *map.get(&v).unwrap();
    if cur == 1 {
        assert_eq!(map.remove(&v).unwrap(), 1);
    } else {
        map.insert(v, cur - 1);
    }
}

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()
    }
}