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)

#[allow(unused_macros)]
macro_rules! input {
  ($($r:tt)*) => {
    let stdin = std::io::stdin();
    let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
    let mut next = move || -> String{
      bytes
        .by_ref()
        .map(|r|r.unwrap() as char)
        .skip_while(|c|c.is_whitespace())
        .take_while(|c|!c.is_whitespace())
        .collect()
    };
    input_inner!{next, $($r)*}
  };
}

#[allow(unused_macros)]
macro_rules! input_inner {
  ($next:expr) => {};
  ($next:expr, ) => {};

  ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
    #[allow(unused_mut)]
    let mut $var = read_value!($next, $t);
    input_inner!{$next $($r)*}
  };
}

#[allow(unused_macros)]
macro_rules! read_value {
  ($next:expr, ( $($t:tt),* )) => {
    ( $(read_value!($next, $t)),* )
  };

  ($next:expr, [ $t:tt ; $len:expr ]) => {
    (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
  };

  ($next:expr, chars) => {
    read_value!($next, String).chars().collect::<Vec<char>>()
  };

  ($next:expr, usize1) => {
    read_value!($next, usize) - 1
  };

  ($next:expr, [ $t:tt ]) => {{
    let len = read_value!($next, usize);
    (0..len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
  }};

  ($next:expr, $t:ty) => {
    $next().parse::<$t>().expect("Parse error")
  };
}

use std::io::*;

fn main() {
  let stack_size = 104_857_600;
  let thd = std::thread::Builder::new().stack_size(stack_size);
  thd.spawn(|| work()).unwrap().join().unwrap();
}

fn work() {
  let out = stdout();
  let mut out = BufWriter::new(out.lock());
  macro_rules! puts {
    ($($format:tt)*) => (write!(out,$($format)*).unwrap());
  }

  input! {
    n: usize,
    a: [usize; n],
  }
  let mut b = vec![0i64; n];
  for x in a {
    b[x - 1] += 1;
  }
  let mut v = Vec::with_capacity(n);
  let mut heap = std::collections::BinaryHeap::new();
  for x in b {
    heap.push(-x);
  }
  v.push(-heap.peek().unwrap());
  for _i in 1..n {
    let x = heap.pop().unwrap();
    let y = heap.pop().unwrap();
    heap.push(x + y);
    v.push(-heap.peek().unwrap());
  }
  for i in 0..n {
    puts!("{}\n", v[n - 1 - i]);
  }
}