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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.*;

public class Main
{
	public static void main(String[] args)
	{
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();

		ArrayList a = new ArrayList<Integer>();
		for(int i = 0 ; i < n ; i++){
			a.add(sc.nextInt());
		}
		Collections.sort(a);
		a.add(-1);

		ArrayList num = new ArrayList<Integer>();
		int tmp = (int)(a.get(0));
		int cnt = 0;
		for(int i = 0 ; i < n+1 ; i++){
			if(tmp == (int)(a.get(i))){
				cnt++;
			}else{
				tmp = (int)(a.get(i));
				num.add(cnt);
				cnt = 1;
			}
		}

		Collections.sort(num, Comparator.reverseOrder());

		int eN = num.size();
		int m = n;

		for(int i = 0 ; i < eN ; i++){
			System.out.println(Math.min(m,n/(i+1)));
			m -= (int)(num.get(i));
		}
		for(int i = eN ; i < n ; i++){
			System.out.println(0);
		}
	}
}