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: Runtime Error)

import java.util.Arrays;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		int A[] = new int[30001];
		for(int i = 0 ; i < N ; ++i){
			int ai = sc.nextInt();
			A[ai]++;
		}
		Arrays.sort(A);
		int freq[] = new int[30001];
		for(int a : A){
			if(a == 0){
				continue;
			}
			freq[a]++;
		}
		int C[] = new int[N + 1];
		int D[] = new int[N + 1];
		for(int f = 1 ; f <= N ; ++f){
			C[f] = C[f - 1] + f * freq[f];
			D[f] = D[f - 1] + freq[f];
		}
		int X[] = new int[N  + 1];
		for(int x = 1 ; x <= N ; ++x){
			int f = C[x] + x * (D[N] - D[x]);
			f = f / x;
			X[x] = f;
		}
		int res[] = new int[N + 1];
		res[1] = N;
		for(int i = N - 1 ; i >= 1 ; --i){
			if(X[i + 1] != X[i]){
				for(int j = X[i + 1] + 1; j <= X[i] ; ++j){
					res[j] = i;
				}
			}
		}
		for(int k = 1 ; k <= N ; ++k){
			System.out.println(res[k]);
		}
	}
}