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 C (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include <stdio.h>
#include <stdlib.h>

int comp(const void *a, const void *b)
{
  return *(int*)b - *(int*)a;
}

int main()
{
  int i,s,t,n;
  int upper,lower;
  int a[300000];
  int hist[300000];
  int ans[300001];

  scanf("%d",&n);
  for(i=0;i<n;i++) hist[i]=0;
  for(i=0;i<n;i++){
    scanf("%d",&a[i]);
    hist[a[i]-1]++;
  }
  qsort(hist,n,sizeof(int),comp);

  for(t=1;t<=n;t++) ans[t]=n/t;
  upper=0;
  lower=n;
  for(s=1;s<n;s++){
    upper+=hist[s-1];
    lower-=hist[s-1];
    for(t=s+1;t<=n;t++)
      if(lower/(t-s)<upper/s && lower/(t-s)<ans[t]) ans[t]=lower/(t-s);
  }
  for(t=1;t<=n;t++) printf("%d\n",ans[t]);
  return 0;
}