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: Runtime Error)

#include<stdio.h>
int cmp(const void *a,const void *b){
  return *(int*)a-*(int*)b;}
int main(){
  int n,i,count=0;
  scanf("%d",&n);
  int a[n];
  for(i=0;i<n;i++)
    scanf("%d",&a[i]);
  qsort(a,n,sizeof(int),cmp);
  for(i=0;i<n-1;i++){
    if(a[i+1]==a[i])
      count++;}
  if(count==0){
    for(i=1;i<n+1-count;i++)
      printf("%d\n",n/i);
    for(i=0;i<count;i++)
      printf("0\n");
  }
  else{
    for(i=0;i<n+1;i++)
      printf("%d\n",n/i);}

  return 0;
}