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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
using namespace std;
int n;
int a;
int c[300100],d[300100];
long long prekdk[300100],sufdk[300100],func[300100];
int main(){
	#ifdef FILIN
		#ifndef LOCAL
			freopen(FILIN,"r",stdin);
			freopen(FILOUT,"w",stdout);
		#endif
	#endif
	cin>>n;
	for(int i=1;i<=n;i++){
		cin>>a;
		c[a]++;
	}
	for(int i=1;i<=n;i++)
		d[c[i]]++;
	for(int i=1;i<=n;i++)
		prekdk[i]=prekdk[i-1]+(long long)(i)*(long long)(d[i]);
	for(int i=n;i>=1;i--)
		sufdk[i]=sufdk[i+1]+(long long)(d[i]);
	for(int i=1;i<=n;i++)
		func[i]=(long long)(prekdk[i]/(long long)(i)+sufdk[i+1]);
	sort(func+1,func+n+1);
	int res;
	for(int i=1;i<=n;i++){
		res=(int)(lower_bound(func+1,func+n+1,(long long)(i))-func);
		cout<<n+1-res<<endl;
	}
	return 0;
}