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;

map<int,int> m;
map<int,int> mp;

int main(){
	int N;
	cin >> N;
	for(int i=0;i<N;i++){
		int A;
		cin >> A;
		A--;
		if(m.find(A)!=m.end())m[A]++;
		else m.insert(make_pair(A,1));
	}
	
	for(auto it=m.begin();it!=m.end();it++){
		int B=it->second;
		if(mp.find(B)!=mp.end())mp[B]++;
		else mp.insert(make_pair(B,1));
	}
	
	vector<pair<int,int>> mpmp;
	for(auto it=mp.begin();it!=mp.end();it++){
		mpmp.push_back(*it);
	}
	int M=mpmp.size();
	
	for(int K=1;K<=N;K++){
		int ok=0,ng=N/K+1;
		while(abs(ok-ng)>1){
			int mid=(ok+ng)/2;
			long long tmp=0;
			for(int i=0;i<M;i++){
				int C=mpmp[i].first,D=mpmp[i].second;
				tmp+=min(mid,C)*D;
			}
			if(tmp>=(long long)mid*K)ok=mid;
			else ng=mid;
		}
		printf("%d\n",ok);
	}
	
	return 0;
}