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: Wrong Answer)

#define _CRT_SECURE_NO_WARNINGS

#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <climits>
#include <cfloat>
#include <cstring>
#include <map>
#include <utility>
#include <set>
#include <iostream>
#include <memory>
#include <string>
#include <vector>
#include <list>
#include <algorithm>
#include <functional>
#include <sstream>
#include <complex>
#include <stack>
#include <queue>
#include <unordered_set>
#include <unordered_map>
#include <array>
#include <cassert>
#include <bitset>
#include <cstdint>
using namespace std;
using LL = long long;

int N;

int main() {
	cin >> N;
	map<int, int>mp;
	for (int i = 0; i < N; ++i) {
		int A;
		cin >> A;
		mp[A]++;
	}
	vector<int>B, C;
	for (auto p : mp) {
		B.push_back(p.second);
	}
	sort(B.begin(), B.end());
	C.push_back(0);
	int M = B.size();
	for (int j = 0; j < M; ++j) {
		C.push_back(C.back() + B[j]);
	}
	for (int k = 1; k <= N; ++k) {
		if (k > M) {
			cout << 0 << endl;
		}
		else if (k == 1) {
			cout << N << endl;
		}
		else {
			if ((C[M] - C[M - k + 1]) / (k - 1) > C[M - k + 1] - C[0]) {
				multiset<int> D;
				for (int elm : B)D.insert(-elm);
				int ans = 0;
				for (;;) {
					auto itr = D.begin();
					bool flag = true;
					for (int i = 0; i < k; ++i) {
						if (*itr >= 0) {
							flag = false;
							break;
						}
						++itr;
					}
					if (!flag)
						break;
					itr = D.begin();
					unordered_multiset<int>E;
					for (int i = 0; i < k; ++i) {
						E.insert(*itr);
						++itr;
					}
					for (int i = 0; i < k; ++i) {
						D.erase(D.begin());
					}
					auto itr2 = E.begin();
					for (int i = 0; i < k; ++i) {
						D.insert(*itr2 + 1);
						++itr2;
					}
					++ans;
				}
				cout << ans << endl;
			}
			else {
				cout << (N / k) << endl;
			}
		}
	}
}