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<iostream>
#include<algorithm>
#include<cstdint>
#include<cstdlib>
template<typename T>
void fin(T const& t){ std::cout << t << std::endl; exit(0); }

int const MAXN = 3e5;
int N, f[MAXN], m[MAXN], d[MAXN+1];

int main() {
  std::cin >> N;
  std::fill_n(m, N+1, 0);
  for(int i = 0; i < N; ++i) { int A; std::cin >> A; ++m[A-1]; }
  std::fill_n(d, N+1, 0);
  for(int i = 0; i < N; ++i) ++d[m[i]];

  int64_t sum = 0;
  for(int64_t x = 0; x < N; ++x) {
    sum += x*d[x];
    f[x] = sum/(x+1);
  }
  sum = d[N];
  for(int x = N-1; x >= 0; --x) {
    f[x] += sum;
    sum += d[x];
  }

  int ans = N;
  for(int k = 1; k <= N; ++k) {
    ans = std::min(ans, N/k);
    while(ans > 0 && k > f[ans-1]) --ans;
    std::cout << ans << std::endl;
  }
  return 0;
}