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)

#include "bits/stdc++.h"
#define rep(i,n) for(int i=0;i<n;i++)
using namespace std;

using ll = long long;
const ll MOD = 998244353;
const ll INF = 1e18;

int main() {
    int N;
    cin >> N;
    vector<int> A(N), B(N, 0);
    rep(i, N) {
        cin >> A[i];
        A[i]--;
        B[A[i]]++;
    }
    int maxB = 0;
    rep(i, N) {
        maxB = max(maxB, B[i]);
    }
    rep(i, N) {
        int c = N, d = maxB;
        while (c / (i + 1) < d) {
            c -= d - c / (i + 1);
            d = maxB - (N - c);
        }
        cout << c / (i + 1) << endl;
    }
}