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 Python (3.4.3) (judge verdict: Runtime Error)

import numpy as np


def bruteforce(c, k):
    c = c.tolist()
    n = 0
    while True:
        if len(c) < k:
            return n
        for i in range(k):
            c[i] -= 1
        c = [ci for ci in c if ci != 0]
        n += 1

def diff(x):
    ret = np.zeros_like(x)
    ret[1:] = np.diff(x)
    return ret

def test(c, k):
    if k == 1:
        return np.sum(c)
    if len(c) < k:
        return 0
    f = np.sort(c[:k])
    remain = sum(c[k:])
    d = diff(f)
    cost = np.arange(len(d)) * d
    for i, cos in enumerate(cost):
        if cos <= remain:
            remain -= cos
        else:
            if i == 0:
                return f[0]
            else:
                return f[i - 1]
    return c[0] + remain // k


def main():
    N = int(input())
    A = list(map(int, input().split()))

    A = sorted(A)
    _, c = np.unique(A, return_counts=True)

    c = np.sort(c)[::-1]
    for k in range(1, N + 1):
        print(test(c, k))
    # for k in range(1, 7):
        # print(test(c, k), bruteforce(c, k))
        # print(bruteforce(c, k))


if __name__ == "__main__":
    main()