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: Time Limit Exceeded)

import collections
import numpy as np

# リストarrからx個の同じ長さの列を取り出す時の最大の長さ
# 発想: x個取り出す時、ある文字をx個より多く取り出して列に含むことはない
#       一方ある文字をその文字がある数よりも取り出して使うこともできない
#       つまり、min(arr.count(a), x)で、x個の同じ長さの列に使えるaの数がわかる
#       さらに、sum(min(arr.count(a),x))で、x個の同じ長さの列に使える文字の数がわかる
#       よって、sum(min(arr.count(a),x))//xで、x個の同じ長さの列の長さがわかる
#       発展的に、longest(arr,x)までの計算状況からlongest(arr,x+1)が計算できる
def longest(arr, x):    # legacy
    return sum(min(arr.count(a), x) for a in arr) // x


n = int(input())
a = list(map(int, input().split()))

nums = list(collections.Counter(a).values())
lastest_add = np.count_nonzero(nums)
building = [0]
longests = [0]
for i in range(1, n+1):
    appended = building[-1] + lastest_add
    building.append(appended)
    longests.append(appended // i)
    lastest_add -= nums.count(i)

for k in range(1, n+1):
    maxindexes = list(i for i, x in enumerate(longests) if x >= k)
    if maxindexes:
        print(max(maxindexes))
    else:
        print(0)