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 sys
input = sys.stdin.readline

#input
N = int(input())
A = list(map(int, input().split()))

#output
from collections import Counter
import bisect as bi

l = Counter(A).most_common()
l = [b for a, b in l]
M = len(l)

number_of_operation = [0] * O
maximum_operation = [0] * N

ll = []
for x in reversed(range(1, N+1)):
    ll.append(sum([min(x, i) for i in l]) / x)

for K in range(M):
    maximum_operation[K] = N-bi.bisect_left(ll, K+1)

for m in maximum_operation:
    print(m)