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)

from collections import Counter

N = int(input())
 
lines = input().split(' ')
 
lis = list(Counter(lines).values())
# dic = {}
# for item in lines:
#     n = int(item)
 
#     if n in dic.keys():
#         dic[n] += 1
#     else:
#         dic[n] = 1
 
# lis = list(dic.values())
# for item in dic.keys():
#     lis += [dic[item]]
 
lis.sort(reverse=True)
 
sublis = []
sublis = lis[:]
 
def cal(k,lis):
    ans = 0
    if (len(lis)<k):
        return 0
    
    while True:
        for k_i in range(k):
            if lis[k_i] == 0:
                return ans
            else:
                lis[k_i] -= 1
        else:
            ans += 1
 
        lis.sort(reverse=True)
 
 
for i in range(N):
    if i == 0:
        print(N)
        continue
    lis = sublis[:]
    print(cal(i+1,lis))