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)

N = input("")
A = input("")
A = A.split(" ")
num = {}
num_key = 0
print(N)
for i in A:
    if not i in num.keys():
        num[i] = A.count(i)
num_key = len(num.keys())
num_value = list(num.values())
num_value.sort(reverse = True)
result = []
for i in range(N+1):
  result.append(0)
i = 2
memory = num_value
while i != N + 1 :
    new_num = []
    if len(num_value) >= i :
        for j in range(i):
            num_value[j] -= 1
        for k in num_value:
            if k != 0:
                new_num.append(k)
        num_value = new_num
        result[i] += 1
    else :
        print(result[i])
        i += 1
        num_value = memory