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.

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.

Constraints

• $1 \le N \le 3 \times 10^5$
• $1 \le A_i \le N$
• All values in input are integers.

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

见题面 Input 部分

见题面 Output 部分