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 $K=t$.

3
2 1 2

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.

5
1 2 3 4 5

5
2
1
1
1

4
1 3 3 3

4
1
0
0