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-----
3
2 1 2

-----Sample Output-----
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.

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