#abc143f. [abc143_f]Distinct Numbers

[abc143_f]Distinct Numbers

Problem Statement

Takahashi has NN cards. The ii-th of these cards has an integer AiA_i written on it.

Takahashi will choose an integer KK, and then repeat the following operation some number of times:

  • Choose exactly KK 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,NK = 1,2, \\ldots, N, find the maximum number of times Takahashi can do the operation.

Constraints

  • 1leNle3times1051 \\le N \\le 3 \\times 10^5
  • 1leAileN1 \\le A_i \\le N
  • All values in input are integers.

Input

Input is given from Standard Input in the following format:

NN A1A_1 A2A_2 ldots\\ldots ANA_N

Output

Print NN integers. The tt-th (1letleN)(1 \\le t \\le N) of them should be the answer for the case K=tK=t.


Sample Input 1

3
2 1 2

Sample Output 1

3
1
0

For K=1K = 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=2K = 2, we can do the operation as follows:

  • Choose the first and second cards to eat.

For K=3K = 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