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 Pascal (FPC 2.6.2) (judge verdict: Accepted)

var
	N,i,t,A,acc:Longint;
	cnt,ans:Array[1..300000]of Longint;
	sum:Array[0..300000]of Longint;
begin
	read(N);
	for i:=1 to N do begin
		read(A);
		inc(sum[cnt[A]]);
		inc(cnt[A]);
	end;
	i:=0;
	for t:=N downto 1 do begin
		while acc>=i*t do begin
			inc(acc,sum[i]);
			inc(i);
		end;
		ans[t]:=i-1;
	end;
	for i:=1 to N do writeln(ans[i]);
end.