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 Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

n=gets.to_i
a=gets.split.map(&:to_i).each_with_object({}){|i,t| t[i]||=0;t[i]+=1; }.values.sort.reverse

sum=a.reduce(:+)

(1..n).each{|t|
    r = a.reduce([[0]*t]){|memo,i|
        memo.flat_map{|x|
            (0...x.size).each_with_object([]){|idx,tt|
                if x[idx] < sum/t + 1
                    tmp = x.dup;
                    tmp[idx] += i 
                    tt << tmp
                end
            }
        }
    }
    p r.map(&:min).max
}