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 PyPy3 (2.4.0) (judge verdict: Time Limit Exceeded)

from copy import copy
n=int(input())
a=list(map(int,input().split()))
a.sort()
b=[]
k=1
for i in range(n-1):
    if a[i]==a[i+1]:
        k+=1
    else:
        b.append(k)
        k=1
b.append(k)
b.sort(reverse=True)
print(n)
l=len(b)
for i in range(2,n+1):
    if l<i:
        print(0)
    else:
        c=copy(b)
        ans=0
        for j in range(n+1):
            if c[i-1]!=0:
                ans += c[i-1]
                for m in range(i):
                    c[m]-=c[i-1]
                c.sort(reverse=True)
            else:
                break
        print(ans)