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: Wrong Answer)

from collections import defaultdict,deque
import sys,heapq,bisect,math,itertools,string,queue,copy,time
sys.setrecursionlimit(10**8)
INF = float('inf')
mod = 10**9+7
eps = 10**-7
def inp(): return int(sys.stdin.readline())
def inpl(): return list(map(int, sys.stdin.readline().split()))
def inpl_str(): return list(sys.stdin.readline().split())

N = inp()
AA = inpl()
cnts = defaultdict(int)
ed = set()
for a in AA:
    cnts[a] += 1
    ed.add(a)

aa1 = defaultdict(int)
for e in ed:
    aa1[cnts[e]] += 1

aa1 = sorted(list(aa1.items()))
aa2 = [0] # 種類数
aa3 = [0] # 実枚数
for t,n in aa1:
    aa2.append(aa2[-1] + n)
    aa3.append(aa3[-1] + n*t)

# print(aa1)
# print(aa2)
# print(aa3)

L = len(aa1)
tmpl_t = []
tmpl_c = []
for i,(t,n) in enumerate(aa1):
    tmp = n + aa3[i]//t
    tmp += aa2[-1] - aa2[i+1]
    tmpl_t.append(t)
    tmpl_c.append(tmp)
    # print(t,'回食べるとき，最大',tmp,'枚までいける')

tmpl_t.reverse()
tmpl_t.append(0)
tmpl_c.reverse()
ans = [0]*N
for i in range(1,N+1):
    idx = bisect.bisect_left(tmpl_c,i)
    if idx == 0:
        ans[i-1] = N//i
    else:
        ans[i-1] = tmpl_t[idx]

print('\n'.join(map(str,ans)))