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.

Examples

Input

3
2 1 2


Output

3
1
0


Input

5
1 2 3 4 5


Output

5
2
1
1
1


Input

4
1 3 3 3


Output

4
1
0
0
from collections import Counter

N = int(input())
A = [int(i) for i in input().split()]

C = [0] * (N + 1)
S = [0] * (N + 1)

for a in Counter(A).values() :
    C[a] += 1
    S[a] += a

for i in range(1, N + 1) :
    C[i] += C[i-1]
    S[i] += S[i-1]

for K in range(1, N + 1) :
    ok, ng = 0, N + 1
    while ng - ok > 1 :
        mid = (ng + ok) // 2
        if S[mid] + mid * (C[-1] - C[mid]) >= K * mid :
            ok = mid
        else :
            ng = mid
    print(ok)