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 = list(map(int, input().split()))
C = list(Counter(A).values())
D = [0] * (N+1)
for k, d in Counter(C).items():
    D[k] = d

ckd, cd = [0] * (N+1), [0] * (N+1)

for i in range(1,N+1):
    cd[i] = cd[i-1] + D[i]
    ckd[i] = ckd[i-1] + i*D[i]

INF = float('inf')
def f(x):
    if x:
        return (x*(cd[-1] - cd[x]) + ckd[x]) // x
    return INF

cur = N
v = f(cur)
for k in range(1,N+1):
    while k > v:
        cur -= 1
        v = f(cur)
    print(cur)
