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
def main():
    N = int(input())
    A = list(map(int, input().split()))
    C = [0] * (N+1)
    Cnt_A = [0] * (N+1)
    for a in A:
        Cnt_A[a] += 1
        cnt = Cnt_A[a]
        C[cnt] += 1
    cum_C = []
    cu = 0
    for c in C:
        cu += c
        cum_C.append(cu)
    Ans = []
    for k in range(1, N+1):
        # K = k のとき、 n 組以上作れる <=> 使えるカードが nk 枚以上
        # n 組以上作れる <=> 同じカードは n 枚以下
        # 同じカードは n 枚以下で全体として nk 枚以上用意できるか？
        ok, ng = 0, N//k+1
        while ok + 1 < ng:
            n = ok+ng>>1
            if cum_C[n] >= n*k:
                ok = n
            else:
                ng = n
        Ans.append(ok)
    print("\n".join(map(str, Ans)))

main()
