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
N = int(input())
 
A = list(map(int,input().split()))
 
dic = {}
 
for a in A:
 
    if a not in dic:
        dic[a] = 1
    else:
        dic[a] += 1
 
B = []
for i in dic:
    B.append(dic[i])
 
B.sort()
 
B_sub = B.copy()
 
for i in range(len(B)-1):
    B_sub[i+1] += B_sub[i] 
 
aind = N + 1
nind = len(B) - 1
 
#print (B,B_sub)
 
for i in range(N):
 
    i += 1
 
    while True:
 
        while nind > 0 and B[nind] > aind - 1:
 
          nind -= 1
 
        if i > len(B):
            print (0)
            break
 
        elif ((len(B) - 1) - nind ) * (aind-1) + B_sub[nind] >= (aind - 1) * i:
            print (aind - 1)
            break
 
        aind -= 1