Distinct Numbers

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

inputFormat

input are integers.

Input

Input is given from Standard Input in the following format:

N A_1 A_2 \ldots A_N

outputFormat

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

样例

5
1 2 3 4 5

5
2
1
1
1

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