3427. Equal Numbers

单点时限: 3.0 sec

内存限制: 256 MB

You are given a list of $n$ integers $a_1, \ldots, a_n$. You can perform the following operation: choose some $a_i$ and multiply it by any positive integer.

Your task is to compute the minimum number of different integers that could be on the list after $k$ operations for all $0 \leq k \leq n$.

输入格式

The first line of the input contains single integer $n$ ($1 \leq n \leq 3 \cdot 10^5$).

The second line of the input contains $n$ integers $a_i$ ($1 \leq a_i \leq 10^6$).

输出格式

Output a single line that contains $n + 1$ integers. The $i$-th integer should be the minimum possible number of different integers in the list after $i - 1$ operations.

样例

Input
6
3 4 1 2 1 2
Output
4 4 3 3 2 2 1

1 人解决,1 人已尝试。

2 份提交通过,共有 2 份提交。

8.9 EMB 奖励。

创建: 2 年,10 月前.

修改: 2 年,10 月前.

最后提交: 2 年,10 月前.

来源: NEERC 2017

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