# 3427. Equal Numbers

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，2 人已尝试。

2 份提交通过，共有 4 份提交。

9.6 EMB 奖励。