You are given a list of n integers a₁, . . . , a_n. You can perform the following operation: choose some a_i and multiply it by any positive integer.</p>

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

입력 형식

The first line of the input contains single integer n (1 ≤ n ≤ 3·10⁵). The second line of the input contains n integers a_i (1 ≤ a_i ≤ 10⁶).

출력 형식

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.

예제 입력

6
3 4 1 2 1 2

예제 출력

4 4 3 3 2 2 1