Problem Statement

Snuke got positive integers $s_1,...,s_N$ from his mother, as a birthday present. There may be duplicate elements.

He will circle some of these $N$ integers. Since he dislikes cubic numbers, he wants to ensure that if both $s_i$ and $s_j (i ≠ j)$ are circled, the product $s_is_j$ is not cubic. For example, when $s_1=1,s_2=1,s_3=2,s_4=4$, it is not possible to circle both $s_1$ and $s_2$ at the same time. It is not possible to circle both $s_3$ and $s_4$ at the same time, either.

Find the maximum number of integers that Snuke can circle.

Constraints

• $1 ≦ N ≦ 10^5$
• $1 ≦ s_i ≦ 10^{10}$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

N
s_1
:
s_N

Output

Print the maximum number of integers that Snuke can circle.