Score : 1100 points
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.
The input is given from Standard Input in the following format:
N s_1 : s_N
Print the maximum number of integers that Snuke can circle.
8 1 2 3 4 5 6 7 8
6
Snuke can circle 1,2,3,5,6,7.
6 2 4 8 16 32 64
3
10 1 10 100 1000000007 10000000000 1000000009 999999999 999 999 999
9