Problem:
Score : 1100 points

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.

Sample Input 1

8
1
2
3
4
5
6
7
8

Sample Output 1

6

Snuke can circle 1,2,3,5,6,7.

Sample Input 2

6
2
4
8
16
32
64

Sample Output 2

3

Sample Input 3

10
1
10
100
1000000007
10000000000
1000000009
999999999
999
999
999

Sample Output 3

9

Solution in Haskell (GHC 7.10.3) (judge verdict: Wrong Answer)

import Data.Function (on)
import Data.List (foldl', sortBy)
import qualified Data.Set as Set

main :: IO ()
main = print . solve . map read . tail . lines =<< getContents

solve :: [Integer] -> Int
solve xs = fst $ foldl' f (0, Set.empty) ys
  where ys = sortBy (compare `on` (length . snd)) [ (x, [ y | y <- xs, isCube (x * y) ]) | x <- xs ]
        f (k, sy) (c, zs) = (k + fromEnum (Set.notMember c sy), Set.fromList zs `Set.union` sy)

isCube :: Integral a => a -> Bool
isCube x = round (fromIntegral x ** (1.0/3)) ^ 3 == x