Buggy python submission (verdict: Runtime Error):
import sys
from subprocess import Popen, PIPE
from itertools import groupby
from collections import Counter

def main():
    sys.stdin.readline()
    S = sys.stdin.read()
    T = []
    inv_dict = {}
    Factors = Popen("factor " + S, stdout=PIPE).communicate()[0].split(b"\n")
    for factors in Factors:
        factors = map(int, factors.split()[1:])
        t = 1
        t_inv = 1
        for f, group in groupby(factors):
            n = len(list(group)) % 3
            if n == 1:
                t *= f
            elif n == 2:
                t_inv *= f
        t, t_inv = t * t_inv * t_inv, t * t * t_inv
        T.append(t)
        inv_dict[t] = t_inv

    counter_T = Counter(T)
    ans = 0
    for t, t_cnt in counter_T.items():
        if t == 1:
            ans += 1
            continue
        t_inv = inv_dict[t]
        t_inv_cnt = counter_T[t_inv]
        if t_cnt > t_inv_cnt or (t_cnt == t_inv_cnt and t > t_inv):
            ans += t_cnt
    print(ans)

main()


Fixed submission:
import sys
from collections import Counter

def make_prime_checker(n):
    # nまでの自然数が素数かどうかを表すリストを返す  O(nloglogn)
    is_prime = [False, True, False, False, False, True] * (n//6+1)
    del is_prime[n+1:]
    is_prime[1:4] = False, True, True
    for i in range(5, int(n**0.5)+1):
        if is_prime[i]:
            is_prime[i*i::i] = [False] * (n//i-i+1)
    return is_prime

def main():
    Primes = [p for p, is_p in enumerate(make_prime_checker(2200)) if is_p]
    def decomp(n):
        res1 = res2 = 1
        for p in Primes:
            cnt = 0
            while n % p == 0:
                n //= p
                cnt += 1
            cnt %= 3
            if cnt == 1:
                res1 *= p
            elif cnt == 2:
                res2 *= p
        if int(n**0.5)**2 == n:
            res2 *= int(n**0.5)
        else:
            res1 *= n
        return res1 * res2 * res2, res1 * res1 * res2

    N, *S = map(int, sys.stdin.buffer.read().split())
    T = []
    inv_dict = {}
    for s in S:
        t, t_inv = decomp(s)
        T.append(t)
        inv_dict[t] = t_inv

    counter_T = Counter(T)
    ans = 0
    for t, t_cnt in counter_T.items():
        if t == 1:
            ans += 1
            continue
        t_inv = inv_dict[t]
        t_inv_cnt = counter_T[t_inv]
        if t_cnt > t_inv_cnt or (t_cnt == t_inv_cnt and t > t_inv):
            ans += t_cnt
    print(ans)

main()

Buggy python submission (verdict: Time Limit Exceeded):
import sys
from subprocess import Popen, PIPE
from itertools import groupby
from collections import Counter

def main():
    N, *S = sys.stdin.read().split()
    T = []
    inv_dict = {}
    for s in S:
        factors = list(map(int, Popen(["factor", s], stdout=PIPE).communicate()[0].split()[1:]))
        t = 1
        t_inv = 1
        for f, group in groupby(factors):
            n = len(list(group)) % 3
            if n == 1:
                t *= f
                t_inv *= f * f
            elif n == 2:
                t *= f * f
                t_inv *= f
        T.append(t)
        inv_dict[t] = t_inv

    counter_T = Counter(T)
    ans = 0
    for t, t_cnt in counter_T.items():
        if t == 1:
            ans += 1
            continue
        t_inv = inv_dict[t]
        t_inv_cnt = counter_T[t_inv]
        if t_cnt > t_inv_cnt or (t_cnt == t_inv_cnt and t > t_inv):
            ans += t_cnt
    print(ans)

main()


Fixed submission:
import sys
from collections import Counter

def make_prime_checker(n):
    # nまでの自然数が素数かどうかを表すリストを返す  O(nloglogn)
    is_prime = [False, True, False, False, False, True] * (n//6+1)
    del is_prime[n+1:]
    is_prime[1:4] = False, True, True
    for i in range(5, int(n**0.5)+1):
        if is_prime[i]:
            is_prime[i*i::i] = [False] * (n//i-i+1)
    return is_prime

def main():
    Primes = [p for p, is_p in enumerate(make_prime_checker(2200)) if is_p]
    def decomp(n):
        res1 = res2 = 1
        for p in Primes:
            cnt = 0
            while n % p == 0:
                n //= p
                cnt += 1
            cnt %= 3
            if cnt == 1:
                res1 *= p
            elif cnt == 2:
                res2 *= p
        if int(n**0.5)**2 == n:
            res2 *= int(n**0.5)
        else:
            res1 *= n
        return res1 * res2 * res2, res1 * res1 * res2

    N, *S = map(int, sys.stdin.buffer.read().split())
    T = []
    inv_dict = {}
    for s in S:
        t, t_inv = decomp(s)
        T.append(t)
        inv_dict[t] = t_inv

    counter_T = Counter(T)
    ans = 0
    for t, t_cnt in counter_T.items():
        if t == 1:
            ans += 1
            continue
        t_inv = inv_dict[t]
        t_inv_cnt = counter_T[t_inv]
        if t_cnt > t_inv_cnt or (t_cnt == t_inv_cnt and t > t_inv):
            ans += t_cnt
    print(ans)

main()