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OI-codes/AtCoder/AGC003/D/D.cpp

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#include <iostream>
#include <algorithm>
#include <cmath>
#include <unordered_map>
#include <utility>
#include <vector>
using std::cin;
using std::cout;
const char endl = '\n';
const int N = 1e5 + 5,
M = 3005;
int n, ans;
std::vector<long long> primes;
bool not_prime[N];
std::unordered_map<long long, int> map;
std::vector<std::pair<long long, long long>> data;
int main() {
std::ios::sync_with_stdio(false);
cin.tie(nullptr);
for (int i = 2; i < M; i++) {
if (!not_prime[i]) primes.emplace_back(i);
for (auto p : primes) {
if (i * p >= M) break;
not_prime[i * p] = true;
if (i % p == 0) break;
}
}
cin >> n;
for (int i = 1; i <= n; i++) {
long long x, y = 1, z = 1;
cin >> x;
for (auto p : primes) {
if (p * p > x) break;
int t = 0;
while (x % p == 0) {
x /= p;
t++;
}
t %= 3;
if (t == 0) continue;
for (int k = 1; k <= t; k++) y *= p;
for (int k = 1; k <= 3 - t; k++) z *= p;
}
y *= x;
if (x > 1) {
long long t = std::sqrt(x);
if (t * t == x) z *= std::sqrt(x);
else z *= x * x;
}
map[y]++;
data.emplace_back(y, z);
}
ans = map[1] > 0;
for (auto o : data) {
if (o.first == 1) continue;
ans += std::max(map[o.first], map[o.second]);
map[o.first] = map[o.second] = 0;
}
cout << ans << endl;
return 0;
}