【数学】【策略】DiviDuelo

https://codeforces.com/gym/105053/problem/D
我发现了p^alpha = N ,alpha % 2 != 0 以及 pq = N,(p，q为素数)的情况下先手玩家有必胜策略，然而我不知道如何用O(sqrt(N))的算法分解出上面的东西

#include<bits/stdc++.h>
 
using namespace std;
std::vector<int> factorize(int n) {
    std::vector<int> factors;
    
    for (int i = 2; i * i <= n; ++i) {
        while (n % i == 0) {
            factors.push_back(i);
            n /= i;
        }
    }
    
    if (n > 1) {
        factors.push_back(n);
    }
    
    return factors;
}
 
bool hasWinningStrategy(int n) {
    std::vector<int> factors = factorize(n);
    int distinctPrimes = 0;
    
    for (int i = 0; i < factors.size(); ++i) {
        if (i == 0 || factors[i] != factors[i - 1]) {
            distinctPrimes++;
        }
    }
    
    if (distinctPrimes == 1 && factors.size() % 2 == 0) {
        return false;
    }
    
    return true;
}
 
int main() {
    int number;
    std::cin >> number;
    if (number == 1) {
    	cout << "N" << endl;
    	return 0;
	}
    
    bool hasStrategy = hasWinningStrategy(number);
    
    if (hasStrategy) {
        std::cout << "Y" << std::endl;
    } else {
        std::cout << "N" << std::endl;
    }
    
    return 0;
}