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#include <iostream>
#include <vector>
#include <map>
#include <iomanip>
#include <cmath>
// using std::cout;
// using std::endl;
using vi=std::vector<int>;
using mii=std::map<int,int>;
int lastprime(vi & primes);
void primefactorization(int num, mii & m);
int main()
{
mii m {};
int num=15593760;
primefactorization(num, m);
// for(const auto &x:m) std::cout << x.first<< " wystepuje "<<x.second<<" razy"<<std::endl;
// std::cout<< std::endl;
//integral//rational
int integral=1;
int root = 3;
for(auto &x:m) {
int times = x.second/root;
if(times) {
integral*=pow(x.first,times);
x.second%=root;
}
}
std::cout << " \n\nR = "<< integral<< " ";
// for(const auto &x:m) if(x.second) std::cout<< " * v"<<root<<"/ " << pow(x.first,x.second)<<x.second<<"| ";
for(const auto &x:m) if(x.second) std::cout<< "* (" << pow(x.first,x.second)<<")^(1/"<<root<<") ";
std::cout<< std::endl;
return 0;
}
int lastprime(vi & primes){
// bool isprimre=true;
auto it=primes.begin();
auto end=primes.end();
int i=primes.back()+1;
for (;it!=end;i++)
for(it=primes.begin();it!=end;it++){
if(i%(*it)==0) {
break;}
}i--;
primes.push_back(i);
return i;
}
void primefactorization(int num, mii & m){ //factorise
vi v{2};
while (num!=1 ){
int currentnum=v.back();
while (num%currentnum==0){
m[currentnum]++;
std::cout<<std::setw(15) <<num<< " | "<<currentnum<<std::endl;
num/=currentnum;
}
lastprime(v);
}
std::cout<<std::setw(15) <<1<< " | "<<std::endl;
// while (lastprime(v)<10);
// for(const auto &x:v) std::cout << x<<' ';
// std::cout<< std::endl;
}
