J. Prime Factors

#include <bits/stdc++.h>

using namespace std;

#define cin(vec) for(auto& i : vec) cin >> i
#define cin_2d(vec, n, m) for(int i = 0; i < n; i++) for(int j = 0; j < m && cin >> vec[i][j]; j++);
#define cout(vec) for(auto& i : vec) cout << i << " "; cout << "\n";
#define cout_2d(vec, n, m) for(int i = 0; i < n; i++, cout << "\n") for(int j = 0; j < m && cout << vec[i][j] << " "; j++);
#define cout_map(mp) for(auto& [f, s] : mp) cout << f << "  " << s << "\n";
#define Time cerr << "Time Taken: " << (float)clock() / CLOCKS_PER_SEC << " Secs" << "\n";
#define fixed(n) fixed << setprecision(n)
#define ceil(n, m) (((n) / (m)) + ((n) % (m) ? 1 : 0))
#define fill(vec, value) memset(vec, value, sizeof(vec));
#define Num_of_Digits(n) ((int)log10(n)+1)
#define all(vec) vec.begin(),vec.end()
#define rall(vec) vec.rbegin(),vec.rend()
#define sz(x) int(x.size())
#define TC int t; cin >> t;   while(t--)
#define fi first
#define se second
#define Pair pair < int, int >
#define ll long long
#define ull unsigned long long
#define Mod  1'000'000'007
#define OO 2'000'000'000
#define EPS 1e-9
#define PI acos(-1)
#define imin INT_MIN
#define imax INT_MAX
#define getline(s) getline(cin >> ws , s) ;

void Abdel3al () {
    ios_base::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr);
#ifndef ONLINE_JUDGE
    freopen("input.txt", "r", stdin), freopen("output.txt", "w", stdout);
#endif
    Time
}

vector < ll > prime_factors ;

vector < ll > prime_factorization (ll n) {
    while (n % 2 == 0) prime_factors.push_back(2) , n /= 2 ;
    for (int i = 3; i <= sqrt(n); i += 2)
        while (n % i == 0) prime_factors.push_back(i) , n /= i ;
    if (n > 2) prime_factors.push_back(n) ;
    return prime_factors ;
}

int main () {
    Abdel3al () ;
    int n ;             cin >> n ;
    vector < ll > factors = prime_factorization(n) ;
    map <ll , int> freq ;
    for (auto& i : factors) freq[i]++ ;
    cout << '(' << factors[0] << '*' << freq[factors[0]] << ')' ;
    for (auto& i : freq)
        cout << '*' << '(' << i.first << '*' << i.second << ')' ;
    return 0 ;
}