Problem p02660 (C++) — buggy submission, verdict: Time Limit Exceeded

#include <bits/stdc++.h>
using namespace std;
#define ll long long
// memo  fixed  setprecision(20);
using vvll = vector<vector<ll>>;
ll mod = 1e9 + 7;
/*"itob" int to "N"base */ template <typename TypeInt>
string itob(const TypeInt v, int base) {
  static const char table[] = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ";
  string ret;
  static numeric_limits<TypeInt> t;
  TypeInt n = v;
  if (t.is_signed) {
    if (v < 0)
      n *= -1;
  }
  while (n >= base) {
    ret += table[n % base];
    n /= base;
  }
  ret += table[n];
  if (t.is_signed) {
    if (v < 0 && base == 10)
      ret += '-';
  }
  reverse(ret.begin(), ret.end());
  return ret;
}
/*"chmin" a = MAX*/ template <class T> inline bool chmin(T &a, T b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
/*"chmax" a = MIN*/ template <class T> inline bool chmax(T &a, T b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
/*"ctoi"  char to int*/ int ctoi(char c) { return c - '0'; }
/*"gcd"   MAX Euclidean */ ll gcd(ll a, ll b) {
  if (b == 0)
    return a;
  return gcd(b, a % b);
}
/*"lcm"   MIN*/ ll lcm(ll a, ll b) {
  ll g = gcd(a, b);
  return a / g * b;
}
/*"primecheck"If prime,return true.*/ bool primecheck(ll n) {
  if (n < 2)
    return false;
  else {
    for (int i = 2; i * i <= n; i++) {
      if (n % i == 0)
        return false;
    }
    return true;
  }
}
string reverserange(string s, ll a, ll b) {
  reverse(s.begin() + a - 1, s.begin() + b);
  return s;
}
ll modpow(ll a, ll n, ll mod) {
  ll res = 1;
  while (n > 0) {
    if (n % 2 == 1) {
      res = res * a % mod;
    }
    a = a * a % mod;
    n /= 2;
  }
  return res;
}
int main() {
  ll n;
  cin >> n;
  vector<int> retu;
  for (ll i = 2; i * i <= n; i++) {
    int x = 0;
    while (n % i == 0) {
      x++;
      n /= i;
    }
    retu.push_back(x);
  }
  if (n != 1)
    retu.push_back(1);
  ll ans = 0;
  for (int i = 0; i < retu.size(); i++) {
    int che = 1;
    while (che <= retu.at(i)) {
      ans++;
      retu.at(i) -= che;
      che++;
    }
  }
  cout << ans << endl;
}


Error: TLE

Fixed submission:

#include <bits/stdc++.h>
using namespace std;
#define ll long long
// memo  fixed  setprecision(20);
using vvll = vector<vector<ll>>;
ll mod = 1e9 + 7;
/*"itob" int to "N"base */ template <typename TypeInt>
string itob(const TypeInt v, int base) {
  static const char table[] = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ";
  string ret;
  static numeric_limits<TypeInt> t;
  TypeInt n = v;
  if (t.is_signed) {
    if (v < 0)
      n *= -1;
  }
  while (n >= base) {
    ret += table[n % base];
    n /= base;
  }
  ret += table[n];
  if (t.is_signed) {
    if (v < 0 && base == 10)
      ret += '-';
  }
  reverse(ret.begin(), ret.end());
  return ret;
}
/*"chmin" a = MAX*/ template <class T> inline bool chmin(T &a, T b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
/*"chmax" a = MIN*/ template <class T> inline bool chmax(T &a, T b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
/*"ctoi"  char to int*/ int ctoi(char c) { return c - '0'; }
/*"gcd"   MAX Euclidean */ ll gcd(ll a, ll b) {
  if (b == 0)
    return a;
  return gcd(b, a % b);
}
/*"lcm"   MIN*/ ll lcm(ll a, ll b) {
  ll g = gcd(a, b);
  return a / g * b;
}
/*"primecheck"If prime,return true.*/ bool primecheck(ll n) {
  if (n < 2)
    return false;
  else {
    for (int i = 2; i * i <= n; i++) {
      if (n % i == 0)
        return false;
    }
    return true;
  }
}
string reverserange(string s, ll a, ll b) {
  reverse(s.begin() + a - 1, s.begin() + b);
  return s;
}
ll modpow(ll a, ll n, ll mod) {
  ll res = 1;
  while (n > 0) {
    if (n % 2 == 1) {
      res = res * a % mod;
    }
    a = a * a % mod;
    n /= 2;
  }
  return res;
}
int main() {
  ll n;
  cin >> n;
  vector<ll> retu;
  for (int i = 2; i * i < n; i++) {
    if (n % i == 0) {
      ll che = 0;
      while (n % i == 0) {
        n /= i;
        che++;
      }
      retu.push_back(che);
    }
  }
  if (n != 1) {
    retu.push_back(1);
  }
  ll ans = 0;
  for (int i = 1; i < 100; i++) {
    for (int j = 0; j < retu.size(); j++) {
      if (retu.at(j) - i >= 0) {
        ans++;
        retu.at(j) -= i;
      }
    }
  }
  cout << ans << endl;
}