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

// C
#ifndef _GLIBCXX_NO_ASSERT
#include <cassert>
#endif
#include <cctype>
#include <cerrno>
#include <cfloat>
#include <ciso646>
#include <climits>
#include <clocale>
#include <cmath>
#include <csetjmp>
#include <csignal>
#include <cstdarg>
#include <cstddef>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>

#if __cplusplus >= 201103L
#include <ccomplex>
#include <cfenv>
#include <cinttypes>
// #include <cstdalign>
#include <cstdbool>
#include <cstdint>
#include <ctgmath>
#include <cwchar>
#include <cwctype>
#endif

// C++
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <exception>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iosfwd>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <locale>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <stdexcept>
#include <streambuf>
#include <string>
#include <typeinfo>
#include <utility>
#include <valarray>
#include <vector>

#if __cplusplus >= 201103L
#include <array>
#include <atomic>
#include <chrono>
#include <condition_variable>
#include <forward_list>
#include <future>
#include <initializer_list>
#include <mutex>
#include <random>
#include <ratio>
#include <regex>
#include <scoped_allocator>
#include <system_error>
#include <thread>
#include <tuple>
#include <type_traits>
#include <typeindex>
#include <unordered_map>
#include <unordered_set>
#endif

using namespace std;
typedef long long int ll;
typedef unsigned long long ull;
typedef long double ld;
#define REP(i, n) for (ll i = 0; i < (n); i++)
#define REPR(i, n) for (ll i = n; i >= 0; i--)
#define FOR(i, m, n) for (ll i = m; i < n; i++)
#define ALL(n) begin(n), end(n)
#define IN(a, x, b) (a <= x && x < b)
#define INIT                                                                   \\
  std::ios::sync_with_stdio(false);                                            \\
  std::cin.tie(0);
template <class T> inline T CHMAX(T &a, const T b) {
  return a = (a < b) ? b : a;
}
template <class T> inline T CHMIN(T &a, const T b) {
  return a = (a > b) ? b : a;
}

const long double EPS = 1e-10;
const long long INF = 1e18;
const long double PI = acos(-1.0L);
const long long MOD = 1000000007;

// ll prim_num[1000010];
ll ans;

void all_devide(ll N) {

  for (long long a = 2; a * a <= N; ++a) {
    if (N % a != 0) {
      continue;
    }
    ll ans_base = 1;
    long long ex = 0; // 指数

    // 割れる限り割り続ける
    while (N % a == 0) {
      ++ex;
      N /= a;
      if (ex >= ans_base) {
        ans++;
        ans_base++;
        ex = 0;
      }
    }
  }
  if (N != 1) {
    ans++;
  }
  /*
      for (int i = 2; i <= input; i++) {
      bool no_prim_flg = true;
      ll ans_base=1;
      ll num=0;

              while (input%i == 0) { // 素数で割り切れなくなるまで割っていく
          //prim_num[i]++;
          num++;
                      input /= i;
          no_prim_flg = false;
          if(num >= ans_base){
              ans++;
              ans_base++;
              num=0;
          }
              }

      // rootnを超えてるなら素数なので終了する。
      if(i*i > base ){
          if(no_prim_flg){
              ans++;
          }
          break;
      }
      }
  */
}

int main(void) {
  ll n;
  cin >> n;
  all_devide(n);

  cout << ans << endl;

  return 0;
}

Error: TLE

Fixed submission:

// C
#ifndef _GLIBCXX_NO_ASSERT
#include <cassert>
#endif
#include <cctype>
#include <cerrno>
#include <cfloat>
#include <ciso646>
#include <climits>
#include <clocale>
#include <cmath>
#include <csetjmp>
#include <csignal>
#include <cstdarg>
#include <cstddef>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>

#if __cplusplus >= 201103L
#include <ccomplex>
#include <cfenv>
#include <cinttypes>
// #include <cstdalign>
#include <cstdbool>
#include <cstdint>
#include <ctgmath>
#include <cwchar>
#include <cwctype>
#endif

// C++
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <exception>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iosfwd>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <locale>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <stdexcept>
#include <streambuf>
#include <string>
#include <typeinfo>
#include <utility>
#include <valarray>
#include <vector>

#if __cplusplus >= 201103L
#include <array>
#include <atomic>
#include <chrono>
#include <condition_variable>
#include <forward_list>
#include <future>
#include <initializer_list>
#include <mutex>
#include <random>
#include <ratio>
#include <regex>
#include <scoped_allocator>
#include <system_error>
#include <thread>
#include <tuple>
#include <type_traits>
#include <typeindex>
#include <unordered_map>
#include <unordered_set>
#endif

using namespace std;
typedef long long int ll;
typedef unsigned long long ull;
typedef long double ld;
#define REP(i, n) for (ll i = 0; i < (n); i++)
#define REPR(i, n) for (ll i = n; i >= 0; i--)
#define FOR(i, m, n) for (ll i = m; i < n; i++)
#define ALL(n) begin(n), end(n)
#define IN(a, x, b) (a <= x && x < b)
#define INIT                                                                   \\
  std::ios::sync_with_stdio(false);                                            \\
  std::cin.tie(0);
template <class T> inline T CHMAX(T &a, const T b) {
  return a = (a < b) ? b : a;
}
template <class T> inline T CHMIN(T &a, const T b) {
  return a = (a > b) ? b : a;
}

const long double EPS = 1e-10;
const long long INF = 1e18;
const long double PI = acos(-1.0L);
const long long MOD = 1000000007;

// ll prim_num[1000010];
ll ans;

void all_devide(ll input) {
  ll base = input;
  for (int i = 2; i <= input; i++) {
    bool no_prim_flg = true;
    ll ans_base = 1;
    ll num = 0;

    while (input % i == 0) { // 素数で割り切れなくなるまで割っていく
      // prim_num[i]++;
      num++;
      input /= i;
      no_prim_flg = false;
      if (num >= ans_base) {
        ans++;
        ans_base++;
        num = 0;
      }
    }

    // rootnを超えてるなら素数なので終了する。
    if (i * i > base) {
      if (no_prim_flg) {
        ans++;
      }
      break;
    }
  }
}

int main(void) {
  ll n;
  cin >> n;
  all_devide(n);

  cout << ans << endl;

  return 0;
}