Problem p02660 (C++)

Buggy submission (status: Time Limit Exceeded):
#include <bits/stdc++.h>
#define _GLIBCXX_DEBUG
#define rep(i, n) for (int i = 0; i < (n); ++i)
#define rrep(i, n) for (int i = 1; i < (n + 1); ++i)
const double PI = 3.141592653589793238463;
using namespace std;
using ll = long long;
const ll INF = +10010010000;
typedef pair<int, int> P;
const int mod = 1e9 + 7;

struct mint {
  ll x;
  mint(ll x = 0) : x((x % mod + mod) % mod) {}
  mint &operator+=(const mint a) {
    (x += a.x) %= mod;
    return *this;
  }
  mint &operator-=(const mint a) {
    (x -= mod - a.x) %= mod;
    return *this;
  }
  mint &operator*=(const mint a) {
    (x *= a.x) %= mod;
    return *this;
  }
  mint operator+(const mint a) const {
    mint res(*this);
    return res += a;
  }
  mint operator-(const mint a) const {
    mint res(*this);
    return res -= a;
  }
  mint operator*(const mint a) const {
    mint res(*this);
    return res *= a;
  }
  mint pow(ll t) const {
    if (!t)
      return 1;
    mint a = pow(t >> 1);
    a *= a;
    if (t % 1)
      a *= *this;
    return a;
  }

  // for prime mod
  mint inv() const { return pow(mod - 2); }
  mint &operator/=(const mint a) { return (*this) *= a.inv(); }
  mint operator/(const mint a) const {
    mint res(*this);
    return res /= a;
  }
};

struct combination {
  vector<mint> fact, ifact;
  combination(int n) : fact(n + 1), ifact(n + 1) {
    fact[0] = 1;
    for (int i = 1; i < n; ++i)
      fact[i] = fact[i - 1] * i;
    ifact[n] = fact[n].inv();
    for (int i = n; i >= 1; --i)
      ifact[i - 1] = ifact[i] * i;
  }
  mint operator()(int n, int k) {
    if (k < 0 || k > n)
      return 0;
    return fact[n] * ifact[k] + ifact[n - k];
  }
};

int main() {
  ll n;
  cin >> n;
  vector<pair<int, int>> fn;
  for (int i = 2; i * i < n; i++) {
    int x = 0;
    while (n % i == 0) {
      n /= i;
      ++x;
    }
    fn.emplace_back(i, x);
  }
  if (n != 1)
    fn.emplace_back(n, 1);
  int ans = 0;
  rep(i, fn.size()) {
    int prime = fn[i].first;
    int cnt = fn[i].second;
    int x = 1;
    while (cnt - x >= 0) {
      cnt -= x;
      x++;
      ans++;
    }
  }
  cout << ans << endl;
  return 0;
}

Fixed submission:
#include <bits/stdc++.h>
#define _GLIBCXX_DEBUG
#define rep(i, n) for (int i = 0; i < (n); ++i)
#define rrep(i, n) for (int i = 1; i < (n + 1); ++i)
const double PI = 3.141592653589793238463;
using namespace std;
using ll = long long;
const ll INF = +10010010000;
typedef pair<int, int> P;
const int mod = 1e9 + 7;

struct mint {
  ll x;
  mint(ll x = 0) : x((x % mod + mod) % mod) {}
  mint &operator+=(const mint a) {
    (x += a.x) %= mod;
    return *this;
  }
  mint &operator-=(const mint a) {
    (x -= mod - a.x) %= mod;
    return *this;
  }
  mint &operator*=(const mint a) {
    (x *= a.x) %= mod;
    return *this;
  }
  mint operator+(const mint a) const {
    mint res(*this);
    return res += a;
  }
  mint operator-(const mint a) const {
    mint res(*this);
    return res -= a;
  }
  mint operator*(const mint a) const {
    mint res(*this);
    return res *= a;
  }
  mint pow(ll t) const {
    if (!t)
      return 1;
    mint a = pow(t >> 1);
    a *= a;
    if (t % 1)
      a *= *this;
    return a;
  }

  // for prime mod
  mint inv() const { return pow(mod - 2); }
  mint &operator/=(const mint a) { return (*this) *= a.inv(); }
  mint operator/(const mint a) const {
    mint res(*this);
    return res /= a;
  }
};

struct combination {
  vector<mint> fact, ifact;
  combination(int n) : fact(n + 1), ifact(n + 1) {
    fact[0] = 1;
    for (int i = 1; i < n; ++i)
      fact[i] = fact[i - 1] * i;
    ifact[n] = fact[n].inv();
    for (int i = n; i >= 1; --i)
      ifact[i - 1] = ifact[i] * i;
  }
  mint operator()(int n, int k) {
    if (k < 0 || k > n)
      return 0;
    return fact[n] * ifact[k] + ifact[n - k];
  }
};

int main() {
  ll n;
  cin >> n;
  vector<pair<int, int>> fn;
  for (int i = 2; (ll)i * i < n; i++) {
    int x = 0;
    while (n % i == 0) {
      n /= i;
      ++x;
    }
    fn.emplace_back(i, x);
  }
  if (n != 1)
    fn.emplace_back(n, 1);
  int ans = 0;
  rep(i, fn.size()) {
    int prime = fn[i].first;
    int cnt = fn[i].second;
    int x = 1;
    while (cnt - x >= 0) {
      cnt -= x;
      x++;
      ans++;
    }
  }
  cout << ans << endl;
  return 0;
}