Problem:
Score : 400 points

Problem Statement

Given is a positive integer N. Consider repeatedly applying the operation below on N:

First, choose a positive integer z satisfying all of the conditions below:

z can be represented as z=p^e, where p is a prime number and e is a positive integer;

z divides N;

z is different from all integers chosen in previous operations.

Then, replace N with N/z.

Find the maximum number of times the operation can be applied.

Constraints

All values in input are integers.

1 \leq N \leq 10^{12}

Input

Input is given from Standard Input in the following format:

N

Output

Print the maximum number of times the operation can be applied.

Sample Input 1

24

Sample Output 1

3

We can apply the operation three times by, for example, making the following choices:

Choose z=2 (=2^1). (Now we have N=12.)

Choose z=3 (=3^1). (Now we have N=4.)

Choose z=4 (=2^2). (Now we have N=1.)

Sample Input 2

1

Sample Output 2

0

We cannot apply the operation at all.

Sample Input 3

64

Sample Output 3

3

We can apply the operation three times by, for example, making the following choices:

Choose z=2 (=2^1). (Now we have N=32.)

Choose z=4 (=2^2). (Now we have N=8.)

Choose z=8 (=2^3). (Now we have N=1.)

Sample Input 4

1000000007

Sample Output 4

1

We can apply the operation once by, for example, making the following choice:

z=1000000007 (=1000000007^1). (Now we have N=1.)

Sample Input 5

997764507000

Sample Output 5

7

Solution in C++ (GCC 9.2.1) (judge verdict: Time Limit Exceeded)

#include <bits/stdc++.h>
typedef uint64_t u64;
typedef int64_t i64;
typedef uint32_t u32;
typedef int32_t i32;

#define MAX_NUM (1000000007)
#define PI 3.14159265358979323846

using namespace std;

template <typename T>
static inline void ArrayInput(vector<T>& A) {
  for (auto itr = A.begin(); itr < A.end(); ++itr) cin >> *itr;
}

template <typename T>
static inline void ArrayPut(const vector<T>& A) {
  for (auto itr = A.begin(); itr < A.end(); ++itr) cout << *itr << " ";
  cout << endl;
}

template <typename T>
static inline T ArraySum(vector<T>& A) {
  T res = 0;
  for (auto itr = A.begin(); itr < A.end(); ++itr) res += *itr;
  return res;
}

bool Sec_compare(pair<uint64_t, uint64_t> a, pair<uint64_t, uint64_t> b) {
  if (a.second != b.second) {
    return a.second < b.second;
  } else {
    return a.first > b.first;
  }
}

u64 dec_dig(u64 num) {
  u64 res = 0;
  while (num > 0) {
    num /= 10;
    ++res;
  }
  return res;
}

i64 modinv(i64 a, i64 m) {
  i64 b = m, u = 1, v = 0;
  while (b) {
    i64 t = a / b;
    a -= t * b;
    swap(a, b);
    u -= t * v;
    swap(u, v);
  }
  u %= m;
  if (u < 0) u += m;
  return u;
}

u64 gcd(u64 a, u64 b) {
  if (a < b) {
    a ^= b;
    b ^= a;
    a ^= b;
  }

  return b ? gcd(b, a % b) : a;
}

i64 My_Comb(u64 n, u64 k, i64 m) {
  if (n < k) return 0;
  if (k == 0 || n == k) return 1;
  u64 res = 1;
  k = (n / 2 < k) ? n - k : k;
  for (u64 i = 1; i <= k; ++i)
    res = (((res * (n + 1 - i)) % m) * modinv(i, m)) % m;
  return res;
}

i64 My_Pow(u64 a, u64 n, i64 m) {
  u64 tmp = n, calc = 1;
  while (tmp > 0) {
    if (tmp % 2) {
      tmp--;
      calc *= a;
      calc %= m;
    } else {
      a *= a;
      a %= m;
      tmp /= 2;
    }
  }
  return calc;
}

class UnionFind {
 public:
  vector<u64> Par;
  vector<u64> sz;

  UnionFind(u64 n);
  u64 root(u64 x);
  bool same(u64 x, u64 y);
  void unite(u64 x, u64 y);
  u64 size(u64 x);
};

UnionFind::UnionFind(u64 n) {
  Par.resize(n);
  sz.assign(n, 1);
  for (u64 i = 0; i < n; ++i) Par[i] = i;
}

u64 UnionFind::root(u64 x) {
  if (Par[x] == x) {
    return x;
  } else {
    return Par[x] = root(Par[x]);
  }
}

bool UnionFind::same(u64 x, u64 y) { return root(x) == root(y); }

u64 UnionFind::size(u64 x) { return sz[root(x)]; }

void UnionFind::unite(u64 x, u64 y) {
  x = root(x);
  y = root(y);
  if (x == y) return;
  if (sz[x] < sz[y]) swap(x, y);
  sz[x] += sz[y];
  Par[y] = x;
}

template <typename T>
i64 BinSearch(vector<T>& V, i64 comp) {
  i64 l = 0, r = V.size() - 1;
  if (V[l] > V[r]) swap(l, r);
  if (V[l] >= comp) return l;
  if (V[r] <= comp) return r;
  while (abs(r - l) > 1) {
    i64 index = (l + r) / 2;
    if (V[index] == comp)
      return index;
    else if (V[index] > comp)
      r = index;
    else
      l = index;
  }
  if (abs(V[l] - comp) < abs(V[r] - comp))
    return l;
  else
    return r;
}

bool Judge(u64 n) {
  if (n == 1 || n == 0) return false;
  if (n == 2) return true;
  if (n % 2 == 0) return false;
  for (u64 i = 3; i * i < n; i += 2) {
    if (n % i == 0) return false;
  }
  return true;
}

int main() {
  cout << setprecision(18);
  u64 N;
  cin >> N;
  map<u64, u64> prime;
  set<u64> key;
  while (N % 2 == 0) {
    N /= 2;
    prime[2]++;
    key.insert(2);
  }
  for (u64 i = 3; N != 1; i += 2) {
    if (Judge(N)) {
      N = 1;
      prime[N]++;
      key.insert(N);
    }
    while (N % i == 0) {
      N /= i;
      prime[i]++;
      key.insert(i);
    }
  }
  u64 res = 0;
  for (auto itr = key.begin(); itr != key.end(); ++itr) {
    u64 cnt = 1;
    while (cnt <= prime[*itr]) {
      prime[*itr] -= cnt;
      ++cnt;
      ++res;
    }
  }
  cout << res << endl;
  return 0;
}