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: Wrong Answer)

//#pragma comment(linker, "/stack:200000000")
//#pragma GCC optimize("Ofast,unroll-loops,no-stack-protector,fast-math")
///#pragma GCC target("avx2")
#define _USE_MATH_DEFINES
#include <iostream>
#include <string>
#include <vector>
#include <map>
#include <set>
#include <algorithm>
#include <fstream>
#include <cmath>
#include <deque>
#include <list>
#include <stack>
#include <queue>
#include <iomanip>
#include <cassert>
#include <functional>
#include <ctime>
#include <unordered_map>
#include <unordered_set>
#include <bitset>
#include <climits>
#include <numeric>

using namespace std;
#define open_streams ifstream fin("olympiad.in");ofstream fout("olympiad.out")
#define close_streams fin.close();fout.close()
#define speed cout.tie(0);cin.tie(0);ios_base::sync_with_stdio(0)
#define ll long long
#define ull unsigned long long
#define all(a) a.begin(),a.end()
#define rall(a) a.rbegin(),a.rend()
#define mp(a,b) make_pair(a,b)
#define pb push_back
#define UNIQ(a) a.resize(unique(all(a)) - a.begin())
#define eps 1e-6
//const double PI = M_PI;
const int INF = INT_MAX;
const ll limit = 1LL*1e18;
const int MOD = 1e9 + 711;
const int MOD2 = 1e9 + 933;
//---------------------------------------------------------------------------
const int mod = 1e9 + 7;
const int maxn = 1e6 + 10;




set<ll> f(ll x) {
    ll d = 2;
    set<ll> res;
    while(d*d <= x) {
        if(x%d==0) {
            res.emplace(d);
        }
        ++d;
    }
    res.emplace(x);
    return res;
}
signed main() {
    speed;
    ll n;
    cin >> n;
    int ans = 0;
    set<ll> d = f(n);
    for(auto &x : d) {
        if(n %x == 0) {
            ++ans;
            n/=x;
        }
    }
    cout << ans;
    return 0;
}