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: Accepted)

#include <bits/stdc++.h>

#pragma region Macro
#define rep(i, n) for(int i = 0; i < (int)(n); i++)
#define FOR(i, m, n) for(int i = m;i < n;i++)
#define SORT(v) sort(v.begin(), v.end())
#define pb(a) push_back(a)
#define eb(a) emplace_back(a)
#define vi vector<int>
#define vvi vector<vector<int>>
#define chmax(x,y) (x = max(x,y))
#define chmin(x,y) (x = min(x,y))

using namespace std;
typedef long long ll;
typedef pair<int, int> P;
#pragma endregion

map<ll,int> factP;

#pragma region Debug
void debug_out() { cout << endl; }

template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
	cout << H << " ";
	debug_out(T...);
}

#ifdef _DEBUG
#define debug(...) debug_out(__VA_ARGS__)
#else
#define debug(...)
#endif
#pragma endregion

// コンパイル時、エイリアス「debug」を使用 --> マクロが使えるように

class Calc
{
    // 宣言
    ll a;

    public:
        // 素因数分解
        void decompositPrime(ll a);
};

/*
 * 素因数分解
 */
void Calc::decompositPrime(ll n)
{
    // 割る数の初期値
    a = 2;
    // √n ≧ a ( n ≧ a * a ) の間ループ処理
    while (n >= a * a) {
        // a で割り切れたら、a は素因数
        // そして、割られる数を a で割る
        // a で割り切れなかったら、 a を 1 増加させる
        if (n % a == 0) {
            factP[a]++;
            n /= a;
        } else {
            a++;
        }
    }
    // 最後に残った n は素因数
    factP[n]++;
}

void solve(){
	#define int ll
	// ここに処理を記述
	// コンパイル時はエイリアス「gpp」--> c++17でコンパイル

	Calc obj;
	ll N;
	cin >> N;
	if(N == 1){
		cout << 0 << endl;
		return;
	}

	obj.decompositPrime(N);
	int ans = 0;

/*
	for(auto [key, value]: factP){
		debug(key, "/", value);
	}
*/

	for(auto [key, value]: factP){
		ll z = key;
		while(N % z == 0){
			N /= z;
			ans++;
			z *= key;
		}
	}

	cout << ans << endl;
}

signed main(){
	cin.tie(0);
	ios::sync_with_stdio(false);
	cout << fixed << setprecision(15);
	
	solve();
	return 0;
}