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)

/* Bismillahirrahmanirrahim */
/* Author : Jehian Norman Saviero (@Reiva5) */
#include <bits/stdc++.h>
 
// MACROS SAMPAH
#define Jehian using
#define Norman namespace
#define Saviero std
 
Jehian Norman Saviero;
 
// MACROS TYPE
typedef long l;
typedef long long ll;
typedef unsigned long ul;
typedef unsigned long long ull;
typedef long double ld;
typedef pair<int,int> pi;
typedef pair<l,l> pl;
typedef pair<ll,ll> pll;
typedef vector<int> vi;
typedef vector<l> vl;
typedef vector<ll> vll;
 
// MACROS FOR PRINT
#define nl printf("\n")
#define sp printf(" ")
 
// MACROS FOR ATTRIBUTE
#define fi first
#define se second
 
// MACROS FOR FUNCTION AND METHOD
#define eb emplace_back
#define mp make_pair
#define pb push_back
#define pf push_front
#define ppb pop_back
#define ppf pop_front
#define ALL(x) (x).begin(), (x).end()
#define ALLN(x,n) (x), (x)+(n)
#define CUBE(x) (SQR(x)*(x))
#define SET(x,y) for (int _qwe = sizeof(x)/sizeof(x[0]); _qwe; ) x[--_qwe] = (y)
#define SQR(x) ((x)*(x))
#define SSORT(x,sz) sort(ALLN(x,sz))
#define RESET(x) memset((x), 0, sizeof(x))
#define VSORT(x) sort(ALL(x))
 
// MACROS READ INPUT
#define sci(x) scanf("%d", &x)
#define scl(x) scanf("%ld", &x)
#define scll(x) scanf("%lld", &x)
#define scul(x) scl(x)
#define scull(x) scll(x)

vll dat;
unordered_map<ll, unordered_map<ll, ll>> dp;

ll eval(ll pos, ll curr) {
	if (pos == dat.size()) return 0;
	if (dp[pos].find(curr) != dp[pos].end()) return dp[pos][curr];
	ll &val = dp[pos][curr];
	val = eval(pos+1, curr);
	if (curr % dat[pos] == 0) {
		val = max(val, 1+eval(pos+1, curr/dat[pos]));
	}
	return val;
}

int main() {
	ll N;
	scll(N);
	for (ll i = 1; i * i <= N; ++i) {
		if (N % i) continue;
		if (i != 1) {
			dat.pb(i);
		}
		ll ot = N/i;
		if (i != ot) {
			dat.pb(ot);
		}
	}
	VSORT(dat);
	printf("%lld\n", eval(0, N));
	return 0;
}