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<cstdio>
#include<vector>
#include<queue>
#include<map>
#include<set>
#include<unordered_map>
#include<stack>
#include<string>
#include<algorithm>
#include<functional>
#include<cstring>
#include<complex>
#include<bitset>
#include<iostream>
#include<cassert>
using namespace std;

typedef long long ll;
typedef unsigned long long ull;
typedef pair<ll, ll> P;
typedef pair<ll, P> Q;
typedef complex<double> C;
#define cx real()
#define cy imag()
#define FOR(i,a,b) for(ll i = (a);i<(b);(i)++)
#define _FOR(i,a,b) for(ll i = (b)-1;i>(a)-1;(i)--)
const ll INF = 1LL << 60;
const double DINF = 1e30;
const ll mod = 1000000007;
const ll dx[4] = { 1, 0, -1, 0 };
const ll dy[4] = { 0, -1, 0, 1 };
const C I = C(0, 1);
const double EPS = 1e-10;
const ll NCK_MAX = 4100000;

ll pw(ll i, ll j) {
	if (j == 0) return 1;
	if (j % 2 == 1) return i * pw(i, j - 1) % mod;
	ll tmp = pw(i, j / 2);
	return tmp * tmp % mod;
}

ll gcd(ll a, ll b) {
	if (b == 0) return a;
	return gcd(b, a % b);
}

ll extgcd(ll a, ll b, ll& x, ll& y) {
	if (b == 0) {
		x = 1, y = 0; return a;
	}
	ll q = a / b, g = extgcd(b, a - q * b, x, y);
	ll z = x - q * y;
	x = y;
	y = z;
	return g;
}

ll invmod(ll a, ll m) { // a^-1 mod m
	ll x, y;
	extgcd(a, m, x, y);
	x %= m;
	if (x < 0) x += m;
	return x;
}

ll* fac, * finv, * inv;

void nCk_init(ll mod) {
	fac = new ll[NCK_MAX];
	finv = new ll[NCK_MAX];
	inv = new ll[NCK_MAX];
	fac[0] = fac[1] = 1;
	finv[0] = finv[1] = 1;
	inv[1] = 1;
	for (ll i = 2; i < NCK_MAX; i++) {
		fac[i] = fac[i - 1] * i % mod;
		inv[i] = mod - inv[mod % i] * (mod / i) % mod;
		finv[i] = finv[i - 1] * inv[i] % mod;
	}
}

ll nCk(ll n, ll k, ll mod) {
	if (fac == NULL) nCk_init(mod);
	if (n < k) return 0;
	if (n < 0 || k < 0) return 0;
	return fac[n] * (finv[k] * finv[n - k] % mod) % mod;
}

template <typename T>
class Zip {
	vector<T> d;
	bool flag;
	void init() {
		sort(d.begin(), d.end());
		d.erase(unique(d.begin(), d.end()), d.end());
		flag = false;
	}
public:
	Zip() {
		flag = false;
	}
	void add(T x) {
		d.push_back(x);
		flag = true;
	}
	ll getNum(T x) {
		if (flag) init();
		return lower_bound(d.begin(), d.end(), x) - d.begin();
	}
	ll size() {
		if (flag) init();
		return (ll)d.size();
	}
};

class UnionFind {
	vector<ll> par, rank; // par > 0: number, par < 0: -par
public:
	UnionFind(ll n) : par(n, 1), rank(n, 0) {}
	ll getSize(ll x) {
		return par[find(x)];
	}
	ll find(ll x) {
		if (par[x] > 0) return x;
		return -(par[x] = -find(-par[x]));
	}
	void merge(ll x, ll y) {
		x = find(x);
		y = find(y);
		if (x == y) return;
		if (rank[x] < rank[y]) {
			par[y] += par[x];
			par[x] = -y;
		}
		else {
			par[x] += par[y];
			par[y] = -x;
			if (rank[x] == rank[y]) rank[x]++;
		}
	}
	bool isSame(ll x, ll y) {
		return find(x) == find(y);
	}
};


template <typename T>
class SegmentTree {
	ll n;
	vector<T> node;
	function<T(T, T)> fun, fun2;
	bool customChange;
	T outValue, initValue;
public:
	void init(ll num, function<T(T, T)> resultFunction, T init, T out, function<T(T, T)> changeFunction = NULL) {
		// changeFunction: (input, beforevalue) => newvalue
		fun = resultFunction;
		fun2 = changeFunction;
		customChange = changeFunction != NULL;
		n = 1;
		while (n < num) n *= 2;
		node.resize(2 * n - 1);
		fill(node.begin(), node.end(), init);
		outValue = out;
		initValue = init;
	}
	void valueChange(ll num, T value) {
		num += n - 1;
		if (customChange) node[num] = fun2(value, node[num]);
		else node[num] = value;
		while (num > 0) num = (num - 1) / 2, node[num] = fun(node[num * 2 + 1], node[num * 2 + 2]);
	}
	T rangeQuery(ll a, ll b, ll l = 0, ll r = -1, ll k = 0) { // [a, b)
		if (r == -1) r = n;
		if (a <= l && r <= b) return node[k];
		if (b <= l || r <= a) return outValue;
		ll mid = (l + r) / 2;
		return fun(rangeQuery(a, b, l, mid, 2 * k + 1), rangeQuery(a, b, mid, r, 2 * k + 2));
	}
};

template <typename T>
class Graph {
	struct edge { ll to; T cost; };
	struct edge_data { ll from, to; T cost; };

	ll v;
	vector<vector<edge>> e, re;
	vector<edge_data> ed;
	vector<bool> used;
	vector<ll> vs, cmp;
	bool isDirected, isMinasEdge;
public:
	Graph(ll _v, bool _isDirected = true, ll range_add = 0) {
		// range_add 0:no / 1:in / 2:out / 3:in+out
		//_v++;
		v = _v, isDirected = _isDirected; isMinasEdge = false;
		e.resize(v), re.resize(v);
	}
	void add_edge(ll s, ll t, T cost = 1) {
		e[s].push_back((edge) { t, cost });
		if (!isDirected) e[t].push_back((edge) { s, cost });
		else re[t].push_back((edge) { s, cost });
		ed.push_back((edge_data) { s, t, cost });
		if (cost < 0) isMinasEdge = true;
	}
	vector<T> dijkstra(ll s) {
		vector<T> d(v, INF);
		d[s] = 0;
		auto edge_cmp = [](const edge& a, const edge& b) { return a.cost > b.cost; };
		priority_queue<edge, vector<edge>, decltype(edge_cmp)> pq(edge_cmp);
		pq.push((edge) { s, 0 });
		while (!pq.empty()) {
			edge temp = pq.top(); pq.pop();
			if (d[temp.to] < temp.cost) continue;
			for (const edge& next : e[temp.to]) {
				T cost = temp.cost + next.cost;
				if (d[next.to] > cost) {
					d[next.to] = cost;
					pq.push((edge) { next.to, cost });
				}
			}
		}
		return d;
	}
	vector<T> bellmanford(ll s) {
		vector<T> d(v, INF);
		d[s] = 0;
		for (ll i = 0; i < v; i++) {
			for (const edge_data& temp : ed) {
				if (d[temp.from] != INF && d[temp.to] > d[temp.from] + temp.cost) d[temp.to] = d[temp.from] + temp.cost;
				if (!isDirected && d[temp.to] != INF && d[temp.from] > d[temp.to] + temp.cost) d[temp.from] = d[temp.to] + temp.cost;
			}
		}
		for (ll i = 0; i < v; i++) {
			for (const edge_data& temp : ed) {
				if (d[temp.from] != INF && d[temp.to] > d[temp.from] + temp.cost) d[temp.to] = -INF;
				if (!isDirected && d[temp.to] != INF && d[temp.from] > d[temp.to] + temp.cost) d[temp.from] = -INF;
			}
		}
		return d;
	}
	vector<T> shortest_path(ll s) {
		if (isMinasEdge) return bellmanford(s);
		else return dijkstra(s);
	}
	T kruskal() {
		// if (isDirected)
		UnionFind uf(v);
		auto edge_data_cmp = [](const edge_data& a, const edge_data& b) { return a.cost < b.cost; };
		sort(ed.begin(), ed.end(), edge_data_cmp);
		T ans = 0;
		for (const edge_data& temp : ed) {
			if (uf.isSame(temp.from, temp.to)) continue;
			uf.merge(temp.from, temp.to);
			ans += temp.cost;
		}
		return ans;
	}
	void scc_dfs(ll s) {
		used[s] = true;
		for (const edge& i : e[s]) if (!used[i.to]) scc_dfs(i.to);
		vs.push_back(s);
	}
	void scc_rdfs(ll s, ll k) {
		used[s] = true;
		cmp[s] = k;
		for (const edge& i : re[s]) if (!used[i.to]) scc_rdfs(i.to, k);
	}
	vector<ll> scc() {
		used.resize(v);
		fill(used.begin(), used.end(), false);
		cmp.resize(v);
		vs.clear();
		for (ll i = 0; i < v; i++) if (!used[i]) scc_dfs(i);
		used.resize(v);
		fill(used.begin(), used.end(), false);
		ll k = 0;
		for (ll i = vs.size() - 1; i >= 0; i--) if (!used[vs[i]]) scc_rdfs(vs[i], k++);
		return cmp;
	}
};

/*****main*****/
ll n,ans = 0;
int main(){
	cin >> n;
	ll _n = n;
	for(ll z=2;z*z<n+1;z++){
		ll counter = 0;
		while(_n%z==0)
			_n/=z,counter++;
		for(ll j = 1;j<counter+1;j++)
			ans++,counter-=j;
	}
	if (_n != 1) ans++;
	cout << ans << endl;
	return 0;
}