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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

/*
    Author: Anthony Ngene
    Created: 11/07/2020 - 16:14
*/
import java.io.*;
import java.util.*;

public class Main {
    private static final FastReader in = new FastReader();
    private static final FastWriter out = new FastWriter();
    static ArrayList<Integer>[] adj;

    public static void main(String[] args) throws IOException {

        long n = in.longNext();
        ArrayList<Integer> primes = generatePrimes(n);
//        out.println(primes);

        long ans = 0;
        for (long prime : primes) {
            if (n % prime == 0) {
                long p = prime;
                while (n % p == 0) {
                    ans++;
                    n /= p;
                    p *= prime;
                }
                while (n % prime == 0) n /= prime;
            }
        }
        if (n > 1) ans++;
        out.println(ans);

        out.close();
    }

    static ArrayList<Integer> generatePrimes(long num) {
        int n = (int)Math.floor(Math.sqrt(num));
        int[] lp = new int[n + 1];
        ArrayList<Integer> pr = new ArrayList<>();

        for (int i = 2; i <= n; ++i) {
            if (lp[i] == 0) {
                lp[i] = i;
                pr.add(i);
            }
            for (int j = 0; j < pr.size() && pr.get(j) <= lp[i] && i * pr.get(j) <= n; ++j) {
                lp[i * pr.get(j)] = pr.get(j);
            }
        }
        return pr;
    }


    static class FastWriter {
        private static final int IO_BUFFERS = 128 * 1024;
        private final StringBuilder out;

        public FastWriter() {
            out = new StringBuilder(IO_BUFFERS);
        }

        public FastWriter p(Object object) {
            out.append(object);
            return this;
        }

        public FastWriter p(String format, Object... args) {
            out.append(String.format(format, args));
            return this;
        }

        public FastWriter println(Object object) {
            out.append(object).append("\n");
            return this;
        }

        public void close() throws IOException {
            System.out.print(out);
        }
    }

    static class FastReader {
        private static final int IO_BUFFERS = 128 * 1024;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;

        public FastReader() {
            din = new DataInputStream(System.in);
            buffer = new byte[IO_BUFFERS];
            bufferPointer = bytesRead = 0;
        }

        public FastReader(String file_name) throws IOException {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[IO_BUFFERS];
            bufferPointer = bytesRead = 0;
        }

        public String readLine() throws IOException {
            byte[] buf = new byte[64]; // line length
            int cnt = 0, c;
            while ((c = read()) != -1) {
                if (c == '\n') break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }

        public int intNext() throws IOException {
            int ret = 0;
            byte c = read();
            while (c <= ' ') c = read();
            boolean neg = (c == '-');
            if (neg) c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');

            if (neg) return -ret;
            return ret;
        }

        public long longNext() throws IOException {
            long ret = 0;
            byte c = read();
            while (c <= ' ') c = read();
            boolean neg = (c == '-');
            if (neg) c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (neg) return -ret;
            return ret;
        }

        public double doubleNext() throws IOException {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ') c = read();
            boolean neg = (c == '-');
            if (neg) c = read();

            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');

            if (c == '.') {
                while ((c = read()) >= '0' && c <= '9') {
                    ret += (c - '0') / (div *= 10);
                }
            }

            if (neg) return -ret;
            return ret;
        }

        public int[] nextIntArray(final int n) throws IOException {
            final int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = intNext();
            return a;
        }

        public long[] nextLongArray(final int n) throws IOException {
            final long[] a = new long[n];
            for (int i = 0; i < n; i++)
                a[i] = longNext();
            return a;
        }

        public ArrayList<Integer>[] adjacencyList(int n, int m) throws IOException {
            ArrayList<Integer>[] adj = new ArrayList[n + 1];
            for (int i = 1; i <= n; i++) adj[i] = new ArrayList<>();
            for (int i = 0; i < m; i++) {
                int a = intNext(), b = intNext();
                adj[a].add(b);
                adj[b].add(a);
            }
            return adj;
        }

        private void fillBuffer() throws IOException {
            bytesRead = din.read(buffer, bufferPointer = 0, IO_BUFFERS);
            if (bytesRead == -1) buffer[0] = -1;
        }

        private byte read() throws IOException {
            if (bufferPointer == bytesRead) fillBuffer();
            return buffer[bufferPointer++];
        }

        public void close() throws IOException {
            if (din == null) return;
            din.close();
        }
    }

    static class util {
        public static int upperBound(long[] array, long obj) {
            int l = 0, r = array.length - 1;
            while (r - l >= 0) {
                int c = (l + r) / 2;
                if (obj < array[c]) {
                    r = c - 1;
                } else {
                    l = c + 1;
                }
            }
            return l;
        }

        public static int upperBound(ArrayList<Long> array, long obj) {
            int l = 0, r = array.size() - 1;
            while (r - l >= 0) {
                int c = (l + r) / 2;
                if (obj < array.get(c)) {
                    r = c - 1;
                } else {
                    l = c + 1;
                }
            }
            return l;
        }

        public static int lowerBound(long[] array, long obj) {
            int l = 0, r = array.length - 1;
            while (r - l >= 0) {
                int c = (l + r) / 2;
                if (obj <= array[c]) {
                    r = c - 1;
                } else {
                    l = c + 1;
                }
            }
            return l;
        }

        public static int lowerBound(ArrayList<Long> array, long obj) {
            int l = 0, r = array.size() - 1;
            while (r - l >= 0) {
                int c = (l + r) / 2;
                if (obj <= array.get(c)) {
                    r = c - 1;
                } else {
                    l = c + 1;
                }
            }
            return l;
        }

        public static void print(long[] arr) {
            System.out.println(Arrays.toString(arr));
        }

        public static void print(int[] arr) {
            System.out.println(Arrays.toString(arr));
        }

        public static void print(char[] arr) {
            System.out.println(Arrays.toString(arr));
        }
    }

    static class Tuple implements Comparable<Tuple> {
        int a;
        int b;

        public Tuple(int a, int b) {
            this.a = a;
            this.b = b;
        }

        public int getA() {
            return a;
        }

        public int getB() {
            return b;
        }

        public int compareTo(Tuple other) {
            if (this.a == other.a) return Integer.compare(this.b, other.b);
            return Integer.compare(this.a, other.a);
        }

        @Override
        public int hashCode() {
            return Arrays.deepHashCode(new Integer[]{a, b});
        }

        @Override
        public boolean equals(Object o) {
            if (!(o instanceof Tuple)) return false;
            Tuple pairo = (Tuple) o;
            return (this.a == pairo.a && this.b == pairo.b);
        }

        @Override
        public String toString() {
            return String.format("%d,%d  ", this.a, this.b);
        }
    }

    static class CF_Reader {
        BufferedReader br;
        StringTokenizer st;

        public CF_Reader() throws IOException {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        public ArrayList<Integer>[] adjacencyList(int n, int m) throws IOException {
            ArrayList<Integer>[] adj = new ArrayList[n + 1];
            for (int i = 1; i <= n; i++) adj[i] = new ArrayList<>();
            for (int i = 0; i < m; i++) {
                int a = intNext(), b = intNext();
                adj[a].add(b);
                adj[b].add(a);
            }
            return adj;
        }

        String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine().trim());
            return st.nextToken();
        }

        long longNext() throws IOException {
            return Long.parseLong(next());
        }

        int intNext() throws IOException {
            return Integer.parseInt(next());
        }

        double doubleNext() throws IOException {
            return Double.parseDouble(next());
        }

        char charNext() throws IOException {
            return next().charAt(0);
        }

        public int[] nextIntArray(final int n) throws IOException {
            final int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = intNext();
            return a;
        }

        public long[] nextLongArray(final int n) throws IOException {
            final long[] a = new long[n];
            for (int i = 0; i < n; i++)
                a[i] = longNext();
            return a;
        }

        String line() throws IOException {
            return br.readLine().trim();
        }
    }

    static <T> T[][] deepCopy(T[][] matrix) {
        return Arrays.stream(matrix).map(el -> el.clone()).toArray($ -> matrix.clone());
    }

    static int[][] deepCopy(int[][] matrix) {
        return Arrays.stream(matrix).map(int[]::clone).toArray($ -> matrix.clone());
    }
}