C: Divisor Game

problem

tsutaj is trying to play about a few games.

In a divisor game, a natural number N of 2 or more is given first, and then the game progresses according to the following procedure.

* Declare one integer from the divisors of N other than N. However, at this time, it is not possible to declare a divisor of an integer that has already been declared.
* Repeat this as long as there is an integer that can be declared, and if there is nothing that can be declared, the game ends.



Find the minimum and maximum number of possible declarations before the end of the game.

Input format

Input is given on one line.


N

Constraint

* 2 \ leq N \ leq 10 ^ {12}



Output format

Output the minimum and maximum number of declarations on one line separated by spaces.

Input example 1


18

Output example 1


twenty five

The following is an example of setting the number of declarations to 2.

* Declare 9.
* Declare 6. (6 is not a divisor of 9, so it can be declared)



If you do this, any integer that is a divisor of 18 and not 18 will be a divisor of the integers you have declared, and the game will end.

Note that you cannot declare anything that is a divisor of an integer that you have already declared. For example, you cannot declare 3 after declaring 9. Because 3 is a divisor of 9.

Input example 2


99

Output example 2


twenty five

Input example 3


10000000019

Output example 3


1 1

The input may not fit in a 32-bit integer type.





Example

Input

18


Output

2 5

import java.util.Arrays;
import java.util.Random;

public class Main {
  private static void solve() {
    long n = nl();
    int[] primes = sieveAtkin(2000000);
    long[] d = enumDivisors(n, primes);
    long[][] f = factorX(n, primes);
    
    System.out.println(f.length + " " + (d.length - 1));
  }
  
  
  static long[][] factorX(long n, int[] primes)
  {
      long[][] ret = new long[20][2];
      int rp = 0;
      for(int p : primes){
          if((long)p * p > n)break;
          int i;
          for(i = 0;n % p == 0;n /= p, i++);
          if(i > 0){
              ret[rp][0] = p;
              ret[rp][1] = i;
              rp++;
          }
      }
      if(n == 1)return Arrays.copyOf(ret, rp);
      
      // P^2
      long sq = (long)Math.sqrt(n);
      for(long u = Math.max(2, sq-2);u <= sq+2;u++){
          if(u*u == n){
              ret[rp][0] = u;
              ret[rp][1] = 2;
              rp++;
              return Arrays.copyOf(ret, rp);
          }
      }
      
      // Prime
      if(doMirrorRabin(n)){
          ret[rp][0] = n;
          ret[rp][1] = 1;
          rp++;
          return Arrays.copyOf(ret, rp);
      }
      
      // P*Q
      long f = rho(n);
      if(f == -1)throw new ArithmeticException();
      if(f > n/f)f = n/f;
      ret[rp][0] = f; ret[rp][1] = 1; rp++;
      ret[rp][0] = n/f; ret[rp][1] = 1; rp++;
      return Arrays.copyOf(ret, rp);
  }
  
  public static long mul(long a, long b, long mod)
  {
      a %= mod;
      long ret = 0;
      int x = 63-Long.numberOfLeadingZeros(b);
      for(;x >= 0;x--){
          ret += ret;
          if(ret >= mod)ret -= mod;
          if(b<<~x<0){
              ret += a;
              if(ret >= mod)ret -= mod;
          }
      }
      return ret;
  }
  
  public static boolean doMirrorRabin(long n)
  {
//    int[] P = {2, 7, 61}; // n<4759123141
      int[] P = {2,3,5,7,11,13,17,19,23}; // n=long
      int s = Long.numberOfTrailingZeros(n-1);
      long d = n-1>>s;
      outer:
      for(int a : P){
          if(a >= n)continue;
          
          long mul = a;
          long ad = 1;
          for(long e = d;e > 0;e>>>=1){
              if((e&1)==1)ad = mul(ad, mul, n);
              mul = mul(mul, mul, n);
          }
          if(ad == 1)continue;
          
          for(int r = 0;r < s;r++){
              if(ad == n-1)continue outer;
              ad = mul(ad, ad, n);
          }
          return false;
      }
      return true;
  }

  static long rho(long n)
  {
      Random gen = new Random();
      for(int u = 0;u < 100;u++){
          long ran = (gen.nextLong()&Long.MAX_VALUE) % n;
          long x = 2, y = 2, d = 1;
          while(d == 1){
              x = (mul(x, x, n)+ran)%n;
              y = (mul(y, y, n)+ran)%n;
              y = (mul(y, y, n)+ran)%n;
              d = gcd(Math.abs(x-y), n);
          }
          if(d < n)return d;
      }
      return -1;
  }
  
  public static long gcd(long a, long b) {
      while (b > 0){
          long c = a;
          a = b;
          b = c % b;
      }
      return a;
  }
  
  public static long[] enumDivisors(long n, int[] primes)
  {
      int m = 1;
      long[] divs = {1L};
      int t = 1;
      long u = n;
      for(int p : primes){
          if((long)p*p > u)break;
          int e = 0;
          while(u % p == 0){
              u /= p;
              e++;
          }
          if(e > 0){
              divs = Arrays.copyOf(divs, t*(e+1));
              for(int q = t-1;q >= 0;q--){
                  long b = divs[q];
                  for(int k = 0;k < e;k++){
                      b *= p;
//                    if((long)b*b <= n)divs[t++] = b;
                      divs[t++] = b;
                  }
              }
              m *= e+1;
          }
      }
      if(u > 1){
          long p = u;
          int e = 1;
          divs = Arrays.copyOf(divs, t*(e+1));
          for(int q = t-1;q >= 0;q--){
              long b = divs[q];
              for(int k = 0;k < e;k++){
                  b *= p;
//                if((long)b*b <= n)divs[t++] = b;
                  divs[t++] = b;
              }
          }
          m *= e+1;
      }
      
      return Arrays.copyOf(divs, t);
  }   
  
  public static int[] sieveAtkin(int size) {
    boolean[] isPrime = new boolean[size + 1];
    int sqrtN = (int) Math.sqrt(size);
    int n;
    for (int x = 1; x <= sqrtN; ++x) {
        for (int y = 1; y <= sqrtN; ++y) {
            n = 4 * x * x + y * y;
            if (n <= size && (n % 12 == 1 || n % 12 == 5)) {
                isPrime[n] = !isPrime[n];
            }
            n = 3 * x * x + y * y;
            if (n <= size && n % 12 == 7) {
                isPrime[n] = !isPrime[n];
            }
            n = 3 * x * x - y * y;
            if (x > y && n <= size && n % 12 == 11) {
                isPrime[n] = !isPrime[n];
            }
        }
    }

    for (n = 5; n <= sqrtN; ++n) {
        if (isPrime[n]) {
            for (int k = n * n; k <= size; k += n * n) {
                isPrime[k] = false;
            }
        }
    }
    isPrime[2] = isPrime[3] = true;
    
    int[] ret = new int[size];
    int count = 0;
    for (int i = 1; i < size; i ++) {
        if (isPrime[i]) {
            ret[count ++] = i;
        }
    }
    return Arrays.copyOf(ret, count);
}

  public static void main(String[] args) {
    new Thread(null, new Runnable() {
      @Override
      public void run() {
        long start = System.currentTimeMillis();
        String debug = args.length > 0 ? args[0] : null;
        if (debug != null) {
          try {
            is = java.nio.file.Files.newInputStream(java.nio.file.Paths.get(debug));
          } catch (Exception e) {
            throw new RuntimeException(e);
          }
        }
        reader = new java.io.BufferedReader(new java.io.InputStreamReader(is), 32768);
        solve();
        out.flush();
        tr((System.currentTimeMillis() - start) + "ms");
      }
    }, "", 64000000).start();
  }

  private static java.io.InputStream is = System.in;
  private static java.io.PrintWriter out = new java.io.PrintWriter(System.out);
  private static java.util.StringTokenizer tokenizer = null;
  private static java.io.BufferedReader reader;

  public static String next() {
    while (tokenizer == null || !tokenizer.hasMoreTokens()) {
      try {
        tokenizer = new java.util.StringTokenizer(reader.readLine());
      } catch (Exception e) {
        throw new RuntimeException(e);
      }
    }
    return tokenizer.nextToken();
  }

  private static double nd() {
    return Double.parseDouble(next());
  }

  private static long nl() {
    return Long.parseLong(next());
  }

  private static int[] na(int n) {
    int[] a = new int[n];
    for (int i = 0; i < n; i++)
      a[i] = ni();
    return a;
  }

  private static char[] ns() {
    return next().toCharArray();
  }

  private static long[] nal(int n) {
    long[] a = new long[n];
    for (int i = 0; i < n; i++)
      a[i] = nl();
    return a;
  }

  private static int[][] ntable(int n, int m) {
    int[][] table = new int[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[i][j] = ni();
      }
    }
    return table;
  }

  private static int[][] nlist(int n, int m) {
    int[][] table = new int[m][n];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[j][i] = ni();
      }
    }
    return table;
  }

  private static int ni() {
    return Integer.parseInt(next());
  }

  private static void tr(Object... o) {
    if (is != System.in)
      System.out.println(java.util.Arrays.deepToString(o));
  }
}

