



'''simple docstring'''





from __future__ import annotations

import math




def lowerCAmelCase    (__A):



     """simple docstring"""



     if num <= 0:
          _a           =    F'''{num}: Invalid input, please enter a positive integer.'''
          raise ValueError(__A)

     _a           =    [True] * (num + 1)
     _a           =    []
     _a           =    2
     _a           =    int(math.sqrt(__A))

     while start <= end:
          # If start is a prime
          if sieve[start] is True:
               prime.append(__A)

               # Set multiples of start be False
               for i in range(start * start    ,      num + 1    ,      __A):
                    if sieve[i] is True:
                         _a           =    False

          start += 1

     for j in range(end + 1    ,      num + 1):
          if sieve[j] is True:
               prime.append(__A)

     return prime


if __name__ == "__main__":
  print(prime_sieve(int(input("Enter a positive integer: ").strip())))








'''simple docstring'''





def lowerCAmelCase    (__A):



     """simple docstring"""



     if not isinstance(__A    ,      __A):
          raise ValueError('''multiplicative_persistence() only accepts integral values''')
     if num < 0:
          raise ValueError('''multiplicative_persistence() does not accept negative values''')

     _a           =    0
     _a           =    str(__A)

     while len(__A) != 1:
          _a           =    [int(__A) for i in num_string]

          _a           =    1
          for i in range(0    ,      len(__A)):
               total *= numbers[i]

          _a           =    str(__A)

          steps += 1
     return steps




def lowerCAmelCase    (__A):



     """simple docstring"""



     if not isinstance(__A    ,      __A):
          raise ValueError('''additive_persistence() only accepts integral values''')
     if num < 0:
          raise ValueError('''additive_persistence() does not accept negative values''')

     _a           =    0
     _a           =    str(__A)

     while len(__A) != 1:
          _a           =    [int(__A) for i in num_string]

          _a           =    0
          for i in range(0    ,      len(__A)):
               total += numbers[i]

          _a           =    str(__A)

          steps += 1
     return steps


if __name__ == "__main__":
  import doctest

  doctest.testmod()



