





import math




def 			lowerCAmelCase_			(				UpperCamelCase_	)  ->		Tuple:
       UpperCamelCase_ 							=	0
       if n % 2 == 0:
              count += 1
              while n % 2 == 0:
                     UpperCamelCase_ 							=	int(n / 2	)
    # the n input value must be odd so that
    # we can skip one element (ie i += 2)

       UpperCamelCase_ 							=	3

       while i <= int(math.sqrt(UpperCamelCase_	)	):
              if n % i == 0:
                     count += 1
                     while n % i == 0:
                            UpperCamelCase_ 							=	int(n / i	)
              UpperCamelCase_ 							=	i + 2

       # this condition checks the prime
       # number n is greater than 2

       if n > 2:
              count += 1
       return count


if __name__ == "__main__":
     _UpperCAmelCase										=					5_1_2_4_2_1_8_3
     print(f'''The number of distinct prime factors is/are {exact_prime_factor_count(n)}''')
     print(f'''The value of log(log(n)) is {math.log(math.log(n)):.4f}''')







from __future__ import annotations





def 							lowerCamelCase    (							UpperCAmelCase_	:      str   ,       UpperCAmelCase_	:      dict[str, str]      )->			str:

       """simple docstring"""




       a   ,      a   ,      a			   ="""""", """""", """"""
       a			   =[]

       for character in message_part:
              tmp.append(character_to_number[character]      )

       for each in tmp:
              one += each[0]
              two += each[1]
              three += each[2]

       return one + two + three





def 							lowerCamelCase    (							UpperCAmelCase_	:      str   ,       UpperCAmelCase_	:      dict[str, str]      )->			tuple[str, str, str]:

       """simple docstring"""




       a   ,      a			   ="""""", """"""
       a			   =[]

       for character in message_part:
              this_part += character_to_number[character]

       for digit in this_part:
              tmp += digit
              if len(UpperCAmelCase_      ) == len(UpperCAmelCase_      ):
                     result.append(UpperCAmelCase_      )
                     a			   =""""""

       return result[0], result[1], result[2]





def 							lowerCamelCase    (							UpperCAmelCase_	:      str   ,       UpperCAmelCase_	:      str      )->			tuple[str, str, dict[str, str], dict[str, str]]:

       """simple docstring"""




       a			   =alphabet.replace(""" """   ,       """"""      ).upper()
       a			   =message.replace(""" """   ,       """"""      ).upper()

       # Check length and characters
       if len(UpperCAmelCase_      ) != 27:
              raise KeyError("""Length of alphabet has to be 27."""      )
       for each in message:
              if each not in alphabet:
                     raise ValueError("""Each message character has to be included in alphabet!"""      )

    # Generate dictionares
       a			   =(
           """111""",
           """112""",
           """113""",
           """121""",
           """122""",
           """123""",
           """131""",
           """132""",
           """133""",
           """211""",
           """212""",
           """213""",
           """221""",
           """222""",
           """223""",
           """231""",
           """232""",
           """233""",
           """311""",
           """312""",
           """313""",
           """321""",
           """322""",
           """323""",
           """331""",
           """332""",
           """333""",
       )
       a			   ={}
       a			   ={}
       for letter, number in zip(UpperCAmelCase_   ,       UpperCAmelCase_      ):
              a			   =number
              a			   =letter

       return message, alphabet, character_to_number, number_to_character





def 							lowerCamelCase    (							UpperCAmelCase_	:      str   ,       UpperCAmelCase_	:      str = "ABCDEFGHIJKLMNOPQRSTUVWXYZ."   ,       UpperCAmelCase_	:      int = 5      )->			str:

       """simple docstring"""




       a   ,      a   ,      a   ,      a			   =__prepare(
           UpperCAmelCase_   ,       UpperCAmelCase_      )
       a   ,      a			   ="""""", """"""

       for i in range(0   ,       len(UpperCAmelCase_      ) + 1   ,       UpperCAmelCase_      ):
              encrypted_numeric += __encrypt_part(
                  message[i : i + period]   ,       UpperCAmelCase_      )

       for i in range(0   ,       len(UpperCAmelCase_      )   ,       3      ):
              encrypted += number_to_character[encrypted_numeric[i : i + 3]]

       return encrypted





def 							lowerCamelCase    (							UpperCAmelCase_	:      str   ,       UpperCAmelCase_	:      str = "ABCDEFGHIJKLMNOPQRSTUVWXYZ."   ,       UpperCAmelCase_	:      int = 5      )->			str:

       """simple docstring"""




       a   ,      a   ,      a   ,      a			   =__prepare(
           UpperCAmelCase_   ,       UpperCAmelCase_      )
       a			   =[]
       a			   =""""""

       for i in range(0   ,       len(UpperCAmelCase_      ) + 1   ,       UpperCAmelCase_      ):
              a   ,      a   ,      a			   =__decrypt_part(message[i : i + period]   ,       UpperCAmelCase_      )

              for j in range(0   ,       len(UpperCAmelCase_      )      ):
                     decrypted_numeric.append(a[j] + b[j] + c[j]      )

       for each in decrypted_numeric:
              decrypted += number_to_character[each]

       return decrypted


if __name__ == "__main__":
    _lowerCamelCase							=      '''DEFEND THE EAST WALL OF THE CASTLE.'''
    _lowerCamelCase							=      encrypt_message(msg, '''EPSDUCVWYM.ZLKXNBTFGORIJHAQ''')
    _lowerCamelCase							=      decrypt_message(encrypted, '''EPSDUCVWYM.ZLKXNBTFGORIJHAQ''')
    print(f"""Encrypted: {encrypted}\nDecrypted: {decrypted}""")
