


from math import pi, sqrt






def 		_A		(		_lowercase )					-> float:


     """simple docstring"""


     if num <= 0:
          raise ValueError('math domain error' )
     if num > 1_71.5:
          raise OverflowError('math range error' )
     elif num - int(_lowercase ) not in (0, 0.5):
          raise NotImplementedError('num must be an integer or a half-integer' )
     elif num == 0.5:
          return sqrt(_lowercase )
     else:
          return 1.0 if num == 1 else (num - 1) * gamma(num - 1 )






def 		_A		(		)					-> None:


     """simple docstring"""


     assert gamma(0.5 ) == sqrt(_lowercase )
     assert gamma(1 ) == 1.0
     assert gamma(2 ) == 1.0


if __name__ == "__main__":
    from doctest import testmod

    testmod()
    __snake_case   							=						1.0
    while num:
        __snake_case   							=						float(input('''Gamma of: '''))
        print(f"""gamma({num}) = {gamma(num)}""")
        print('''\nEnter 0 to exit...''')






__snake_case   							=						{
    '''a''': '''AAAAA''',
    '''b''': '''AAAAB''',
    '''c''': '''AAABA''',
    '''d''': '''AAABB''',
    '''e''': '''AABAA''',
    '''f''': '''AABAB''',
    '''g''': '''AABBA''',
    '''h''': '''AABBB''',
    '''i''': '''ABAAA''',
    '''j''': '''BBBAA''',
    '''k''': '''ABAAB''',
    '''l''': '''ABABA''',
    '''m''': '''ABABB''',
    '''n''': '''ABBAA''',
    '''o''': '''ABBAB''',
    '''p''': '''ABBBA''',
    '''q''': '''ABBBB''',
    '''r''': '''BAAAA''',
    '''s''': '''BAAAB''',
    '''t''': '''BAABA''',
    '''u''': '''BAABB''',
    '''v''': '''BBBAB''',
    '''w''': '''BABAA''',
    '''x''': '''BABAB''',
    '''y''': '''BABBA''',
    '''z''': '''BABBB''',
    ''' ''': ''' ''',
}


__snake_case   							=						{value: key for key, value in encode_dict.items()}






def 		_A		(		_lowercase )					-> str:


     """simple docstring"""


     __UpperCamelCase =			''
     for letter in word.lower():
          if letter.isalpha() or letter == " ":
               encoded += encode_dict[letter]
          else:
               raise Exception('encode() accepts only letters of the alphabet and spaces' )
     return encoded






def 		_A		(		_lowercase )					-> str:


     """simple docstring"""


     if set(_lowercase ) - {"A", "B", " "} != set():
          raise Exception('decode() accepts only \'A\', \'B\' and spaces' )
     __UpperCamelCase =			''
     for word in coded.split():
          while len(_lowercase ) != 0:
               decoded += decode_dict[word[:5]]
               __UpperCamelCase =			word[5:]
          decoded += " "
     return decoded.strip()


if __name__ == "__main__":
    from doctest import testmod

    testmod()


