


'''simple docstring'''



A__		:					Optional[int]												=  """ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/"""



def 			UpperCAmelCase__					(	UpperCAmelCase_    :				bytes							)     ->		bytes:
     # Make sure the supplied data is a bytes-like object
     if not isinstance(UpperCAmelCase_      ,    UpperCAmelCase_							):
          __lowerCamelCase   :	Dict								=		F'a bytes-like object is required, not \'{data.__class__.__name__}\''
          raise TypeError(UpperCAmelCase_							)

     __lowerCamelCase   :	Optional[int]								=		''.join(bin(UpperCAmelCase_							)[2:].zfill(8							) for byte in data							)

     __lowerCamelCase   :	Any								=		len(UpperCAmelCase_							) % 6 != 0

     if padding_needed:
          # The padding that will be added later
          __lowerCamelCase   :	int								=		B'=' * ((6 - len(UpperCAmelCase_							) % 6) // 2)

          # Append binary_stream with arbitrary binary digits (0's by default) to make its
          # length a multiple of 6.
          binary_stream += "0" * (6 - len(UpperCAmelCase_							) % 6)
     else:
          __lowerCamelCase   :	str								=		B''

     # Encode every 6 binary digits to their corresponding Base64 character
     return (
         "".join(
             B64_CHARSET[int(binary_stream[index : index + 6]      ,    2							)]
             for index in range(0      ,    len(UpperCAmelCase_							)      ,    6							)							).encode()
         + padding
     )



def 			UpperCAmelCase__					(	UpperCAmelCase_    :				str							)     ->		bytes:
     # Make sure encoded_data is either a string or a bytes-like object
     if not isinstance(UpperCAmelCase_      ,    UpperCAmelCase_							) and not isinstance(UpperCAmelCase_      ,    UpperCAmelCase_							):
          __lowerCamelCase   :	Dict								=		(
              'argument should be a bytes-like object or ASCII string, '
              F'not \'{encoded_data.__class__.__name__}\''
          )
          raise TypeError(UpperCAmelCase_							)

     # In case encoded_data is a bytes-like object, make sure it contains only
     # ASCII characters so we convert it to a string object
     if isinstance(UpperCAmelCase_      ,    UpperCAmelCase_							):
          try:
               __lowerCamelCase   :	int								=		encoded_data.decode('utf-8'							)
          except UnicodeDecodeError:
               raise ValueError('base64 encoded data should only contain ASCII characters'							)

     __lowerCamelCase   :	Union[str, Any]								=		encoded_data.count('='							)

     # Check if the encoded string contains non base64 characters
     if padding:
          assert all(
              char in B64_CHARSET for char in encoded_data[:-padding]							), "Invalid base64 character(s) found."
     else:
          assert all(
              char in B64_CHARSET for char in encoded_data							), "Invalid base64 character(s) found."

     # Check the padding
     assert len(UpperCAmelCase_							) % 4 == 0 and padding < 3, "Incorrect padding"

     if padding:
          # Remove padding if there is one
          __lowerCamelCase   :	Any								=		encoded_data[:-padding]

          __lowerCamelCase   :	Optional[Any]								=		''.join(
              bin(B64_CHARSET.index(UpperCAmelCase_							)							)[2:].zfill(6							) for char in encoded_data							)[: -padding * 2]
     else:
          __lowerCamelCase   :	Any								=		''.join(
              bin(B64_CHARSET.index(UpperCAmelCase_							)							)[2:].zfill(6							) for char in encoded_data							)

     __lowerCamelCase   :	str								=		[
         int(binary_stream[index : index + 8]      ,    2							)
         for index in range(0      ,    len(UpperCAmelCase_							)      ,    8							)
     ]

     return bytes(UpperCAmelCase_							)


if __name__ == "__main__":
      import doctest

      doctest.testmod()










'''simple docstring'''



def 			UpperCAmelCase__					(	UpperCAmelCase_    :				List[Any]							)     ->		str:
     __lowerCamelCase   :	Tuple								=		0
     __lowerCamelCase   :	Optional[int]								=		len(UpperCAmelCase_							)

     for i in range(n - 1							):
          for j in range(i + 1      ,    UpperCAmelCase_							):
               if arr[i] > arr[j]:
                    num_inversions += 1

     return num_inversions



def 			UpperCAmelCase__					(	UpperCAmelCase_    :				str							)     ->		Optional[int]:
     if len(UpperCAmelCase_							) <= 1:
          return arr, 0
     __lowerCamelCase   :	str								=		len(UpperCAmelCase_							) // 2
     __lowerCamelCase   :	List[Any]								=		arr[0:mid]
     __lowerCamelCase   :	List[str]								=		arr[mid:]

     __lowerCamelCase				,       __lowerCamelCase   :	int								=		count_inversions_recursive(UpperCAmelCase_							)
     __lowerCamelCase				,       __lowerCamelCase   :	Optional[Any]								=		count_inversions_recursive(UpperCAmelCase_							)
     __lowerCamelCase				,       __lowerCamelCase   :	Any								=		_count_cross_inversions(UpperCAmelCase_      ,    UpperCAmelCase_							)

     __lowerCamelCase   :	Optional[int]								=		inversion_p + inversions_q + cross_inversions
     return c, num_inversions



def 			UpperCAmelCase__					(	UpperCAmelCase_    :				List[Any]      ,    UpperCAmelCase_    :				List[str]							)     ->		Optional[Any]:
     __lowerCamelCase   :	List[str]								=		[]
     __lowerCamelCase   :	Optional[int]								=		0
     while i < len(UpperCAmelCase_							) and j < len(UpperCAmelCase_							):
          if p[i] > q[j]:
               # if P[1] > Q[j], then P[k] > Q[k] for all  i < k <= len(P)
               # These are all inversions. The claim emerges from the
               # property that P is sorted.
               num_inversion += len(UpperCAmelCase_							) - i
               r.append(q[j]							)
               j += 1
          else:
               r.append(p[i]							)
               i += 1

     if i < len(UpperCAmelCase_							):
          r.extend(p[i:]							)
     else:
          r.extend(q[j:]							)

     return r, num_inversion



def 			UpperCAmelCase__					(	)     ->		List[str]:
     __lowerCamelCase   :	Any								=		[10, 2, 1, 5, 5, 2, 11]

     # this arr has 8 inversions:
     # (10, 2), (10, 1), (10, 5), (10, 5), (10, 2), (2, 1), (5, 2), (5, 2)

     __lowerCamelCase   :	Optional[Any]								=		count_inversions_bf(UpperCAmelCase_							)
     __lowerCamelCase				,       __lowerCamelCase   :	Dict								=		count_inversions_recursive(UpperCAmelCase_							)

     assert num_inversions_bf == num_inversions_recursive == 8

     print('number of inversions = '      ,    UpperCAmelCase_							)

     # testing an array with zero inversion (a sorted arr_1)

     arr_a.sort()
     __lowerCamelCase   :	Optional[Any]								=		count_inversions_bf(UpperCAmelCase_							)
     __lowerCamelCase				,       __lowerCamelCase   :	int								=		count_inversions_recursive(UpperCAmelCase_							)

     assert num_inversions_bf == num_inversions_recursive == 0
     print('number of inversions = '      ,    UpperCAmelCase_							)

     # an empty list should also have zero inversions
     __lowerCamelCase   :	Dict								=		[]
     __lowerCamelCase   :	Optional[Any]								=		count_inversions_bf(UpperCAmelCase_							)
     __lowerCamelCase				,       __lowerCamelCase   :	Union[str, Any]								=		count_inversions_recursive(UpperCAmelCase_							)

     assert num_inversions_bf == num_inversions_recursive == 0
     print('number of inversions = '      ,    UpperCAmelCase_							)


if __name__ == "__main__":
      main()






