






from __future__ import annotations
def 		_a					(   a				:list[int]				)							->    list[int]:
 if not list_of_ints:
  return []

 if min(a				) < 0:
  raise ValueError('''All numbers must be positive'''				)

 a							=   max(len(bin(a				)[2:]				) for x in list_of_ints				)
 return _msd_radix_sort(a			,							a				)
def 		_a					(   a				:list[int]			,							a				:int				)							->    list[int]:
 if bit_position == 0 or len(a				) in [0, 1]:
  return list_of_ints

 a							=   []
 a							=   []
 # Split numbers based on bit at bit_position from the right
 for number in list_of_ints:
  if (number >> (bit_position - 1)) & 1:
   # number has a one at bit bit_position
   ones.append(a				)
  else:
   # number has a zero at bit bit_position
   zeros.append(a				)

    # recursively split both lists further
 a							=   _msd_radix_sort(a			,							bit_position - 1				)
 a							=   _msd_radix_sort(a			,							bit_position - 1				)

 # recombine lists
 a							=   zeros
 res.extend(a				)

 return res
def 		_a					(   a				:list[int]				)							->    List[str]:
 a							=   len(a				)
 if not list_of_ints or length == 1:
  return

 if min(a				) < 0:
  raise ValueError('''All numbers must be positive'''				)

 a							=   max(len(bin(a				)[2:]				) for x in list_of_ints				)
 _msd_radix_sort_inplace(a			,							a			,							0			,							a				)
def 		_a					(   a				:list[int]			,							a				:int			,							a				:int			,							a				:int				)							->    Optional[Any]:
 if bit_position == 0 or end_index - begin_index <= 1:
  return

 bit_position -= 1

 a							=   begin_index
 a							=   end_index - 1
 while i <= j:
  a							=   False
  if not (list_of_ints[i] >> bit_position) & 1:
   # found zero at the beginning
   i += 1
   a							=   True
  if (list_of_ints[j] >> bit_position) & 1:
   # found one at the end
   j -= 1
   a							=   True

  if changed:
   continue

  a						,  a							=   list_of_ints[j], list_of_ints[i]
  j -= 1
  if j != i:
   i += 1

 _msd_radix_sort_inplace(a			,							a			,							a			,							a				)
 _msd_radix_sort_inplace(a			,							a			,							a			,							a				)


if __name__ == "__main__":
     import doctest

     doctest.testmod()










import numpy as np

UpperCAmelCase__            =	[
    ["a", "b", "c", "d", "e"],
    ["f", "g", "h", "i", "k"],
    ["l", "m", "n", "o", "p"],
    ["q", "r", "s", "t", "u"],
    ["v", "w", "x", "y", "z"],
]






class 	lowercase_      :






      '''simple docstring'''




      def __init__(   self   :		Optional[Any]						)					->None:




       """simple docstring"""


       a							=   np.array(__UpperCAmelCase						)







      def    __lowerCAmelCase      (   self   :		List[str]				,      __UpperCAmelCase   :		str						)					->np.ndarray:




       """simple docstring"""


       a						,  a							=   np.where(letter == self.SQUARE						)
       a							=   np.concatenate([indexa + 1, indexa + 1]						)
       return indexes







      def    __lowerCAmelCase      (   self   :		int				,      __UpperCAmelCase   :		int				,      __UpperCAmelCase   :		int						)					->str:




       """simple docstring"""


       return self.SQUARE[indexa - 1, indexa - 1]







      def    __lowerCAmelCase      (   self   :		Tuple				,      __UpperCAmelCase   :		str						)					->str:




       """simple docstring"""


       a							=   message.lower()
       a							=   message.replace('''j'''				,      '''i'''						)

       a							=   ''''''
       for letter_index in range(len(__UpperCAmelCase						)						):
        if message[letter_index] != " ":
         a							=   self.letter_to_numbers(message[letter_index]						)
         a							=   encoded_message + str(numbers[0]						) + str(numbers[1]						)
        elif message[letter_index] == " ":
         a							=   encoded_message + ''' '''

       return encoded_message







      def    __lowerCAmelCase      (   self   :		Any				,      __UpperCAmelCase   :		str						)					->str:




       """simple docstring"""


       a							=   message.replace(''' '''				,      '''  '''						)
       a							=   ''''''
       for numbers_index in range(int(len(__UpperCAmelCase						) / 2						)						):
        if message[numbers_index * 2] != " ":
         a							=   message[numbers_index * 2]
         a							=   message[numbers_index * 2 + 1]

         a							=   self.numbers_to_letter(int(__UpperCAmelCase						)				,      int(__UpperCAmelCase						)						)
         a							=   decoded_message + letter
        elif message[numbers_index * 2] == " ":
         a							=   decoded_message + ''' '''

       return decoded_message


