



"""simple docstring"""




from __future__ import annotations



def 	UpperCAmelCase__   (				A__   )      ->      list[int]:




   """simple docstring"""





   if len(_lowerCamelCase   ) == 0:
      return array

   lowerCamelCase__						=			min(_lowerCamelCase   ), max(_lowerCamelCase   )

   # Compute the variables
   lowerCamelCase__						=			_max - _min + 1
   lowerCamelCase__						=			[0] * holes_range, [0] * holes_range

   # Make the sorting.
   for i in array:
      lowerCamelCase__						=			i - _min
      lowerCamelCase__						=			i
      holes_repeat[index] += 1

   # Makes the array back by replacing the numbers.
   lowerCamelCase__						=			0
   for i in range(_lowerCamelCase   ):
      while holes_repeat[i] > 0:
         lowerCamelCase__						=			holes[i]
         index += 1
         holes_repeat[i] -= 1

    # Returns the sorted array.
   return array


if __name__ == "__main__":
     import doctest

     doctest.testmod()
     SCREAMING_SNAKE_CASE_     :			Any	  =			input('''Enter numbers separated by comma:\n''')
     SCREAMING_SNAKE_CASE_     :			str	  =			[int(x) for x in user_input.split(''',''')]
     print(pigeon_sort(unsorted))







"""simple docstring"""




def 	UpperCAmelCase__   (				A__   )      ->      list[int]:




   """simple docstring"""

   if length <= 0 or not isinstance(A__	,    A__   ):
      raise ValueError("Length must be a positive integer."   )
   return [n * (2 * n - 1) for n in range(A__   )]


if __name__ == "__main__":
     print(hexagonal_numbers(length=5))
     print(hexagonal_numbers(length=10))




