





def      lowerCAmelCase_ (       __a		)     ->		List[Any]:







  """simple docstring"""





  if collection == []:
    return []

  # get some information about the collection
  lowerCamelCase__:      List[Any]			  =len(__a		)
  lowerCamelCase__:      List[str]			  =max(__a		)
  lowerCamelCase__:      Dict			  =min(__a		)

  # create the counting array
  lowerCamelCase__:      Tuple			  =coll_max + 1 - coll_min
  lowerCamelCase__:      Optional[int]			  =[0] * counting_arr_length

  # count how much a number appears in the collection
  for number in collection:
    counting_arr[number - coll_min] += 1

  # sum each position with it's predecessors. now, counting_arr[i] tells
  # us how many elements <= i has in the collection
  for i in range(1	,    __a		):
    lowerCamelCase__:      int			  =counting_arr[i] + counting_arr[i - 1]

  # create the output collection
  lowerCamelCase__:      Dict			  =[0] * coll_len

  # place the elements in the output, respecting the original order (stable
  # sort) from end to begin, updating counting_arr
  for i in reversed(range(0	,    __a		)		):
    lowerCamelCase__:      int			  =collection[i]
    counting_arr[collection[i] - coll_min] -= 1

  return ordered





def      lowerCAmelCase_ (       __a		)     ->		str:







  """simple docstring"""





  return "".join([chr(__a		) for i in counting_sort([ord(__a		) for c in string]		)]		)


if __name__ == "__main__":
     # Test string sort
     assert counting_sort_string("thisisthestring") == "eghhiiinrsssttt"

     __A									=				input("Enter numbers separated by a comma:\n").strip()
     __A									=				[int(item) for item in user_input.split(",")]
     print(counting_sort(unsorted))








from math import ceil, sqrt





def      lowerCAmelCase_ (       __a = 1000000		)     ->		int:







  """simple docstring"""





  lowerCamelCase__:      Optional[int]			  =0

  for outer_width in range(3	,    (limit // 4) + 2		):
    if outer_width**2 > limit:
      lowerCamelCase__:      Dict			  =max(ceil(sqrt(outer_width**2 - limit		)		)	,    1		)
    else:
      lowerCamelCase__:      str			  =1
    if (outer_width - hole_width_lower_bound) % 2:
      hole_width_lower_bound += 1

    answer += (outer_width - hole_width_lower_bound - 2) // 2 + 1

  return answer


if __name__ == "__main__":
     print(f'{solution() = }')

