





def 					lowerCAmelCase_			(	__a		)					->		Optional[int]:







  """simple docstring"""





  if collection == []:
    return []

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

  # create the counting array
  lowerCamelCase__:				List[str]        =coll_max + 1 - coll_min
  lowerCamelCase__:				Optional[Any]        =[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__:				List[Any]        =counting_arr[i] + counting_arr[i - 1]

  # create the output collection
  lowerCamelCase__:				List[str]        =[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__:				Tuple        =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))








def 					lowerCAmelCase_			(	__a     ,   __a		)					->		Tuple:







  """simple docstring"""





  assert x is not None
  assert y is not None

  lowerCamelCase__:				Any        =len(__a		)
  lowerCamelCase__:				int        =len(__a		)

  # declaring the array for storing the dp values
  lowerCamelCase__:				List[Any]        =[[0] * (n + 1) for _ in range(m + 1		)]  # noqa: E741

  for i in range(1     ,   m + 1		):
    for j in range(1     ,   n + 1		):
      lowerCamelCase__:				str        =1 if x[i - 1] == y[j - 1] else 0

      lowerCamelCase__:				str        =max(l[i - 1][j]     ,   l[i][j - 1]     ,   l[i - 1][j - 1] + match		)

  lowerCamelCase__:				Any        =""
  lowerCamelCase__  , lowerCamelCase__:				str        =m, n
  while i > 0 and j > 0:
    lowerCamelCase__:				Union[str, Any]        =1 if x[i - 1] == y[j - 1] else 0

    if l[i][j] == l[i - 1][j - 1] + match:
      if match == 1:
        lowerCamelCase__:				Any        =x[i - 1] + seq
      i -= 1
      j -= 1
    elif l[i][j] == l[i - 1][j]:
      i -= 1
    else:
      j -= 1

  return l[m][n], seq


if __name__ == "__main__":
     __A     =    "AGGTAB"
     __A     =    "GXTXAYB"
     __A     =    4
     __A     =    "GTAB"

     __A ,     __A     =    longest_common_subsequence(a, b)
     print("len =", ln, ", sub-sequence =", subseq)
     import doctest

     doctest.testmod()

