


import math

def       lowercase_		(		_A			:    list    ,					_A			:    int = 0    ,					_A			:    int = 0						):

      """simple docstring"""




      lowerCamelCase__		:				str    =  end or len(_A						)
      for i in range(_A    ,					_A						):
            lowerCamelCase__		:				Optional[Any]    =  i
            lowerCamelCase__		:				List[str]    =  array[i]
            while temp_index != start and temp_index_value < array[temp_index - 1]:
                  lowerCamelCase__		:				int    =  array[temp_index - 1]
                  temp_index -= 1
            lowerCamelCase__		:				Tuple    =  temp_index_value
      return array

def       lowercase_		(		_A			:    list    ,					_A			:    int    ,					_A			:    int						):  # Max Heap

      """simple docstring"""




      lowerCamelCase__		:				List[str]    =  index
      lowerCamelCase__		:				Union[str, Any]    =  2 * index + 1  # Left Node
      lowerCamelCase__		:				str    =  2 * index + 2  # Right Node

      if left_index < heap_size and array[largest] < array[left_index]:
            lowerCamelCase__		:				Any    =  left_index

      if right_index < heap_size and array[largest] < array[right_index]:
            lowerCamelCase__		:				List[str]    =  right_index

      if largest != index:
            lowerCamelCase__    ,   lowerCamelCase__		:				int    =  array[largest], array[index]
            heapify(_A    ,					_A    ,					_A						)

def       lowercase_		(		_A			:    list						):

      """simple docstring"""




      lowerCamelCase__		:				Union[str, Any]    =  len(_A						)

      for i in range(n // 2    ,					-1    ,					-1						):
            heapify(_A    ,					_A    ,					_A						)

      for i in range(n - 1    ,					0    ,					-1						):
            lowerCamelCase__    ,   lowerCamelCase__		:				Dict    =  array[0], array[i]
            heapify(_A    ,					0    ,					_A						)

      return array

def       lowercase_		(		_A			:    list    ,					_A			:    int    ,					_A			:    int    ,					_A			:    int						):

      """simple docstring"""




      if (array[first_index] > array[middle_index]) != (
          array[first_index] > array[last_index]
      ):
            return array[first_index]
      elif (array[middle_index] > array[first_index]) != (
          array[middle_index] > array[last_index]
      ):
            return array[middle_index]
      else:
            return array[last_index]

def       lowercase_		(		_A			:    list    ,					_A			:    int    ,					_A			:    int    ,					_A			:    int						):

      """simple docstring"""




      lowerCamelCase__		:				Optional[Any]    =  low
      lowerCamelCase__		:				Tuple    =  high
      while True:
            while array[i] < pivot:
                  i += 1
            j -= 1
            while pivot < array[j]:
                  j -= 1
            if i >= j:
                  return i
            lowerCamelCase__    ,   lowerCamelCase__		:				List[Any]    =  array[j], array[i]
            i += 1

def       lowercase_		(		_A			:    list						):

      """simple docstring"""




      if len(_A						) == 0:
            return array
      lowerCamelCase__		:				List[str]    =  2 * math.ceil(math.loga(len(_A						)						)						)
      lowerCamelCase__		:				Dict    =  16
      return intro_sort(_A    ,					0    ,					len(_A						)    ,					_A    ,					_A						)

def       lowercase_		(		_A			:    list    ,					_A			:    int    ,					_A			:    int    ,					_A			:    int    ,					_A			:    int						):

      """simple docstring"""




      while end - start > size_threshold:
            if max_depth == 0:
                  return heap_sort(_A						)
            max_depth -= 1
            lowerCamelCase__		:				int    =  median_of_a(_A    ,					_A    ,					start + ((end - start) // 2) + 1    ,					end - 1						)
            lowerCamelCase__		:				Optional[int]    =  partition(_A    ,					_A    ,					_A    ,					_A						)
            intro_sort(_A    ,					_A    ,					_A    ,					_A    ,					_A						)
            lowerCamelCase__		:				Tuple    =  p
      return insertion_sort(_A    ,					_A    ,					_A						)


if __name__ == "__main__":
    import doctest

    doctest.testmod()

    A      :    int		=					input("Enter numbers separated by a comma : ").strip()
    A      :    Union[str, Any]		=					[float(item) for item in user_input.split(",")]
    print(sort(unsorted))






def       lowercase_		(		_A			:    int    ,					_A			:    list						):

      """simple docstring"""




      _enforce_args(_A    ,					_A						)
      if n == 0:
            return 0
      lowerCamelCase__		:				Union[str, Any]    =  float("-inf"						)
      for i in range(1    ,					n + 1						):
            lowerCamelCase__		:				int    =  max(
                _A    ,					prices[i - 1] + naive_cut_rod_recursive(n - i    ,					_A						)						)

      return max_revue

def       lowercase_		(		_A			:    int    ,					_A			:    list						):

      """simple docstring"""




      _enforce_args(_A    ,					_A						)
      lowerCamelCase__		:				int    =  [float("-inf"						) for _ in range(n + 1						)]
      return _top_down_cut_rod_recursive(_A    ,					_A    ,					_A						)

def       lowercase_		(		_A			:    int    ,					_A			:    list    ,					_A			:    list						):

      """simple docstring"""




      if max_rev[n] >= 0:
            return max_rev[n]
      elif n == 0:
            return 0
      else:
            lowerCamelCase__		:				Dict    =  float("-inf"						)
            for i in range(1    ,					n + 1						):
                  lowerCamelCase__		:				int    =  max(
                      _A    ,					prices[i - 1] + _top_down_cut_rod_recursive(n - i    ,					_A    ,					_A						)    ,					)

            lowerCamelCase__		:				List[Any]    =  max_revenue

      return max_rev[n]

def       lowercase_		(		_A			:    int    ,					_A			:    list						):

      """simple docstring"""




      _enforce_args(_A    ,					_A						)

      # length(max_rev) = n + 1, to accommodate for the revenue obtainable from a rod of
      # length 0.
      lowerCamelCase__		:				int    =  [float("-inf"						) for _ in range(n + 1						)]
      lowerCamelCase__		:				Optional[int]    =  0

      for i in range(1    ,					n + 1						):
            lowerCamelCase__		:				Union[str, Any]    =  max_rev[i]
            for j in range(1    ,					i + 1						):
                  lowerCamelCase__		:				Any    =  max(_A    ,					prices[j - 1] + max_rev[i - j]						)

            lowerCamelCase__		:				Any    =  max_revenue_i

      return max_rev[n]

def       lowercase_		(		_A			:    int    ,					_A			:    list						):

      """simple docstring"""




      if n < 0:
            lowerCamelCase__		:				Optional[int]    =  F"n must be greater than or equal to 0. Got n = {n}"
            raise ValueError(_A						)

      if n > len(_A						):
            lowerCamelCase__		:				Optional[int]    =  (
                "Each integral piece of rod must have a corresponding price. "
                F"Got n = {n} but length of prices = {len(_A						)}"
            )
            raise ValueError(_A						)

def       lowercase_		(		):

      """simple docstring"""




      lowerCamelCase__		:				Optional[Any]    =  [6, 10, 12, 15, 20, 23]
      lowerCamelCase__		:				Dict    =  len(_A						)

      # the best revenue comes from cutting the rod into 6 pieces, each
      # of length 1 resulting in a revenue of 6 * 6 = 36.
      lowerCamelCase__		:				int    =  36

      lowerCamelCase__		:				List[Any]    =  top_down_cut_rod(_A    ,					_A						)
      lowerCamelCase__		:				List[Any]    =  bottom_up_cut_rod(_A    ,					_A						)
      lowerCamelCase__		:				List[Any]    =  naive_cut_rod_recursive(_A    ,					_A						)

      assert expected_max_revenue == max_rev_top_down
      assert max_rev_top_down == max_rev_bottom_up
      assert max_rev_bottom_up == max_rev_naive


if __name__ == "__main__":
    main()


