





"""simple docstring"""




def 		UpperCAmelCase__						(	_UpperCAmelCase					,   _UpperCAmelCase					,   _UpperCAmelCase					,   _UpperCAmelCase   ):






  """simple docstring"""





  if start == end:
    return start if lst[start] > item else start + 1
  if start > end:
    return start

  A_    :			List[str]									=    (start + end) // 2
  if lst[mid] < item:
    return binary_search(_UpperCAmelCase					,   _UpperCAmelCase					,   mid + 1					,   _UpperCAmelCase   )
  elif lst[mid] > item:
    return binary_search(_UpperCAmelCase					,   _UpperCAmelCase					,   _UpperCAmelCase					,   mid - 1   )
  else:
    return mid





def 		UpperCAmelCase__						(	_UpperCAmelCase   ):






  """simple docstring"""





  A_    :			Union[str, Any]									=    len(_UpperCAmelCase   )

  for index in range(1					,   _UpperCAmelCase   ):
    A_    :			Optional[int]									=    lst[index]
    A_    :			Optional[int]									=    binary_search(_UpperCAmelCase					,   _UpperCAmelCase					,   0					,   index - 1   )
    A_    :			Union[str, Any]									=    lst[:pos] + [value] + lst[pos:index] + lst[index + 1 :]

  return lst





def 		UpperCAmelCase__						(	_UpperCAmelCase					,   _UpperCAmelCase   ):






  """simple docstring"""





  if not left:
    return right

  if not right:
    return left

  if left[0] < right[0]:
    return [left[0], *merge(left[1:]					,   _UpperCAmelCase   )]

  return [right[0], *merge(_UpperCAmelCase					,   right[1:]   )]





def 		UpperCAmelCase__						(	_UpperCAmelCase   ):






  """simple docstring"""





  A_    :			Tuple									=    len(_UpperCAmelCase   )
  A_		,			A_    :			Union[str, Any]									=    [], []
  A_    :			str									=    [lst[0]]
  A_    :			Union[str, Any]									=    []
  A_    :			Union[str, Any]									=    1
  while i < length:
    if lst[i] < lst[i - 1]:
      runs.append(_UpperCAmelCase   )
      A_    :			Any									=    [lst[i]]
    else:
      new_run.append(lst[i]   )
    i += 1
  runs.append(_UpperCAmelCase   )

  for run in runs:
    sorted_runs.append(insertion_sort(_UpperCAmelCase   )   )
  for run in sorted_runs:
    A_    :			str									=    merge(_UpperCAmelCase					,   _UpperCAmelCase   )

  return sorted_array





def 		UpperCAmelCase__						(	):






  """simple docstring"""





  A_    :			Optional[int]									=    [5, 9, 10, 3, -4, 5, 178, 92, 46, -18, 0, 7]
  A_    :			Tuple									=    tim_sort(_UpperCAmelCase   )
  print(_UpperCAmelCase   )


if __name__ == "__main__":
   main()

def 					SCREAMING_SNAKE_CASE  (   __UpperCamelCase			:    Dict				,    __UpperCamelCase			:    Dict							)			->							List[Any]:

				"""simple docstring"""







				if len(str(__UpperCamelCase							)							) == 1 or len(str(__UpperCamelCase							)							) == 1:
								return a * b

				A__	:						List[str]								=				max(len(str(__UpperCamelCase							)							)				,    len(str(__UpperCamelCase							)							)							)
				A__	:						Any								=				ma // 2

				A__							,				A__	:						Union[str, Any]								=				divmod(__UpperCamelCase				,    10**ma							)
				A__							,				A__	:						Tuple								=				divmod(__UpperCamelCase				,    10**ma							)

				A__	:						Optional[int]								=				karatsuba(__UpperCamelCase				,    __UpperCamelCase							)
				A__	:						Tuple								=				karatsuba((aa + aa)				,    (ba + ba)							)
				A__	:						Optional[int]								=				karatsuba(__UpperCamelCase				,    __UpperCamelCase							)

				return (z * 10 ** (2 * ma)) + ((y - z - x) * 10 ** (ma)) + (x)

def 					SCREAMING_SNAKE_CASE  (   )			->							Dict:

				"""simple docstring"""







				print(karatsuba(1_54_63				,    2_34_89							)							)


if __name__ == "__main__":
					main()