




def  lowerCAmelCase  (	UpperCAmelCase,	UpperCAmelCase,	UpperCAmelCase,	UpperCAmelCase       )  ->List[Any]:






					"""simple docstring"""






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

					__magic_name__					:							Union[str, Any]		   =							(start + end) // 2
					if lst[mid] < item:
										return binary_search(a__,	a__,	mid + 1,	a__       )
					elif lst[mid] > item:
										return binary_search(a__,	a__,	a__,	mid - 1       )
					else:
										return mid







def  lowerCAmelCase  (	UpperCAmelCase       )  ->List[str]:






					"""simple docstring"""






					__magic_name__					:							Optional[int]		   =							len(a__       )

					for index in range(1,	a__       ):
										__magic_name__					:							Tuple		   =							lst[index]
										__magic_name__					:							List[str]		   =							binary_search(a__,	a__,	0,	index - 1       )
										__magic_name__					:							str		   =							lst[:pos] + [value] + lst[pos:index] + lst[index + 1 :]

					return lst







def  lowerCAmelCase  (	UpperCAmelCase,	UpperCAmelCase       )  ->List[Any]:






					"""simple docstring"""






					if not left:
										return right

					if not right:
										return left

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

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







def  lowerCAmelCase  (	UpperCAmelCase       )  ->Any:






					"""simple docstring"""






					__magic_name__					:							Optional[Any]		   =							len(a__       )
					__magic_name__   , __magic_name__					:							Optional[int]		   =							[], []
					__magic_name__					:							Optional[int]		   =							[lst[0]]
					__magic_name__					:							Dict		   =							[]
					__magic_name__					:							Any		   =							1
					while i < length:
										if lst[i] < lst[i - 1]:
															runs.append(a__       )
															__magic_name__					:							Dict		   =							[lst[i]]
										else:
															new_run.append(lst[i]       )
										i += 1
					runs.append(a__       )

					for run in runs:
										sorted_runs.append(insertion_sort(a__       )       )
					for run in sorted_runs:
										__magic_name__					:							Optional[Any]		   =							merge(a__,	a__       )

					return sorted_array







def  lowerCAmelCase  (	)  ->int:






					"""simple docstring"""






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


if __name__ == "__main__":
				main()









'''simple docstring'''
def 				snake_case_  (   a__		:	int			):



    """simple docstring"""




    if not isinstance(a__    ,a__			) or number < 0:
        raise ValueError("""Input must be a non-negative integer"""			)

    __lowercase							=						number & ~(number - 1)
    __lowercase							=						0
    while intermediate:
        intermediate >>= 1
        index += 1
    return index - 1


if __name__ == "__main__":
  import doctest

  doctest.testmod(verbose=True)




