


def lowerCAmelCase__(__snake_case	,__snake_case	,__snake_case	,__snake_case							)    ->				Optional[Any]:







	'''simple docstring'''







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

	lowerCamelCase__        =		(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 lowerCAmelCase__(__snake_case							)    ->				Dict:







	'''simple docstring'''







	lowerCamelCase__        =		len(UpperCamelCase_							)

	for index in range(1	,UpperCamelCase_							):
		lowerCamelCase__        =		lst[index]
		lowerCamelCase__        =		binary_search(UpperCamelCase_	,UpperCamelCase_	,0	,index - 1							)
		lowerCamelCase__        =		lst[:pos] + [value] + lst[pos:index] + lst[index + 1 :]

	return lst





def lowerCAmelCase__(__snake_case	,__snake_case							)    ->				Tuple:







	'''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 lowerCAmelCase__(__snake_case							)    ->				str:







	'''simple docstring'''







	lowerCamelCase__        =		len(UpperCamelCase_							)
	lowerCamelCase__    ,     lowerCamelCase__        =		[], []
	lowerCamelCase__        =		[lst[0]]
	lowerCamelCase__        =		[]
	lowerCamelCase__        =		1
	while i < length:
		if lst[i] < lst[i - 1]:
			runs.append(UpperCamelCase_							)
			lowerCamelCase__        =		[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:
		lowerCamelCase__        =		merge(UpperCamelCase_	,UpperCamelCase_							)

	return sorted_array





def lowerCAmelCase__()    ->				List[str]:







	'''simple docstring'''







	lowerCamelCase__        =		[5, 9, 10, 3, -4, 5, 178, 92, 46, -18, 0, 7]
	lowerCamelCase__        =		tim_sort(UpperCamelCase_							)
	print(UpperCamelCase_							)


if __name__ == "__main__":
			main()










def lowerCAmelCase__(__snake_case							)    ->				int:







	'''simple docstring'''







	lowerCamelCase__        =		str(__snake_case							).strip()
	if not bin_string:
		raise ValueError('''Empty string was passed to the function'''							)
	lowerCamelCase__        =		bin_string[0] == '''-'''
	if is_negative:
		lowerCamelCase__        =		bin_string[1:]
	if not all(char in '''01''' for char in bin_string							):
		raise ValueError('''Non-binary value was passed to the function'''							)
	lowerCamelCase__        =		0
	for char in bin_string:
		lowerCamelCase__        =		2 * decimal_number + int(__snake_case							)
	return -decimal_number if is_negative else decimal_number


if __name__ == "__main__":
			from doctest import testmod

			testmod()



