


'''simple docstring'''


from __future__ import annotations

import bisect






def        __lowerCAmelCase       (__lowerCAmelCase					,       __lowerCAmelCase					,       __lowerCAmelCase = 0					,       __lowerCAmelCase = -1      ):
		if hi < 0:
				_UpperCAmelCase						:				Union[str, Any]	    =					len(__lowerCAmelCase      )

		while lo < hi:
				_UpperCAmelCase						:				Union[str, Any]	    =					lo + (hi - lo) // 2
				if sorted_collection[mid] < item:
						_UpperCAmelCase						:				int	    =					mid + 1
				else:
						_UpperCAmelCase						:				Optional[Any]	    =					mid

		return lo






def        __lowerCAmelCase       (__lowerCAmelCase					,       __lowerCAmelCase					,       __lowerCAmelCase = 0					,       __lowerCAmelCase = -1      ):
		if hi < 0:
				_UpperCAmelCase						:				Dict	    =					len(__lowerCAmelCase      )

		while lo < hi:
				_UpperCAmelCase						:				Any	    =					lo + (hi - lo) // 2
				if sorted_collection[mid] <= item:
						_UpperCAmelCase						:				Optional[int]	    =					mid + 1
				else:
						_UpperCAmelCase						:				List[str]	    =					mid

		return lo






def        __lowerCAmelCase       (__lowerCAmelCase					,       __lowerCAmelCase					,       __lowerCAmelCase = 0					,       __lowerCAmelCase = -1      ):
		sorted_collection.insert(bisect_left(__lowerCAmelCase					,       __lowerCAmelCase					,       __lowerCAmelCase					,       __lowerCAmelCase      )					,       __lowerCAmelCase      )






def        __lowerCAmelCase       (__lowerCAmelCase					,       __lowerCAmelCase					,       __lowerCAmelCase = 0					,       __lowerCAmelCase = -1      ):
		sorted_collection.insert(bisect_right(__lowerCAmelCase					,       __lowerCAmelCase					,       __lowerCAmelCase					,       __lowerCAmelCase      )					,       __lowerCAmelCase      )






def        __lowerCAmelCase       (__lowerCAmelCase					,       __lowerCAmelCase      ):
		_UpperCAmelCase						:				Tuple	    =					0
		_UpperCAmelCase						:				List[Any]	    =					len(__lowerCAmelCase      ) - 1

		while left <= right:
				_UpperCAmelCase						:				List[Any]	    =					left + (right - left) // 2
				_UpperCAmelCase						:				Any	    =					sorted_collection[midpoint]
				if current_item == item:
						return midpoint
				elif item < current_item:
						_UpperCAmelCase						:				List[str]	    =					midpoint - 1
				else:
						_UpperCAmelCase						:				int	    =					midpoint + 1
		return None






def        __lowerCAmelCase       (__lowerCAmelCase					,       __lowerCAmelCase      ):
		_UpperCAmelCase						:				Optional[Any]	    =					bisect.bisect_left(__lowerCAmelCase					,       __lowerCAmelCase      )
		if index != len(__lowerCAmelCase      ) and sorted_collection[index] == item:
				return index
		return None






def        __lowerCAmelCase       (__lowerCAmelCase					,       __lowerCAmelCase					,       __lowerCAmelCase					,       __lowerCAmelCase      ):
		if right < left:
				return None

		_UpperCAmelCase						:				List[Any]	    =					left + (right - left) // 2

		if sorted_collection[midpoint] == item:
				return midpoint
		elif sorted_collection[midpoint] > item:
				return binary_search_by_recursion(__lowerCAmelCase					,       __lowerCAmelCase					,       __lowerCAmelCase					,       midpoint - 1      )
		else:
				return binary_search_by_recursion(__lowerCAmelCase					,       __lowerCAmelCase					,       midpoint + 1					,       __lowerCAmelCase      )


if __name__ == "__main__":
						lowerCamelCase__					=   input('Enter numbers separated by comma:\n').strip()
						lowerCamelCase__					=   sorted(int(item) for item in user_input.split(','))
						lowerCamelCase__					=   int(input('Enter a single number to be found in the list:\n'))
						lowerCamelCase__					=   binary_search(collection, target)
						if result is None:
												print(F'''{target} was not found in {collection}.''')
						else:
												print(F'''{target} was found at position {result} in {collection}.''')







'''simple docstring'''


def        __lowerCAmelCase       (__lowerCAmelCase					,       __lowerCAmelCase      ):

		if density <= 0:
				raise ValueError("Impossible fluid density"      )
		if bulk_modulus <= 0:
				raise ValueError("Impossible bulk modulus"      )

		return (bulk_modulus / density) ** 0.5


if __name__ == "__main__":
						import doctest

						doctest.testmod()



