



'''simple docstring'''






import os
from typing import Dict, List, Tuple, TypeVar, Union


UpperCamelCase__:   List[str]								=			TypeVar("T")

UpperCamelCase__:   Any								=			Union[List[T], Tuple[T, ...]]
UpperCamelCase__:   Dict								=			Union[T, List[T], Dict[str, T]]
UpperCamelCase__:   Optional[Any]								=			Union[str, bytes, os.PathLike]










'''simple docstring'''






from __future__ import annotations


def  snake_case_     (					_lowerCAmelCase  :						list[int | float]   ,      _lowerCAmelCase  :						int   ,      _lowerCAmelCase  :						int  )      ->   int | float:
							if len(_lowerCAmelCase  ) == 0:
														raise ValueError('''find_max() arg is an empty sequence'''  )
							if (
							    left >= len(_lowerCAmelCase  )
							    or left < -len(_lowerCAmelCase  )
							    or right >= len(_lowerCAmelCase  )
							    or right < -len(_lowerCAmelCase  )
							):
														raise IndexError('''list index out of range'''  )
							if left == right:
														return nums[left]
							UpperCAmelCase :       List[Any] 							=		(left + right) >> 1  # the middle
							UpperCAmelCase :       Optional[Any] 							=		find_max(_lowerCAmelCase   ,      _lowerCAmelCase   ,      _lowerCAmelCase  )  # find max in range[left, mid]
							UpperCAmelCase :       Dict 							=		find_max(_lowerCAmelCase   ,      mid + 1   ,      _lowerCAmelCase  )  # find max in range[mid + 1, right]

							return left_max if left_max >= right_max else right_max


if __name__ == "__main__":
						import doctest

						doctest.testmod(verbose=True)





