'''simple docstring'''




from __future__ import annotations

import math




def 							lowerCamelCase	(      UpperCAmelCase__       :					int      ,      UpperCAmelCase__       :					int      ,      UpperCAmelCase__       :					bool      ,      UpperCAmelCase__       :					list[int]      ,      UpperCAmelCase__       :					float )			->      int:

							if depth < 0:
														raise ValueError("""Depth cannot be less than 0""" )

							if len(UpperCAmelCase__ ) == 0:
														raise ValueError("""Scores cannot be empty""" )

							if depth == height:
														return scores[node_index]

							if is_max:
														return max(
														    minimax(depth + 1      ,      node_index * 2      ,      UpperCAmelCase__      ,      UpperCAmelCase__      ,      UpperCAmelCase__ )      ,      minimax(depth + 1      ,      node_index * 2 + 1      ,      UpperCAmelCase__      ,      UpperCAmelCase__      ,      UpperCAmelCase__ )      ,      )

							return min(
							    minimax(depth + 1      ,      node_index * 2      ,      UpperCAmelCase__      ,      UpperCAmelCase__      ,      UpperCAmelCase__ )      ,      minimax(depth + 1      ,      node_index * 2 + 1      ,      UpperCAmelCase__      ,      UpperCAmelCase__      ,      UpperCAmelCase__ )      ,      )




def 							lowerCamelCase	(      )			->      None:
							lowercase_					:			Dict										=       [90, 23, 6, 33, 21, 65, 123, 34423]
							lowercase_					:			Any										=       math.log(len(UpperCAmelCase__ )      ,      2 )
							print("""Optimal value : """      ,      end="""""" )
							print(minimax(0      ,      0      ,      UpperCAmelCase__      ,      UpperCAmelCase__      ,      UpperCAmelCase__ ) )


if __name__ == "__main__":
						import doctest

						doctest.testmod()
						main()






'''simple docstring'''




_lowercase						: str						=						tuple[float, float, float]
_lowercase						: List[Any]						=						tuple[float, float, float]




def 							lowerCamelCase	(      UpperCAmelCase__       :					Pointad      ,      UpperCAmelCase__       :					Pointad )			->      Vectorad:
							lowercase_					:			List[str]										=       end_pointa[0] - end_pointa[0]
							lowercase_					:			Union[str, Any]										=       end_pointa[1] - end_pointa[1]
							lowercase_					:			List[Any]										=       end_pointa[2] - end_pointa[2]
							return (x, y, z)




def 							lowerCamelCase	(      UpperCAmelCase__       :					Vectorad      ,      UpperCAmelCase__       :					Vectorad )			->      Vectorad:
							lowercase_					:			List[Any]										=       ab[1] * ac[2] - ab[2] * ac[1]  # *i
							lowercase_					:			Union[str, Any]										=       (ab[0] * ac[2] - ab[2] * ac[0]) * -1  # *j
							lowercase_					:			List[str]										=       ab[0] * ac[1] - ab[1] * ac[0]  # *k
							return (x, y, z)




def 							lowerCamelCase	(      UpperCAmelCase__       :					Vectorad      ,      UpperCAmelCase__       :					int )			->      bool:
							return tuple(round(UpperCAmelCase__      ,      UpperCAmelCase__ ) for x in vector ) == (0, 0, 0)




def 							lowerCamelCase	(      UpperCAmelCase__       :					Pointad      ,      UpperCAmelCase__       :					Pointad      ,      UpperCAmelCase__       :					Pointad      ,      UpperCAmelCase__       :					int = 10 )			->      bool:
							lowercase_					:			Dict										=       create_vector(UpperCAmelCase__      ,      UpperCAmelCase__ )
							lowercase_					:			Optional[int]										=       create_vector(UpperCAmelCase__      ,      UpperCAmelCase__ )
							return is_zero_vector(get_ad_vectors_cross(UpperCAmelCase__      ,      UpperCAmelCase__ )      ,      UpperCAmelCase__ )





