





"""simple docstring"""




from __future__ import annotations

import math





def 	a_    (							_lowercase	,						_lowercase	,						_lowercase	,						_lowercase	,						_lowercase       ):

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

						if not scores:
												raise ValueError('''Scores cannot be empty'''       )

						if depth == height:
												return scores[node_index]

						return (
						    max(
						        minimax(depth + 1	,						node_index * 2	,						_lowercase	,						_lowercase	,						_lowercase       )	,						minimax(depth + 1	,						node_index * 2 + 1	,						_lowercase	,						_lowercase	,						_lowercase       )	,						)
						    if is_max
						    else min(
						        minimax(depth + 1	,						node_index * 2	,						_lowercase	,						_lowercase	,						_lowercase       )	,						minimax(depth + 1	,						node_index * 2 + 1	,						_lowercase	,						_lowercase	,						_lowercase       )	,						)
						)





def 	a_    (							):
						_UpperCamelCase      : Any         =   [90, 23, 6, 33, 21, 65, 123, 3_4423]
						_UpperCamelCase      : Optional[Any]         =   math.log(len(_lowercase       )	,						2       )
						print(F"""Optimal value : {minimax(0	,						0	,						_lowercase	,						_lowercase	,						_lowercase       )}"""       )


if __name__ == "__main__":
						import doctest

						doctest.testmod()
						main()










"""simple docstring"""




class 			_a						:






				def __init__(			self		:   Optional[int],			lowerCAmelCase__		:   list							)     ->				None:




										'''simple docstring'''



										_UpperCamelCase      : Optional[int]         =   set_counts
										_UpperCamelCase      : Any         =   max(lowerCAmelCase__							)
										_UpperCamelCase      : int         =   len(lowerCAmelCase__							)
										_UpperCamelCase      : int         =   [1] * num_sets
										_UpperCamelCase      : List[Any]         =   list(range(lowerCAmelCase__							)							)






				def     snake_case     (			self		:   int,			lowerCAmelCase__		:   int,			lowerCAmelCase__		:   int							)     ->				bool:




										'''simple docstring'''



										_UpperCamelCase      : Optional[Any]         =   self.get_parent(lowerCAmelCase__							)
										_UpperCamelCase      : Any         =   self.get_parent(lowerCAmelCase__							)

										if src_parent == dst_parent:
																return False

										if self.ranks[dst_parent] >= self.ranks[src_parent]:
																self.set_counts[dst_parent] += self.set_counts[src_parent]
																_UpperCamelCase      : List[Any]         =   0
																_UpperCamelCase      : str         =   dst_parent
																if self.ranks[dst_parent] == self.ranks[src_parent]:
																						self.ranks[dst_parent] += 1
																_UpperCamelCase      : Union[str, Any]         =   self.set_counts[dst_parent]
										else:
																self.set_counts[src_parent] += self.set_counts[dst_parent]
																_UpperCamelCase      : Tuple         =   0
																_UpperCamelCase      : Optional[Any]         =   src_parent
																_UpperCamelCase      : int         =   self.set_counts[src_parent]

										_UpperCamelCase      : Optional[Any]         =   max(self.max_set,			lowerCAmelCase__							)
										return True






				def     snake_case     (			self		:   Optional[Any],			lowerCAmelCase__		:   int							)     ->				int:




										'''simple docstring'''



										if self.parents[disj_set] == disj_set:
																return disj_set
										_UpperCamelCase      : Union[str, Any]         =   self.get_parent(self.parents[disj_set]							)
										return self.parents[disj_set]



