



from __future__ import annotations

import math






def        __lowerCAmelCase		(	__lowerCamelCase						:     int					, __lowerCamelCase						:     int					, __lowerCamelCase						:     bool					, __lowerCamelCase						:     list[int]					, __lowerCamelCase						:     float						)	->    int:

					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					, lowerCAmelCase__					, lowerCAmelCase__					, lowerCAmelCase__						)					, minimax(depth + 1					, node_index * 2 + 1					, lowerCAmelCase__					, lowerCAmelCase__					, lowerCAmelCase__						)					, )
					    if is_max
					    else min(
					        minimax(depth + 1					, node_index * 2					, lowerCAmelCase__					, lowerCAmelCase__					, lowerCAmelCase__						)					, minimax(depth + 1					, node_index * 2 + 1					, lowerCAmelCase__					, lowerCAmelCase__					, lowerCAmelCase__						)					, )
					)






def        __lowerCAmelCase		(	)	->    None:
					__lowerCAmelCase						 =[90, 23, 6, 33, 21, 65, 123, 34423]
					__lowerCAmelCase						 =math.log(len(lowerCAmelCase__						)					, 2						)
					print(f"""Optimal value : {minimax(0					, 0					, lowerCAmelCase__					, lowerCAmelCase__					, lowerCAmelCase__						)}"""						)


if __name__ == "__main__":
				import doctest

				doctest.testmod()
				main()











"""simple docstring"""






from maths.is_square_free import is_square_free
from maths.prime_factors import prime_factors






def      lowercase__ (					lowerCAmelCase__   :			int			)    ->			int:



			'''simple docstring'''
			a__  :	Tuple		 =			prime_factors(lowerCAmelCase__			)
			if is_square_free(lowerCAmelCase__			):
						return -1 if len(lowerCAmelCase__			) % 2 else 1
			return 0


if __name__ == "__main__":
		import doctest

		doctest.testmod()