





from __future__ import annotations

import math





def 						__SCREAMING_SNAKE_CASE  (				UpperCamelCase__			,			UpperCamelCase__			,			UpperCamelCase__			,			UpperCamelCase__			,			UpperCamelCase__ )  ->				int:







			'''simple docstring'''

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





def 						__SCREAMING_SNAKE_CASE  (				)  ->				None:







			'''simple docstring'''

			UpperCAmelCase   		=				[90, 23, 6, 33, 21, 65, 123, 3_4423]
			UpperCAmelCase   		=				math.log(len(UpperCamelCase__ )			,			2 )
			print(F"""Optimal value : {minimax(0			,			0			,			UpperCamelCase__			,			UpperCamelCase__			,			UpperCamelCase__ )}""" )


if __name__ == "__main__":
				import doctest

				doctest.testmod()
				main()










def 						__SCREAMING_SNAKE_CASE  (				UpperCamelCase__ )  ->				list[int]:







			'''simple docstring'''

			if length <= 0 or not isinstance(UpperCamelCase__			,			UpperCamelCase__ ):
						raise ValueError('''Length must be a positive integer.''' )
			return [n * (2 * n - 1) for n in range(UpperCamelCase__ )]


if __name__ == "__main__":
				print(hexagonal_numbers(length=5))
				print(hexagonal_numbers(length=10))



