





from __future__ import annotations

import math


def        SCREAMING_SNAKE_CASE      (       _UpperCAmelCase						,	_UpperCAmelCase						,	_UpperCAmelCase						,	_UpperCAmelCase						,	_UpperCAmelCase )			->     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						,	_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:
    lowerCamelCase__    :      int					 =		[90, 23, 6, 33, 21, 65, 123, 3_4423]
    lowerCamelCase__    :      Any					 =		math.log(len(_UpperCAmelCase )						,	2 )
    print(F"""Optimal value : {minimax(0						,	0						,	_UpperCAmelCase						,	_UpperCAmelCase						,	_UpperCAmelCase )}""" )


if __name__ == "__main__":
    import doctest

    doctest.testmod()
    main()











from functools import lru_cache





@lru_cache
def __UpperCamelCase			(       _A  ):
						if num < 0:
												raise ValueError('''Number should not be negative.'''  )

						return 1 if num in (0, 1) else num * factorial(num - 1  )


if __name__ == "__main__":
						import doctest

						doctest.testmod()




