
from __future__ import annotations

import math


def     UpperCAmelCase_  (						__lowerCAmelCase	,					__lowerCAmelCase	,					__lowerCAmelCase	,					__lowerCAmelCase	,					__lowerCAmelCase	) ->						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     UpperCAmelCase_  (						) ->						None:
    __lowercase		:			Tuple	    =       [90, 23, 6, 33, 21, 65, 123, 34_423]
    __lowercase		:			Optional[int]	    =       math.log(len(__lowerCAmelCase	)	,					2	)
    print(F'Optimal value : {minimax(0	,					0	,					__lowerCAmelCase	,					__lowerCAmelCase	,					__lowerCAmelCase	)}'	)


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 main()




from math import factorial

__lowerCAmelCase					:			Dict			      =		{str(d): factorial(d) for d in range(10)}


def     UpperCAmelCase_  (						__lowerCAmelCase	) ->						int:
    return sum(DIGIT_FACTORIAL[d] for d in str(__lowerCAmelCase	)	)


def     UpperCAmelCase_  (						) ->						int:
    __lowercase		:			int	    =       7 * factorial(9	) + 1
    return sum(i for i in range(3	,					__lowerCAmelCase	) if sum_of_digit_factorial(__lowerCAmelCase	) == i	)


if __name__ == "__main__":
 print(F'{solution() = }')


