
'''simple docstring'''
from functools import lru_cache




@lru_cache
def    _UpperCamelCase						(       SCREAMING_SNAKE_CASE__			)  ->							int:


		'''simple docstring'''


		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()





from __future__ import annotations

import math




def 			lowerCAmelCase(      SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			)->						int:



    """simple docstring"""






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

    if len(SCREAMING_SNAKE_CASE_			) == 0:
        raise ValueError("Scores cannot be empty"			)

    if depth == height:
        return scores[node_index]

    if is_max:
        return max(
            minimax(depth + 1			,						node_index * 2			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			)			,						minimax(depth + 1			,						node_index * 2 + 1			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			)			,						)

    return min(
        minimax(depth + 1			,						node_index * 2			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			)			,						minimax(depth + 1			,						node_index * 2 + 1			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			)			,						)




def 			lowerCAmelCase(      )->						None:



    """simple docstring"""






    UpperCamelCase_			  =						[9_0, 2_3, 6, 3_3, 2_1, 6_5, 1_2_3, 3_4_4_2_3]
    UpperCamelCase_			  =						math.log(len(SCREAMING_SNAKE_CASE_			)			,						2			)
    print("Optimal value : "			,						end=""			)
    print(minimax(0			,						0			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			)			)


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 main()
