

'''simple docstring'''

from __future__ import annotations

import math




def 							_UpperCamelCase				(   lowerCAmelCase__:					int		,lowerCAmelCase__:					int		,lowerCAmelCase__:					bool		,lowerCAmelCase__:					list[int]		,lowerCAmelCase__:					float   )      -> int:

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

							if len(lowerCAmelCase__   ) == 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		,lowerCAmelCase__		,lowerCAmelCase__		,lowerCAmelCase__   )		,minimax(depth + 1		,node_index * 2 + 1		,lowerCAmelCase__		,lowerCAmelCase__		,lowerCAmelCase__   )		,)

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




def 							_UpperCamelCase				(   )      -> None:
							SCREAMING_SNAKE_CASE_				=				[90, 23, 6, 33, 21, 65, 123, 3_4423]
							SCREAMING_SNAKE_CASE_				=				math.log(len(lowerCAmelCase__   )		,2   )
							print('Optimal value : '		,end=''   )
							print(minimax(0		,0		,lowerCAmelCase__		,lowerCAmelCase__		,lowerCAmelCase__   )   )


if __name__ == "__main__":
							import doctest

							doctest.testmod()
							main()








'''simple docstring'''

SCREAMING_SNAKE_CASE							:				Union[str, Any]     	=			0  # The first color of the flag.
SCREAMING_SNAKE_CASE							:				List[str]     	=			1  # The second color of the flag.
SCREAMING_SNAKE_CASE							:				Optional[Any]     	=			2  # The third color of the flag.
SCREAMING_SNAKE_CASE							:				Tuple     	=			(red, white, blue)




def 							_UpperCamelCase				(   lowerCAmelCase__:					list   )      -> list:
							if not sequence:
														return []
							if len(lowerCAmelCase__   ) == 1:
														return list(lowerCAmelCase__   )
							SCREAMING_SNAKE_CASE_				=				0
							SCREAMING_SNAKE_CASE_				=				len(lowerCAmelCase__   ) - 1
							SCREAMING_SNAKE_CASE_				=				0
							while mid <= high:
														if sequence[mid] == colors[0]:
																					SCREAMING_SNAKE_CASE_				,    SCREAMING_SNAKE_CASE_				=				sequence[mid], sequence[low]
																					low += 1
																					mid += 1
														elif sequence[mid] == colors[1]:
																					mid += 1
														elif sequence[mid] == colors[2]:
																					SCREAMING_SNAKE_CASE_				,    SCREAMING_SNAKE_CASE_				=				sequence[high], sequence[mid]
																					high -= 1
														else:
																					SCREAMING_SNAKE_CASE_				=				F"""The elements inside the sequence must contains only {colors} values"""
																					raise ValueError(lowerCAmelCase__   )
							return sequence


if __name__ == "__main__":
							import doctest

							doctest.testmod()

							SCREAMING_SNAKE_CASE							:				str     	=			input("Enter numbers separated by commas:\n").strip()
							SCREAMING_SNAKE_CASE							:				List[Any]     	=			[int(item.strip()) for item in user_input.split(",")]
							print(f"{dutch_national_flag_sort(unsorted)}")





