
from __future__ import annotations




def 		A_       (							snake_case							:      List[str]       )					->			list[int]:  # This function is recursive



						'''simple docstring'''

						__UpperCamelCase        =	len(__UpperCAmelCase       )
						# If the array contains only one element, we return it (it's the stop condition of
						# recursion)
						if array_length <= 1:
												return array
												# Else
						__UpperCamelCase        =	array[0]
						__UpperCamelCase        =	False
						__UpperCamelCase        =	1
						__UpperCamelCase        =	[]
						while not is_found and i < array_length:
												if array[i] < pivot:
																		__UpperCamelCase        =	True
																		__UpperCamelCase        =	[element for element in array[i:] if element >= array[i]]
																		__UpperCamelCase        =	longest_subsequence(__UpperCAmelCase       )
																		if len(__UpperCAmelCase       ) > len(__UpperCAmelCase       ):
																								__UpperCamelCase        =	temp_array
												else:
																		i += 1

						__UpperCamelCase        =	[element for element in array[1:] if element >= pivot]
						__UpperCamelCase        =	[pivot, *longest_subsequence(__UpperCAmelCase       )]
						if len(__UpperCAmelCase       ) > len(__UpperCAmelCase       ):
												return temp_array
						else:
												return longest_subseq


if __name__ == "__main__":
				import doctest

				doctest.testmod()










'''simple docstring'''

from __future__ import annotations

import math


def 		__magic_name__    (	__UpperCAmelCase,      __UpperCAmelCase,      __UpperCAmelCase,      __UpperCAmelCase,      __UpperCAmelCase	)		->					int:

					'''simple docstring'''

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

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

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


def 		__magic_name__    (	)		->					None:

					'''simple docstring'''

					snake_case_									=				[90, 23, 6, 33, 21, 65, 123, 3_4423]
					snake_case_									=				math.log(len(__UpperCAmelCase	),      2	)
					print('''Optimal value : ''',      end=''''''	)
					print(minimax(0,      0,      __UpperCAmelCase,      __UpperCAmelCase,      __UpperCAmelCase	)	)


if __name__ == "__main__":
							import doctest

							doctest.testmod()
							main()

