




'''simple docstring'''

from __future__ import annotations


def 		__magic_name__    (	__UpperCAmelCase,      __UpperCAmelCase,      __UpperCAmelCase,      __UpperCAmelCase	)		->					str:  # noqa: E741

					'''simple docstring'''

					while r - l > 1:
										snake_case_									=				(l + r) // 2
										if v[m] >= key:
															snake_case_									=				m
										else:
															snake_case_									=				m  # noqa: E741
					return r


def 		__magic_name__    (	__UpperCAmelCase	)		->					int:

					'''simple docstring'''

					if len(__UpperCAmelCase	) == 0:
										return 0

					snake_case_									=				[0] * len(__UpperCAmelCase	)
					snake_case_									=				1

					snake_case_									=				v[0]

					for i in range(1,      len(__UpperCAmelCase	)	):
										if v[i] < tail[0]:
															snake_case_									=				v[i]
										elif v[i] > tail[length - 1]:
															snake_case_									=				v[i]
															length += 1
										else:
															snake_case_									=				v[i]

					return length


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()

