





'''simple docstring'''






from __future__ import annotations






def      __A						(							a_						:  Optional[int]      ,a_						:  Dict      ,a_						:  Any      ,a_						:  Optional[Any]	):  # noqa: E741
		while r - l > 1:
				lowerCAmelCase     :    str						=   (l + r) // 2
				if v[m] >= key:
						lowerCAmelCase     :    Any						=   m
				else:
						lowerCAmelCase     :    Union[str, Any]						=   m  # noqa: E741
		return r






def      __A						(							a_						:  list[int]	):
		if len(a_	) == 0:
				return 0

		lowerCAmelCase     :    str						=   [0] * len(a_	)
		lowerCAmelCase     :    Any						=   1

		lowerCAmelCase     :    Optional[Any]						=   v[0]

		for i in range(1      ,len(a_	)	):
				if v[i] < tail[0]:
						lowerCAmelCase     :    Union[str, Any]						=   v[i]
				elif v[i] > tail[length - 1]:
						lowerCAmelCase     :    Any						=   v[i]
						length += 1
				else:
						lowerCAmelCase     :    Dict						=   v[i]

		return length


if __name__ == "__main__":
					import doctest

					doctest.testmod()










'''simple docstring'''






import numpy as np






def      __A						(							a_						:  np.array	):
		return 1 / (1 + np.exp(-vector	))


if __name__ == "__main__":
					import doctest

					doctest.testmod()



