



from __future__ import annotations





def   lowerCamelCase__       (       UpperCamelCase__     :    List[Any]    ,      UpperCamelCase__     :    Optional[Any]    ,      UpperCamelCase__     :    str    ,      UpperCamelCase__     :    List[str]  )     ->	List[Any]:  # 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   lowerCamelCase__       (       UpperCamelCase__     :    list[int]  )     ->	Union[str, Any]:



					'''simple docstring'''




					if len(__lowerCAmelCase  ) == 0:
										return 0

					_snake_case													=			[0] * len(__lowerCAmelCase  )
					_snake_case													=			1

					_snake_case													=			v[0]

					for i in range(1    ,      len(__lowerCAmelCase  )  ):
										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()










def   lowerCamelCase__       (       UpperCamelCase__     :    Tuple    ,      UpperCamelCase__     :    Optional[int]  )     ->	Tuple:



					'''simple docstring'''




					_snake_case													=			[0 for i in range(r + 1  )]
					# nc0 = 1
					_snake_case													=			1
					for i in range(1    ,      n + 1  ):
										# to compute current row from previous row.
										_snake_case													=			min(UpperCamelCase__    ,      UpperCamelCase__  )
										while j > 0:
															c[j] += c[j - 1]
															j -= 1
					return c[r]




print(binomial_coefficient(n=10, r=5))



