
'''simple docstring'''

def 	A  (   UpperCamelCase_       :  int   )       ->							str:







			'''simple docstring'''



			lowerCAmelCase__										=				int(UpperCamelCase_   )
			if decimal in (0, 1):  # Exit cases for the recursion
						return str(UpperCamelCase_   )
			lowerCAmelCase__						,lowerCAmelCase__										=				divmod(UpperCamelCase_    ,						2   )
			return binary_recursive(UpperCamelCase_   ) + str(UpperCamelCase_   )







def 	A  (   UpperCamelCase_       :  str   )       ->							str:







			'''simple docstring'''



			lowerCAmelCase__										=				str(UpperCamelCase_   ).strip()
			if not number:
						raise ValueError("No input value was provided"   )
			lowerCAmelCase__										=				"-" if number.startswith("-"   ) else ""
			lowerCAmelCase__										=				number.lstrip("-"   )
			if not number.isnumeric():
						raise ValueError("Input value is not an integer"   )
			return F"""{negative}0b{binary_recursive(int(UpperCamelCase_   )   )}"""


if __name__ == "__main__":
		from doctest import testmod

		testmod()













from __future__ import annotations


def 				__lowerCamelCase     (							__lowerCAmelCase							:					str					,							__lowerCAmelCase							:					Tuple					,							__lowerCAmelCase							:					int					,							__lowerCAmelCase							:					Tuple							)     ->  Optional[Any]:  # noqa: E741
   while r - l > 1:
      __UpperCamelCase	:			int					=					(l + r) // 2
      if v[m] >= key:
         __UpperCamelCase	:			Dict					=					m
      else:
         __UpperCamelCase	:			Optional[Any]					=					m  # noqa: E741
   return r


def 				__lowerCamelCase     (							__lowerCAmelCase							:					list[int]							)     ->  int:
   if len(__lowerCAmelCase							) == 0:
      return 0

   __UpperCamelCase	:			Optional[Any]					=					[0] * len(__lowerCAmelCase							)
   __UpperCamelCase	:			Optional[int]					=					1

   __UpperCamelCase	:			Union[str, Any]					=					v[0]

   for i in range(1					,							len(__lowerCAmelCase							)							):
      if v[i] < tail[0]:
         __UpperCamelCase	:			Dict					=					v[i]
      elif v[i] > tail[length - 1]:
         __UpperCamelCase	:			Optional[int]					=					v[i]
         length += 1
      else:
         __UpperCamelCase	:			List[Any]					=					v[i]

   return length


if __name__ == "__main__":
       import doctest

       doctest.testmod()



