



from math import loga







def       lowerCAmelCase_     (lowerCAmelCase__:						int   ):





			"""simple docstring"""


			if a < 0:
						raise ValueError("""Input value must be a positive integer"""   )
			elif isinstance(snake_case_						,		snake_case_   ):
						raise TypeError("""Input value must be a \'int\' type"""   )
			return 0 if (a == 0) else int(loga(a & -a   )   )


if __name__ == "__main__":
	import doctest

	doctest.testmod()













from __future__ import annotations






def lowerCamelCase__    (							snake_case_	:  list[int]       )      ->				list[int]:  # This function is recursive
   __snake_case							       =   len(snake_case_       )
   # If the array contains only one element, we return it (it's the stop condition of
   # recursion)
   if array_length <= 1:
      return array
      # Else
   __snake_case							       =   array[0]
   __snake_case							       =   False
   __snake_case							       =   1
   __snake_case							       =   []
   while not is_found and i < array_length:
      if array[i] < pivot:
         __snake_case							       =   True
         __snake_case							       =   [element for element in array[i:] if element >= array[i]]
         __snake_case							       =   longest_subsequence(snake_case_       )
         if len(snake_case_       ) > len(snake_case_       ):
            __snake_case							       =   temp_array
      else:
         i += 1

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


if __name__ == "__main__":
    import doctest

    doctest.testmod()

