

'''simple docstring'''

def 				UpperCamelCase(					UpperCAmelCase_     ):
 if not isinstance(UpperCAmelCase_  ,	UpperCAmelCase_     ):
  raise ValueError('Input must be an integer'     )
 if input_num <= 0:
  raise ValueError('Input must be positive'     )
 return sum(
     divisor for divisor in range(1  ,	input_num // 2 + 1     ) if input_num % divisor == 0     )


if __name__ == "__main__":
 import doctest

 doctest.testmod()







'''simple docstring'''

from __future__ import annotations




def 				UpperCamelCase(					UpperCAmelCase_  ,	UpperCAmelCase_  ,	UpperCAmelCase_     ):
 if len(UpperCAmelCase_     ) == 0:
  raise ValueError('find_max() arg is an empty sequence'     )
 if (
     left >= len(UpperCAmelCase_     )
     or left < -len(UpperCAmelCase_     )
     or right >= len(UpperCAmelCase_     )
     or right < -len(UpperCAmelCase_     )
 ):
  raise IndexError('list index out of range'     )
 if left == right:
  return nums[left]
 UpperCAmelCase	:     Optional[int]						 =			(left + right) >> 1  # the middle
 UpperCAmelCase	:     Any						 =			find_max(UpperCAmelCase_  ,	UpperCAmelCase_  ,	UpperCAmelCase_     )  # find max in range[left, mid]
 UpperCAmelCase	:     Union[str, Any]						 =			find_max(UpperCAmelCase_  ,	mid + 1  ,	UpperCAmelCase_     )  # find max in range[mid + 1, right]

 return left_max if left_max >= right_max else right_max


if __name__ == "__main__":
 import doctest

 doctest.testmod(verbose=True)




