




from __future__ import annotations






def 				UpperCAmelCase__  (							_A      ,      _A      ,      _A			):






  """simple docstring"""


  if len(_SCREAMING_SNAKE_CASE			) == 0:
    raise ValueError('''find_min() arg is an empty sequence'''			)
  if (
      left >= len(_SCREAMING_SNAKE_CASE			)
      or left < -len(_SCREAMING_SNAKE_CASE			)
      or right >= len(_SCREAMING_SNAKE_CASE			)
      or right < -len(_SCREAMING_SNAKE_CASE			)
  ):
    raise IndexError('''list index out of range'''			)
  if left == right:
    return nums[left]
  a_		    =  (left + right) >> 1  # the middle
  a_		    =  find_min(_SCREAMING_SNAKE_CASE      ,      _SCREAMING_SNAKE_CASE      ,      _SCREAMING_SNAKE_CASE			)  # find min in range[left, mid]
  a_		    =  find_min(_SCREAMING_SNAKE_CASE      ,      mid + 1      ,      _SCREAMING_SNAKE_CASE			)  # find min in range[mid + 1, right]

  return left_min if left_min <= right_min else right_min


if __name__ == "__main__":
  import doctest

  doctest.testmod(verbose=True)


'''simple docstring'''






from __future__ import annotations







def 		SCREAMING_SNAKE_CASE__					(							_SCREAMING_SNAKE_CASE  ,					_SCREAMING_SNAKE_CASE  ,					_SCREAMING_SNAKE_CASE  ):
		if len(_SCREAMING_SNAKE_CASE  ) == 0:
				raise ValueError('''find_min() arg is an empty sequence'''  )
		if (
		    left >= len(_SCREAMING_SNAKE_CASE  )
		    or left < -len(_SCREAMING_SNAKE_CASE  )
		    or right >= len(_SCREAMING_SNAKE_CASE  )
		    or right < -len(_SCREAMING_SNAKE_CASE  )
		):
				raise IndexError('''list index out of range'''  )
		if left == right:
				return nums[left]
		lowerCAmelCase_   :       Dict    							=(left + right) >> 1  # the middle
		lowerCAmelCase_   :       Optional[int]    							=find_min(_SCREAMING_SNAKE_CASE  ,					_SCREAMING_SNAKE_CASE  ,					_SCREAMING_SNAKE_CASE  )  # find min in range[left, mid]
		lowerCAmelCase_   :       Any    							=find_min(_SCREAMING_SNAKE_CASE  ,					mid + 1  ,					_SCREAMING_SNAKE_CASE  )  # find min in range[mid + 1, right]

		return left_min if left_min <= right_min else right_min


if __name__ == "__main__":
							import doctest

							doctest.testmod(verbose=True)






