


from __future__ import annotations






def 	__lowerCAmelCase   (SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE )->  int | float:




      """simple docstring"""

      if len(SCREAMING_SNAKE_CASE ) == 0:
            raise ValueError('''find_max() 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]
      snake_case_	=				(left + right) >> 1  # the middle
      snake_case_	=				find_max(SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE )  # find max in range[left, mid]
      snake_case_	=				find_max(SCREAMING_SNAKE_CASE , mid + 1 , SCREAMING_SNAKE_CASE )  # 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)



def 	__lowerCAmelCase   (SCREAMING_SNAKE_CASE )->  int:




      """simple docstring"""

      if not isinstance(SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE ):
            snake_case_	=				f'''Input value of [number={number}] must be an integer'''
            raise TypeError(SCREAMING_SNAKE_CASE )

      if number < 1:
            snake_case_	=				f'''Input value of [number={number}] must be > 0'''
            raise ValueError(SCREAMING_SNAKE_CASE )

      snake_case_	=				1

      for i in range(1 , SCREAMING_SNAKE_CASE ):
            current_number *= 4 * i - 2
            current_number //= i + 1

      return current_number


if __name__ == "__main__":
   import doctest

   doctest.testmod()