

"""simple docstring"""

def 				__UpperCamelCase   (    a__: int = 1_00 ,	a__: int = 1_00			)				->			int:




					"""simple docstring"""



					return max(
					    sum(int(a__			) for x in str(base**power			)			)
					    for base in range(a__			)
					    for power in range(a__			)			)


# Tests
if __name__ == "__main__":
							import doctest

							doctest.testmod()





"""simple docstring"""

def 				__UpperCamelCase   (    a__: int ,	a__: int = 10_00			)				->			str:




					"""simple docstring"""



					if (not isinstance(a__ ,	a__			)) or (digit_position <= 0):
										raise ValueError('''Digit position must be a positive integer'''			)
					elif (not isinstance(a__ ,	a__			)) or (precision < 0):
										raise ValueError('''Precision must be a nonnegative integer'''			)

					# compute an approximation of (16 ** (n - 1)) * pi whose fractional part is mostly
					# accurate
					__lowercase												=			(
					    4 * _subsum(a__ ,	1 ,	a__			)
					    - 2 * _subsum(a__ ,	4 ,	a__			)
					    - _subsum(a__ ,	5 ,	a__			)
					    - _subsum(a__ ,	6 ,	a__			)
					)

					# return the first hex digit of the fractional part of the result
					return hex(int((sum_result % 1) * 16			)			)[2:]





def 				__UpperCamelCase   (    a__: int ,	a__: int ,	a__: int			)				->			float:




					"""simple docstring"""



					__lowercase												=			0.0
					for sum_index in range(digit_pos_to_extract + precision			):
										__lowercase												=			8 * sum_index + denominator_addend
										if sum_index < digit_pos_to_extract:
															# if the exponential term is an integer and we mod it by the denominator
															# before dividing, only the integer part of the sum will change;
															# the fractional part will not
															__lowercase												=			pow(
															    16 ,	digit_pos_to_extract - 1 - sum_index ,	a__			)
										else:
															__lowercase												=			pow(16 ,	digit_pos_to_extract - 1 - sum_index			)
										total += exponential_term / denominator
					return total


if __name__ == "__main__":
							import doctest

							doctest.testmod()


