
"""simple docstring"""


def     _lowerCamelCase(__UpperCamelCase    , __UpperCamelCase = 1000       )				-> str:
	if (not isinstance(__UpperCamelCase    , __UpperCamelCase       )) or (digit_position <= 0):
		raise ValueError("""Digit position must be a positive integer"""       )
	elif (not isinstance(__UpperCamelCase    , __UpperCamelCase       )) 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
	_lowerCAmelCase								=(
	    4 * _subsum(__UpperCamelCase    , 1    , __UpperCamelCase       )
	    - 2 * _subsum(__UpperCamelCase    , 4    , __UpperCamelCase       )
	    - _subsum(__UpperCamelCase    , 5    , __UpperCamelCase       )
	    - _subsum(__UpperCamelCase    , 6    , __UpperCamelCase       )
	)

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



def     _lowerCamelCase(__UpperCamelCase    , __UpperCamelCase    , __UpperCamelCase       )				-> float:
	_lowerCAmelCase								=0.0
	for sum_index in range(digit_pos_to_extract + precision       ):
		_lowerCAmelCase								=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
			_lowerCAmelCase								=pow(
			    16    , digit_pos_to_extract - 1 - sum_index    , __UpperCamelCase       )
		else:
			_lowerCAmelCase								=pow(16    , digit_pos_to_extract - 1 - sum_index       )
		total += exponential_term / denominator
	return total


if __name__ == "__main__":
			import doctest

			doctest.testmod()





"""simple docstring"""


def     _lowerCamelCase(__UpperCamelCase = 4000000       )				-> int:
	_lowerCAmelCase								=1
	_lowerCAmelCase								=2
	_lowerCAmelCase								=0
	while j <= n:
		if j % 2 == 0:
			total += j
		_lowerCAmelCase						,							_lowerCAmelCase								=j, i + j

	return total


if __name__ == "__main__":
			print(F"""{solution() = }""")



