


"""simple docstring"""
from math import gcd






def 						lowercase				(	_snake_case		: int = 12_000	)	->int:
	"""simple docstring"""





	__snake_case      :		List[str]         =							0
	for d in range(max_d + 1	):
		for n in range(d // 3 + 1	,  (d + 1) // 2	):
			if gcd(_snake_case	,  _snake_case	) == 1:
				fractions_number += 1
	return fractions_number


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











def 							__lowerCAmelCase			(UpperCAmelCase_		):
    return n * (2 * n - 1)
def 							__lowerCAmelCase			(UpperCAmelCase_		):
    a__  			=							(1 + 24 * n) ** 0.5
    return ((1 + root) / 6) % 1 == 0
def 							__lowerCAmelCase			(UpperCAmelCase_ = 144		):
    a__  			=							start
    a__  			=							hexagonal_num(UpperCAmelCase_		)
    while not is_pentagonal(UpperCAmelCase_		):
        n += 1
        a__  			=							hexagonal_num(UpperCAmelCase_		)
    return num


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






