



from numpy import exp, pi, sqrt






def      lowerCAmelCase__		(   lowerCamelCase_		:		List[Any]	,lowerCamelCase_		:		float = 0.0	,lowerCamelCase_		:		float = 1.0):





				'''simple docstring'''

				return 1 / sqrt(2 * pi * sigma**2) * exp(-((x - mu) ** 2) / (2 * sigma**2))


if __name__ == "__main__":
							import doctest

							doctest.testmod()






def      lowerCAmelCase__		(   lowerCamelCase_		:		int = 1000000):





				'''simple docstring'''

				lowerCAmelCase__					:    int												=					set(range(3	,lowerCamelCase_	,2))
				primes.add(2)
				for p in range(3	,lowerCamelCase_	,2):
								if p not in primes:
												continue
								primes.difference_update(set(range(p * p	,lowerCamelCase_	,lowerCamelCase_)))

				lowerCAmelCase__					:    int												=					[float(lowerCamelCase_) for n in range(limit + 1)]

				for p in primes:
								for n in range(lowerCamelCase_	,limit + 1	,lowerCamelCase_):
												phi[n] *= 1 - 1 / p

				return int(sum(phi[2:]))


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

