



"""simple docstring"""







from collections import defaultdict


def  __SCREAMING_SNAKE_CASE (  __UpperCAmelCase = 5      ):
		_lowercase				: str     =   defaultdict(__UpperCAmelCase      )
		_lowercase				: Any     =   0

		while True:
				_lowercase				: List[str]     =   get_digits(__UpperCAmelCase      )
				freqs[digits].append(__UpperCAmelCase      )

				if len(freqs[digits]      ) == max_base:
						_lowercase				: Optional[Any]     =   freqs[digits][0] ** 3
						return base

				num += 1


def  __SCREAMING_SNAKE_CASE (  __UpperCAmelCase      ):
		return "".join(sorted(str(num**3      )      )      )


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








"""simple docstring"""







import math
from collections.abc import Generator


def  __SCREAMING_SNAKE_CASE (  __UpperCAmelCase      ):
		_lowercase				: Generator     =   (i for i in range(1   ,				(max_n + 1)      ))
		for i in (n for n in numbers if n > 1):
				for j in range(2   ,				__UpperCAmelCase      ):
						if (i % j) == 0:
								break
				else:
						yield i


def  __SCREAMING_SNAKE_CASE (  __UpperCAmelCase      ):
		_lowercase				: Generator     =   (i for i in range(1   ,				(max_n + 1)      ))
		for i in (n for n in numbers if n > 1):
				# only need to check for factors up to sqrt(i)
				_lowercase				: Union[str, Any]     =   int(math.sqrt(__UpperCAmelCase      )      ) + 1
				for j in range(2   ,				__UpperCAmelCase      ):
						if (i % j) == 0:
								break
				else:
						yield i


def  __SCREAMING_SNAKE_CASE (  __UpperCAmelCase      ):
		_lowercase				: Generator     =   (i for i in range(1   ,				(max_n + 1)   ,				2      ))
		# It's useless to test even numbers as they will not be prime
		if max_n > 2:
				yield 2  # Because 2 will not be tested, it's necessary to yield it now
		for i in (n for n in numbers if n > 1):
				_lowercase				: str     =   int(math.sqrt(__UpperCAmelCase      )      ) + 1
				for j in range(3   ,				__UpperCAmelCase   ,				2      ):
						# As we removed the even numbers, we don't need them now
						if (i % j) == 0:
								break
				else:
						yield i


def  __SCREAMING_SNAKE_CASE (  ):
		from timeit import timeit

		_lowercase				: Tuple     =   """from __main__ import slow_primes, primes, fast_primes"""
		print(timeit("""slow_primes(1_000_000_000_000)"""   ,				setup=__UpperCAmelCase   ,				number=1000000      )      )
		print(timeit("""primes(1_000_000_000_000)"""   ,				setup=__UpperCAmelCase   ,				number=1000000      )      )
		print(timeit("""fast_primes(1_000_000_000_000)"""   ,				setup=__UpperCAmelCase   ,				number=1000000      )      )


if __name__ == "__main__":
		UpperCAmelCase:  int			     =				int(input("""Calculate primes up to:\n>> """).strip())
		for ret in primes(number):
				print(ret)
		benchmark()



