





"""simple docstring"""




import math





def 			a_							(				_lowercase  ):
						_UpperCamelCase     :   int      =       0
						if n % 2 == 0:
												count += 1
												while n % 2 == 0:
																		_UpperCamelCase     :   Optional[Any]      =       int(n / 2  )
    # the n input value must be odd so that
    # we can skip one element (ie i += 2)

						_UpperCamelCase     :   List[str]      =       3

						while i <= int(math.sqrt(_lowercase  )  ):
												if n % i == 0:
																		count += 1
																		while n % i == 0:
																								_UpperCamelCase     :   Any      =       int(n / i  )
												_UpperCamelCase     :   str      =       i + 2

						# this condition checks the prime
						# number n is greater than 2

						if n > 2:
												count += 1
						return count


if __name__ == "__main__":
						UpperCamelCase_	 =51_242_183
						print(F"The number of distinct prime factors is/are {exact_prime_factor_count(n)}")
						print(F"The value of log(log(n)) is {math.log(math.log(n)):.4f}")







from __future__ import annotations

import math
from itertools import permutations

def 		snake_case_   (				lowercase__     :    int     ):






				'''simple docstring'''






				if 1 < number < 4:
								# 2 and 3 are primes
								return True
				elif number < 2 or number % 2 == 0 or number % 3 == 0:
								# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
								return False

				# All primes number are in format of 6k +/- 1
				for i in range(5       ,     int(math.sqrt(lowercase__     ) + 1     )       ,     6     ):
								if number % i == 0 or number % (i + 2) == 0:
												return False
				return True

def 		snake_case_   (				lowercase__     :    int = 7     ):






				'''simple docstring'''






				_lowerCAmelCase  						="""""".join(str(lowercase__     ) for i in range(1       ,     n + 1     )     )
				_lowerCAmelCase  						=[int("""""".join(lowercase__     )     ) for i in permutations(lowercase__       ,     lowercase__     )]
				_lowerCAmelCase  						=[num for num in perm_list if is_prime(lowercase__     )]
				return max(lowercase__     ) if pandigitals else 0


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

