

'''simple docstring'''


from __future__ import annotations

import math
from itertools import permutations







def     SCREAMING_SNAKE_CASE(	UpperCamelCase	)     ->     bool:







	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(UpperCamelCase	) + 1	) ,6	):
		if number % i == 0 or number % (i + 2) == 0:
			return False
	return True







def     SCREAMING_SNAKE_CASE(	UpperCamelCase = 7	)     ->     int:
	UpperCAmelCase_		:   Any													=       ''''''.join(str(UpperCamelCase	) for i in range(1 ,n + 1	)	)
	UpperCAmelCase_		:   Optional[int]													=       [int(''.join(UpperCamelCase	)	) for i in permutations(UpperCamelCase ,UpperCamelCase	)]
	UpperCAmelCase_		:   Any													=       [num for num in perm_list if is_prime(UpperCamelCase	)]
	return max(UpperCamelCase	) if pandigitals else 0


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









"""simple docstring"""
import math







def       UpperCamelCase_					(     lowerCamelCase							:					int   )						->     list:



       """simple docstring"""







       if n <= 0:
              raise ValueError('''Only positive integers have prime factors'''   )
       __magic_name__			:		Union[str, Any]        =     []
       while n % 2 == 0:
              pf.append(2   )
              __magic_name__			:		Union[str, Any]        =     int(n / 2   )
       for i in range(3     , int(math.sqrt(lowerCamelCase   )   ) + 1     , 2   ):
              while n % i == 0:
                     pf.append(lowerCamelCase   )
                     __magic_name__			:		Any        =     int(n / i   )
       if n > 2:
              pf.append(lowerCamelCase   )
       return pf







def       UpperCamelCase_					(     lowerCamelCase							:					int   )						->     int:



       """simple docstring"""







       if n <= 0:
              raise ValueError('''Only positive numbers are accepted'''   )
       __magic_name__			:		List[Any]        =     1
       __magic_name__			:		Dict        =     1
       while n % 2 == 0:
              temp += 1
              __magic_name__			:		Dict        =     int(n / 2   )
       div *= temp
       for i in range(3     , int(math.sqrt(lowerCamelCase   )   ) + 1     , 2   ):
              __magic_name__			:		Dict        =     1
              while n % i == 0:
                     temp += 1
                     __magic_name__			:		Union[str, Any]        =     int(n / i   )
              div *= temp
       if n > 1:
              div *= 2
       return div







def       UpperCamelCase_					(     lowerCamelCase							:					int   )						->     int:



       """simple docstring"""







       if n <= 0:
              raise ValueError('''Only positive numbers are accepted'''   )
       __magic_name__			:		int        =     1
       __magic_name__			:		Dict        =     1
       while n % 2 == 0:
              temp += 1
              __magic_name__			:		List[Any]        =     int(n / 2   )
       if temp > 1:
              s *= (2**temp - 1) / (2 - 1)
       for i in range(3     , int(math.sqrt(lowerCamelCase   )   ) + 1     , 2   ):
              __magic_name__			:		Any        =     1
              while n % i == 0:
                     temp += 1
                     __magic_name__			:		Any        =     int(n / i   )
              if temp > 1:
                     s *= (i**temp - 1) / (i - 1)
       return int(lowerCamelCase   )







def       UpperCamelCase_					(     lowerCamelCase							:					int   )						->     int:



       """simple docstring"""







       __magic_name__			:		str        =     n
       for x in set(prime_factors(lowerCamelCase   )   ):
              s *= (x - 1) / x
       return int(lowerCamelCase   )


if __name__ == "__main__":
 import doctest

 doctest.testmod()
