

"""simple docstring"""




from __future__ import annotations

import math
from itertools import permutations



def 						UpperCAmelCase__ (					A__ )   ->   bool:




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



def 						UpperCAmelCase__ (					A__ = 7 )   ->   int:




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


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







"""simple docstring"""




SCREAMING_SNAKE_CASE_  :      Optional[int]							=      {0: [1, 2], 1: [0, 3], 2: [0], 3: [1], 4: [5, 6], 5: [4, 6], 6: [4, 5]}

SCREAMING_SNAKE_CASE_  :      str							=      {0: [1, 2, 3], 1: [0, 3], 2: [0], 3: [0, 1], 4: [], 5: []}



def 						UpperCAmelCase__ (					A__						,     A__						,     A__ )   ->   list:




   """simple docstring"""
   lowerCamelCase__						       =      True
   lowerCamelCase__						       =      []

   for neighbour in graph[vert]:
      if not visited[neighbour]:
         connected_verts += dfs(A__						,     A__						,     A__ )

   return [vert, *connected_verts]



def 						UpperCAmelCase__ (					A__ )   ->   list:




   """simple docstring"""
   lowerCamelCase__						       =      len(A__ )
   lowerCamelCase__						       =      graph_size * [False]
   lowerCamelCase__						       =      []

   for i in range(A__ ):
      if not visited[i]:
         lowerCamelCase__						       =      dfs(A__						,     A__						,     A__ )
         components_list.append(A__ )

   return components_list


if __name__ == "__main__":
     import doctest

     doctest.testmod()




