






def     _snake_case    (__lowercase):

   if p < 2:
      raise ValueError('p should not be less than 2!')
   elif p == 2:
      return True

   UpperCamelCase_									=     4
   UpperCamelCase_									=     (1 << p) - 1
   for _ in range(p - 2):
      UpperCamelCase_									=     ((s * s) - 2) % m
   return s == 0


if __name__ == "__main__":
 print(lucas_lehmer_test(7))
 print(lucas_lehmer_test(1_1))













def     _snake_case    (__lowercase    ,      __lowercase    ,      __lowercase):
   return not any(
       neighbour == 1 and colored_vertices[i] == color
       for i, neighbour in enumerate(__lowercase))






def     _snake_case    (__lowercase    ,      __lowercase    ,      __lowercase    ,      __lowercase):

   # Base Case
   if index == len(__lowercase):
      return True

   # Recursive Step
   for i in range(__lowercase):
      if valid_coloring(graph[index]    ,      __lowercase    ,      __lowercase):
         # Color current vertex
         UpperCamelCase_									=     i
         # Validate coloring
         if util_color(__lowercase    ,      __lowercase    ,      __lowercase    ,      index + 1):
            return True
         # Backtrack
         UpperCamelCase_									=     -1
   return False






def     _snake_case    (__lowercase    ,      __lowercase):
   UpperCamelCase_									=     [-1] * len(__lowercase)

   if util_color(__lowercase    ,      __lowercase    ,      __lowercase    ,      0):
      return colored_vertices

   return []





