


'''simple docstring'''







def    lowerCAmelCase__ (       lowerCamelCase  :    list     ):
       _A  :			str											=      len(lowerCamelCase     )

       # Set the gap value to be decreased by a factor of 1.3
       # after each iteration
       _A  :			Optional[int]											=      1.3

       # Continue sorting until the gap is 1
       while gap > 1:
              # Decrease the gap value
              _A  :			str											=      int(gap / shrink     )

              # Sort the elements using insertion sort
              for i in range(lowerCamelCase						,len(lowerCamelCase     )     ):
                     _A  :			Dict											=      collection[i]
                     _A  :			List[Any]											=      i
                     while j >= gap and collection[j - gap] > temp:
                            _A  :			int											=      collection[j - gap]
                            j -= gap
                     _A  :			int											=      temp

       return collection


if __name__ == "__main__":
   import doctest

   doctest.testmod()










'''simple docstring'''







import math






def    lowerCAmelCase__ (       lowerCamelCase  :    int     ):

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






def    lowerCAmelCase__ (       lowerCamelCase  :    int = 1000						,lowerCamelCase  :    int = 1000     ):
       _A  :			int											=      [0, 0, 0]  # length, a, b
       for a in range((a_limit * -1) + 1						,lowerCamelCase     ):
              for b in range(2						,lowerCamelCase     ):
                     if is_prime(lowerCamelCase     ):
                            _A  :			Dict											=      0
                            _A  :			Tuple											=      0
                            while is_prime((n**2) + (a * n) + b     ):
                                   count += 1
                                   n += 1
                            if count > longest[0]:
                                   _A  :			List[str]											=      [count, a, b]
       _A  :			str											=      longest[1] * longest[2]
       return ans


if __name__ == "__main__":
   print(solution(1000, 1000))






