'''simple docstring'''

import math


def __a			(						__lowerCamelCase      :    int					)						->				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(__lowerCamelCase					) + 1					)			,		6					):
            if number % i == 0 or number % (i + 2) == 0:
                  return False
      return True


def __a			(						__lowerCamelCase      :    int = 1_000			,		__lowerCamelCase      :    int = 1_000					)						->				int:
      '''simple docstring'''


      lowercase_     			=   [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					):
                        lowercase_     			=   0
                        lowercase_     			=   0
                        while is_prime((n**2) + (a * n) + b					):
                              count += 1
                              n += 1
                        if count > longest[0]:
                              lowercase_     			=   [count, a, b]
      lowercase_     			=   longest[1] * longest[2]
      return ans


if __name__ == "__main__":
       print(solution(1_000, 1_000))







'''simple docstring'''

import timeit





class 				lowercase    :


   def __init__( self					:						Dict ,		__lowerCAmelCase					:						Any)   ->       Optional[int]:
         if isinstance(__lowerCAmelCase ,		__lowerCAmelCase):  # Initializes a matrix identical to the one provided.
               lowercase_     			=   arg
               lowercase_     			=   len(__lowerCAmelCase)
         else:  # Initializes a square matrix of the given size and set values to zero.
               lowercase_     			=   arg
               lowercase_     			=   [[0 for _ in range(self.n)] for _ in range(self.n)]


   def __mul__( self					:						int ,		__lowerCAmelCase					:						List[str])   ->       Union[str, Any]:
         lowercase_     			=   Matrix(self.n)
         for i in range(self.n):
               for j in range(self.n):
                     for k in range(self.n):
                           matrix.t[i][j] += self.t[i][k] * b.t[k][j]
         return matrix




def __a			(						__lowerCamelCase      :    List[str]			,		__lowerCamelCase      :    Dict					)						->				Optional[Any]:
      '''simple docstring'''


      lowercase_     			=   Matrix([[1, 0], [0, 1]]					)
      while b > 0:
            if b & 1:
                  matrix *= a
            a *= a
            b >>= 1
      return matrix


def __a			(						__lowerCamelCase      :    Tuple			,		__lowerCamelCase      :    Tuple			,		__lowerCamelCase      :    List[Any]					)						->				Dict:
      '''simple docstring'''


      if n == 1:
            return fa
      elif n == 2:
            return fa
      lowercase_     			=   Matrix([[1, 1], [1, 0]]					)
      lowercase_     			=   modular_exponentiation(__lowerCamelCase			,		n - 2					)
      return fa * matrix.t[0][0] + fa * matrix.t[0][1]


def __a			(						__lowerCamelCase      :    List[Any]			,		__lowerCamelCase      :    Union[str, Any]			,		__lowerCamelCase      :    List[str]					)						->				Optional[Any]:
      '''simple docstring'''


      if n == 1:
            return fa
      elif n == 2:
            return fa

      lowercase_     			=   fa
      lowercase_     			=   fa
      n -= 2

      while n > 0:
            lowercase_			,				lowercase_     			=   fn_a + fn_a, fn_a
            n -= 1

      return fn_a


def __a			(						)						->				str:
      '''simple docstring'''


      lowercase_     			=   "\nfrom random import randint\nfrom __main__ import fibonacci_with_matrix_exponentiation\n"
      lowercase_     			=   "fibonacci_with_matrix_exponentiation(randint(1,70000), 1, 1)"
      lowercase_     			=   timeit.timeit(setup=__lowerCamelCase			,		stmt=__lowerCamelCase			,		number=100					)
      print("With matrix exponentiation the average execution time is "			,		exec_time / 100					)
      return exec_time


def __a			(						)						->				Optional[Any]:
      '''simple docstring'''


      lowercase_     			=   "\nfrom random import randint\nfrom __main__ import simple_fibonacci\n"
      lowercase_     			=   "simple_fibonacci(randint(1,70000), 1, 1)"
      lowercase_     			=   timeit.timeit(setup=__lowerCamelCase			,		stmt=__lowerCamelCase			,		number=100					)
      print(
          "Without matrix exponentiation the average execution time is "			,		exec_time / 100					)
      return exec_time


def __a			(						)						->				Tuple:
      '''simple docstring'''


      matrix_exponentiation_time()
      simple_fibonacci_time()


if __name__ == "__main__":
       main()






