


'''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__					:float = 0.1						)				->					int:




     '''simple docstring'''



     _a      =							3
     _a      =							3

     while primes / (2 * j - 1) >= ratio:
          for i in range(j * j + j + 1			,  (j + 2) * (j + 2)			,  j + 1						):
               primes += is_prime(lowerCAmelCase__						)
          j += 2
     return j


if __name__ == "__main__":
 import doctest

 doctest.testmod()





'''simple docstring'''






def 		_A			(lowerCAmelCase__					:int						)				->					int:




     '''simple docstring'''



     assert (
         isinstance(lowerCAmelCase__			,  lowerCAmelCase__						) and number_of_steps > 0
     ), f'number_of_steps needs to be positive integer, your input {number_of_steps}'
     if number_of_steps == 1:
          return 1
     _a ,				_a      =							1, 1
     for _ in range(number_of_steps - 1						):
          _a ,				_a      =							current + previous, current
     return current


if __name__ == "__main__":
 import doctest

 doctest.testmod()

