





'''simple docstring'''

import math







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







def  a__    (    lowercase :					float = 0.1				)		->		int:





     """simple docstring"""

     _UpperCamelCase       =	3
     _UpperCamelCase       =	3

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


if __name__ == "__main__":
   import doctest

   doctest.testmod()










'''simple docstring'''

from __future__ import annotations







def  a__    (    lowercase :					list[int], lowercase :					list[int], lowercase :					int				)		->		tuple[float, list[float]]:





     """simple docstring"""

     _UpperCamelCase       =	list(range(len(lowercase				)				)				)
     _UpperCamelCase       =	[v / w for v, w in zip(lowercase, lowercase				)]
     index.sort(key=lambda lowercase				: ratio[i], reverse=lowercase				)

     _UpperCamelCase       =	0
     _UpperCamelCase       =	[0] * len(lowercase				)
     for i in index:
          if weight[i] <= capacity:
               _UpperCamelCase       =	1
               max_value += value[i]
               capacity -= weight[i]
          else:
               _UpperCamelCase       =	capacity / weight[i]
               max_value += value[i] * capacity / weight[i]
               break

     return max_value, fractions


if __name__ == "__main__":
   import doctest

   doctest.testmod()



