




from __future__ import annotations

def      A      (      _SCREAMING_SNAKE_CASE    )	-> list[int]:
       lowerCamelCase   :      Optional[Any]			 =					[True] * limit
       lowerCamelCase   :      Any			 =					False
       lowerCamelCase   :      int			 =					False
       lowerCamelCase   :      List[str]			 =					True

       for i in range(3 ,int(limit**0.5 + 1    ) ,2    ):
              lowerCamelCase   :      Dict			 =					i * 2
              while index < limit:
                     lowerCamelCase   :      str			 =					False
                     lowerCamelCase   :      Union[str, Any]			 =					index + i

       lowerCamelCase   :      int			 =					[2]

       for i in range(3 ,lowerCAmelCase_ ,2    ):
              if is_prime[i]:
                     primes.append(lowerCAmelCase_    )

       return primes

def      A      (      _SCREAMING_SNAKE_CASE = 100_0000    )	-> int:
       lowerCamelCase   :      str			 =					prime_sieve(lowerCAmelCase_    )
       lowerCamelCase   :      Dict			 =					0
       lowerCamelCase   :      Dict			 =					0

       for i in range(len(lowerCAmelCase_    )    ):
              for j in range(i + length ,len(lowerCAmelCase_    )    ):
                     lowerCamelCase   :      Optional[int]			 =					sum(primes[i:j]    )
                     if sol >= ceiling:
                            break

                     if sol in primes:
                            lowerCamelCase   :      Any			 =					j - i
                            lowerCamelCase   :      List[Any]			 =					sol

       return largest


if __name__ == "__main__":
       print(f'''{solution() = }''')











'''simple docstring'''






from __future__ import annotations

from numpy import array, cos, cross, floataa, radians, sin
from numpy.typing import NDArray




def     snake_case_					(     lowerCAmelCase_       ,   lowerCAmelCase_       ,   lowerCAmelCase_ = False		)->		list[float]:





       '''simple docstring'''


       if radian_mode:
              return [magnitude * cos(lowerCAmelCase_		), magnitude * sin(lowerCAmelCase_		)]
       return [magnitude * cos(radians(lowerCAmelCase_		)		), magnitude * sin(radians(lowerCAmelCase_		)		)]




def     snake_case_					(     lowerCAmelCase_       ,   lowerCAmelCase_       ,   lowerCAmelCase_ = 10**-1		)->		bool:





       '''simple docstring'''


       _UpperCAmelCase  :						NDArray[floataa]			     = cross(lowerCAmelCase_       ,   lowerCAmelCase_		)
       _UpperCAmelCase  :						float			     = sum(lowerCAmelCase_		)
       return abs(lowerCAmelCase_		) < eps


if __name__ == "__main__":
   # Test to check if it works
   A_							: str						 =	array(
       [
           polar_force(718.4, 1_8_0 - 3_0),
           polar_force(879.54, 4_5),
           polar_force(1_0_0, -9_0),
       ]
   )

   A_							: NDArray[floataa]						 =	array([[0, 0], [0, 0], [0, 0]])

   assert in_static_equilibrium(forces, location)

   # Problem 1 in image_data/2D_problems.jpg
   A_							: List[str]						 =	array(
       [
           polar_force(3_0 * 9.81, 1_5),
           polar_force(2_1_5, 1_8_0 - 4_5),
           polar_force(2_6_4, 9_0 - 3_0),
       ]
   )

   A_							: Tuple						 =	array([[0, 0], [0, 0], [0, 0]])

   assert in_static_equilibrium(forces, location)

   # Problem in image_data/2D_problems_1.jpg
   A_							: Dict						 =	array([[0, -2_0_0_0], [0, -1_2_0_0], [0, 1_5_6_0_0], [0, -1_2_4_0_0]])

   A_							: Union[str, Any]						 =	array([[0, 0], [6, 0], [1_0, 0], [1_2, 0]])

   assert in_static_equilibrium(forces, location)

   import doctest

   doctest.testmod()



