
"""simple docstring"""
from __future__ import annotations

_a      :			str					=							[True] * 1_000_001
_a      :			Optional[Any]					=							2
while i * i <= 1_000_000:
    if seive[i]:
        for j in range(i * i, 1_000_001, i):
            _a      :			Tuple					=							False
    i += 1
def 				a__   (   a   :				str		):

  """simple docstring"""







  return seive[n]
def 				a__   (   a   :				Tuple		):

  """simple docstring"""







  return any(digit in "02468" for digit in str(__UpperCamelCase		)		)
def 				a__   (   a   :				Any = 1_000_000		):

  """simple docstring"""







  _snake_case     :						Any						=   [2]  # result already includes the number 2.
  for num in range(3       ,     limit + 1       ,     2		):
    if is_prime(__UpperCamelCase		) and not contains_an_even_digit(__UpperCamelCase		):
      _snake_case     :						int						=   str(__UpperCamelCase		)
      _snake_case     :						Union[str, Any]						=   [int(str_num[j:] + str_num[:j]		) for j in range(len(__UpperCamelCase		)		)]
      if all(is_prime(__UpperCamelCase		) for i in list_nums		):
        result.append(__UpperCamelCase		)
  return result
def 				a__   (   ):

  """simple docstring"""







  return len(find_circular_primes()		)


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

"""simple docstring"""
from __future__ import annotations

from numpy import array, cos, cross, floataa, radians, sin
from numpy.typing import NDArray
def 				a__   (   a   :				float       ,     a   :				float       ,     a   :				bool = False		):

  """simple docstring"""







  if radian_mode:
    return [magnitude * cos(a		), magnitude * sin(a		)]
  return [magnitude * cos(radians(a		)		), magnitude * sin(radians(a		)		)]
def 				a__   (   a   :				NDArray[floataa]       ,     a   :				NDArray[floataa]       ,     a   :				float = 10**-1		):

  """simple docstring"""







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


if __name__ == "__main__":
    # Test to check if it works
    _a      :			Tuple					=							array(
        [
            polar_force(718.4, 180 - 30),
            polar_force(879.54, 45),
            polar_force(100, -90),
        ]
    )

    _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[Any]					=							array(
        [
            polar_force(30 * 9.81, 15),
            polar_force(215, 180 - 45),
            polar_force(264, 90 - 30),
        ]
    )

    _a      :			List[Any]					=							array([[0, 0], [0, 0], [0, 0]])

    assert in_static_equilibrium(forces, location)

    # Problem in image_data/2D_problems_1.jpg
    _a      :			List[str]					=							array([[0, -2_000], [0, -1_200], [0, 15_600], [0, -12_400]])

    _a      :			Optional[int]					=							array([[0, 0], [6, 0], [10, 0], [12, 0]])

    assert in_static_equilibrium(forces, location)

    import doctest

    doctest.testmod()

