from __future__ import annotations

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







def 						A__  (					__A   , __A   , __A = 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   , __A   , __A = 10**-1	):







    '''simple docstring'''
    _lowerCamelCase     :		NDArray[floataa] 						=						cross(__A   , __A	)
    _lowerCamelCase     :		float 						=						sum(__A	)
    return abs(__A	) < eps


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

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

    assert in_static_equilibrium(forces, location)

    # Problem 1 in image_data/2D_problems.jpg
    lowerCAmelCase			:							Any     =			array(
        [
            polar_force(30 * 9.81, 15),
            polar_force(215, 180 - 45),
            polar_force(264, 90 - 30),
        ]
    )

    lowerCAmelCase			:							int     =			array([[0, 0], [0, 0], [0, 0]])

    assert in_static_equilibrium(forces, location)

    # Problem in image_data/2D_problems_1.jpg
    lowerCAmelCase			:							List[str]     =			array([[0, -2000], [0, -1200], [0, 15600], [0, -12400]])

    lowerCAmelCase			:							Any     =			array([[0, 0], [6, 0], [10, 0], [12, 0]])

    assert in_static_equilibrium(forces, location)

    import doctest

    doctest.testmod()





lowerCAmelCase			:							Tuple     =0  # The first color of the flag.
lowerCAmelCase			:							Union[str, Any]     =1  # The second color of the flag.
lowerCAmelCase			:							Any     =2  # The third color of the flag.
lowerCAmelCase			:							List[str]     =(red, white, blue)







def 						A__  (					__A	):







    '''simple docstring'''
    if not sequence:
        return []
    if len(__A	) == 1:
        return list(__A	)
    _lowerCamelCase     :		int 						=						0
    _lowerCamelCase     :		Dict 						=						len(__A	) - 1
    _lowerCamelCase     :		str 						=						0
    while mid <= high:
        if sequence[mid] == colors[0]:
            _lowerCamelCase						,							_lowerCamelCase     :		Tuple 						=						sequence[mid], sequence[low]
            low += 1
            mid += 1
        elif sequence[mid] == colors[1]:
            mid += 1
        elif sequence[mid] == colors[2]:
            _lowerCamelCase						,							_lowerCamelCase     :		str 						=						sequence[high], sequence[mid]
            high -= 1
        else:
            _lowerCamelCase     :		int 						=						F"""The elements inside the sequence must contains only {colors} values"""
            raise ValueError(__A	)
    return sequence


if __name__ == "__main__":
    import doctest

    doctest.testmod()

    lowerCAmelCase			:							List[str]     =input("Enter numbers separated by commas:\n").strip()
    lowerCAmelCase			:							Dict     =[int(item.strip()) for item in user_input.split(",")]
    print(F"""{dutch_national_flag_sort(unsorted)}""")




