



'''simple docstring'''






from __future__ import annotations

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


def  snake_case_     (					_lowerCAmelCase  :						float   ,      _lowerCAmelCase  :						float   ,      _lowerCAmelCase  :						bool = False  )      ->   list[float]:
							if radian_mode:
														return [magnitude * cos(_lowerCAmelCase  ), magnitude * sin(_lowerCAmelCase  )]
							return [magnitude * cos(radians(_lowerCAmelCase  )  ), magnitude * sin(radians(_lowerCAmelCase  )  )]


def  snake_case_     (					_lowerCAmelCase  :						NDArray[floataa]   ,      _lowerCAmelCase  :						NDArray[floataa]   ,      _lowerCAmelCase  :						float = 10**-1  )      ->   bool:
							UpperCAmelCase :       NDArray[floataa] 							=		cross(_lowerCAmelCase   ,      _lowerCAmelCase  )
							UpperCAmelCase :       float 							=		sum(_lowerCAmelCase  )
							return abs(_lowerCAmelCase  ) < eps


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

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

						assert in_static_equilibrium(forces, location)

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

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

						assert in_static_equilibrium(forces, location)

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

						UpperCamelCase__:   List[str]								=			array([[0, 0], [6, 0], [10, 0], [12, 0]])

						assert in_static_equilibrium(forces, location)

						import doctest

						doctest.testmod()







'''simple docstring'''







from __future__ import annotations

import string
from itertools import cycle, product
from pathlib import Path

lowercase    :							str      =					(
    string.ascii_letters + string.digits + string.punctuation + string.whitespace
)
lowercase    :							list[int]      =					[ord(letter) for letter in string.ascii_lowercase]
lowercase    :							set[int]      =					{ord(char) for char in VALID_CHARS}

lowercase    :							list[str]      =					["the", "be", "to", "of", "and", "in", "that", "have"]







def 				SCREAMING_SNAKE_CASE__	(   __A			,				__A	)       ->	str | None:
	_snake_case   						=		""
	_snake_case   						=		42
	_snake_case   						=		42
	_snake_case   						=		42

	for keychar, cipherchar in zip(cycle(__A	)			,				__A	):
		_snake_case   						=		cipherchar ^ keychar
		if decodedchar not in VALID_INTS:
			return None
		decoded += chr(__A	)

	return decoded







def 				SCREAMING_SNAKE_CASE__	(   __A	)       ->	list[str]:
	_snake_case   						=		[]
	for key in product(__A			,				repeat=3	):
		_snake_case   						=		try_key(__A			,				__A	)
		if encoded is not None:
			possibles.append(__A	)
	return possibles







def 				SCREAMING_SNAKE_CASE__	(   __A			,				__A	)       ->	list[str]:
	return [possible for possible in possibles if common_word in possible.lower()]







def 				SCREAMING_SNAKE_CASE__	(   __A = "p059_cipher.txt"	)       ->	int:
	_snake_case   						=		42
	_snake_case   						=		42
	_snake_case   						=		42
	_snake_case   						=		42
	_snake_case   						=		Path(__A	).parent.joinpath(__A	).read_text(encoding='utf-8'	)

	_snake_case   						=		[int(__A	) for number in data.strip().split(','	)]

	_snake_case   						=		filter_valid_chars(__A	)
	for common_word in COMMON_WORDS:
		_snake_case   						=		filter_common_word(__A			,				__A	)
		if len(__A	) == 1:
			break

	_snake_case   						=		possibles[0]
	return sum(ord(__A	) for char in decoded_text	)


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

