




import functools


def 					_a							(					lowerCAmelCase    ,						lowerCAmelCase )->	int:

		# Validation
		if not isinstance(lowerCAmelCase    ,						lowerCAmelCase ) or not all(isinstance(lowerCAmelCase    ,						lowerCAmelCase ) for day in days ):
				raise ValueError('The parameter days should be a list of integers' )

		if len(lowerCAmelCase ) != 3 or not all(isinstance(lowerCAmelCase    ,						lowerCAmelCase ) for cost in costs ):
				raise ValueError('The parameter costs should be a list of three integers' )

		if len(lowerCAmelCase ) == 0:
				return 0

		if min(lowerCAmelCase ) <= 0:
				raise ValueError('All days elements should be greater than 0' )

		if max(lowerCAmelCase ) >= 366:
				raise ValueError('All days elements should be less than 366' )

		SCREAMING_SNAKE_CASE_					      =							set(lowerCAmelCase )

		@functools.cache
		def dynamic_programming(lowerCAmelCase ) -> int:
				if index > 365:
						return 0

				if index not in days_set:
						return dynamic_programming(index + 1 )

				return min(
				    costs[0] + dynamic_programming(index + 1 )    ,						costs[1] + dynamic_programming(index + 7 )    ,						costs[2] + dynamic_programming(index + 30 )    ,						)

		return dynamic_programming(1 )


if __name__ == "__main__":
						import doctest

						doctest.testmod()





from math import sqrt

import numpy as np
from sympy import symbols

# Coefficient
# Speed of light (m/s)
SCREAMING_SNAKE_CASE:     Optional[int]									= 2_9_9_7_9_2_4_5_8

# Symbols
SCREAMING_SNAKE_CASE				,					SCREAMING_SNAKE_CASE				,					SCREAMING_SNAKE_CASE				,					SCREAMING_SNAKE_CASE:     Tuple									= symbols('''ct x y z''')


def 					_a							(					lowerCAmelCase )->	float:
		if velocity > c:
				raise ValueError('Speed must not exceed light speed 299,792,458 [m/s]!' )
		elif velocity < 1:
				# Usually the speed should be much higher than 1 (c order of magnitude)
				raise ValueError('Speed must be greater than or equal to 1!' )

		return velocity / c


def 					_a							(					lowerCAmelCase )->	float:
		return 1 / sqrt(1 - beta(lowerCAmelCase ) ** 2 )


def 					_a							(					lowerCAmelCase )->	np.ndarray:
		return np.array(
		    [
		        [gamma(lowerCAmelCase ), -gamma(lowerCAmelCase ) * beta(lowerCAmelCase ), 0, 0],
		        [-gamma(lowerCAmelCase ) * beta(lowerCAmelCase ), gamma(lowerCAmelCase ), 0, 0],
		        [0, 0, 1, 0],
		        [0, 0, 0, 1],
		    ] )


def 					_a							(					lowerCAmelCase    ,						lowerCAmelCase = None )->	np.ndarray:
		# Ensure event is not empty
		if event is None:
				SCREAMING_SNAKE_CASE_					      =							np.array([ct, x, y, z] )  # Symbolic four vector
		else:
				event[0] *= c  # x0 is ct (speed of light * time)

		return transformation_matrix(lowerCAmelCase ) @ event


if __name__ == "__main__":
						import doctest

						doctest.testmod()

						# Example of symbolic vector:
						SCREAMING_SNAKE_CASE:     int									= transform(2_9_9_7_9_2_4_5)
						print('''Example of four vector: ''')
						print(f"""ct' = {four_vector[0]}""")
						print(f"""x' = {four_vector[1]}""")
						print(f"""y' = {four_vector[2]}""")
						print(f"""z' = {four_vector[3]}""")

						# Substitute symbols with numerical values
						SCREAMING_SNAKE_CASE:     List[Any]									= {ct: c, x: 1, y: 1, z: 1}
						SCREAMING_SNAKE_CASE:     Optional[Any]									= [four_vector[i].subs(sub_dict) for i in range(4)]

						print(f"""\n{numerical_vector}""")