


import functools




def      UpperCAmelCase__ (lowerCAmelCase_						,		lowerCAmelCase_     ):




					'''simple docstring'''


					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()




"""simple docstring"""







from math import asin, atan, cos, radians, sin, sqrt, tan

a__       :							List[str]        =  6_37_81_37.0
a__       :							Tuple        =  6_35_67_52.31_42_45
a__       :							str        =  6_3_7_8_1_3_7




def      UpperCAmelCase__ (lowerCAmelCase_						,		lowerCAmelCase_						,		lowerCAmelCase_						,		lowerCAmelCase_     ):




					'''simple docstring'''


					__SCREAMING_SNAKE_CASE		     =       (AXIS_A - AXIS_B) / AXIS_A
					__SCREAMING_SNAKE_CASE		     =       atan((1 - flattening) * tan(radians(lowerCAmelCase_     )     )     )
					__SCREAMING_SNAKE_CASE		     =       atan((1 - flattening) * tan(radians(lowerCAmelCase_     )     )     )
					__SCREAMING_SNAKE_CASE		     =       radians(lowerCAmelCase_     )
					__SCREAMING_SNAKE_CASE		     =       radians(lowerCAmelCase_     )
					# Equation
					__SCREAMING_SNAKE_CASE		     =       sin((phi_a - phi_a) / 2     )
					__SCREAMING_SNAKE_CASE		     =       sin((lambda_a - lambda_a) / 2     )
					# Square both values
					sin_sq_phi *= sin_sq_phi
					sin_sq_lambda *= sin_sq_lambda
					__SCREAMING_SNAKE_CASE		     =       sqrt(sin_sq_phi + (cos(lowerCAmelCase_     ) * cos(lowerCAmelCase_     ) * sin_sq_lambda)     )
					return 2 * RADIUS * asin(lowerCAmelCase_     )


if __name__ == "__main__":
		import doctest

		doctest.testmod()
