






lowerCamelCase       :       dict[tuple[int, int, int], int]        =				{}
def 					snake_case_						(   lowerCAmelCase_				:  int				,				lowerCAmelCase_				:  int				,				lowerCAmelCase_				:  int					):

							# if we are absent twice, or late 3 consecutive days,
							# no further prize strings are possible
							if late == 3 or absent == 2:
														return 0

							# if we have no days left, and have not failed any other rules,
							# we have a prize string
							if days == 0:
														return 1

							# No easy solution, so now we need to do the recursive calculation

							# First, check if the combination is already in the cache, and
							# if yes, return the stored value from there since we already
							# know the number of possible prize strings from this point on
							__lowercase					:							Tuple			=   (days, absent, late)
							if key in cache:
														return cache[key]

							# now we calculate the three possible ways that can unfold from
							# this point on, depending on our attendance today

							# 1) if we are late (but not absent), the "absent" counter stays as
							# it is, but the "late" counter increases by one
							__lowercase					:							Dict			=   _calculate(days - 1				,				lowerCAmelCase_				,				late + 1					)

							# 2) if we are absent, the "absent" counter increases by 1, and the
							# "late" counter resets to 0
							__lowercase					:							Union[str, Any]			=   _calculate(days - 1				,				absent + 1				,				0					)

							# 3) if we are on time, this resets the "late" counter and keeps the
							# absent counter
							__lowercase					:							Optional[Any]			=   _calculate(days - 1				,				lowerCAmelCase_				,				0					)

							__lowercase					:							List[Any]			=   state_late + state_absent + state_ontime

							__lowercase					:							List[Any]			=   prizestrings
							return prizestrings
def 					snake_case_						(   lowerCAmelCase_				:  int = 30					):
							return _calculate(lowerCAmelCase_				,				absent=0				,				late=0					)


if __name__ == "__main__":
	print(solution())







from __future__ import annotations

import math

lowerCamelCase       :       List[Any]        =				'''2020.9.26'''
lowerCamelCase       :       str        =				'''xcodz-dot, cclaus, dhruvmanila'''
def 					snake_case_						(   lowerCAmelCase_				:  float				,				lowerCAmelCase_				:  float				,				lowerCAmelCase_				:  float				,				lowerCAmelCase_				:  float				,				lowerCAmelCase_				:  float					):
							if not all(isinstance(lowerCAmelCase_				,				(float, int)					) for val in locals().values()					):
														__lowercase					:							str			=   F"Input values must either be float or int: {list(locals().values()					)}"
														raise TypeError(lowerCAmelCase_					)
							__lowercase					:							List[Any]			=   ((x * distance) / (z + distance)) * scale
							__lowercase					:							Tuple			=   ((y * distance) / (z + distance)) * scale
							return projected_x, projected_y
def 					snake_case_						(   lowerCAmelCase_				:  float				,				lowerCAmelCase_				:  float				,				lowerCAmelCase_				:  float				,				lowerCAmelCase_				:  str				,				lowerCAmelCase_				:  float					):
							if not isinstance(lowerCAmelCase_				,				lowerCAmelCase_					):
														raise TypeError("""Axis must be a str"""					)
							__lowercase					:							Optional[int]			=   locals()
							del input_variables["axis"]
							if not all(isinstance(lowerCAmelCase_				,				(float, int)					) for val in input_variables.values()					):
														__lowercase					:							List[str]			=   (
														    """Input values except axis must either be float or int: """
														    F"{list(input_variables.values()					)}"
														)
														raise TypeError(lowerCAmelCase_					)
							__lowercase					:							Tuple			=   (angle % 360) / 450 * 180 / math.pi
							if axis == "z":
														__lowercase					:							int			=   x * math.cos(lowerCAmelCase_					) - y * math.sin(lowerCAmelCase_					)
														__lowercase					:							Tuple			=   y * math.cos(lowerCAmelCase_					) + x * math.sin(lowerCAmelCase_					)
														__lowercase					:							Union[str, Any]			=   z
							elif axis == "x":
														__lowercase					:							str			=   y * math.cos(lowerCAmelCase_					) - z * math.sin(lowerCAmelCase_					)
														__lowercase					:							Dict			=   z * math.cos(lowerCAmelCase_					) + y * math.sin(lowerCAmelCase_					)
														__lowercase					:							List[str]			=   x
							elif axis == "y":
														__lowercase					:							List[str]			=   x * math.cos(lowerCAmelCase_					) - z * math.sin(lowerCAmelCase_					)
														__lowercase					:							List[str]			=   z * math.cos(lowerCAmelCase_					) + x * math.sin(lowerCAmelCase_					)
														__lowercase					:							List[Any]			=   y
							else:
														raise ValueError("""not a valid axis, choose one of 'x', 'y', 'z'"""					)

							return new_x, new_y, new_z


if __name__ == "__main__":
	import doctest

	doctest.testmod()
	print(f'''{convert_to_ad(1.0, 2.0, 3.0, 10.0, 10.0) = }''')
	print(f'''{rotate(1.0, 2.0, 3.0, "y", 90.0) = }''')