






from math import radians as angle_to_radians
from math import sin

# Acceleration Constant on Earth (unit m/s^2)
__lowerCamelCase						= 9.8_06_65






def    UpperCamelCase__  (   UpperCAmelCase    ,	UpperCAmelCase     )     ->		None:







							"""simple docstring"""





							if not isinstance(UpperCAmelCase    ,	(int, float)     ):
														raise TypeError('''Invalid velocity. Should be a positive number.'''     )

							if not isinstance(UpperCAmelCase    ,	(int, float)     ):
														raise TypeError('''Invalid angle. Range is 1-90 degrees.'''     )

							# Ensure valid angle
							if angle > 90 or angle < 1:
														raise ValueError('''Invalid angle. Range is 1-90 degrees.'''     )

							# Ensure valid velocity
							if init_velocity < 0:
														raise ValueError('''Invalid velocity. Should be a positive number.'''     )






def    UpperCamelCase__  (   UpperCAmelCase    ,	UpperCAmelCase     )     ->		float:







							"""simple docstring"""





							check_args(UpperCAmelCase    ,	UpperCAmelCase     )
							_a  :    Dict			=						angle_to_radians(2 * angle     )
							return round(init_velocity**2 * sin(UpperCAmelCase     ) / g    ,	2     )






def    UpperCamelCase__  (   UpperCAmelCase    ,	UpperCAmelCase     )     ->		float:







							"""simple docstring"""





							check_args(UpperCAmelCase    ,	UpperCAmelCase     )
							_a  :    Union[str, Any]			=						angle_to_radians(UpperCAmelCase     )
							return round(init_velocity**2 * sin(UpperCAmelCase     ) ** 2 / (2 * g)    ,	2     )






def    UpperCamelCase__  (   UpperCAmelCase    ,	UpperCAmelCase     )     ->		float:







							"""simple docstring"""





							check_args(UpperCAmelCase    ,	UpperCAmelCase     )
							_a  :    str			=						angle_to_radians(UpperCAmelCase     )
							return round(2 * init_velocity * sin(UpperCAmelCase     ) / g    ,	2     )






def    UpperCamelCase__  (   )     ->		None:







							"""simple docstring"""





							_a		,					_a  :    Any			=						25, 20
							assert horizontal_distance(UpperCAmelCase    ,	UpperCAmelCase     ) == 4_0.9_7
							assert max_height(UpperCAmelCase    ,	UpperCAmelCase     ) == 3.7_3
							assert total_time(UpperCAmelCase    ,	UpperCAmelCase     ) == 1.7_4


if __name__ == "__main__":
						from doctest import testmod

						testmod()

						# Get input from user
						__lowerCamelCase						= float(input('Initial Velocity: ').strip())

						# Get input from user
						__lowerCamelCase						= float(input('angle: ').strip())

						# Print results
						print()
						print('Results: ')
						print(F'''Horizontal Distance: {horizontal_distance(init_vel, angle)!s} [m]''')
						print(F'''Maximum Height: {max_height(init_vel, angle)!s} [m]''')
						print(F'''Total Time: {total_time(init_vel, angle)!s} [s]''')







def    UpperCamelCase__  (   UpperCAmelCase     )     ->		tuple[int, int]:







							"""simple docstring"""





							if len(UpperCAmelCase     ) == 1:
														return a[0], a[0]
							else:
														# split A into half.
														_a  :    Union[str, Any]			=						a[: len(UpperCAmelCase     ) // 2]
														_a  :    Optional[Any]			=						a[len(UpperCAmelCase     ) // 2 :]

														# 2 sub problems, 1/2 of original size.
														_a		,					_a  :    Union[str, Any]			=						max_difference(UpperCAmelCase     )
														_a		,					_a  :    List[Any]			=						max_difference(UpperCAmelCase     )

														# get min of first and max of second
														# linear time
														_a  :    Union[str, Any]			=						min(UpperCAmelCase     )
														_a  :    Any			=						max(UpperCAmelCase     )

														# 3 cases, either (small1, big1),
														# (min_first, max_second), (small2, big2)
														# constant comparisons
														if biga - smalla > max_second - min_first and biga - smalla > biga - smalla:
																					return smalla, biga
														elif biga - smalla > max_second - min_first:
																					return smalla, biga
														else:
																					return min_first, max_second


if __name__ == "__main__":
						import doctest

						doctest.testmod()