



from __future__ import annotations



def  __a  (					lowerCAmelCase_     :      int       )   ->				int | None:






						'''simple docstring'''



						for r in range(1    ,lowerCAmelCase_       ):
												UpperCAmelCase_=     []
												for x in range(n - 1       ):
																		UpperCAmelCase_=     pow(lowerCAmelCase_    ,lowerCAmelCase_    ,lowerCAmelCase_       )
																		if val in li:
																								break
																		li.append(lowerCAmelCase_       )
												else:
																		return r
						return None


if __name__ == "__main__":
	__A       					=		int(input('''Enter a prime number q: '''))
	__A       					=		find_primitive(q)
	if a is None:
		print(f'Cannot find the primitive for the value: {a!r}')
	else:
		__A       					=		int(input('''Enter private key of A: '''))
		__A       					=		pow(a, a_private, q)
		__A       					=		int(input('''Enter private key of B: '''))
		__A       					=		pow(a, b_private, q)

		__A       					=		pow(b_public, a_private, q)
		__A       					=		pow(a_public, b_private, q)

		print('''The key value generated by A is: ''', a_secret)
		print('''The key value generated by B is: ''', b_secret)









from math import radians as angle_to_radians
from math import sin

# Acceleration Constant on Earth (unit m/s^2)
__A       					=		9.8_0_6_6_5



def  __a  (					lowerCAmelCase_     :      float    ,lowerCAmelCase_     :      float       )   ->				None:






						'''simple docstring'''



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

						if not isinstance(lowerCAmelCase_    ,(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  __a  (					lowerCAmelCase_     :      float    ,lowerCAmelCase_     :      float       )   ->				float:






						'''simple docstring'''



						check_args(lowerCAmelCase_    ,lowerCAmelCase_       )
						UpperCAmelCase_=     angle_to_radians(2 * angle       )
						return round(init_velocity**2 * sin(lowerCAmelCase_       ) / g    ,2       )



def  __a  (					lowerCAmelCase_     :      float    ,lowerCAmelCase_     :      float       )   ->				float:






						'''simple docstring'''



						check_args(lowerCAmelCase_    ,lowerCAmelCase_       )
						UpperCAmelCase_=     angle_to_radians(lowerCAmelCase_       )
						return round(init_velocity**2 * sin(lowerCAmelCase_       ) ** 2 / (2 * g)    ,2       )



def  __a  (					lowerCAmelCase_     :      float    ,lowerCAmelCase_     :      float       )   ->				float:






						'''simple docstring'''



						check_args(lowerCAmelCase_    ,lowerCAmelCase_       )
						UpperCAmelCase_=     angle_to_radians(lowerCAmelCase_       )
						return round(2 * init_velocity * sin(lowerCAmelCase_       ) / g    ,2       )



def  __a  (					)   ->				None:






						'''simple docstring'''



						UpperCAmelCase_,     UpperCAmelCase_=     25, 20
						assert horizontal_distance(lowerCAmelCase_    ,lowerCAmelCase_       ) == 40.97
						assert max_height(lowerCAmelCase_    ,lowerCAmelCase_       ) == 3.73
						assert total_time(lowerCAmelCase_    ,lowerCAmelCase_       ) == 1.74


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

	testmod()

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

	# Get input from user
	__A       					=		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]')




