"""simple docstring"""







from math import radians as angle_to_radians
from math import sin

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



def       A__    (	lowercase_     :	float      , lowercase_     :	float						)  ->							None:

   # Ensure valid instance
   if not isinstance(lowercase_      , (int, float)						):
      raise TypeError('Invalid velocity. Should be a positive number.'						)

   if not isinstance(lowercase_      , (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__    (	lowercase_     :	float      , lowercase_     :	float						)  ->							float:
   check_args(lowercase_      , lowercase_						)
   __lowerCamelCase    		=					angle_to_radians(2 * angle						)
   return round(init_velocity**2 * sin(lowercase_						) / g      , 2						)



def       A__    (	lowercase_     :	float      , lowercase_     :	float						)  ->							float:
   check_args(lowercase_      , lowercase_						)
   __lowerCamelCase    		=					angle_to_radians(lowercase_						)
   return round(init_velocity**2 * sin(lowercase_						) ** 2 / (2 * g)      , 2						)



def       A__    (	lowercase_     :	float      , lowercase_     :	float						)  ->							float:
   check_args(lowercase_      , lowercase_						)
   __lowerCamelCase    		=					angle_to_radians(lowercase_						)
   return round(2 * init_velocity * sin(lowercase_						) / g      , 2						)



def       A__    (	)  ->							None:
   __lowerCamelCase		,__lowerCamelCase    		=					25, 20
   assert horizontal_distance(lowercase_      , lowercase_						) == 4_0.9_7
   assert max_height(lowercase_      , lowercase_						) == 3.7_3
   assert total_time(lowercase_      , lowercase_						) == 1.7_4


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

     testmod()

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

     # Get input from user
     _SCREAMING_SNAKE_CASE	:		int   =   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       _a (		SCREAMING_SNAKE_CASE_				:							int , SCREAMING_SNAKE_CASE_				:							int	):
					if a < b:
										return gcd(SCREAMING_SNAKE_CASE_ , SCREAMING_SNAKE_CASE_	)
					if a % b == 0:
										return b
					return gcd(SCREAMING_SNAKE_CASE_ , a % b	)







def       _a (		SCREAMING_SNAKE_CASE_				:							int , SCREAMING_SNAKE_CASE_				:							int , SCREAMING_SNAKE_CASE_				:							int	):
					if y == 0:
										return 1
					__lowerCAmelCase							  =			power(SCREAMING_SNAKE_CASE_ , y // 2 , SCREAMING_SNAKE_CASE_	) % mod
					__lowerCAmelCase							  =			(temp * temp) % mod
					if y % 2 == 1:
										__lowerCAmelCase							  =			(temp * x) % mod
					return temp







def       _a (		SCREAMING_SNAKE_CASE_				:							int	):
					__lowerCAmelCase							  =			2
					while b < n:
										if gcd(SCREAMING_SNAKE_CASE_ , SCREAMING_SNAKE_CASE_	) == 1 and power(SCREAMING_SNAKE_CASE_ , n - 1 , SCREAMING_SNAKE_CASE_	) != 1:
															return False
										b += 1
					return True


if __name__ == "__main__":
					UpperCamelCase__            =     int(input("""Enter number: """).strip())
					if is_carmichael_number(number):
										print(f'''{number} is a Carmichael Number.''')
					else:
										print(f'''{number} is not a Carmichael Number.''')




