




from math import radians as angle_to_radians
from math import sin

# Acceleration Constant on Earth (unit m/s^2)
__A						:		Optional[Any]          =						9.8_06_65





def      UpperCAmelCase  (						UpperCamelCase__						,			UpperCamelCase__   )     ->     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      UpperCAmelCase  (						UpperCamelCase__						,			UpperCamelCase__   )     ->     float:







				'''simple docstring'''


				check_args(lowerCamelCase__						,			lowerCamelCase__   )
				__lowerCAmelCase					=  angle_to_radians(2 * angle   )
				return round(init_velocity**2 * sin(lowerCamelCase__   ) / g						,			2   )





def      UpperCAmelCase  (						UpperCamelCase__						,			UpperCamelCase__   )     ->     float:







				'''simple docstring'''


				check_args(lowerCamelCase__						,			lowerCamelCase__   )
				__lowerCAmelCase					=  angle_to_radians(lowerCamelCase__   )
				return round(init_velocity**2 * sin(lowerCamelCase__   ) ** 2 / (2 * g)						,			2   )





def      UpperCAmelCase  (						UpperCamelCase__						,			UpperCamelCase__   )     ->     float:







				'''simple docstring'''


				check_args(lowerCamelCase__						,			lowerCamelCase__   )
				__lowerCAmelCase					=  angle_to_radians(lowerCamelCase__   )
				return round(2 * init_velocity * sin(lowerCamelCase__   ) / g						,			2   )





def      UpperCAmelCase  (						)     ->     None:







				'''simple docstring'''


				__lowerCAmelCase					=  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						:		Dict          =						float(input("Initial Velocity: ").strip())

	# Get input from user
	__A						:		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]""")













import math




class 	lowerCamelCase__				:






      def __init__(self					:    int		,		_snake_case					:    Dict		)       ->   Union[str, Any]:


       """simple docstring"""






       lowerCamelCase_							:    Optional[Any]							=     len(_snake_case		)
       lowerCamelCase_							:    Optional[Any]							=     [0] * (
           4 * self.N
       )  # approximate the overall size of segment tree with array N
       self.build(1		,		0		,		self.N - 1		)






      def      UpperCAmelCase_     (self					:    List[str]		,		_snake_case					:    List[str]		)       ->   int:


       """simple docstring"""






       return idx * 2






      def      UpperCAmelCase_     (self					:    Tuple		,		_snake_case					:    Dict		)       ->   Optional[Any]:


       """simple docstring"""






       return idx * 2 + 1






      def      UpperCAmelCase_     (self					:    List[Any]		,		_snake_case					:    List[Any]		,		_snake_case					:    str		,		_snake_case					:    List[Any]		)       ->   Optional[Any]:  # noqa: E741


       """simple docstring"""






       if l == r:
        lowerCamelCase_							:    List[Any]							=     A[l]
       else:
        lowerCamelCase_							:    int							=     (l + r) // 2
        self.build(self.left(_snake_case		)		,		_snake_case		,		_snake_case		)
        self.build(self.right(_snake_case		)		,		mid + 1		,		_snake_case		)
        lowerCamelCase_							:    Tuple							=     max(self.st[self.left(_snake_case		)]		,		self.st[self.right(_snake_case		)]		)






      def      UpperCAmelCase_     (self					:    str		,		_snake_case					:    Tuple		,		_snake_case					:    Any		,		_snake_case					:    str		)       ->   Tuple:


       """simple docstring"""






       return self.update_recursive(1		,		0		,		self.N - 1		,		a - 1		,		b - 1		,		_snake_case		)






      def      UpperCAmelCase_     (self					:    Tuple		,		_snake_case					:    List[str]		,		_snake_case					:    Tuple		,		_snake_case					:    Optional[int]		,		_snake_case					:    int		,		_snake_case					:    Tuple		,		_snake_case					:    List[str]		)       ->   Optional[Any]:  # noqa: E741


       """simple docstring"""






       if r < a or l > b:
        return True
       if l == r:
        lowerCamelCase_							:    Tuple							=     val
        return True
       lowerCamelCase_							:    Optional[int]							=     (l + r) // 2
       self.update_recursive(self.left(_snake_case		)		,		_snake_case		,		_snake_case		,		_snake_case		,		_snake_case		,		_snake_case		)
       self.update_recursive(self.right(_snake_case		)		,		mid + 1		,		_snake_case		,		_snake_case		,		_snake_case		,		_snake_case		)
       lowerCamelCase_							:    Union[str, Any]							=     max(self.st[self.left(_snake_case		)]		,		self.st[self.right(_snake_case		)]		)
       return True






      def      UpperCAmelCase_     (self					:    List[Any]		,		_snake_case					:    List[Any]		,		_snake_case					:    Optional[int]		)       ->   str:


       """simple docstring"""






       return self.query_recursive(1		,		0		,		self.N - 1		,		a - 1		,		b - 1		)






      def      UpperCAmelCase_     (self					:    Any		,		_snake_case					:    List[Any]		,		_snake_case					:    Optional[Any]		,		_snake_case					:    int		,		_snake_case					:    Optional[int]		,		_snake_case					:    Optional[Any]		)       ->   str:  # noqa: E741


       """simple docstring"""






       if r < a or l > b:
        return -math.inf
       if l >= a and r <= b:
        return self.st[idx]
       lowerCamelCase_							:    int							=     (l + r) // 2
       lowerCamelCase_							:    Optional[Any]							=     self.query_recursive(self.left(_snake_case		)		,		_snake_case		,		_snake_case		,		_snake_case		,		_snake_case		)
       lowerCamelCase_							:    Union[str, Any]							=     self.query_recursive(self.right(_snake_case		)		,		mid + 1		,		_snake_case		,		_snake_case		,		_snake_case		)
       return max(_snake_case		,		_snake_case		)






      def      UpperCAmelCase_     (self					:    str		)       ->   Tuple:


       """simple docstring"""






       lowerCamelCase_							:    Dict							=     []
       for i in range(1		,		N + 1		):
        show_list += [self.query(_snake_case		,		_snake_case		)]
       print(_snake_case		)


if __name__ == "__main__":
       UpperCamelCase											=      [1, 2, -4, 7, 3, -5, 6, 1_1, -2_0, 9, 1_4, 1_5, 5, 2, -8]
       UpperCamelCase											=      1_5
       UpperCamelCase											=      SegmentTree(A)
       print(segt.query(4, 6))
       print(segt.query(7, 1_1))
       print(segt.query(7, 1_2))
       segt.update(1, 3, 1_1_1)
       print(segt.query(1, 1_5))
       segt.update(7, 8, 2_3_5)
       segt.show_data()
