



from __future__ import annotations

import random

from matplotlib import animation
from matplotlib import pyplot as plt

# Frame rate of the animation
__A				    =						20

# Time between time steps in seconds
__A				    =						INTERVAL / 1000






class 		lowercase						:






	"""simple docstring"""


	def __init__(	self	:						List[Any]						,  __UpperCAmelCase	:						float						,  __UpperCAmelCase	:						float						,  __UpperCAmelCase	:						float						,  __UpperCAmelCase	:						float						,  __UpperCAmelCase	:						float = 1.0						,  __UpperCAmelCase	:						float = 1.0						,  __UpperCAmelCase	:						str = "blue"						,  )			-> None:
							UpperCAmelCase_=   position_x
							UpperCAmelCase_=   position_y
							UpperCAmelCase_=   velocity_x
							UpperCAmelCase_=   velocity_y
							UpperCAmelCase_=   mass
							UpperCAmelCase_=   size
							UpperCAmelCase_=   color




	@property
	def   _SCREAMING_SNAKE_CASE		(	self	:						Optional[Any]     )			-> tuple[float, float]:
							return self.position_x, self.position_y




	@property
	def   _SCREAMING_SNAKE_CASE		(	self	:						str     )			-> tuple[float, float]:
							return self.velocity_x, self.velocity_y




	def   _SCREAMING_SNAKE_CASE		(	self	:						Tuple						,  __UpperCAmelCase	:						float						,  __UpperCAmelCase	:						float						,  __UpperCAmelCase	:						float     )			-> None:
							self.velocity_x += force_x * delta_time
							self.velocity_y += force_y * delta_time




	def   _SCREAMING_SNAKE_CASE		(	self	:						str						,  __UpperCAmelCase	:						float     )			-> None:
							self.position_x += self.velocity_x * delta_time
							self.position_y += self.velocity_y * delta_time






class 		lowercase						:






	"""simple docstring"""


	def __init__(	self	:						Optional[int]						,  __UpperCAmelCase	:						list[Body]						,  __UpperCAmelCase	:						float = 1.0						,  __UpperCAmelCase	:						float = 1.0						,  __UpperCAmelCase	:						float = 0.0						,  )			-> None:
							UpperCAmelCase_=   bodies
							UpperCAmelCase_=   gravitation_constant
							UpperCAmelCase_=   time_factor
							UpperCAmelCase_=   softening_factor




	def __len__(	self	:						List[str]     )			-> int:
							return len(self.bodies     )




	def   _SCREAMING_SNAKE_CASE		(	self	:						int						,  __UpperCAmelCase	:						float     )			-> None:
							for bodya in self.bodies:
													UpperCAmelCase_=   0.0
													UpperCAmelCase_=   0.0
													for bodya in self.bodies:
																			if bodya != bodya:
																									UpperCAmelCase_=   bodya.position_x - bodya.position_x
																									UpperCAmelCase_=   bodya.position_y - bodya.position_y

																									# Calculation of the distance using Pythagoras's theorem
																									# Extra factor due to the softening technique
																									UpperCAmelCase_=   (dif_x**2 + dif_y**2 + self.softening_factor) ** (
																									    1 / 2
																									)

																									# Newton's law of universal gravitation.
																									force_x += (
																									    self.gravitation_constant * bodya.mass * dif_x / distance**3
																									)
																									force_y += (
																									    self.gravitation_constant * bodya.mass * dif_y / distance**3
																									)

            # Update the body's velocity once all the force components have been added
													bodya.update_velocity(__UpperCAmelCase						,  __UpperCAmelCase						,  delta_time * self.time_factor     )

							# Update the positions only after all the velocities have been updated
							for body in self.bodies:
													body.update_position(delta_time * self.time_factor     )



def        __a     (    lowerCAmelCase_   :					BodySystem			,lowerCAmelCase_   :					float			,lowerCAmelCase_   :					list[plt.Circle]				)      -> None:






						'''simple docstring'''



						body_system.update_system(lowerCAmelCase_				)

						# Update the positions of the patches
						for patch, body in zip(lowerCAmelCase_			,body_system.bodies				):
												UpperCAmelCase_=   (body.position_x, body.position_y)



def        __a     (    lowerCAmelCase_   :					str			,lowerCAmelCase_   :					BodySystem			,lowerCAmelCase_   :					float = -1			,lowerCAmelCase_   :					float = 1			,lowerCAmelCase_   :					float = -1			,lowerCAmelCase_   :					float = 1			,)      -> None:






						'''simple docstring'''



						UpperCAmelCase_=   plt.figure()
						fig.canvas.set_window_title(lowerCAmelCase_				)
						UpperCAmelCase_=   plt.axes(
						    xlim=(x_start, x_end)			,ylim=(y_start, y_end)				)  # Set section to be plotted
						plt.gca().set_aspect("""equal"""				)  # Fix aspect ratio

						# Each body is drawn as a patch by the plt-function
						UpperCAmelCase_=   [
						    plt.Circle((body.position_x, body.position_y)			,body.size			,fc=body.color				)
						    for body in body_system.bodies
						]

						for patch in patches:
												ax.add_patch(lowerCAmelCase_				)

						# Function called at each step of the animation
						def update(lowerCAmelCase_   :					int				) -> list[plt.Circle]:
												update_step(lowerCAmelCase_			,lowerCAmelCase_			,lowerCAmelCase_				)
												return patches

						UpperCAmelCase_=   animation.FuncAnimation(  # noqa: F841
						    lowerCAmelCase_			,lowerCAmelCase_			,interval=lowerCAmelCase_			,blit=lowerCAmelCase_				)

						plt.show()



def        __a     (    )      -> BodySystem:






						'''simple docstring'''



						UpperCAmelCase_=   0.9_700_436
						UpperCAmelCase_=   -0.24_308_753
						UpperCAmelCase_=   0.466_203_685
						UpperCAmelCase_=   0.43_236_573

						UpperCAmelCase_=   [
						    Body(lowerCAmelCase_			,lowerCAmelCase_			,lowerCAmelCase_			,lowerCAmelCase_			,size=0.2			,color="""red"""				),
						    Body(-position_x			,-position_y			,lowerCAmelCase_			,lowerCAmelCase_			,size=0.2			,color="""green"""				),
						    Body(0			,0			,-2 * velocity_x			,-2 * velocity_y			,size=0.2			,color="""blue"""				),
						]
						return BodySystem(lowerCAmelCase_			,time_factor=3				)



def        __a     (    )      -> BodySystem:






						'''simple docstring'''



						UpperCAmelCase_=   7.3476E22
						UpperCAmelCase_=   5.972E24
						UpperCAmelCase_=   10_22
						UpperCAmelCase_=   3_84_39_90_00
						UpperCAmelCase_=   6.674E-11

						# Calculation of the respective velocities so that total impulse is zero,
						# i.e. the two bodies together don't move
						UpperCAmelCase_=   earth_mass * velocity_dif / (earth_mass + moon_mass)
						UpperCAmelCase_=   moon_velocity - velocity_dif

						UpperCAmelCase_=   Body(-earth_moon_distance			,0			,0			,lowerCAmelCase_			,lowerCAmelCase_			,10_00_00_00			,"""grey"""				)
						UpperCAmelCase_=   Body(0			,0			,0			,lowerCAmelCase_			,lowerCAmelCase_			,50_00_00_00			,"""blue"""				)
						return BodySystem([earth, moon]			,lowerCAmelCase_			,time_factor=1_00_00_00				)



def        __a     (    )      -> BodySystem:






						'''simple docstring'''



						UpperCAmelCase_=   []
						for _ in range(10				):
												UpperCAmelCase_=   random.uniform(-0.5			,0.5				)
												UpperCAmelCase_=   random.uniform(-0.5			,0.5				)

												# Bodies are created pairwise with opposite velocities so that the
												# total impulse remains zero
												bodies.append(
												    Body(
												        random.uniform(-0.5			,0.5				)			,random.uniform(-0.5			,0.5				)			,lowerCAmelCase_			,lowerCAmelCase_			,size=0.05			,)				)
												bodies.append(
												    Body(
												        random.uniform(-0.5			,0.5				)			,random.uniform(-0.5			,0.5				)			,-velocity_x			,-velocity_y			,size=0.05			,)				)
						return BodySystem(lowerCAmelCase_			,0.01			,10			,0.1				)


if __name__ == "__main__":
	plot('''Figure-8 solution to the 3-body-problem''', example_a(), -2, 2, -2, 2)
	plot(
	    '''Moon\'s orbit around the earth''',
	    example_a(),
	    -4_3000_0000,
	    4_3000_0000,
	    -4_3000_0000,
	    4_3000_0000,
	)
	plot('''Random system with many bodies''', example_a(), -1.5, 1.5, -1.5, 1.5)









def        __a     (    lowerCAmelCase_   :					int				)      -> int:






						'''simple docstring'''



						if number != int(lowerCAmelCase_				):
												raise ValueError("""factorial() only accepts integral values"""				)
						if number < 0:
												raise ValueError("""factorial() not defined for negative values"""				)
						UpperCAmelCase_=   1
						for i in range(1			,number + 1				):
												value *= i
						return value



def        __a     (    lowerCAmelCase_   :					int				)      -> int:






						'''simple docstring'''



						if not isinstance(lowerCAmelCase_			,lowerCAmelCase_				):
												raise ValueError("""factorial() only accepts integral values"""				)
						if n < 0:
												raise ValueError("""factorial() not defined for negative values"""				)
						return 1 if n == 0 or n == 1 else n * factorial(n - 1				)


if __name__ == "__main__":
	import doctest

	doctest.testmod()

	__A				    =						int(input('''Enter a positive integer: ''').strip() or 0)
	print(f'factorial{n} is {factorial(n)}')




