




"""simple docstring"""




def       __UpperCAmelCase      (				__UpperCamelCase = 10_00					):
			__lowercase	:       Optional[Any]				=   0
			for i in range(__UpperCamelCase					):
						if i % 3 == 0 or i % 5 == 0:
									result += i
			return result


if __name__ == "__main__":
			print(F"{solution() = }")









"""simple docstring"""




from __future__ import annotations

import random

from matplotlib import animation
from matplotlib import pyplot as plt

# Frame rate of the animation
a_            =   2_0

# Time between time steps in seconds
a_            =   INTERVAL / 1_0_0_0

class        UpperCAmelCase_  :
		def __init__(		self							,		UpperCamelCase_							,		UpperCamelCase_							,		UpperCamelCase_							,		UpperCamelCase_							,		UpperCamelCase_ = 1.0							,		UpperCamelCase_ = 1.0							,		UpperCamelCase_ = "blue"							,		)		->   None:
					__lowercase	:       Optional[int]				=   position_x
					__lowercase	:       List[Any]				=   position_y
					__lowercase	:       Optional[int]				=   velocity_x
					__lowercase	:       List[str]				=   velocity_y
					__lowercase	:       List[Any]				=   mass
					__lowercase	:       Tuple				=   size
					__lowercase	:       Tuple				=   color
		@property
		def 					_lowerCamelCase    (		self   )		->   tuple[float, float]:
					return self.position_x, self.position_y
		@property
		def 					_lowerCamelCase    (		self   )		->   tuple[float, float]:
					return self.velocity_x, self.velocity_y
		def 					_lowerCamelCase    (		self							,		UpperCamelCase_							,		UpperCamelCase_							,		UpperCamelCase_   )		->   None:
					self.velocity_x += force_x * delta_time
					self.velocity_y += force_y * delta_time
		def 					_lowerCamelCase    (		self							,		UpperCamelCase_   )		->   None:
					self.position_x += self.velocity_x * delta_time
					self.position_y += self.velocity_y * delta_time


class        UpperCAmelCase_  :
		def __init__(		self							,		UpperCamelCase_							,		UpperCamelCase_ = 1.0							,		UpperCamelCase_ = 1.0							,		UpperCamelCase_ = 0.0							,		)		->   None:
					__lowercase	:       int				=   bodies
					__lowercase	:       Dict				=   gravitation_constant
					__lowercase	:       List[Any]				=   time_factor
					__lowercase	:       List[str]				=   softening_factor
		def __len__(		self   )		->   int:
					return len(self.bodies   )
		def 					_lowerCamelCase    (		self							,		UpperCamelCase_   )		->   None:
					for bodya in self.bodies:
								__lowercase	:       Optional[Any]				=   0.0
								__lowercase	:       Any				=   0.0
								for bodya in self.bodies:
											if bodya != bodya:
														__lowercase	:       Union[str, Any]				=   bodya.position_x - bodya.position_x
														__lowercase	:       str				=   bodya.position_y - bodya.position_y

														# Calculation of the distance using Pythagoras's theorem
														# Extra factor due to the softening technique
														__lowercase	:       str				=   (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       __UpperCAmelCase      (				__UpperCamelCase					,							__UpperCamelCase					,							__UpperCamelCase					):
			body_system.update_system(__UpperCamelCase					)

			# Update the positions of the patches
			for patch, body in zip(__UpperCamelCase					,							body_system.bodies					):
						__lowercase	:       List[str]				=   (body.position_x, body.position_y)







def       __UpperCAmelCase      (				__UpperCamelCase					,							__UpperCamelCase					,							__UpperCamelCase = -1					,							__UpperCamelCase = 1					,							__UpperCamelCase = -1					,							__UpperCamelCase = 1					,							):
			__lowercase	:       List[str]				=   plt.figure()
			fig.canvas.set_window_title(__UpperCamelCase					)
			__lowercase	:       List[Any]				=   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
			__lowercase	:       Any				=   [
			    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(__UpperCamelCase					)

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

			__lowercase	:       Tuple				=   animation.FuncAnimation(  # noqa: F841
			    __UpperCamelCase					,							__UpperCamelCase					,							interval=__UpperCamelCase					,							blit=__UpperCamelCase					)

			plt.show()







def       __UpperCAmelCase      (				):
			__lowercase	:       Dict				=   0.9_700_436
			__lowercase	:       Tuple				=   -0.24_308_753
			__lowercase	:       Any				=   0.466_203_685
			__lowercase	:       str				=   0.43_236_573

			__lowercase	:       int				=   [
			    Body(__UpperCamelCase					,							__UpperCamelCase					,							__UpperCamelCase					,							__UpperCamelCase					,							size=0.2					,							color='''red'''					),
			    Body(-position_x					,							-position_y					,							__UpperCamelCase					,							__UpperCamelCase					,							size=0.2					,							color='''green'''					),
			    Body(0					,							0					,							-2 * velocity_x					,							-2 * velocity_y					,							size=0.2					,							color='''blue'''					),
			]
			return BodySystem(__UpperCamelCase					,							time_factor=3					)







def       __UpperCAmelCase      (				):
			__lowercase	:       Tuple				=   7.3_476e22
			__lowercase	:       Optional[int]				=   5.972e24
			__lowercase	:       str				=   10_22
			__lowercase	:       Any				=   3_84_39_90_00
			__lowercase	:       Optional[int]				=   6.674e-11

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

			__lowercase	:       Tuple				=   Body(-earth_moon_distance					,							0					,							0					,							__UpperCamelCase					,							__UpperCamelCase					,							10_00_00_00					,							'''grey'''					)
			__lowercase	:       Dict				=   Body(0					,							0					,							0					,							__UpperCamelCase					,							__UpperCamelCase					,							50_00_00_00					,							'''blue'''					)
			return BodySystem([earth, moon]					,							__UpperCamelCase					,							time_factor=1_00_00_00					)







def       __UpperCAmelCase      (				):
			__lowercase	:       Optional[Any]				=   []
			for _ in range(10					):
						__lowercase	:       str				=   random.uniform(-0.5					,							0.5					)
						__lowercase	:       int				=   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					)					,							__UpperCamelCase					,							__UpperCamelCase					,							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(__UpperCamelCase					,							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_3_0_0_0_0_0_0_0,
			    4_3_0_0_0_0_0_0_0,
			    -4_3_0_0_0_0_0_0_0,
			    4_3_0_0_0_0_0_0_0,
			)
			plot('Random system with many bodies', example_a(), -1.5, 1.5, -1.5, 1.5)



