

"""simple docstring"""




from __future__ import annotations

import random

from matplotlib import animation
from matplotlib import pyplot as plt

# Frame rate of the animation
__A     :    Any    =		20

# Time between time steps in seconds
__A     :    Union[str, Any]    =		INTERVAL / 10_00





class 			__UpperCamelCase :


		def __init__(self :		Tuple     ,     __SCREAMING_SNAKE_CASE :		float     ,     __SCREAMING_SNAKE_CASE :		float     ,     __SCREAMING_SNAKE_CASE :		float     ,     __SCREAMING_SNAKE_CASE :		float     ,     __SCREAMING_SNAKE_CASE :		float = 1.0     ,     __SCREAMING_SNAKE_CASE :		float = 1.0     ,     __SCREAMING_SNAKE_CASE :		str = "blue"     ,     ):
							A			=					position_x
							A			=					position_y
							A			=					velocity_x
							A			=					velocity_y
							A			=					mass
							A			=					size
							A			=					color


		@property
		def 					SCREAMING_SNAKE_CASE__   (self :		int):
							return self.position_x, self.position_y


		@property
		def 					SCREAMING_SNAKE_CASE__   (self :		Dict):
							return self.velocity_x, self.velocity_y


		def 					SCREAMING_SNAKE_CASE__   (self :		int     ,     __SCREAMING_SNAKE_CASE :		float     ,     __SCREAMING_SNAKE_CASE :		float     ,     __SCREAMING_SNAKE_CASE :		float):
							self.velocity_x += force_x * delta_time
							self.velocity_y += force_y * delta_time


		def 					SCREAMING_SNAKE_CASE__   (self :		int     ,     __SCREAMING_SNAKE_CASE :		float):
							self.position_x += self.velocity_x * delta_time
							self.position_y += self.velocity_y * delta_time





class 			__UpperCamelCase :


		def __init__(self :		int     ,     __SCREAMING_SNAKE_CASE :		list[Body]     ,     __SCREAMING_SNAKE_CASE :		float = 1.0     ,     __SCREAMING_SNAKE_CASE :		float = 1.0     ,     __SCREAMING_SNAKE_CASE :		float = 0.0     ,     ):
							A			=					bodies
							A			=					gravitation_constant
							A			=					time_factor
							A			=					softening_factor


		def __len__(self :		Tuple):
							return len(self.bodies)


		def 					SCREAMING_SNAKE_CASE__   (self :		Any     ,     __SCREAMING_SNAKE_CASE :		float):
							for bodya in self.bodies:
												A			=					0.0
												A			=					0.0
												for bodya in self.bodies:
																	if bodya != bodya:
																						A			=					bodya.position_x - bodya.position_x
																						A			=					bodya.position_y - bodya.position_y

																						# Calculation of the distance using Pythagoras's theorem
																						# Extra factor due to the softening technique
																						A			=					(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(__SCREAMING_SNAKE_CASE     ,     __SCREAMING_SNAKE_CASE     ,     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    __SCREAMING_SNAKE_CASE						(						lowercase__			,							lowercase__			,							lowercase__      ):
					"""simple docstring"""
					body_system.update_system(lowercase__      )

					# Update the positions of the patches
					for patch, body in zip(lowercase__			,							body_system.bodies      ):
										A			=					(body.position_x, body.position_y)
def    __SCREAMING_SNAKE_CASE						(						lowercase__			,							lowercase__			,							lowercase__ = -1			,							lowercase__ = 1			,							lowercase__ = -1			,							lowercase__ = 1			,							):
					"""simple docstring"""
					A			=					plt.figure()
					fig.canvas.set_window_title(lowercase__      )
					A			=					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
					A			=					[
					    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(lowercase__      )

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

					A			=					animation.FuncAnimation(  # noqa: F841
					    lowercase__			,							lowercase__			,							interval=lowercase__			,							blit=lowercase__      )

					plt.show()
def    __SCREAMING_SNAKE_CASE						(						):
					"""simple docstring"""
					A			=					0.9_70_04_36
					A			=					-0.24_30_87_53
					A			=					0.4_66_20_36_85
					A			=					0.43_23_65_73

					A			=					[
					    Body(lowercase__			,							lowercase__			,							lowercase__			,							lowercase__			,							size=0.2			,							color="red"      ),
					    Body(-position_x			,							-position_y			,							lowercase__			,							lowercase__			,							size=0.2			,							color="green"      ),
					    Body(0			,							0			,							-2 * velocity_x			,							-2 * velocity_y			,							size=0.2			,							color="blue"      ),
					]
					return BodySystem(lowercase__			,							time_factor=3      )
def    __SCREAMING_SNAKE_CASE						(						):
					"""simple docstring"""
					A			=					7.3476e22
					A			=					5.972e24
					A			=					1_022
					A			=					384_399_000
					A			=					6.674e-11

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

					A			=					Body(-earth_moon_distance			,							0			,							0			,							lowercase__			,							lowercase__			,							10_000_000			,							"grey"      )
					A			=					Body(0			,							0			,							0			,							lowercase__			,							lowercase__			,							50_000_000			,							"blue"      )
					return BodySystem([earth, moon]			,							lowercase__			,							time_factor=1_000_000      )
def    __SCREAMING_SNAKE_CASE						(						):
					"""simple docstring"""
					A			=					[]
					for _ in range(10      ):
										A			=					random.uniform(-0.5			,							0.5      )
										A			=					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      )			,							lowercase__			,							lowercase__			,							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(lowercase__			,							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_30_00_00_00,
	    4_30_00_00_00,
	    -4_30_00_00_00,
	    4_30_00_00_00,
	)
	plot('Random system with many bodies', example_a(), -1.5, 1.5, -1.5, 1.5)








"""simple docstring"""




def    __SCREAMING_SNAKE_CASE						(						lowercase__			,							lowercase__			,							lowercase__      ):
					"""simple docstring"""
					A			=					index
					A			=					2 * index + 1
					A			=					2 * index + 2
					if left_index < heap_size and unsorted[left_index] > unsorted[largest]:
										A			=					left_index

					if right_index < heap_size and unsorted[right_index] > unsorted[largest]:
										A			=					right_index

					if largest != index:
										A			,    A			=					unsorted[index], unsorted[largest]
										heapify(lowercase__			,							lowercase__			,							lowercase__      )
def    __SCREAMING_SNAKE_CASE						(						lowercase__      ):
					"""simple docstring"""
					A			=					len(lowercase__      )
					for i in range(n // 2 - 1			,							-1			,							-1      ):
										heapify(lowercase__			,							lowercase__			,							lowercase__      )
					for i in range(n - 1			,							0			,							-1      ):
										A			,    A			=					unsorted[i], unsorted[0]
										heapify(lowercase__			,							0			,							lowercase__      )
					return unsorted


if __name__ == "__main__":
	__A     :    List[Any]    =		input('Enter numbers separated by a comma:\n').strip()
	__A     :    List[str]    =		[int(item) for item in user_input.split(',')]
	print(heap_sort(unsorted))





