



"""simple docstring"""




import random
import sys

import numpy as np
from matplotlib import pyplot as plt
from matplotlib.colors import ListedColormap

lowerCAmelCase__		:					Dict							='''Usage of script: script_name <size_of_canvas:int>'''

lowerCAmelCase__		:					Dict							=[0] * 100 + [1] * 10
random.shuffle(choice)






def      __lowercase       (			a__       )    ->			list[list[bool]]:
							__SCREAMING_SNAKE_CASE									= [[False for i in range(__lowerCAmelCase       )] for j in range(__lowerCAmelCase       )]
							return canvas






def      __lowercase       (			a__       )    ->			None:
							for i, row in enumerate(__lowerCAmelCase       ):
														for j, _ in enumerate(__lowerCAmelCase       ):
																					__SCREAMING_SNAKE_CASE									= bool(random.getrandbits(1       )       )






def      __lowercase       (			a__       )    ->			list[list[bool]]:
							__SCREAMING_SNAKE_CASE									= np.array(__lowerCAmelCase       )
							__SCREAMING_SNAKE_CASE									= np.array(create_canvas(current_canvas.shape[0]       )       )
							for r, row in enumerate(__lowerCAmelCase       ):
														for c, pt in enumerate(__lowerCAmelCase       ):
																					__SCREAMING_SNAKE_CASE									= __judge_point(
																					    __lowerCAmelCase							,       current_canvas[r - 1 : r + 2, c - 1 : c + 2]       )

							__SCREAMING_SNAKE_CASE									= next_gen_canvas
							del next_gen_canvas  # cleaning memory as we move on.
							__SCREAMING_SNAKE_CASE									= current_canvas.tolist()
							return return_canvas






def      __lowercase       (			a__							,       a__       )    ->			bool:
							__SCREAMING_SNAKE_CASE									= 0
							__SCREAMING_SNAKE_CASE									= 0
							# finding dead or alive neighbours count.
							for i in neighbours:
														for status in i:
																					if status:
																												alive += 1
																					else:
																												dead += 1

    # handling duplicate entry for focus pt.
							if pt:
														alive -= 1
							else:
														dead -= 1

							# running the rules of game here.
							__SCREAMING_SNAKE_CASE									= pt
							if pt:
														if alive < 2:
																					__SCREAMING_SNAKE_CASE									= False
														elif alive == 2 or alive == 3:
																					__SCREAMING_SNAKE_CASE									= True
														elif alive > 3:
																					__SCREAMING_SNAKE_CASE									= False
							else:
														if alive == 3:
																					__SCREAMING_SNAKE_CASE									= True

							return state


if __name__ == "__main__":
			if len(sys.argv) != 2:
						raise Exception(usage_doc)

			lowerCAmelCase__		:					str							=int(sys.argv[1])
			# main working structure of this module.
			lowerCAmelCase__		:					List[str]							=create_canvas(canvas_size)
			seed(c)
			lowerCAmelCase__						,					lowerCAmelCase__		:					Tuple							=plt.subplots()
			fig.show()
			lowerCAmelCase__		:					Optional[int]							=ListedColormap(['''w''', '''k'''])
			try:
						while True:
									lowerCAmelCase__		:					str							=run(c)
									ax.matshow(c, cmap=cmap)
									fig.canvas.draw()
									ax.cla()
			except KeyboardInterrupt:
						# do nothing.
						pass











def      __lowercase       (			a__ = 10_00       )    ->			int:
							__SCREAMING_SNAKE_CASE									= -1
							__SCREAMING_SNAKE_CASE									= 0
							for a in range(1							,       n // 3       ):
														# Solving the two equations a**2+b**2=c**2 and a+b+c=N eliminating c
														__SCREAMING_SNAKE_CASE									= (n * n - 2 * a * n) // (2 * n - 2 * a)
														__SCREAMING_SNAKE_CASE									= n - a - b
														if c * c == (a * a + b * b):
																					__SCREAMING_SNAKE_CASE									= a * b * c
																					if candidate >= product:
																												__SCREAMING_SNAKE_CASE									= candidate
							return product


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






