






'''simple docstring'''







import random
import sys

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

_A	:			List[str]         ='''Usage of script: script_name <size_of_canvas:int>'''

_A	:			List[str]         =[0] * 100 + [1] * 10
random.shuffle(choice)





def  SCREAMING_SNAKE_CASE_       (UpperCamelCase      )      ->       list[list[bool]]:
							lowerCamelCase__					:	int         =       [[False for i in range(UpperCamelCase      )] for j in range(UpperCamelCase      )]
							return canvas





def  SCREAMING_SNAKE_CASE_       (UpperCamelCase      )      ->       None:
							for i, row in enumerate(UpperCamelCase      ):
														for j, _ in enumerate(UpperCamelCase      ):
																					lowerCamelCase__					:	List[str]         =       bool(random.getrandbits(1      )      )





def  SCREAMING_SNAKE_CASE_       (UpperCamelCase      )      ->       list[list[bool]]:
							lowerCamelCase__					:	Any         =       np.array(UpperCamelCase      )
							lowerCamelCase__					:	Optional[int]         =       np.array(create_canvas(current_canvas.shape[0]      )      )
							for r, row in enumerate(UpperCamelCase      ):
														for c, pt in enumerate(UpperCamelCase      ):
																					lowerCamelCase__					:	List[str]         =       __judge_point(
																					    UpperCamelCase				,			current_canvas[r - 1 : r + 2, c - 1 : c + 2]      )

							lowerCamelCase__					:	Optional[Any]         =       next_gen_canvas
							del next_gen_canvas  # cleaning memory as we move on.
							lowerCamelCase__					:	list[list[bool]]         =       current_canvas.tolist()
							return return_canvas





def  SCREAMING_SNAKE_CASE_       (UpperCamelCase				,			UpperCamelCase      )      ->       bool:
							lowerCamelCase__					:	Tuple         =       0
							lowerCamelCase__					:	Any         =       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.
							lowerCamelCase__					:	Tuple         =       pt
							if pt:
														if alive < 2:
																					lowerCamelCase__					:	Union[str, Any]         =       False
														elif alive == 2 or alive == 3:
																					lowerCamelCase__					:	str         =       True
														elif alive > 3:
																					lowerCamelCase__					:	List[str]         =       False
							else:
														if alive == 3:
																					lowerCamelCase__					:	Any         =       True

							return state


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

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









'''simple docstring'''







def  SCREAMING_SNAKE_CASE_       (UpperCamelCase = 1000      )      ->       int:
							lowerCamelCase__					:	str         =       -1
							lowerCamelCase__					:	Dict         =       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
														lowerCamelCase__					:	Dict         =       (n * n - 2 * a * n) // (2 * n - 2 * a)
														lowerCamelCase__					:	Any         =       n - a - b
														if c * c == (a * a + b * b):
																					lowerCamelCase__					:	Dict         =       a * b * c
																					if candidate >= product:
																												lowerCamelCase__					:	Union[str, Any]         =       candidate
							return product


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

