






from math import ceil, sqrt







def   SCREAMING_SNAKE_CASE       (				snake_case_      :							int = 1000000     ):
	snake_case__				:   Tuple     =						0

	for outer_width in range(3  ,						(limit // 4) + 2     ):
		if outer_width**2 > limit:
			snake_case__				:   int     =						max(ceil(sqrt(outer_width**2 - limit     )     )  ,						1     )
		else:
			snake_case__				:   Union[str, Any]     =						1
		if (outer_width - hole_width_lower_bound) % 2:
			hole_width_lower_bound += 1

		answer += (outer_width - hole_width_lower_bound - 2) // 2 + 1

	return answer


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











def   SCREAMING_SNAKE_CASE       (				snake_case_      :							str     ):
	snake_case__				:   Any     =						[0] * len(snake_case_     )

	for i in range(1  ,						len(snake_case_     )     ):
		# use last results for better performance - dynamic programming
		snake_case__				:   Union[str, Any]     =						prefix_result[i - 1]
		while j > 0 and input_string[i] != input_string[j]:
			snake_case__				:   str     =						prefix_result[j - 1]

		if input_string[i] == input_string[j]:
			j += 1
		snake_case__				:   int     =						j

	return prefix_result







def   SCREAMING_SNAKE_CASE       (				snake_case_      :							str     ):
	return max(prefix_function(snake_case_     )     )


if __name__ == "__main__":
	import doctest

	doctest.testmod()



