





from collections import defaultdict
from math import ceil, sqrt


def 					A__	(       SCREAMING_SNAKE_CASE_ = 1_0_0_0_0_0_0							,       SCREAMING_SNAKE_CASE_ = 1_0		)   ->     int:
		lowerCamelCase   : defaultdict								=defaultdict(SCREAMING_SNAKE_CASE_		)

		for outer_width in range(3							,       (t_limit // 4) + 2		):
				if outer_width * outer_width > t_limit:
						lowerCamelCase   : Any								=max(
						    ceil(sqrt(outer_width * outer_width - t_limit		)		)							,       1		)
				else:
						lowerCamelCase   : str								=1

				hole_width_lower_bound += (outer_width - hole_width_lower_bound) % 2

				for hole_width in range(SCREAMING_SNAKE_CASE_							,       outer_width - 1							,       2		):
						count[outer_width * outer_width - hole_width * hole_width] += 1

		return sum(1 for n in count.values() if 1 <= n <= 1_0		)


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








import string


def 					A__	(       SCREAMING_SNAKE_CASE_		)   ->     str:
		lowerCamelCase   : Optional[Any]								=''''''
		for i in sequence:
				lowerCamelCase   : int								=ord(SCREAMING_SNAKE_CASE_		)
				if 6_5 <= extract <= 9_0:
						output += chr(1_5_5 - extract		)
				elif 9_7 <= extract <= 1_2_2:
						output += chr(2_1_9 - extract		)
				else:
						output += i
		return output


def 					A__	(       SCREAMING_SNAKE_CASE_		)   ->     str:
		lowerCamelCase   : Tuple								=string.ascii_letters
		lowerCamelCase   : int								=string.ascii_lowercase[::-1] + string.ascii_uppercase[::-1]
		return "".join(
		    letters_reversed[letters.index(SCREAMING_SNAKE_CASE_		)] if c in letters else c for c in sequence		)


def 					A__	(       )   ->     None:
		from timeit import timeit

		print('''Running performance benchmarks...'''		)
		lowerCamelCase   : Tuple								='''from string import printable ; from __main__ import atbash, atbash_slow'''
		print(F"> atbash_slow(): {timeit('atbash_slow(printable)'							,       setup=SCREAMING_SNAKE_CASE_		)} seconds"		)
		print(F">      atbash(): {timeit('atbash(printable)'							,       setup=SCREAMING_SNAKE_CASE_		)} seconds"		)


if __name__ == "__main__":
				for example in ("ABCDEFGH", "123GGjj", "testStringtest", "with space"):
								print(F"""{example} encrypted in atbash: {atbash(example)}""")
				benchmark()

