

'''simple docstring'''



from collections import defaultdict
from math import ceil, sqrt
def 						__lowerCamelCase	(       __snake_case					:		int = 1_000_000,		__snake_case					:		int = 10	)	->							int:






						"""simple docstring"""





						A__					:       defaultdict     =defaultdict(__snake_case	)

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

												hole_width_lower_bound += (outer_width - hole_width_lower_bound) % 2

												for hole_width in range(__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 <= 10	)


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




'''simple docstring'''



from __future__ import annotations

from math import pi
from typing import Protocol

import matplotlib.pyplot as plt
import numpy as np



class lowerCamelCase			(  lowercase_						):



			'''simple docstring'''






			def lowercase__						(				self	:						Any		,      lowerCAmelCase_	:						float			)      ->		float:





									'''simple docstring'''
									return 0.0


def 						__lowerCamelCase	(       __snake_case					:		np.ndarray,		__snake_case					:		int	)	->							tuple[int | float, int | float]:






						"""simple docstring"""





						A__					:       Tuple     =min([-20, np.min(fft_results[1 : samplerate // 2 - 1]	)]	)
						A__					:       str     =max([20, np.max(fft_results[1 : samplerate // 2 - 1]	)]	)
						return lowest, highest
def 						__lowerCamelCase	(       __snake_case					:		FilterType,		__snake_case					:		int	)	->							None:






						"""simple docstring"""





						A__					:       Any     =512
						A__					:       int     =[1] + [0] * (size - 1)
						A__					:       int     =[filter_type.process(__snake_case	) for item in inputs]

						A__					:       Union[str, Any]     =[0] * (samplerate - size)  # zero-padding
						outputs += filler
						A__					:       List[Any]     =np.abs(np.fft.fft(__snake_case	)	)
						A__					:       int     =20 * np.logaa(__snake_case	)

						# Frequencies on log scale from 24 to nyquist frequency
						plt.xlim(24,		samplerate / 2 - 1	)
						plt.xlabel("""Frequency (Hz)"""	)
						plt.xscale("""log"""	)

						# Display within reasonable bounds
						A__					:       Union[str, Any]     =get_bounds(__snake_case,		__snake_case	)
						plt.ylim(max([-80, bounds[0]]	),		min([80, bounds[1]]	)	)
						plt.ylabel("""Gain (dB)"""	)

						plt.plot(__snake_case	)
						plt.show()
def 						__lowerCamelCase	(       __snake_case					:		FilterType,		__snake_case					:		int	)	->							None:






						"""simple docstring"""





						A__					:       List[Any]     =512
						A__					:       List[Any]     =[1] + [0] * (size - 1)
						A__					:       Dict     =[filter_type.process(__snake_case	) for item in inputs]

						A__					:       Union[str, Any]     =[0] * (samplerate - size)  # zero-padding
						outputs += filler
						A__					:       str     =np.angle(np.fft.fft(__snake_case	)	)

						# Frequencies on log scale from 24 to nyquist frequency
						plt.xlim(24,		samplerate / 2 - 1	)
						plt.xlabel("""Frequency (Hz)"""	)
						plt.xscale("""log"""	)

						plt.ylim(-2 * pi,		2 * pi	)
						plt.ylabel("""Phase shift (Radians)"""	)
						plt.plot(np.unwrap(__snake_case,		-2 * pi	)	)
						plt.show()

