
'''simple docstring'''







def 				SCREAMING_SNAKE_CASE__	(   __A = 1_000_000	)       ->	int:
	_snake_case   						=		[i - 1 for i in range(limit + 1	)]

	for i in range(2			,				limit + 1	):
		if phi[i] == i - 1:
			for j in range(2 * i			,				limit + 1			,				__A	):
				phi[j] -= phi[j] // i

	return sum(phi[2 : limit + 1]	)


if __name__ == "__main__":
					print(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 						__UpperCAmelCase      (					_lowerCamelCase						):


							def  lowerCamelCase				(       self    ,   lowerCAmelCase_  ):





								"""simple docstring"""






								return 0.0







def 				SCREAMING_SNAKE_CASE__	(   __A			,				__A	)       ->	tuple[int | float, int | float]:
	_snake_case   						=		min([-20, np.min(fft_results[1 : samplerate // 2 - 1]	)]	)
	_snake_case   						=		max([20, np.max(fft_results[1 : samplerate // 2 - 1]	)]	)
	return lowest, highest







def 				SCREAMING_SNAKE_CASE__	(   __A			,				__A	)       ->	None:
	_snake_case   						=		512
	_snake_case   						=		[1] + [0] * (size - 1)
	_snake_case   						=		[filter_type.process(__A	) for item in inputs]

	_snake_case   						=		[0] * (samplerate - size)  # zero-padding
	outputs += filler
	_snake_case   						=		np.abs(np.fft.fft(__A	)	)
	_snake_case   						=		20 * np.logaa(__A	)

	# 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
	_snake_case   						=		get_bounds(__A			,				__A	)
	plt.ylim(max([-80, bounds[0]]	)			,				min([80, bounds[1]]	)	)
	plt.ylabel('Gain (dB)'	)

	plt.plot(__A	)
	plt.show()







def 				SCREAMING_SNAKE_CASE__	(   __A			,				__A	)       ->	None:
	_snake_case   						=		512
	_snake_case   						=		[1] + [0] * (size - 1)
	_snake_case   						=		[filter_type.process(__A	) for item in inputs]

	_snake_case   						=		[0] * (samplerate - size)  # zero-padding
	outputs += filler
	_snake_case   						=		np.angle(np.fft.fft(__A	)	)

	# 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(__A			,				-2 * pi	)	)
	plt.show()

