from maths.is_square_free import is_square_free
from maths.prime_factors import prime_factors







def 						A__  (					__A	):







    '''simple docstring'''
    _lowerCamelCase     :		List[Any] 						=						prime_factors(__A	)
    if is_square_free(__A	):
        return -1 if len(__A	) % 2 else 1
    return 0


if __name__ == "__main__":
    import doctest

    doctest.testmod()





from __future__ import annotations

from math import pi
from typing import Protocol

import matplotlib.pyplot as plt
import numpy as np




class 	__snake_case	( __lowerCAmelCase		):





      '''simple docstring'''






      def 	_SCREAMING_SNAKE_CASE    (					self     :				Optional[Any]    ,  _UpperCamelCase     :				float)				->float:


          """simple docstring"""


          return 0.0







def 						A__  (					__A   , __A	):







    '''simple docstring'''
    _lowerCamelCase     :		int 						=						min([-20, np.min(fft_results[1 : samplerate // 2 - 1]	)]	)
    _lowerCamelCase     :		Tuple 						=						max([20, np.max(fft_results[1 : samplerate // 2 - 1]	)]	)
    return lowest, highest







def 						A__  (					__A   , __A	):







    '''simple docstring'''
    _lowerCamelCase     :		Tuple 						=						512
    _lowerCamelCase     :		Tuple 						=						[1] + [0] * (size - 1)
    _lowerCamelCase     :		Optional[Any] 						=						[filter_type.process(__A	) for item in inputs]

    _lowerCamelCase     :		Optional[Any] 						=						[0] * (samplerate - size)  # zero-padding
    outputs += filler
    _lowerCamelCase     :		Tuple 						=						np.abs(np.fft.fft(__A	)	)
    _lowerCamelCase     :		List[Any] 						=						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
    _lowerCamelCase     :		Any 						=						get_bounds(__A   , __A	)
    plt.ylim(max([-80, bounds[0]]	)   , min([80, bounds[1]]	)	)
    plt.ylabel("""Gain (dB)"""	)

    plt.plot(__A	)
    plt.show()







def 						A__  (					__A   , __A	):







    '''simple docstring'''
    _lowerCamelCase     :		Tuple 						=						512
    _lowerCamelCase     :		Union[str, Any] 						=						[1] + [0] * (size - 1)
    _lowerCamelCase     :		int 						=						[filter_type.process(__A	) for item in inputs]

    _lowerCamelCase     :		Optional[Any] 						=						[0] * (samplerate - size)  # zero-padding
    outputs += filler
    _lowerCamelCase     :		Any 						=						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()




