




from __future__ import annotations

from math import pi
from typing import Protocol

import matplotlib.pyplot as plt
import numpy as np




class       a__	( UpperCamelCase__				):







     def       lowerCAmelCase_    (     self  ,		A			)  ->   float:



          '''simple docstring'''



          return 0.0







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

def  SCREAMING_SNAKE_CASE							(       __UpperCamelCase		, __UpperCamelCase)      ->					None:
     a     =				5_12
     a     =				[1] + [0] * (size - 1)
     a     =				[filter_type.process(__UpperCamelCase) for item in inputs]

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

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

     plt.plot(__UpperCamelCase)
     plt.show()





def  SCREAMING_SNAKE_CASE							(       __UpperCamelCase		, __UpperCamelCase)      ->					None:
     a     =				5_12
     a     =				[1] + [0] * (size - 1)
     a     =				[filter_type.process(__UpperCamelCase) for item in inputs]

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

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







import math
import sys

def  SCREAMING_SNAKE_CASE							(       __UpperCamelCase)      ->					int:
     if number != int(__UpperCamelCase):
          raise ValueError("the value of input must be a natural number")
     if number < 0:
          raise ValueError("the value of input must not be a negative number")
     if number == 0:
          return 1
     a     =				[-1] * (number + 1)
     a     =				0
     for i in range(1		, number + 1):
          a     =				sys.maxsize
          a     =				int(math.sqrt(__UpperCamelCase))
          for j in range(1		, root + 1):
               a     =				1 + answers[i - (j**2)]
               a     =				min(__UpperCamelCase		, __UpperCamelCase)
          a     =				answer
     return answers[number]


if __name__ == "__main__":
   import doctest

   doctest.testmod()

