

'''simple docstring'''
import random

from .binary_exp_mod import bin_exp_mod







def 					_A		(	snake_case		,							snake_case=10_00     )			->	int:




   if n < 2:
      return False

   if n % 2 == 0:
      return n == 2

   # this means n is odd
   _lowercase			:      int			     =   n - 1
   _lowercase			:      Optional[Any]			     =   0
   while d % 2 == 0:
      d /= 2
      exp += 1

   # n - 1=d*(2**exp)
   _lowercase			:      Dict			     =   0
   while count < prec:
      _lowercase			:      Union[str, Any]			     =   random.randint(2		,							n - 1     )
      _lowercase			:      Dict			     =   bin_exp_mod(_lowerCamelCase		,							_lowerCamelCase		,							_lowerCamelCase     )
      if b != 1:
         _lowercase			:      Tuple			     =   True
         for _ in range(_lowerCamelCase     ):
            if b == n - 1:
               _lowercase			:      str			     =   False
               break
            _lowercase			:      Any			     =   b * b
            b %= n
         if flag:
            return False
         count += 1
   return True


if __name__ == "__main__":
    _snake_case     =  abs(int(input('Enter bound : ').strip()))
    print('Here\'s the list of primes:')
    print(', '.join(str(i) for i in range(n + 1) if is_prime_big(i)))











from __future__ import annotations

from math import pi
from typing import Protocol

import matplotlib.pyplot as plt
import numpy as np



class   UpperCAmelCase_    (       a):







							def    snake_case__      (   self,			__a):

														'''simple docstring'''

														return 0.0






def 				A				(					_lowerCamelCase				, _lowerCamelCase  ):





							'''simple docstring'''




							_lowerCAmelCase     :							Optional[Any]    =    min([-20, np.min(fft_results[1 : samplerate // 2 - 1]  )]  )
							_lowerCAmelCase     :							Optional[int]    =    max([20, np.max(fft_results[1 : samplerate // 2 - 1]  )]  )
							return lowest, highest






def 				A				(					_lowerCamelCase				, _lowerCamelCase  ):





							'''simple docstring'''




							_lowerCAmelCase     :							int    =    512
							_lowerCAmelCase     :							Union[str, Any]    =    [1] + [0] * (size - 1)
							_lowerCAmelCase     :							Optional[Any]    =    [filter_type.process(_lowerCamelCase  ) for item in inputs]

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

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

							plt.plot(_lowerCamelCase  )
							plt.show()






def 				A				(					_lowerCamelCase				, _lowerCamelCase  ):





							'''simple docstring'''




							_lowerCAmelCase     :							Union[str, Any]    =    512
							_lowerCAmelCase     :							Optional[Any]    =    [1] + [0] * (size - 1)
							_lowerCAmelCase     :							str    =    [filter_type.process(_lowerCamelCase  ) for item in inputs]

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

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