






import sys

__a:     str   					=					(
    '''73167176531330624919225119674426574742355349194934'''
    '''96983520312774506326239578318016984801869478851843'''
    '''85861560789112949495459501737958331952853208805511'''
    '''12540698747158523863050715693290963295227443043557'''
    '''66896648950445244523161731856403098711121722383113'''
    '''62229893423380308135336276614282806444486645238749'''
    '''30358907296290491560440772390713810515859307960866'''
    '''70172427121883998797908792274921901699720888093776'''
    '''65727333001053367881220235421809751254540594752243'''
    '''52584907711670556013604839586446706324415722155397'''
    '''53697817977846174064955149290862569321978468622482'''
    '''83972241375657056057490261407972968652414535100474'''
    '''82166370484403199890008895243450658541227588666881'''
    '''16427171479924442928230863465674813919123162824586'''
    '''17866458359124566529476545682848912883142607690042'''
    '''24219022671055626321111109370544217506941658960408'''
    '''07198403850962455444362981230987879927244284909188'''
    '''84580156166097919133875499200524063689912560717606'''
    '''05886116467109405077541002256983155200055935729725'''
    '''71636269561882670428252483600823257530420752963450'''
)




def       _SCREAMING_SNAKE_CASE (							__snake_case = N )				->						int:
       _UpperCAmelCase							=    -sys.maxsize - 1
       for i in range(len(__snake_case ) - 1_2 ):
              _UpperCAmelCase							=    1
              for j in range(1_3 ):
                     product *= int(n[i + j] )
              if product > largest_product:
                     _UpperCAmelCase							=    product
       return largest_product


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      A(  lowerCamelCase__		):

		"""simple docstring"""





		def   _UpperCamelCase( self					,				SCREAMING_SNAKE_CASE__   )      ->	float:

					"""simple docstring"""



					return 0.0





def 				A_       ( snake_case__       ,					snake_case__		)					->  tuple[int | float, int | float]:
			_UpperCamelCase					:Union[str, Any]					     =	min([-20, np.min(fft_results[1 : samplerate // 2 - 1]		)]		)
			_UpperCamelCase					:Optional[int]					     =	max([20, np.max(fft_results[1 : samplerate // 2 - 1]		)]		)
			return lowest, highest





def 				A_       ( snake_case__       ,					snake_case__		)					->  None:
			_UpperCamelCase					:List[str]					     =	5_12
			_UpperCamelCase					:int					     =	[1] + [0] * (size - 1)
			_UpperCamelCase					:Union[str, Any]					     =	[filter_type.process(snake_case__		) for item in inputs]

			_UpperCamelCase					:Any					     =	[0] * (samplerate - size)  # zero-padding
			outputs += filler
			_UpperCamelCase					:int					     =	np.abs(np.fft.fft(snake_case__		)		)
			_UpperCamelCase					:str					     =	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
			_UpperCamelCase					:Tuple					     =	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 				A_       ( snake_case__       ,					snake_case__		)					->  None:
			_UpperCamelCase					:Tuple					     =	5_12
			_UpperCamelCase					:Union[str, Any]					     =	[1] + [0] * (size - 1)
			_UpperCamelCase					:List[Any]					     =	[filter_type.process(snake_case__		) for item in inputs]

			_UpperCamelCase					:str					     =	[0] * (samplerate - size)  # zero-padding
			outputs += filler
			_UpperCamelCase					:Tuple					     =	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()

